Question

The electrical resistance of a column of 0.05 M NaOH solution of diameter 1 cm and length 50 cm is $5.55\times {10}^3$ ohm. Calculate its resistivity, conductivity and molar conductivity.

Answer 1

$A=\pi r^2=3.14\times (0.5{)}^2=0.785c{m}^2,l=50cm$
$R=\frac{\rho l}{A}\rho =\frac{AR}{l}=\frac{5.55\times {10}^{-3}\times 0.785}{50}$
$\rho =87.18\Omega cm$
Conductivity, $K=\frac{l}{\rho }=0.01147Sc{m}^{-1}$
Molar Conductivity $=\frac{1000\times K}{C}=\frac{0.01147\times 1000}{0.05}$
${\Lambda }_m=229.4Sc{m}^{2}mo{l}^{-1}$

Molar conductivity, ${\Lambda }_m=229.4Sc{m}^{2}mo{l}^{-1}$