General formula for Calcium carbonate

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How do u derive a general formula (without undue approximations) to calculate the solubility of CaCO3(s) in a aqueous solution at any pH?

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Start with all equations describing the solution - like dissociation equilibria, Kso, water ion product. Add to that charge balace and mass balances for carbonates and calcium. Solve for concentration of calcium.

That's the most general approach possible.

See pH calculation lectures, and especially lecture on pH of polyprotic acids. Equations 9.11, 9.12 and 9.13 can give you some hints.

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