A certain amount of $H_2CO_3$ & $HCl$ are dissolved to form $1$ litre solution. At equilibrium it is found that concentration of $H_2CO_3$ & $CO_3^{-\,-}$ are $0.1\,M$ & $0.01\,M$ respectively. Calculate the $pH$ of solution. Given that for $H_2CO_3$ $K_{a_1} =10^{-5}$ & $K_{a_2} =10^{-8}$

For a weak acid $HA,$ Ostwald's dilution law is represented by the equation

At $298$ $K$ temperature, the ${K_b}$ of ${\left( {C{H_3}} \right)_2}NH$ is $5.4 \times {10^{ – 4}}$ $0.25$ $M$ solution.

Given

$(i)$ $\begin{gathered}
  HCN\left( {aq} \right) + {H_2}O\left( l \right) \rightleftharpoons {H_3}{O^ + }\left( {aq} \right) + C{N^ – }\left( {aq} \right) \hfill \\
  {K_a} = 6.2 \times {10^{ – 10}} \hfill \\ 
\end{gathered} $

$(ii)$ $\begin{gathered}
  C{N^ – }\left( {aq} \right) + {H_2}O\left( l \right) \rightleftharpoons HCN\left( {aq} \right) + O{H^ – }\left( {aq} \right) \hfill \\
  {K_b} = 1.6 \times {10^{ – 5}} \hfill \\ 
\end{gathered} $

These equilibria show the following order of the relative base strength

The solution of $N{a_2}C{O_3}$ has $pH$