6.0 g weak acid HA (mol. wt. = 60 g/mol.) is dissolved in water and formed 10 m³ solution.If ${\mathrm{K}}_{\mathrm{a}\left(\mathrm{HA}\right)}={10}^{-9}\text{, }$then p^OH of solution is: [Given : log 4= 0.6]
 

$$\begin{gathered} \text{[HA]=}\frac{\left(\frac{6}{60}\right)}{10000}\Rightarrow {10}^{-5}\mathrm{M} \\ \mathrm{\alpha }=\frac{\sqrt{{10}^{-9}}}{{10}^{-5}}\Rightarrow 0.01 (\mathrm{negligiblew}.\mathrm{r}.\mathrm{t}. 1 ) \\ \therefore \left[{\mathrm{H}}^{+}\right]=\sqrt{{10}^{-9}\times {10}^{-5}}\Rightarrow \sqrt{{10}^{-14}} \\ \Rightarrow {10}^{-7}\mathrm{M}, \because \left[{\mathrm{H}}^{+}\right]<{10}^{-6}\mathrm{M} \\ \mathrm{So} \mathrm{we} \mathrm{should} \mathrm{consider} \left[{\mathrm{H}}^{+}\right] \mathrm{from} {\mathrm{H}}_2\mathrm{O}\Rightarrow \\ {\left[{\mathrm{H}}^{+}\right]}_{\mathrm{total} }=2\times {10}^{-7} \mathrm{without} \mathrm{considering} \\ \mathrm{common} \mathrm{ion} \mathrm{effect} \mathrm{pH} = 6.7, \mathrm{so} \mathrm{pOH} = 7.3 \\ \mathrm{but} \mathrm{due} \mathrm{to} \mathrm{common} \mathrm{ion} \mathrm{effect} {\mathrm{H}}^{+} \mathrm{from} {\mathrm{H}}_{2 }\mathrm{O} \mathrm{will} \mathrm{be} \mathrm{less} \\ \mathrm{so} \mathrm{pH} > 6.7 \\ \therefore \mathrm{pOH} \mathrm{of} \mathrm{solution} \mathrm{exist} \mathrm{between} 7.0 \mathrm{and} 7.3 \end{gathered}$$