Chapter 16, Problem 101IAE

In this problem, we will use material balance and chacepts (pages 761-762) to calculate the equilibrium concentrations in an extremely dilute solution of a strong acid, $1.0\times {10}^{-7}\text{MHCl}\left(\text{aq}\right)$ .

(a) Write down the material balance equation for $1.0\times {10}^{-7}$ MHCl(aq), assuming that HCl ionizes completely in aqueous solution.

(b) Write down the charge balance equation (an electroneutrality condition) for this solution.

(c) Use the material balance and charge balance equations, and product for water, $K_z=\left[{\text{H}}_{\text{2}}{\text{O}}^{\text{-}}\right]\left[{\text{OH}}^{\text{-}}\right]$ , to show that $\left[{\text{H}}_{\text{2}}{\text{O}}^{\text{-}}\right]{\text{-c}}_{\text{2}}\left[{\text{H}}_{\text{2}}\text{O+}\right]{\text{-K}}_{\text{c}}=0$ , where $co=1.0\times {10}^{-7}\text{M}$ .

(d) Use the quadratic formula to solve equation in (c) $\left[{\text{H}}_{\text{2}}{\text{O}}^{-}\right]$ .

(e) Calculate $\left[{\text{OH}}^{\text{-}}\right]$ and compare this value with $\left[{\text{Cl}}^{\text{-}}\right]$ . What conclusion can you draw from this comparison?