Question

The dissociation constant of n-butyl acid $1.6\times {10}^{-5}$ and the molar conductivity at infinite dilution is $380\times {10}^{-4}S{m}^{2}mo{l}^{-1}$. The specific conductance of the 0.01 M acid solution is:

• A. $1.52\times {10}^{-5}S{m}^{-1}$
• B. $1.52\times {10}^{-2}S{m}^{-1}$
• C. $1.52\times {10}^{-3}S{m}^{-1}$
• D. none of the above

Answer 1

The correct option is A $1.52\times {10}^{-5}S{m}^{-1}$

Dissociation constant $\left(K_a\right)=1.6\times {10}^{-5}=16\times {10}^{-6}$

${\Lambda }_m^{\infty }=3.8\times {10}^{-2}C=0.01M{K}_a=C{\alpha }^2⟹\frac{16\times {10}^{-6}}{0.01}={\alpha }^2⟹\alpha =4\times {10}^{-2}\frac{{\Lambda }_m}{{\Lambda }_m^{\infty }}=4\times {10}^{-2}⟹{\Lambda }_m=4\times {10}^{-2}\times 3.8\times {10}^{-2}=15.2\times {10}^{-4}{\Lambda }_m=K\times \frac{1000\times {10}^{-3}}{0.01}⟹K=1.52\times {10}^{-3}\times {10}^{-2}=1.52\times {10}^{-5}$