Question

The molar conductivity of $0.007 \,M$ acetic acid is $20\, S\, cm ^{2} mol ^{-1}$. What is the dissociation constant of acetic acid? Choose the correct option. $[\Lambda_{ H ^{+}}^{\circ}=350 \,S \,cm ^{2} mol ^{-1}, ]$
$[\Lambda_{ CH _{3} COO ^{-}}^{\circ}=50\, S\, cm ^{2} mol ^{-1}]$

• A. $1.75 \times 10^{-4}\, mol\, L ^{-1}$
• B. $2.50 \times 10^{-4}\, mol\, L ^{-1}$
• C. $1.75 \times 10^{-5}\, mol\, L ^{-1}$
• D. $2.50 \times 10^{-5} \, mol\, L ^{-1}$

Answer 1

Answer: (C)

Degree of dissociation $(\alpha)$ of $CH _{3} COOH$
$=\frac{\Lambda_{ C }}{\Lambda_{0}}=\frac{20}{350+50}=\frac{1}{20}$
$ K _{ a }=\frac{ C \alpha^{2}}{1-\alpha} $
$1-\alpha \approx 1 $
$K _{ a }= C \alpha^{2} $
$ K _{ a }=0.007 \times \frac{1}{20} \times \frac{1}{20} $
$ K _{ a }=1.75 \times 10^{-5}$