Question

A weak acid $HA$ after treatment with $12\text{ml}$ of $0.1\text{M}$ strong base $BOH$ has $pH=5$. At the end point, the volume of same base required is $13.2\text{ml}$. $K_a$ of acid is:

• A. ${10}^{-6}$
• B. ${10}^{-5}$
• C. ${10}^{-4}$
• D. ${10}^{-7}$

Answer 1

The correct option is C ${10}^{-4}$

According to the question, $12\text{mL}$ of $0.1\text{M}$ strong base is used. Thus, at the end point, the volume of same base required is $13.2\text{mL}$
$HA+BOH\rightleftharpoons BA+H_{2}Ot=0a12\times 0.100t=eq(a-1.2)01.21.2$

Given, at the end point, the volume of same base required is $13.2\text{ml}$
Thus, Meq of $HA$ = Meq of $BOH$
Meq of $BOH$ at the end point $=13.2\times 0.1=1.32$
$\therefore$ Meq of $HA$ left $=1.32-1.2=0.12$
Now, $pH=p{K}_a+\log \frac{\left[Salt\right]}{[\text{acid]}}$
$5=-\log K_a+\log \frac{1.2}{\left(0.12\right)}\Rightarrow 5=-log{K}_a+1\Rightarrow K_a={10}^{-4}$