Chemistry - Ionic Equilibrium Question with Solution | TestHub

${\mathrm{k}}_{\mathrm{b}}=\frac{(\mathrm{C}\mathrm{\alpha }{)}^2}{\mathrm{C}\left(1-\mathrm{\alpha }\right)}=\frac{\mathrm{C}{\mathrm{\alpha }}^2}{1-\mathrm{\alpha }}$

negligible$\left(1-\mathrm{\alpha }\right)=1$

${\mathrm{k}}_{\mathrm{b}}=\mathrm{C}{\mathrm{\alpha }}^2$

$\mathrm{\alpha }=\sqrt{\frac{{\mathrm{k}}_{\mathrm{b}}}{\mathrm{C}}}=\sqrt{\frac{2\times 10^{-5}}{0.1}}=\sqrt{2\times 10^{-4}}$

$\mathrm{\alpha }=1.41\times 10^{-2}$

$\mathrm{\alpha }=1.4\mathrm{\%}$

$\left[\mathrm{O}{\mathrm{H}}^{-}\right]=\mathrm{C}\mathrm{\alpha }=0.1\times 1.4\times 10^{-2}$

$=1.4\times 10^{-3}\mathrm{M}$

$\left[{\mathrm{H}}^{-}\right]=\frac{{\mathrm{K}}_{\mathrm{w}}}{\left[\mathrm{O}{\mathrm{H}}^{-}\right]}=\frac{10^{-14}}{1.4\times 10^{-3}}$

$=7.09\times 10^{-12}\mathrm{M}$