7.60 The pH of 0.1M solution of cyanic acid (HCNO) is 2.34. Calculate the ionization constant of the acid and its degree of ionization in the solution.

c = 0.1 M

pH = 2.34

$-\mathrm{log}\left[{\mathrm{H}}^{+}\right]=\mathrm{pH}\phantom{\rule{0ex}{0ex}}-\mathrm{log}\left[{\mathrm{H}}^{+}\right]=2.34\phantom{\rule{0ex}{0ex}}\left[{\mathrm{H}}^{+}\right]=4.5×{10}^{-3}\phantom{\rule{0ex}{0ex}}\mathrm{Also},\phantom{\rule{0ex}{0ex}}\left[{\mathrm{H}}^{+}\right]=\mathrm{c\alpha }\phantom{\rule{0ex}{0ex}}4.5×{10}^{-3}=0.1×\mathrm{\alpha }\phantom{\rule{0ex}{0ex}}\frac{4.5×{10}^{-3}}{0.1}=\mathrm{\alpha }\phantom{\rule{0ex}{0ex}}\mathrm{\alpha }=45×{10}^{-3}=.045\phantom{\rule{0ex}{0ex}}\mathrm{Then},\phantom{\rule{0ex}{0ex}}{\mathrm{K}}_{\mathrm{\alpha }}={\mathrm{c\alpha }}^{2}\phantom{\rule{0ex}{0ex}}=0.1×{\left(45×{10}^{-3}\right)}^{2}\phantom{\rule{0ex}{0ex}}=202.5×{10}^{-6}\phantom{\rule{0ex}{0ex}}=2.02×{10}^{-4}$