Question

Compare the acidic nature of $0.1MHCNO$ with that of $0.2MHCN.$ (Given $K_a$ for $HCNO=1.2\times {10}^{-4}$ and $K_a$ for $HCN=4.0\times {10}^{-10}$ at $298K.$)

• A. $HCNO$ solution is $2.6\times {10}^{-3}$ times more acidic
• B. $HCNO$ solution is $3\times {10}^5$ times more acidic
• C. $HCNO$ solution is $3.9\times {10}^2$ times more acidic
• D. none of these

Answer 1

Answer: (C)

$HCNO$ solution is $3.9\times {10}^2$ times more acidic

$HCNO\rightleftharpoons H^{+}+{CNO}^{-}$

$0.1M$

$\therefore 1.2\times {10}^{-4}=\frac{\left[H^{+}\right]\left[{CNO}^{-}\right]}{0.1}$

$\therefore {\left[H^{+}\right]}^2=1.2\times {10}^{-5}(\because \left[H^{+}\right]=\left[{CNO}^{-}\right])$

$\therefore \left[H^{+}\right]=0.35\times {10}^{-2}M$

$HCN\rightleftharpoons H^{+}+{CN}^{-}$

$0.4\times {10}^{-10}=\frac{{\left[H^{+}\right]}^2}{\left[HCN\right]}(\because \left[H^{+}\right]=\left[{CN}^{-}\right])$

$\therefore {\left[H^{+}\right]}^2=0.8\times {10}^{-10}$

$\therefore \left[H^{+}\right]=0.89\times {10}^{-5}$

$\therefore HCNO$ is $\frac{0.35\times {10}^{-2}}{0.89\times {10}^{-5}}$ times more acidic than $HCN$

i.e.$0.39\times {10}^{+3}$ times

$\therefore HCNO$ is $3.9\times {10}^2$ times more acidic than $HCN$