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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">SE</journal-id>
<journal-title-group>
<journal-title>Solid Earth</journal-title>
<abbrev-journal-title abbrev-type="publisher">SE</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Solid Earth</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1869-9529</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/se-7-415-2016</article-id><title-group><article-title>Ion association in water solution of soil and vadose zone of chestnut saline solonetz as a driver of terrestrial carbon sink</article-title>
      </title-group><?xmltex \runningtitle{Ion association in water solution of soil and vadose zone}?><?xmltex \runningauthor{A.-M.~A.~Batukaev et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Batukaev</surname><given-names>Abdul-Malik A.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Endovitsky</surname><given-names>Anatoly P.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Andreev</surname><given-names>Andrey G.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Kalinichenko</surname><given-names>Valery P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2217-4592</ext-link></contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff2">
          <name><surname>Minkina</surname><given-names>Tatiana M.</given-names></name>
          <email>tminkina@mail.ru</email>
        <ext-link>https://orcid.org/0000-0003-3022-0883</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Dikaev</surname><given-names>Zaurbek S.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Mandzhieva</surname><given-names>Saglara S.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6000-2209</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Sushkova</surname><given-names>Svetlana N.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Institute of Fertility of Soils of South Russia, Persianovka, Rostov Oblast, Russia</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Southern Federal University, Rostov-on-Don, Russia</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Chechen State University, Grozny, Russia</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Tatiana M. Minkina (tminkina@mail.ru)</corresp></author-notes><pub-date><day>15</day><month>March</month><year>2016</year></pub-date>
      
      <volume>7</volume>
      <issue>2</issue>
      <fpage>415</fpage><lpage>423</lpage>
      <history>
        <date date-type="received"><day>5</day><month>January</month><year>2016</year></date>
           <date date-type="rev-request"><day>18</day><month>January</month><year>2016</year></date>
           <date date-type="rev-recd"><day>22</day><month>February</month><year>2016</year></date>
           <date date-type="accepted"><day>1</day><month>March</month><year>2016</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://se.copernicus.org/articles/.html">This article is available from https://se.copernicus.org/articles/.html</self-uri>
<self-uri xlink:href="https://se.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://se.copernicus.org/articles/.pdf</self-uri>


      <abstract>
    <p>The assessment of soil and vadose zone as the drains for carbon sink and proper
modeling of the effects and extremes of biogeochemical cycles in
the terrestrial biosphere are the key components to understanding the carbon cycle,
global climate system, and aquatic and terrestrial system uncertainties.
Calcium carbonate equilibrium causes saturation of solution with CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>,
and it determines its material composition, migration and accumulation of salts. In
a solution electrically neutral ion pairs are formed: CaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>,
CaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, MgCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, and MgSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, as well as
charged ion pairs CaHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, MgHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, NaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
NaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, CaOH<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>, and MgOH<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>. The calcium carbonate
equilibrium algorithm, mathematical model and original software to calculate
the real equilibrium forms of ions and to determine the nature of
calcium carbonate balance in a solution were developed. This approach conducts the quantitative
assessment of real ion forms of solution in solonetz soil and vadose zone of
dry steppe taking into account the ion association at high ionic strength
of saline soil solution. The concentrations of free and associated ion form
were calculated according to analytical ion concentration in real solution.
In the iteration procedure, the equations were used to find the following: ion material balance, a
linear interpolation of equilibrium constants, a method of ionic pairs, the
laws of initial concentration preservation, operating masses of equilibrium
system, and the concentration constants of ion pair dissociation. The
coefficient of ion association <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was determined as the ratio of
ions free form to analytical content of ion <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">ass</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">an</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. Depending on soil and vadose
zone layer, concentration and composition of solution in the ionic pair's
form are 11–52 % Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>; 22.2–54.6 % Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>; 1.1–10.5 %
Na<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>; 3.7–23.8 HCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, 23.3–61.6 % SO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>, and up to
85.7 % CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>. The carbonate system of soil and vadose zone water
solution helps to explain the evolution of salted soils, vadose and
saturation zones, and landscape. It also helps to improve the soil maintenance, plant
nutrition and irrigation.</p>
    <p>The association of ions in soil solutions is one of the drivers promoting
transformation of solution, excessive fluxes of carbon in the soil, and loss of
carbon from soil through vadose zone.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>The problem of carbon sequestration is based on water solution in soil
and vadose zone as the drains for carbon sink (Shein et al., 2014;
Sammartino et al, 2015). Physical
and biogeochemical model improvement is proposed (Romanou et al., 2014).
The chemical composition of soil and vadose
zone water solution is influenced by calcium carbonate equilibrium (CCE).
CCE depends on the state of the chemical composition, pH, Eh, buffering
properties of liquid phase, dissolution, migration, precipitation of
carbonates in the soil profile and landscape, and ion exchange processes at the
interface of solid and liquid phases (Minkina et al., 2012b). Biosphere
uncertainties and climate extremes are linked to biogeochemical cycles in the
terrestrial biosphere (Bahn et al., 2015), which have profound implications
for ecosystems, society and the climate system (Reichstein et al., 2013).
Proper understanding is required of the effects, drivers and extremes which
alter the biogeochemical cycles of terrestrial biosphere, especially soil,
vadose and saturation zone as a continuum of salt (including carbon)
transfer (Shein et al., 2015; Kalinichenko, 2014, 2015a, b; Kalinichenko and
Starcev, 2015; Kalinichenko et al., 2012, 2014a, b; Sobgayda and Solodkova,
2015; Glazko and Glazko, 2015; Yuan et al., 2014).</p>
      <p>The heterogeneity in carbon stream out of the soil and biosphere is caused
by landscape (Ågren et al., 2014), anthropogenic influence on the
carbon cycle (Berger et al., 2014), change of carbon stocks (Munir et al.,
2014), sinking of carbon (Lima et al., 2014; Turi et al., 2014), saturation
of water with CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> and Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> (Evans et al., 2014), and the
function of vegetation (Melton and Arora, 2014). The CCE in water solution
of soil, vadose and saturation zones provides understanding of
biogeochemical element cycles, models of anthropogenic emission of
greenhouse gases (Peng et al., 2014), and anthropogenic CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> sink to the
ocean (Ishii et al., 2014).</p>
      <p>There are significant uncertainties in understanding the role of soil
mineral and organic carbon deposits in the global C cycle and its models
(Z. Wang et al., 2014) and biogeochemical cycles (Caldararu et al., 2014).</p>
      <p>The water solution is the most mobile, volatile and active agent of soil, vadose
and saturation zones, and landscape properties (Amakor et al., 2013; Hunenberger
and Relf, 2011; Visconti and de Paz, 2012; Anisimov et al.,
2015; Endovitskii et al., 2014; Endovitsky et al., 2012; Chaplygin et al., 2014).</p>
      <p>The properties and structure of water solution are the function of its
chemical equilibrium (Debye and Hückel, 1923; Bjerrum et al., 1958;
Davies, 1962; Garrels and Christ, 1965; Butler, 1998). The higher the ionic
strength of the solution is, the more ions pass to form ion associates
(Lewis and Randell, 1921; Adams, 1971; Sposito, 1984, 1989; Sparks,
1984). This fact is known for the waters of ocean and low mineralized waters
of storage reservoirs (Levchenko, 1966). Ion association in CCE helps to
explain the natural water oversaturation with carbonates, migration and
accumulation of carbonates (Minkin et al., 1977; Minkin and
Yendovitskii, 1986). The reason for excess saturation of water with
CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is the ion association into the ionic mineral and organic
complexes. The carbonate system of water solution is under the influence of
biological process, soil–atmosphere gas exchange, partial pressure and
seasonal cycles of CO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula>. The soil solution determines the dynamics of
its material composition, migration and accumulation of salts into the
disperse system of soil continuum, vadose, saturation zones and landscape,
genesis and evolution of biosphere. In soil solutions, electrically
neutral ion pairs CaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, CaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>,
MgCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, and MgSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> are formed, as well as charged ion pairs
CaHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, MgHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, NaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, NaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
CaOH<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>, and MgOH<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>. Communication between the associated ions in soil
solution is much more diverse compared to water systems (Hunenberger and
Relf, 2011; Stoyanov et al., 2011; Zhang et al., 2012; Tertre et al., 2011).</p>
      <p>Another important aspect of soil solution is its strong dependence on the
soil moisture and the interaction between soil solution and soil disperse system.
The sampling of a soil solution leads to destruction of its links to disperse
system of soil. So the solution extracted from soil does not completely
correspond to properties of native soil solution. For this reason the
modeling of soil solution composition at different stages of water, salt
and organic matter content in the soil, vadose, saturation zones to the some
extent is more important than the direct analysis of extracted solution itself.
Ionic strength of the soil solution, water solution of vadose, and saturation
zones varies from 0.05 (almost ideal chemical solution after rain in upper
horizon of non-saline soil) to 0.5 and more (dry saline soil), and it can be
observed in a rather short time period in the same discrete part of soil,
vadose, saturation zone continuum. In some cases, the ionic strength of
solution can be so high that it is better to use the lows of quasicrystalline
water structure and supercritical water (Johnston et al., 2010; Plugatyr et
al., 2011) to describe the system properly.</p>
      <p>Modern non-thermodynamic techniques are used for modeling the
associated ion pairs in nanotubes (Izgorodina et al., 2014; Luo et al.,
2013), in supercritical water (Chialvo et al., 1995; Plugatyr et al., 2011),
and hybrid excitations in solution (Nicholson and Quirke, 2003; Reznikov and
Shaposhnik, 2005; Maiti and Rogers, 2011; Lui et al., 2011; Farnum et al.,
2011; Kielpinski, 2013). In recent years, the improved methods of direct ion
pair study have been used (Westerlund et al., 2011; Besser-Rogac et al., 2011;
T. Wang et al., 2014).</p>
      <p>For most cases of water solution, it is enough to use the lows of
thermodynamics. A thermodynamic mathematical model and software of soil,
vadose, saturation zone of water solution equilibrium have been proposed. The model
was tested by experimental data.</p>
</sec>
<sec id="Ch1.S2">
  <title>Materials and methods</title>
<sec id="Ch1.S2.SS1">
  <title>Study area</title>
      <p>The studied area is situated in the southeast of the Russian Federation, Rostov Oblast, called Lower Don.</p>
      <p>The subject of research is the dry steppe chestnut saline solonetzic soil of
southern Russia. The climate is arid, with an annual precipitation of 300–350 mm.
The parent rocks are carbonate and carbonate–sulfate loess-like loam and
clay. The landscape is semi-hydromorphic.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>Sampling and analysis</title>
      <p>The solonetz soil is moderately thick at 0–40 cm, moderately solonized, humus
2.6 %, physical clay 47.7 %, clay 29.5 %, CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> 0.15 % (up to
3–10 % at the depth of 0.8–1.5 m), pH <inline-formula><mml:math display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 7.8, with exchangeable cations
Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> – 182 mmol kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> – 65 mmol kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and Na<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula> – 34 mmol kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.
The landscape is semi-hydromorphic; vadose zone under the solonetz soil is
vast – the depth of ground water varying up to 7–10 m. Solid residual in
vadose zone is up to 2.0 %.</p>
      <p>Soil and vadose zone species were sampled from a section wall down to a
depth of 1 m. Samples from the deeper vadose zone layers were taken by
soil auger, with a drill cup diameter of 5 cm. During preparation the samples were
crushed and sifted, with openings of 2 mm, and then mixed with quartz sand in a
ratio of <inline-formula><mml:math display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> (Carter and Gregorich, 2007; Minkina et al., 2012a). The mixture from every soil
and vadose zone layer was put into glass tube with an inner diameter of
3.4 cm and a length of 100 cm. At the bottom of the tube an outlet was mounted to drain the solution. Soil solution was allocated by direct displacement method with
ethyl alcohol poured on the top of the soil column. The volume of soil solution
emitted from every soil column was 20–60 mL.</p>
      <p>Soil and vadose zone solution was analyzed by standard methods (Carter
and Gregorich, 2007; Visconti and de Paz, 2012). Moisture of soil was
determined by thermostat 105 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C method. Dry residual of the soil
was determined by thermostat 105 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C method. pH was measured in
thermostat (20 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.2 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) by a pH meter with a glass electrode.
The carbonate and bicarbonate anions were titrated directly by 0.01 M
hydrochloric acid detecting titration, endpoint on color change of
indicators – phenolphthalein and methyl orange. The chloride ion was
detected by argentometric method with potassium chromate. The total content
of Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> and Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> was measured by complexometric titration. In
another aliquot Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> was determined by complexometric. Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> was
calculated as a difference. The sulfate was analyzed by BaSO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula>
sedimentation method and Na<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula> by flame photometric detection. The
experiment was performed in triplicate. All statistical calculations were
performed using Microsoft Excel 2010.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results</title>
      <p>Carbonate system of soil solution includes dynamic equilibriums (Fig. 1).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p>Calcium carbonate equilibrium system of soil solution.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://se.copernicus.org/articles/7/415/2016/se-7-415-2016-f01.png"/>

      </fig>

      <p>CCE system of soil solution is an adsorption–hydration balance between
solution, gas phase, and bioorganic phase, including step dissociation of
carbonic acid, as well as calcium carbonate equilibrium between solution, soil
absorbing complex, sediments of CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> and solid phase, and the ion
equilibrium of water. The deposition or dissolution of CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is caused
by receipt or removal of Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>, HCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> from
solution and carbonate equilibrium shift. It is influence by ionic composition of
soil solution, and it determines the type of migration and accumulation of
various forms of carbonate forms through the soil profile.</p>
      <p>The dry residual of soil and vadose zone solution is rather high. Analytical
composition is typical for dry steppe chestnut saline solonetzic soil of
southern Russia (Table 1). The state of ions in such a solution is influenced
by the high ionic strength and ion association in soil and vadose zone
solution.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Soil solution of chestnut saline solonetz, measured in mmol-eq L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.80}[.80]?><oasis:tgroup cols="11">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left"/>
     <oasis:colspec colnum="9" colname="col9" align="left"/>
     <oasis:colspec colnum="10" colname="col10" align="left"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1">Layer,</oasis:entry>  
         <oasis:entry colname="col2">Moisture,</oasis:entry>  
         <oasis:entry colname="col3">Solid residue,</oasis:entry>  
         <oasis:entry colname="col4">pH</oasis:entry>  
         <oasis:entry colname="col5">Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col6">Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col7">Na<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col8">CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col9">HCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col10">SO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col11">Cl<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>-</mml:mo></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">cm</oasis:entry>  
         <oasis:entry colname="col2">%</oasis:entry>  
         <oasis:entry colname="col3">g L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"/>  
         <oasis:entry colname="col5"/>  
         <oasis:entry colname="col6"/>  
         <oasis:entry colname="col7"/>  
         <oasis:entry colname="col8"/>  
         <oasis:entry colname="col9"/>  
         <oasis:entry colname="col10"/>  
         <oasis:entry colname="col11"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">0–5</oasis:entry>  
         <oasis:entry colname="col2">22.4 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.9</oasis:entry>  
         <oasis:entry colname="col3">1.64 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.39</oasis:entry>  
         <oasis:entry colname="col4">7.82 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.06</oasis:entry>  
         <oasis:entry colname="col5">4.94 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.65</oasis:entry>  
         <oasis:entry colname="col6">6.78 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.25</oasis:entry>  
         <oasis:entry colname="col7">11.22 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.02</oasis:entry>  
         <oasis:entry colname="col8">absent</oasis:entry>  
         <oasis:entry colname="col9">4.75 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.36</oasis:entry>  
         <oasis:entry colname="col10">10.44 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.28</oasis:entry>  
         <oasis:entry colname="col11">7.75 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.95</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">5–14</oasis:entry>  
         <oasis:entry colname="col2">30.7 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.8</oasis:entry>  
         <oasis:entry colname="col3">6.74 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.23</oasis:entry>  
         <oasis:entry colname="col4">9.02 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.08</oasis:entry>  
         <oasis:entry colname="col5">12.33 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.98</oasis:entry>  
         <oasis:entry colname="col6">28.72 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.75</oasis:entry>  
         <oasis:entry colname="col7">60.21 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 7.42</oasis:entry>  
         <oasis:entry colname="col8">1.95 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.88</oasis:entry>  
         <oasis:entry colname="col9">8.64 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.99</oasis:entry>  
         <oasis:entry colname="col10">59.45 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 4.58</oasis:entry>  
         <oasis:entry colname="col11">31.22 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.02</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">14–30</oasis:entry>  
         <oasis:entry colname="col2">37.4 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.3</oasis:entry>  
         <oasis:entry colname="col3">18.10 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.82</oasis:entry>  
         <oasis:entry colname="col4">8.76 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.07</oasis:entry>  
         <oasis:entry colname="col5">23.17 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.24</oasis:entry>  
         <oasis:entry colname="col6">94.15 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 12.56</oasis:entry>  
         <oasis:entry colname="col7">165.73 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 14.65</oasis:entry>  
         <oasis:entry colname="col8">0.99 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.71</oasis:entry>  
         <oasis:entry colname="col9">8.31 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.45</oasis:entry>  
         <oasis:entry colname="col10">184.31 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 13.22</oasis:entry>  
         <oasis:entry colname="col11">89.44 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 5.24</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">30–40</oasis:entry>  
         <oasis:entry colname="col2">28.7 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1</oasis:entry>  
         <oasis:entry colname="col3">35.54 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.65</oasis:entry>  
         <oasis:entry colname="col4">8.68 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.05</oasis:entry>  
         <oasis:entry colname="col5">24.84 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.78</oasis:entry>  
         <oasis:entry colname="col6">130.22 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 13.43</oasis:entry>  
         <oasis:entry colname="col7">400.27 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 21.21</oasis:entry>  
         <oasis:entry colname="col8">0.82 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.68</oasis:entry>  
         <oasis:entry colname="col9">7.74 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.82</oasis:entry>  
         <oasis:entry colname="col10">358.32 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 25.69</oasis:entry>  
         <oasis:entry colname="col11">188.45 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 13.89</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">70–80</oasis:entry>  
         <oasis:entry colname="col2">27.0 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1</oasis:entry>  
         <oasis:entry colname="col3">50.58 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 6.21</oasis:entry>  
         <oasis:entry colname="col4">8.20 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04</oasis:entry>  
         <oasis:entry colname="col5">35.74 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.68</oasis:entry>  
         <oasis:entry colname="col6">349.46 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 30.67</oasis:entry>  
         <oasis:entry colname="col7">444.42 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 20.33</oasis:entry>  
         <oasis:entry colname="col8">absent</oasis:entry>  
         <oasis:entry colname="col9">6.93 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.91</oasis:entry>  
         <oasis:entry colname="col10">467.48 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 24.86</oasis:entry>  
         <oasis:entry colname="col11">355.21 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 17.34</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">140–150</oasis:entry>  
         <oasis:entry colname="col2">25.2 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>  
         <oasis:entry colname="col3">38.86 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 4.27</oasis:entry>  
         <oasis:entry colname="col4">8.02 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.7</oasis:entry>  
         <oasis:entry colname="col5">20.41 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.79</oasis:entry>  
         <oasis:entry colname="col6">194.28 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 16.28</oasis:entry>  
         <oasis:entry colname="col7">414.09 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 30.77</oasis:entry>  
         <oasis:entry colname="col8">absent</oasis:entry>  
         <oasis:entry colname="col9">7.15 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.38</oasis:entry>  
         <oasis:entry colname="col10">327.28 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 24.12</oasis:entry>  
         <oasis:entry colname="col11">294.35 <inline-formula><mml:math display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 18.01</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <p>The measure of real participation of salts and separate ions in soil
chemical reactions is their activity. The real state of the main ions in
soil solutions was determined on the basis of ionic strength and ion
association in the soil solution. Algorithms were proposed for soil and
vadose zone solution equilibrium calculation (Endovitskii and Minkin, 1979;
Endovitskii et al., 1985; Endovitskii et al, 2009). On the basis of analytical data (Table 1) using our own
software, the forms of main ions in the soil solution were calculated
according the method of ionic pairs (MIP) (Adams, 1971): the law of initial
concentration preservation and the law of the operating masses of chemical
equilibrium system.</p>
      <p>The concentration was calculated of free and associated forms of ions
according to the sum of the ion's analytical concentration. To carry out the
calculation, the following was used: iteration to solve the system of algebraic equations
of the material balance of ions and linear interpolation to calculate the
values of tabulated equilibrium constants according calculated data.</p>
      <p>The equations of main ions material balance are as follows:

              <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mfenced close="]" open="["><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">Ca</mml:mi></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CaCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CaHCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E1"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CaSO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mfenced close="]" open="["><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">Mg</mml:mi></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">MgCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">MgHCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E2"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">MgSO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p><?xmltex \hack{\newpage}?>
          <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msup><mml:mrow class="chem"><mml:mi mathvariant="normal">Na</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mrow class="chem"><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mspace width="0.125em" linebreak="nobreak"/></mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">NaCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mrow class="chem"><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">NaSO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

              <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CaCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">MgCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E4"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">NaCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msubsup><mml:mrow class="chem"><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">HCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">HCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CaHCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">MgHCO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

              <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">SO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">SO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">2</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">CaSO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">MgSO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E6"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mrow class="chem"><mml:mi mathvariant="normal">NaSO</mml:mi></mml:mrow><mml:mrow class="chem"><mml:mn mathvariant="normal">4</mml:mn></mml:mrow><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          where [Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>] and [Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>] are the equilibrium concentrations of the free
form of the ions, and [CaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>] and [MgCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>] are equilibrium
concentrations of ion in associated form (ion pair).</p>
      <p>For groups of cations, the concentration constants of ionic pair dissociation
follow the law of operating masses given via Eqs. (7)–(9):
          <disp-formula id="Ch1.E7" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mspace width="0.25em" linebreak="nobreak"/><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CaHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">CaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E8" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">MgHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:mi>M</mml:mi><mml:msup><mml:mi>g</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">MgSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E9" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">NaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">NaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
        The equilibrium concentration of ionic pair was replaced in Eqs. (1)–(6)
with its value according to relevant dissociation constant from Eqs. (7)–(9).
The system of equations of material balance of ions was transformed
as follows according to Eqs. (10)–(15):
          <disp-formula id="Ch1.E10" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8}{8}\selectfont$\displaystyle}?><mml:mo movablelimits="false">∑</mml:mo><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E11" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:mo movablelimits="false">∑</mml:mo><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E12" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced><mml:mfenced open="(" close=")"><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E13" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:mo movablelimits="false">∑</mml:mo><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E14" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mo movablelimits="false">∑</mml:mo><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          <disp-formula id="Ch1.E15" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{8.5}{8.5}\selectfont$\displaystyle}?><mml:mo movablelimits="false">∑</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>.</mml:mo><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
        According to Davies equation for constants, the concentration constant of
dissociation in Eqs. (10)–(15) was recalculated:
          <disp-formula id="Ch1.E16" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mi>p</mml:mi><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mi>p</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mi>A</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:msup><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mfenced open="(" close=")"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:msqrt><mml:mi>I</mml:mi></mml:msqrt><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>+</mml:mo><mml:msqrt><mml:mi>I</mml:mi></mml:msqrt></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mi>I</mml:mi></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> denotes the concentration constant of dissociation of ionic couple,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi>K</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> the corresponding thermodynamic constant, <inline-formula><mml:math display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> the Debye–Huckel
constant 0.5042 at 20 <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C, <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>A</mml:mi><mml:msup><mml:mi>Z</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> the algebraic sum of squares of a
charge of the particles in the equation of dissociation constant, and <inline-formula><mml:math display="inline"><mml:mi>I</mml:mi></mml:math></inline-formula> the ionic
strength of solution.</p>
      <p>The calculated <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mi>K</mml:mi></mml:mrow></mml:math></inline-formula> value with Eq. (16) corresponds to Bjerrum et
al. (1958), Garrels and Christ (1965), Debye and Huckel (1923), and Sposito (1984).</p>
      <p>Thermodynamic constants of dissociation are as follows (Lurie, 1986; Handbook of
chemist 21; Sposito, 1989):
          <disp-formula id="Ch1.Ex5"><mml:math display="block"><mml:mtable class="array" columnalign="left left left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mn>3.2</mml:mn><mml:mo>;</mml:mo><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>1.26</mml:mn><mml:mo>;</mml:mo><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">CaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>2.31.</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mn>3.4</mml:mn><mml:mo>;</mml:mo><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>1.16</mml:mn><mml:mo>;</mml:mo><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">MgSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>2.36.</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1.27</mml:mn><mml:mo>;</mml:mo><mml:mi>p</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">NaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mn>0.72.</mml:mn></mml:mrow></mml:mtd><mml:mtd/></mml:mtr></mml:mtable></mml:math></disp-formula>
        The formal ionic strength of soil solution was calculated with the data of
analytical ion concentration according to Eq. (17):
          <disp-formula id="Ch1.E17" content-type="numbered"><mml:math display="block"><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>[</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>(</mml:mo><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>(</mml:mo><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="normal">Cl</mml:mi><mml:mo>-</mml:mo></mml:msup><mml:mo>)</mml:mo><mml:mo>]</mml:mo><mml:mo>,</mml:mo><mml:mi mathvariant="normal">mol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
        The equilibrium concentrations of ion free forms were designated as
unknown values of the equation system. The analytical concentration of all
ion forms was used as a total value of every chemical element. The system
was obtained with six equations with six unknowns.</p>
      <p>The iteration was used to find out the value of the equilibrium
concentrations of free ions. The equilibrium concentrations of ion pairs
were determined according equations for dissociation constants (Eqs. 7–9).</p>
      <p>The effective ionic force of solution was calculated according to the
values of equilibrium concentration of all ion forms according to Eq. (18):
          <disp-formula id="Ch1.E18" content-type="numbered"><mml:math display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{9.5}{9.5}\selectfont$\displaystyle}?><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mi>I</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mfenced close="" open="{"><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mfenced open="[" close="]"><mml:msup><mml:mi mathvariant="normal">Mg</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msup><mml:mi mathvariant="normal">Na</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced close="]" open="["><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:msup><mml:mn mathvariant="normal">2</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">CaHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">MgHCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">NaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:mfenced open="[" close="]"><mml:msubsup><mml:mi mathvariant="normal">NaSO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mfenced><mml:mo>+</mml:mo><mml:mfenced open="." close="}"><mml:mfenced open="[" close=")"><mml:msup><mml:mi mathvariant="normal">Cl</mml:mi><mml:mo>-</mml:mo></mml:msup></mml:mfenced></mml:mfenced><mml:mo>,</mml:mo><mml:mi mathvariant="normal">mol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable><?xmltex \hack{$\egroup}?></mml:mrow></mml:math></disp-formula>
        As a result of the first step of iteration procedure, the
concentration constants of dissociation were calculated (Eq. 16). The new system of
equations of material balance was obtained. On the new set of the system, components made
the next iteration of Eqs. (10)–(15). By the iteration sequence calculated the ion
forms in soil solution.</p>
      <p>The coefficient of ion association <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is proposed as a ratio of
ion free form to its analytical content:
          <disp-formula id="Ch1.E19" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>e</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">ass</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">an</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">ass</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is calculated ion content in solution taking into account
its association with another ions and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">an</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is analytical concentration of
an ion.</p>
      <p>An activity coefficient is a factor used in thermodynamics to account for
deviations from ideal behavior in a mixture of chemical
substances. Activity coefficients may be determined experimentally, and it can be
calculated theoretically using the Debye–Hückel equation and other
models. The <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi>e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> factor in Eq. (19) is not a result of direct
determination or direct calculation, but rather it is an integral product of several
stages of modeling taking into account laws of a solution's chemical
thermodynamics and corresponding to Eqs. (1)–(18).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Forms of ions (cations) in the soil solution of chestnut saline
solonetz, % of the total ion content.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.91}[.91]?><oasis:tgroup cols="12">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left"/>
     <oasis:colspec colnum="9" colname="col9" align="left" colsep="1"/>
     <oasis:colspec colnum="10" colname="col10" align="left"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:colspec colnum="12" colname="col12" align="left"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1">Depth, cm</oasis:entry>  
         <oasis:entry rowsep="1" namest="col2" nameend="col5" align="center" colsep="1">Calcium </oasis:entry>  
         <oasis:entry rowsep="1" namest="col6" nameend="col9" align="center" colsep="1">Magnesium </oasis:entry>  
         <oasis:entry rowsep="1" namest="col10" nameend="col12" align="center">Sodium </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">[Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col3">[CaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col4">[CaHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col5">[CaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col6">[Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col7">[MgCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col8">[MgHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col9">[MgSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col10">[Na<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col11">[NaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col12">[NaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">0–5</oasis:entry>  
         <oasis:entry colname="col2">78.96</oasis:entry>  
         <oasis:entry colname="col3">absent</oasis:entry>  
         <oasis:entry colname="col4">3.43</oasis:entry>  
         <oasis:entry colname="col5">17.61</oasis:entry>  
         <oasis:entry colname="col6">77.83</oasis:entry>  
         <oasis:entry colname="col7">absent</oasis:entry>  
         <oasis:entry colname="col8">2.69</oasis:entry>  
         <oasis:entry colname="col9">19.48</oasis:entry>  
         <oasis:entry colname="col10">98.91</oasis:entry>  
         <oasis:entry colname="col11">absent</oasis:entry>  
         <oasis:entry colname="col12">1.09</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">5–14</oasis:entry>  
         <oasis:entry colname="col2">63.14</oasis:entry>  
         <oasis:entry colname="col3">2.46</oasis:entry>  
         <oasis:entry colname="col4">3.17</oasis:entry>  
         <oasis:entry colname="col5">31.23</oasis:entry>  
         <oasis:entry colname="col6">60.36</oasis:entry>  
         <oasis:entry colname="col7">3.72</oasis:entry>  
         <oasis:entry colname="col8">2.41</oasis:entry>  
         <oasis:entry colname="col9">33.50</oasis:entry>  
         <oasis:entry colname="col10">96.28</oasis:entry>  
         <oasis:entry colname="col11">0.13</oasis:entry>  
         <oasis:entry colname="col12">3.59</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">14–30</oasis:entry>  
         <oasis:entry colname="col2">56.47</oasis:entry>  
         <oasis:entry colname="col3">0.44</oasis:entry>  
         <oasis:entry colname="col4">1.93</oasis:entry>  
         <oasis:entry colname="col5">41.16</oasis:entry>  
         <oasis:entry colname="col6">53.84</oasis:entry>  
         <oasis:entry colname="col7">0.66</oasis:entry>  
         <oasis:entry colname="col8">1.46</oasis:entry>  
         <oasis:entry colname="col9">44.03</oasis:entry>  
         <oasis:entry colname="col10">93.10</oasis:entry>  
         <oasis:entry colname="col11">0.03</oasis:entry>  
         <oasis:entry colname="col12">6.86</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">30–40</oasis:entry>  
         <oasis:entry colname="col2">48.09</oasis:entry>  
         <oasis:entry colname="col3">0.24</oasis:entry>  
         <oasis:entry colname="col4">1.39</oasis:entry>  
         <oasis:entry colname="col5">50.29</oasis:entry>  
         <oasis:entry colname="col6">45.37</oasis:entry>  
         <oasis:entry colname="col7">0.35</oasis:entry>  
         <oasis:entry colname="col8">1.04</oasis:entry>  
         <oasis:entry colname="col9">53.23</oasis:entry>  
         <oasis:entry colname="col10">89.53</oasis:entry>  
         <oasis:entry colname="col11">0.02</oasis:entry>  
         <oasis:entry colname="col12">10.44</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">70–80</oasis:entry>  
         <oasis:entry colname="col2">49.58</oasis:entry>  
         <oasis:entry colname="col3">absent</oasis:entry>  
         <oasis:entry colname="col4">1.11</oasis:entry>  
         <oasis:entry colname="col5">49.31</oasis:entry>  
         <oasis:entry colname="col6">46.87</oasis:entry>  
         <oasis:entry colname="col7">absent</oasis:entry>  
         <oasis:entry colname="col8">0.83</oasis:entry>  
         <oasis:entry colname="col9">52.29</oasis:entry>  
         <oasis:entry colname="col10">90.12</oasis:entry>  
         <oasis:entry colname="col11">absent</oasis:entry>  
         <oasis:entry colname="col12">9.88</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">140–150</oasis:entry>  
         <oasis:entry colname="col2">53.78</oasis:entry>  
         <oasis:entry colname="col3">absent</oasis:entry>  
         <oasis:entry colname="col4">1.36</oasis:entry>  
         <oasis:entry colname="col5">44.86</oasis:entry>  
         <oasis:entry colname="col6">51.13</oasis:entry>  
         <oasis:entry colname="col7">absent</oasis:entry>  
         <oasis:entry colname="col8">1.02</oasis:entry>  
         <oasis:entry colname="col9">47.85</oasis:entry>  
         <oasis:entry colname="col10">91.47</oasis:entry>  
         <oasis:entry colname="col11">absent</oasis:entry>  
         <oasis:entry colname="col12">8.53</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><caption><p>Forms of ions (anions) in the soil solution of chestnut saline
solonetz, % of the total ion content.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.82}[.82]?><oasis:tgroup cols="13">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left" colsep="1"/>
     <oasis:colspec colnum="9" colname="col9" align="left"/>
     <oasis:colspec colnum="10" colname="col10" align="left"/>
     <oasis:colspec colnum="11" colname="col11" align="left"/>
     <oasis:colspec colnum="12" colname="col12" align="left" colsep="1"/>
     <oasis:colspec colnum="13" colname="col13" align="left"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1">Depth, cm</oasis:entry>  
         <oasis:entry rowsep="1" namest="col2" nameend="col5" align="center" colsep="1">Sulfates </oasis:entry>  
         <oasis:entry rowsep="1" namest="col6" nameend="col8" align="center" colsep="1">Hydrocarbons </oasis:entry>  
         <oasis:entry rowsep="1" namest="col9" nameend="col12" align="center" colsep="1">Carbonates </oasis:entry>  
         <oasis:entry colname="col13">Chlorides</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">[SO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col3">[CaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col4">[MgSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col5">[NaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col6">[HCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col7">[CaHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col8">[MgHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col9">[CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col10">[CaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col11">[MgCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col12">[NaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>]</oasis:entry>  
         <oasis:entry colname="col13"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">0–5</oasis:entry>  
         <oasis:entry colname="col2">76.69</oasis:entry>  
         <oasis:entry colname="col3">8.33</oasis:entry>  
         <oasis:entry colname="col4">12.65</oasis:entry>  
         <oasis:entry colname="col5">2.33</oasis:entry>  
         <oasis:entry colname="col6">96.30</oasis:entry>  
         <oasis:entry colname="col7">1.78</oasis:entry>  
         <oasis:entry colname="col8">1.92</oasis:entry>  
         <oasis:entry colname="col9">absent</oasis:entry>  
         <oasis:entry colname="col10">absent</oasis:entry>  
         <oasis:entry colname="col11">absent</oasis:entry>  
         <oasis:entry colname="col12">absent</oasis:entry>  
         <oasis:entry colname="col13">100</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">5–14</oasis:entry>  
         <oasis:entry colname="col2">70.07</oasis:entry>  
         <oasis:entry colname="col3">6.48</oasis:entry>  
         <oasis:entry colname="col4">16.19</oasis:entry>  
         <oasis:entry colname="col5">7.27</oasis:entry>  
         <oasis:entry colname="col6">93.73</oasis:entry>  
         <oasis:entry colname="col7">2.26</oasis:entry>  
         <oasis:entry colname="col8">4.00</oasis:entry>  
         <oasis:entry colname="col9">21.65</oasis:entry>  
         <oasis:entry colname="col10">15.54</oasis:entry>  
         <oasis:entry colname="col11">54.84</oasis:entry>  
         <oasis:entry colname="col12">7.97</oasis:entry>  
         <oasis:entry colname="col13">100</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">14–30</oasis:entry>  
         <oasis:entry colname="col2">59.99</oasis:entry>  
         <oasis:entry colname="col3">5.17</oasis:entry>  
         <oasis:entry colname="col4">22.49</oasis:entry>  
         <oasis:entry colname="col5">12.34</oasis:entry>  
         <oasis:entry colname="col6">89.02</oasis:entry>  
         <oasis:entry colname="col7">2.69</oasis:entry>  
         <oasis:entry colname="col8">8.29</oasis:entry>  
         <oasis:entry colname="col9">15.36</oasis:entry>  
         <oasis:entry colname="col10">10.28</oasis:entry>  
         <oasis:entry colname="col11">63.14</oasis:entry>  
         <oasis:entry colname="col12">11.21</oasis:entry>  
         <oasis:entry colname="col13">100</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">30–40</oasis:entry>  
         <oasis:entry colname="col2">53.83</oasis:entry>  
         <oasis:entry colname="col3">3.49</oasis:entry>  
         <oasis:entry colname="col4">19.35</oasis:entry>  
         <oasis:entry colname="col5">23.33</oasis:entry>  
         <oasis:entry colname="col6">89.01</oasis:entry>  
         <oasis:entry colname="col7">2.23</oasis:entry>  
         <oasis:entry colname="col8">8.76</oasis:entry>  
         <oasis:entry colname="col9">14.32</oasis:entry>  
         <oasis:entry colname="col10">7.20</oasis:entry>  
         <oasis:entry colname="col11">56.44</oasis:entry>  
         <oasis:entry colname="col12">22.03</oasis:entry>  
         <oasis:entry colname="col13">100</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">70–80</oasis:entry>  
         <oasis:entry colname="col2">38.35</oasis:entry>  
         <oasis:entry colname="col3">3.77</oasis:entry>  
         <oasis:entry colname="col4">39.09</oasis:entry>  
         <oasis:entry colname="col5">18.79</oasis:entry>  
         <oasis:entry colname="col6">76.13</oasis:entry>  
         <oasis:entry colname="col7">2.86</oasis:entry>  
         <oasis:entry colname="col8">21.01</oasis:entry>  
         <oasis:entry colname="col9">absent</oasis:entry>  
         <oasis:entry colname="col10">absent</oasis:entry>  
         <oasis:entry colname="col11">absent</oasis:entry>  
         <oasis:entry colname="col12">absent</oasis:entry>  
         <oasis:entry colname="col13">100</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">140–150</oasis:entry>  
         <oasis:entry colname="col2">47.22</oasis:entry>  
         <oasis:entry colname="col3">2.80</oasis:entry>  
         <oasis:entry colname="col4">28.40</oasis:entry>  
         <oasis:entry colname="col5">21.58</oasis:entry>  
         <oasis:entry colname="col6">84.17</oasis:entry>  
         <oasis:entry colname="col7">1.93</oasis:entry>  
         <oasis:entry colname="col8">13.90</oasis:entry>  
         <oasis:entry colname="col9">absent</oasis:entry>  
         <oasis:entry colname="col10">absent</oasis:entry>  
         <oasis:entry colname="col11">absent</oasis:entry>  
         <oasis:entry colname="col12">absent</oasis:entry>  
         <oasis:entry colname="col13">100</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table></table-wrap>

      <p>For calculation, the software product was used, developed by
Endovitskii and Minkin (1979) and Endovitskii et al. (1985, 2009).</p>
</sec>
<sec id="Ch1.S4">
  <title>Discussion</title>
      <p>Equations (7)–(19) were used to model the association of ions at a given
analytical composition of solution (Table 1).</p>
      <p>At high ionic strength of soil solution, the biological processes in plant
and mass transfer in vadose zone are extremely slow. In this respect the
modeling at soil solution ionic strength of more than 1.0 is excessive. The
circumstance is significant for soil of medium salinity, where the solution
in soil and aeration zone had an ionic strength of about 1.0 at low soil
moisture, and it is not available to remove from dispersed systems without
disturbing the structure and linkages with the solid and gas soil systems,
and direct analytical composition determination.</p>
      <p>A range of estimated ionic strength from 0.05 to 1.2 corresponds to the
activity of ions useful for plants and moveable in vadose zone
concentrated solutions. At higher ionic strength, the soil biological
processes, plant growth and mass transfer in vadose zone are extremely slow.</p>
      <p>To obtain the baseline data for thermodynamic model's testing, a
standard physical modeling method was used. The method has drawbacks. Instead of proper
soil, the substrate of soil and sand is used. Otherwise, the extraction of
soil solution from the native soil of heavy structure and corresponding
granulometric composition is impossible. The presence of sand in the
substrate dramatically increases the hydraulic conductivity of the
artificial system. It is distinguished from natural chestnut soil. The next
lack of direct soil solution extraction methods is that links are broken in
the system “solid–liquid phase”.</p>
      <p>Chestnut soil has low humidity. But at low soil moisture the soil solution
displacement method is useless, so in the experiment the high soil moisture was
applied. This leads to inadequate generalization of the object's simulation,
but another version of the direct study of soil solution composition is not
currently available. This disadvantage of method is a reason for
thermodynamic model development. It allows for extrapolation of the solution's
state in soil and vadose zone to the range of low humidity of soil complex
components.</p>
      <p>The real equilibrium concentration of ion forms in soil solution and vadose
zone depends on concentration and composition of soil solution (Tables 2, 3).
The higher the salinity of the solution, the more the ions are associated. In the
form of ionic pairs in saline horizons of soil and vadose zone, there are
11–52 % Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>; 22.2–54.6 % Mg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula>; 1.1–10.5 % Na<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>;
3.7–23.8 HCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, 23.3–61.6 % SO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>, and up to 85.7 %
CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>. In non-saline soil horizon at 0–5 cm at soil humidity of
22.4 %, most of the ions are in free form.</p>
      <p>Due to ion association, the mobility of dry steppe chestnut saline solonetzic
soil and vadose zone water solution components is higher compared to
previous estimates, especially for carbonates. In such circumstances the
preferred water fluxes in the soil and vadose zone cause the loss of soil
mineral phase to deep soil horizons, then to vadose zone, saturation zone
and landscape. The vertical and lateral salt redistribution is high. The
association of ions in saline carbonate water solution is a cause of high
salt mobility through the vadose and saturation zones. It is dangerous in a
view of biosphere carbon loss, and this indicates the need for measures to reduce
this seepage. The carbon sequestration theory should not be understood as
a carbon isolation but rather as the transformation of carbon gaseous phase to
biological phase.</p>
      <p>Association of ions in water solutions of soil and vadose zone promotes
innovative solutions in the field of soil water regime and water saving (El
Marazky et al., 2011; Kalinichenko, 2014; Seitkaziev et al., 2015).</p>
      <p>The nature of CCE in soils is a reason why, using an analytical concentration
of ions, only the high calculated saturation degree of soil solutions with
CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> is observed. Accounting processes of ion association reduces the
supersaturation of soil solutions with CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> for 10–50 times. The
similar effect on soil solution has its ionic strength. In view of
complexation of Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> with soluble organic substance, the degree of
calculated soil solution saturation with CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> reduces up to 1.5–2.0 times.</p>
      <p>Accounting association and activity of ions and calculating degree of soil
solution saturation with chemicals provides new understanding of
migration and accumulation of chemical compounds in soils, vadose and
saturation zones, and landscapes concerning CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula>.</p>
      <p>Along with salt dynamics in soil profile, the lateral
transfer of substances in landscapes and watersheds is important. The developed approach is
closely linked to these objects due to the fact that, given the association
of ions in the soil solution, assessment of the likelihood of substance
mobility in landscape and watershed is significantly higher than previously
thought.</p>
      <p>The dynamics of solution composition is related to moisture of soil and
aeration zone. According to the simulation, the transfer of substances
in the soil and vadose zone is noticeable at low soil moisture. With this
point of view, the transfer of a substance in disperse systems should be
considered not only as the unbroken mass transfer flux but also taking into
account the formation of micro-basins of solution. As the humidity reduces,
the mass transfer zone of the actual transfer of water and dissolved
substances becomes more discrete. The reason for discontinuity of the flow
is the difference of water thermodynamic potential in individual
capillaries, inner surfaces of soil, and water surface curvature variations.
After subsequent wetting of soil, the agent of transfer does not pass the
dissolution stage, but it quickly enters into a geochemical transfer process. The
micro-basin formation, on the one hand, is useful as a source of plant
nutrients, but, on the other hand, it is dangerous in terms of easy loss of
useful substances from the soil and vice versa – the receipt of unwanted
substances.</p>
      <p>In agriculture, there is a danger of distortion of calcium carbonate system
of soil and aeration zone. This determines a need for new findings in
management of soil and aeration zone focused on reducing mobility of
matter, especially for technological tools that will overcome an entrainment
of useful substances from the soil, as well as receipt and accumulation of
unfavorable substances at agriculture and irrigation.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <title>Conclusions</title>
      <p>The result obtained in experiment and modeling shows the fundamental
peculiarities of behavior of calcium carbonate system in soil and vadose
zone water solution taking into account the ion association. At high ionic
force in soil solution, electrically neutral ion pairs
CaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, CaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, MgCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula>, and
MgSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mn mathvariant="normal">0</mml:mn></mml:msubsup></mml:mrow></mml:math></inline-formula> are formed, as well as charged ion pairs CaHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>,
MgHCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, NaCO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, NaSO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, CaOH<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>, and
MgOH<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>+</mml:mo></mml:msup></mml:math></inline-formula>. The association of ions shows that the thermodynamic
preconditions of CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> sedimentation in soil and vadose zone occur at
a much higher concentration of Ca<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> and CO<inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> ions in soil
solution than was considered previously. Therefore, there is a
significant probability of high mobility of CaCO<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:math></inline-formula> in soil, vadose and
saturation zones, and landscape, which was underestimated earlier.</p>
      <p>The quantitative solving of water solution thermodynamic model shows that
mobility of matter, especially carbon, in terrestrial system is much higher
than was known before. The prediction of soil, vadose and saturation
zone,and  landscape evolution will be properly carried out.</p>
      <p>This research shows that uncertainty of terrestrial carbon sink
from soil through vadose zone is linked to high mobility of carbon in the form
of carbonates in the soil solution of dry steppe chestnut saline solonetzic
soil of southern Russia. The soil geochemical barriers for carbonates are
probably less stable than was known before. The association of ions in
soil solutions is one of the drivers promoting transformation of solution,
excessive fluxes of carbon into soil, and loss of carbon from soil and
vadose zone.</p>
      <p>The revealed regularities represent the evolution model of soil complexes
under halogenesis on the global scale</p>
</sec>

      
      </body>
    <back><notes notes-type="authorcontribution">

      <p>Abdul-Malik A. Batukaev, the head of investigation, designed the plan of
research and organized the study and data analysis, which were coordinated by Tatiana M. Minkina.
The idea of ion association in soil solution was by provided by
Anatoly P. Endovitsky, who also gave the system of equations. The mathematical model
was developed by Andrey G. Andreev. This model was interpreted by Valery P.
Kalinichenko. Svetlana N. Sushkova collected the field data and performed the
statistical analysis. Zaurbek S. Dikaev, Tatiana M. Minkina and Saglara S. Mandzhieva carried
out the experiment. All the authors
contributed in writing of the paper.</p>
  </notes><ack><title>Acknowledgements</title><p>This research was supported by projects
of Ministry of Education and Science of Russia, no. 5.885.2014/K, Russian
Foundation for Basic Research, no. 14-05-00586_a, and the grant of the
President of Russian Federation, no. MK-6827.2015.4.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: A. Jordán</p></ack><ref-list>
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    <!--<article-title-html>Ion association in water solution of soil and vadose zone of chestnut saline solonetz as a driver of terrestrial carbon sink</article-title-html>
<abstract-html><p class="p">The assessment of soil and vadose zone as the drains for carbon sink and proper
modeling of the effects and extremes of biogeochemical cycles in
the terrestrial biosphere are the key components to understanding the carbon cycle,
global climate system, and aquatic and terrestrial system uncertainties.
Calcium carbonate equilibrium causes saturation of solution with CaCO<sub>3</sub>,
and it determines its material composition, migration and accumulation of salts. In
a solution electrically neutral ion pairs are formed: CaCO<sub>3</sub><sup>0</sup>,
CaSO<sub>4</sub><sup>0</sup>, MgCO<sub>3</sub><sup>0</sup>, and MgSO<sub>4</sub><sup>0</sup>, as well as
charged ion pairs CaHCO<sub>3</sub><sup>+</sup>, MgHCO<sub>3</sub><sup>+</sup>, NaCO<sub>3</sub><sup>−</sup>,
NaSO<sub>4</sub><sup>−</sup>, CaOH<sup>+</sup>, and MgOH<sup>+</sup>. The calcium carbonate
equilibrium algorithm, mathematical model and original software to calculate
the real equilibrium forms of ions and to determine the nature of
calcium carbonate balance in a solution were developed. This approach conducts the quantitative
assessment of real ion forms of solution in solonetz soil and vadose zone of
dry steppe taking into account the ion association at high ionic strength
of saline soil solution. The concentrations of free and associated ion form
were calculated according to analytical ion concentration in real solution.
In the iteration procedure, the equations were used to find the following: ion material balance, a
linear interpolation of equilibrium constants, a method of ionic pairs, the
laws of initial concentration preservation, operating masses of equilibrium
system, and the concentration constants of ion pair dissociation. The
coefficient of ion association <i>γ</i><sub><i>e</i></sub> was determined as the ratio of
ions free form to analytical content of ion <i>γ</i><sub><i>e</i></sub> = <i>C</i><sub>ass</sub>∕<i>C</i><sub>an</sub>. Depending on soil and vadose
zone layer, concentration and composition of solution in the ionic pair's
form are 11–52 % Ca<sup>2+</sup>; 22.2–54.6 % Mg<sup>2+</sup>; 1.1–10.5 %
Na<sup>+</sup>; 3.7–23.8 HCO<sub>3</sub><sup>−</sup>, 23.3–61.6 % SO<sub>4</sub><sup>2−</sup>, and up to
85.7 % CO<sub>3</sub><sup>2−</sup>. The carbonate system of soil and vadose zone water
solution helps to explain the evolution of salted soils, vadose and
saturation zones, and landscape. It also helps to improve the soil maintenance, plant
nutrition and irrigation.</p><p class="p">The association of ions in soil solutions is one of the drivers promoting
transformation of solution, excessive fluxes of carbon in the soil, and loss of
carbon from soil through vadose zone.</p></abstract-html>
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