A geochemist is modeling the fate of two calcium‐containing minerals in mildly acidic…

CHEMISTRY · Multi-part · AP · Chemistry · Acids and Bases · Acids and Bases

Problem

A geochemist is modeling the fate of two calcium‐containing minerals in mildly acidic groundwater at 25 ∘C25\ ^\circ\text{C}. • CaCO3\text{CaCO}_3 (Ksp=3.8×10−9K_{sp}=3.8\times10^{-9}) • CaSO4\text{CaSO}_4 (Ksp=2.4×10−5K_{sp}=2.4\times10^{-5}) The groundwater is buffered at pH=6.00\text{pH}=6.00. For carbonate chemistry, the following acid–base data may be assumed: Ka2(H2CO3)=4.8×10−11K_{a2}(\text{H}_2\text{CO}_3)=4.8\times10^{-11} (a) Derive an expression for the molar solubility of CaCO3\text{CaCO}_3 that is valid at the given pH, clearly defining all symbols used. (b) Using the expression from part (a), calculate the molar solubility of CaCO3\text{CaCO}_3 in the groundwater. (c) Calculate the molar solubility of CaSO4\text{CaSO}_4 at the same pH. (d) Rank the two minerals from greater to lesser solubility under the stated conditions, and explain how pH contributes to the observed difference.

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