How and to what extent soil temperature affect the solubility of CO2 in soil (under optimal moisture condition)?
pH and Ca+2 affect CO2 concentration in calcite solution, https://eprints.nwisrl.ars.usda.gov/436/1/548.pdf. The equilibrium with temperature and roots is much more uncertain for soil heterogeneity https://www.pc-progress.com/Documents/Jirka/CO2(1)_WRR93.pdf
In general, the hotter the soil, less CO2(g) in it. It may not be true in chalcareous soils
Solutions of CO2 in water contain both CO2 and bicarbonate at the range of typical soil pHs. The concentration of bicarbonate increases with increasing pH. The concentration of CO2 is almost independent of pH. There are international tables of these data and there are equilibrium speciation models that incorporate the effects of other components, e.g. GEOCHEM-EZ is free
Scientific area that I do the pathophysiology and pathology of animal nutrition LIKE transgenic animals
In general, the solubility of CO2 in water decreases with increasing temperature from 0 C up to 100 C. As some of the other answers describe, there are many other factors including pH, pressure, and the concentrations of other ions among others that will also affect CO2 solubility. And as Paul Milham mentions in another answer, CO2 is part of the inorganic carbon system that includes bicarbonate and at high pH values, carbonate as well. There are many good reference materials including aqueous geochemistry texts like Stumm and Morgan that discuss the inorganic carbon system in detail.
There are physical controls associated with CO2 solubility as noted above. However, there are also controls over CO2 production associated with soil respiration. Soil temperature is also an important determinant of CO2 production in most environments (ex. arid/hyperarid). This relates to the metabolic controls over microbial respiration, which is responsible for the higher partial pressure of CO2 within the soil zone (often peaks in B horizon). In cold environments CO2 respiration rates will be lower than in warmer environments assuming that soil moisture is not limiting. Therefore, it is important to consider the role of soil temperature over both the solubility of CO2 and microbial metabolism.
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