Question

The ionisation constant of $H_{2}C{O}_3$ as an acid in aqueous solution at room temperature is $X$. If the first and second ionisation constants of $H_{2}C{O}_3$ are $X_1$ and $X_2$ respectively, then:

• A. $X=\frac{X_1}{X_2}$
• B. $X=\frac{X_2}{X_1}$
• C. $X=X_1{X}_2$
• D. $X=\frac{X_1{X}_2}{2}$

Answer 1

The correct option is C $X=X_1{X}_2$

Steps for ionisation of $H_2{CO}_3$ is

$H_2{CO}_3+H_{2}O\to {HCO}_3^{-}+H_3{O}^{+},K_{a1}=X_1{HCO}_3^{-}+H_{2}O\to {CO}_3^{2-}+H_3{O}^{+},K_{a2}=X_{2}For{H}_2{CO}_3,X=\frac{\left[{CO}_3^{2-}\right]\left[H_3{O}^{+}\right]}{{[H}_2{CO}_3\left]\right[H_{2}O]}{X}_1=\frac{{[HCO}_3^{-}\left]\right[H_3{O}^{+}]}{\left[H_2{CO}_3\right]\left[H_{2}O\right]}{X}_2=\frac{\left[{CO}_3^{2-}\right]\left[H_3{O}^{+}\right]}{\left[{HCO}_3^{-}\right]\left[H_{2}O\right]}$

From above equations it is clear that,

$X=X_1.X_2$

So, correct answer is option C.