Question

The $pH$ of a buffer solution prepared by dissolving $30g$ of ${Na}_2{CO}_3$ in $500mL$ of an aqueous solution containing $150mL$ of $1M$ $HCl$.

$K_a$ for $H{CO}_3^{-}=5.63\times {10}^{-11}$ is:

• A. $9.86$
• B. $10$
• C. $10.2$
• D. $10.86$

Answer 1

The correct option is C $10.2$

${Na}_2{CO}_3+HCl⟶NaCl+NaH{CO}_3$
Meq. before reaction
$\frac{30}{106}\times 1000=283150\times 1=150$ $0$ $0$

Meq. after reaction

$133$ $0$ $150$ $150$

The solution contains ${Na}_2{CO}_3$ and $H{CO}_3^{-}$ and thus acts as buffer.

$\therefore$ $pH=-\log K_a+\log \frac{\left[{CO}_3^{2-}\right]}{\left[H{CO}_3^{-}\right]}$

$pH=-\log K_a+\log \frac{133}{150}$

$=-\log [5.63\times {10}^{-11}]+\log \frac{133}{150}$

$=10.249-0.052$

$pH=10.197$