Abstract. 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 3 , and it determines its material composition, migration and accumulation of salts. In a solution electrically neutral ion pairs are formed: CaCO 0 3 , CaSO 0 4 , MgCO 0 3 , and MgSO 0 4 , as well as charged ion pairs CaHCO, CaOH + , and MgOH + . 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 γ e was determined as the ratio of ions free form to analytical content of ion γ e = C ass /C an . Depending on soil and vadose zone layer, concentration and composition of solution in the ionic pair's form are 11-52 % Ca 2+ ; 22.2-54.6 % Mg 2+ ;1.1-10.5 % Na + ; 3.7-23.8 HCO 3 . 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.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.

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Biogeosystem change is linked to ion's association in soil solution. The concern of carbon sequestration problem is a soil as carbon sink drain. The carbonate calcium equilibrium (CCE) in soil solutions is important to characterize the degree soil solutions saturation with CaCO3 as a factor of terrestrial system carbonate geochemical cycle. CCE depends on the state of the chemical composition, pH, Eh, buffering properties of soil liquid phase, dissolution, migration, precipitation of carbonates in the soil profile and landscape, ion exchange processes at the interface of solid and liquid phases. At high ionic force in soil solution are formed electrically neutral ion pairs СаСО3°; CaSO4°, MgCO3°, MgSO4°, charged ion pairs CaHCO3 + , MgHCO3 + , NaCO3 -, NaSO4 -, CaOH + , MgOH + .The object of research -Southern Russia; saline chestnut soil, dry steppe zone; non-saline chernozem, steppe zone. The soil solution was extracted from soil layers 0-150 cm. Composition of soil solution was determined using standard analytical methods. The soil system is the object of mathematical thermodynamic modeling, because it is impossible to remove the solution from dry soil, on the other hand, the extraction of solution change the chemical equilibrium in solution. The approach to soil disperse system model is proposed as a discreet partially insulated form one another microwater-basins on the internal surfaces of soil. This approach gives a new understanding of water-salt transfer, geochemical barrier functions and ecological properties of soil.On the basis of CCE algorithm, the computer programs were developed to calculate the real equilibrium ion forms and determine the nature of carbonate-calcium balance in the soil solution. The mathematical model shows the real state of associated ions at different ionic strength of low saline and saline soil solution. The concentration of free and associated macro-ion forms were calculated in iteration procedure according analytical ion concentration considering ion material balance, linear interpolation of equilibrium constants, method of ionic pairs, laws of: initial Biogeosystem Technique, 2015, Vol.(5), Is. 3 268 concentration preservation, operating masses of equilibrium system. Concentration constants of ion pairs dissociation were calculated following the law of operating masses. Were determined the quantity of ion free form and coefficient of ion association γe as a ratio of ions free form to its analytical contents e ass an C / C  . The association of ions is higher in saline soil layers. Depending on composition and ionic force c of soil solution in the form of ionic pairs