Question

Find the concentration of $H^{+},HC{O}_3^{-}$ and ${CO}_3^{2-}$ in a $0.01M$ solution of carbonic acid if the pH of the solution is $4.18$, $K_1=4.45\times {10}^{-7},K_2=4.69\times {10}^{-11}$.

Answer 1

$H_{2}C{O}_3\rightleftharpoons H^{+}+HC{O}_3^{-}$

$HC{O}_3^{-}\rightleftharpoons H^{+}+C{O}_3^{2-}$
$K_1=\frac{\left[H^{+}\right]\left[HC{O}_3^{-}\right]}{\left[H_2{CO}_3\right]}=4.45\times {10}^{-7}$
$K_2=\frac{\left[H^{+}\right]\left[{CO}_3^{2-}\right]}{\left[HC{O}_3^{-}\right]}=4.69\times {10}^{-11}$

As $pH=4.18$ so $[H{]}^{+}=6.61\times {10}^{-5}$ and $\left[H_{2}C{O}_3\right]=0.01M$

On putting this value in eq(1) we will get $\left[HC{O}_3^{-}\right]=6.73\times {10}^{-5}$

Similarly we get $\left[C{O}_3^{2-}\right]=4.78\times {10}^{-11}M$

$\left[H^{+}\right]=6.61\times {10}^{-5}M,\left[HC{O}_3^{-}\right]=6.73\times {10}^{-5}M,\left[{CO}_3^{2-}\right]=4.78\times {10}^{-11}mol{L}^{-1}$