Question

A buffer of $pH$ $9.26$ is made by dissolving $x$ moles of ammonium sulphate and $0.1$ mole of ammonia into $100mL$ solution. If $p{K}_b$ of ammonia is $4.74$, calculate value of $x$.

• A. $0.05$ mol
• B. $0.5$
• C. $1$
• D. $0.005$

Answer 1

The correct option is A $0.05$ mol

${\left({NH}_4\right)}_2{SO}_4$
Molarity of ${\left({NH}_4\right)}_2{SO}_4=\left(\frac{x}{100}\right)$
Molarity of ${NH}_4^{+}=\left(\frac{2x}{100}\right)$
Molarity of ${NH}_{4}OH=\left(\frac{0.1}{100}\right)={10}^{-3}$
$14-9.26=4.24+\log \left(\frac{2x/100}{0.1/100}\right)$
$⟹0=\log \left(20x\right)$ $\Rightarrow$ $1=20x$
$⟹x=\frac{1}{20}$ moles
$⟹x=0.05$ moles