Question

A weak acid $\left(HA\right)$ after treatment with $12mL$ of $0.1M$ strong base $\left(BOH\right)$ solution has a $pH$ of $5$. At the end point, the volume of the same base solution required is $27mL.K_a$ of acid is:

• A. $1.8\times {10}^{-5}$
• B. $8\times {10}^{-6}$
• C. $1.8\times {10}^{-6}$
• D. $8\times {10}^{-5}$

Answer 1

The correct option is B $8\times {10}^{-6}$

At end point, $M_1{V}_1=M_2{V}_2$

$M_1{V}_1=27\times 0.1=2.7$ millimoles

$\therefore$ Millimoles of acid present= $2.7$

Millimoles of salt formed= $1.2$

$\left[Salt\right]=\frac{1.2}{V},\left[acid\right]=2.7-1.2=\frac{1.5}{V}$

$\Rightarrow pH=p{K}_a+\log \frac{\left[Salt\right]}{\left[acid\right]}$

$\Rightarrow 5=p{K}_a+\log \frac{1.2/V}{1.5/V}$

$\therefore p{K}_a=5-\log \frac{1.2}{1.5}=5.0969$

$-\log K_a=5.0969$

$\therefore K_a=8\times {10}^{-6}$