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That the solution is alkaline is not surprising, given that the carbonate ion, as weak bases go, is a moderately strong one.

### PROBLEM 13-13

Repeat the calculation of the solubility of calcium carbonate by the approximate single equilibrium method using a realistic wintertime water temperature of 5°C; at that temperature, ksp = 8.1 X 1CT9 for CaC03, ka = 2.8 X 1CT11 for HC03and kw = 0.2 X lu"14. By comparing the result with that in the foregoing text for 25 °C, decide whether the solubility of calcium carbonate increases or decreases with increasing temperature.

PROBLEM 13-14

What is the net reaction when reactions (1) and (3) are added together? How is the equilibrium constant for this combined process related to kl and Ky Show that the pH of the aqueous solution resulting from a C02 partial pressure of 0.00037 atm in the combined process has the same value of 5.6 as is determined by considering the individual reactions consecutively, as in Problem 3-10.

In the analysis above, it has been assumed that calcium carbonate is dissolving in pure water and that the reaction of carbonate with water determines the pH. In some real-world situations, the pH of the aqueous solution is predetermined by the presence of some dominant source of H+ or OH", so the contribution from calcium carbonate is negligible. In such cases, the ratio of bicarbonate to carbonate ion can be determined from kb and the known, fixed [OH"*"]:

[HC031/[C032-] = Kb/[OH"]

and thus

[HC03-] = Kb[C032l/[0H-]

The solubility S of calcium carbonate, and the resulting dissolved calcium ion concentration, here equal the sum of the carbonate and bicarbonate ion concentrations, so

S = [Ca2+] = [C0321 + [HCOs i = [C032-] + Kb[C032l/[0Hl = [C032! (1 + fCb/[OH"])

If, for convenience, we temporarily define / = (1 + Kb/[OH ]), then

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