Question

The conductivity of a weak acid $HA$ of concentration $0.001{\text{mol L}}^{-1}$ is $2.0\times {10}^{-5}Sc{m}^{-1}$.

If ${\Lambda }_m^o\left(HA\right)=190Sc{m}^2{\text{mol}}^{-1}$, the ionization constant $\left(K_a\right)$ of $HA$ is equal to ____ $\times {10}^{-6}$.
(Round off to the Nearest Integer)

• A. 12.00
• B. 12
• C. 12.0

Answer 1

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

$C=0.001{\text{mol L}}^{-1}$

$K=2\times {10}^{-5}Sc{m}^{-1}$

${\Lambda }_m^{\infty }\left(HA\right)=190Sc{m}^2{\text{mol}}^{-1}$

${\Lambda }_m=\frac{K}{C}\times 1000$

${\Lambda }_m=\frac{2\times {10}^{-5}\times {10}^3}{0.001}$

${\Lambda }_m=20$

$\alpha =\frac{{\Lambda }_m}{{\Lambda }_m^{\infty }}=\frac{20}{190}$
For a weak acid $HA$

$K_a=\frac{C{\alpha }^2}{1-\alpha }=\frac{{10}^{-3}{\left(\frac{20}{190}\right)}^2}{1-\frac{20}{190}}$

$K_a=1.2383\times {10}^{-5}$

$K_a=12.38\times {10}^{-6}$
Nearest integer is 12