Question

At ${25}^{o}C,$ the dissociation constant $\left(K_a\right)$of a weak monoprotic acid, $HA$ is numerically equal to the dissociation constant $\left(K_b\right)$ of its conjugate base, $A^{-}.$ Which of the following statements (s) is/are correct?

• A. The dissociation constant of the acid, HA, is ${10}^{-7}$
  
• B. The pH of $0.1M$ aqueous solution of the acid, $HA$, is $4.0$
  
• C. The pH of $0.1M$ aqueous solution of the conjugate base $\left(A^{-}\right)$ is $10.0$
  
• D. The pH of an aqueous solution containing $0.1MHA$ and $0.01MHCl$ is $2.0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The dissociation constant of the acid, HA, is ${10}^{-7}$

B The pH of $0.1M$ aqueous solution of the acid, $HA$, is $4.0$

C The pH of $0.1M$ aqueous solution of the conjugate base $\left(A^{-}\right)$ is $10.0$

D The pH of an aqueous solution containing $0.1MHA$ and $0.01MHCl$ is $2.0$

(A) For conjugate pairs, $K_a.K_b=K_w={10}^{-14}$
$\therefore K_a=K_b={10}^{-7}$
(B) $pH=\frac{1}{2}(p{K}_a-logC)$
$=\frac{1}{2}(7-log0.1)=4.0$
(C) $pO{H}_{\left(A^{-}\right)}=\frac{1}{2}(p{K}_a-logC)$
$=\frac{1}{2}(7-log0.1)=4.0$
$pH=14-pOH$
$pH=14-4=10$

(D) As HA is a weak acid then $[H{]}^{+}$ ions furnished from it is very very less than the $[H{]}^{+}$ ion furnished from strong acid HCl. $[H^{+}{]}_{total}=[H^{+}{]}_{HA}+[H^{+}{]}_{HCl}\approx 0.01M$
$\therefore pH=2.0$