Chemistry

Problem

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

25\ ^\circ\text{C}

. •

\text{CaCO}_3

(

K_{sp}=3.8\times10^{-9}

) •

\text{CaSO}_4

(

K_{sp}=2.4\times10^{-5}

) The groundwater is buffered at

\text{pH}=6.00

. For carbonate chemistry, the following acid–base data may be assumed:

K_{a2}(\text{H}_2\text{CO}_3)=4.8\times10^{-11}

(a) Derive an expression for the molar solubility of

\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

\text{CaCO}_3

in the groundwater. (c) Calculate the molar solubility of

\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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