Question

$0.1$ mole of $C{H}_{3}N{H}_2(K_b=5\times {10}^{-4})$ is mixed with $0.08$ mole of $HCl$ and diluted to one litre. What will be the $H^{+}$ concentration in the solution?

• A. $8\times {10}^{-2}M$
• B. $8\times {10}^{-11}M$
• C. $1.6\times {10}^{-11}M$
• D. $8\times {10}^{-5}M$

Answer 1

The correct option is B $8\times {10}^{-11}M$

This is an example of a basic buffer solution. It contains $0.02$ moles of base and $0.08$ moles of salt in $1$ litre of solution.

The expression for the hydroxide ion concentration is $\left[O{H}^{-}\right]=K_b\times \frac{\text{Base}}{\text{Salt}}$.

Substitute values in the above expression.

$\left[O{H}^{-}\right]=5\times {10}^{-4}\times \frac{0.02}{0.08}=1.25\times {10}^{-4}$

But $\left[H^{+}\right]\left[O{H}^{-}\right]=K_w=1\times {10}^{-14}$

Hence, $\left[H^{+}\right]=\frac{1\times {10}^{-14}}{\left[O{H}^{-}\right]}=\frac{1\times {10}^{-14}}{1.25\times {10}^{-4}}=8\times {10}^{-11}$.

Hence, the correct option is $\text{B}$