Question

Calculate the change in pH of one litre buffer solution containing $0.10mole$ each of ${NH}_3$ and ${NH}_{4}Cl$ upon addition of (i) $0.02$ mole of dissolved gaseous $HCl$, (ii) $0.02mole$ of dissolved $NaOH$. Assume no change in volume $K_b$ for ${NH}_3=1.8\times {10}^{-5}$)

Answer 1

$pOH$ of ${NH}_3$ and ${NH}_{4}Cl$ buffer

$pOH=-\log K_b+\log \frac{\left[Salt\right]}{\left[Base\right]}$

$\Rightarrow pOH=-\log 1.8\times {10}^{-5}+\log \frac{0.1}{0.1}=4.75$

$pH=14-4.75=9.25$

First Case:

${NH}_3+HCl⟶{NH}_{4}Cl$

$\left[Salt\right]=(0.1+0.02)=0.12M$

$\left[Base\right]=(0.1-0.02)=0.08M$

$pOH=-\log K_b+\log \frac{0.12}{0.08}=4.926$

$pH=(14-4.926)=9.074$

$\Delta pH=(9.25-9.074)=0.176$

Second case:

${NH}_{4}Cl+NaOH⟶{NH}_3+NaCl$

$\left[Salt\right]=(0.1-0.02)=0.08M$

$\left[Base\right]=(0.1+0.02)=0.12M$

$pOH=-\log K_b+\log \frac{0.08}{0.12}=4.574$

$pH=(14-4.574)=9.426$

$\Delta pH=(9.426-9.25)=0.176$