Problem $7$

The calcium $(C{a}^{2+})$ concentration of the water in a lake is $2ppb.$ Please estimate its $pH.$ Note that the ${10}^{-10\mathrm{.}33}.K_H={10}^{-1\mathrm{.}47}\frac{M}{a}tm$ for the dissolution of $C{O}_2.$ Keep three significant figures in the answer.

$(12$ Points$)$