Question

The pH of $0.05M$ aqueous solution of diethylamine is $12$. Calculate its $K_b$.

Answer 1

We know that, $pH+pOH=14$

or $pOH=14-pH=14-12-2$

So, $\left[{OH}^{-}\right]={10}^{-2}$

${\left(C_2{H}_5\right)}_{2}NH+H_{2}O\rightleftharpoons {\left(C_2{H}_5\right)}_2{NH}_2^{+}+{OH}^{-}$

At equilibrium,$\left[{\left(C_2{H}_5\right)}_{2}NH\right]=0.05-x,\left[{\left(C_2{H}_5\right)}_2{N{H}_2}^{+}\right]=x,\left[O{H}^{-}\right]=x$

where $x=0.01mol$

$K_b=\frac{\left[{\left(C_2{H}_5\right)}_2{NH}_2^{+}\right]\left[{OH}^{-}\right]}{\left[{\left(C_2{H}_5\right)}_{2}NH\right]}=\frac{0.01\times 0.01}{0.05-0.01}=\frac{0.01}{4}=2.5\times {10}^{-3}$