Question

Calculate the ratio of pH of a solution containing 1 mol. of $C{H}_{3}COONa+1mol$ of HCl per litre and of other solution containing 1 mol of $C{H}_{3}COONa+1mol$ of $C{H}_{3}COOH$ per litre.

Answer 1

Case I: pH when 1 mol CH and 1 mol HCI are present
$C{H}_{3}COONa+HCl⟶C{H}_{3}COOH+NaCl$
Before reaction 1 1 0 0
After reaction 0 0 1 1

$\therefore \left[C{H}_{3}COOH\right]=1M$

$\therefore \left[H^{\oplus }\right]=C\cdot \alpha =C\sqrt{\left(\frac{K_a}{C}\right)}=\sqrt{K_a\cdot C}=\sqrt{\left(K_a\right)}(\because C=1)$

$\therefore p{H}_1=-\frac{1}{2}log{K}_a$

Case II: pH when 1 mol $C{H}_{3}COONa$ and 1 mole of $C{H}_{3}COOH$; a buffer solution

$\therefore p{H}_2=-log{K}_a+log\frac{\left[Salt\right]}{\left[Acid\right]}$

$\left[\begin{array}{c}\therefore \left[Salt\right]=1M\\ \therefore \left[Acid\right]=1M\end{array}\right]$

$p{H}_2=-log{K}_a$

$\therefore \frac{p{H}_1}{p{H}_2}=\frac{1}{2}=0.5$