Question

What is the concentration of acetic acid which can be added to $0.5$ M $HCOOH$ solution, so that dissociation of both will be the same?

(Given: $K_{C{H}_{3}COOH}=1.8\times {10}^{-5};K_{HCOOH}=2.4\times {10}^{-4}$)

• A. $8.6$ M
• B. $7.8$ M
• C. $6.6$ M
• D. $10.2$ M

Answer 1

Answer: (C)

$6.6$ M

The equilibrium for the dissociation of formic acid is $HCOOH\rightleftharpoons [H^{+}{]}_1+HCO{O}^{-}$

The equilibrium for the dissociation of acetic acid is $C{H}_{3}COOH\rightleftharpoons [H^{+}{]}_2+C{H}_{3}CO{O}^{-}$

Since, both acids are present in same mixture, $[H^{+}{]}_1=[H^{+}{]}_2.$

$C_1{\alpha }_1=C_2{\alpha }_2$

$\sqrt{K_{a_1}{C}_1}=\sqrt{K_{a_2}{C}_2}.$

$\sqrt{2.4\times {10}^{-4}\times 0.5}=\sqrt{1.8\times {10}^{-5}\times C_2}$

On solving, $C_2=6.66M$

The dissociation of both acids will be same when, $C_{C{H}_{3}COOH}=6.66M$.