Chemistry

Chemistry

Problem

A chemist needs to dissolve at least 1.0×10−3 mol1.0\times10^{-3}\,\text{mol} of CoCO3_3(s) per liter of solution at 25 °C. The solubility product is Ksp(CoCO3)=1.4×10−13K_{sp}(\text{CoCO}_3)=1.4\times10^{-13} and the second acid-dissociation constant of carbonic acid is Ka2=4.8×10−11K_{a2}=4.8\times10^{-11}. Assuming no other significant carbonate sources, what minimum pH will achieve the required solubility? a) 2.702.70 b) 6.506.50 c) 3.463.46 d) 3.003.00
Intuitive explanation

Dissolving CoCO₃ requires both the salt to dissociate and the carbonate ion to be removed from equilibrium by protonation—the key is that lowering pH shifts the carbonate equilibrium toward CO2\text{CO}_2, freeing up more CO32−\text{CO}_3^{2-} to dissolve more solid. You'll use KspK_{sp} to relate [Co2+][\text{Co}^{2+}] and [CO32−][\text{CO}_3^{2-}], then Ka2K_{a2} to connect [CO32−][\text{CO}_3^{2-}] to [H+][\text{H}^+], working backward from your target dissolution amount to find the required acidity.

Intuitive explanation

Dissolving CoCO₃ requires both the salt to dissociate and the carbonate ion to be removed from equilibrium by protonation—the key is that lowering pH shifts the carbonate equilibrium toward CO2\text{CO}_2, freeing up more CO32−\text{CO}_3^{2-} to dissolve more solid. You'll use KspK_{sp} to relate [Co2+][\text{Co}^{2+}] and [CO32−][\text{CO}_3^{2-}], then Ka2K_{a2} to connect [CO32−][\text{CO}_3^{2-}] to [H+][\text{H}^+], working backward from your target dissolution amount to find the required acidity.

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