Question

The electrical resistance of a column of $0.05mol{L}^{-1}NaOH$ solution of diameter $1cm$ and length $50cm$ is $5.55\times 10^3$ ohm. The conductivity is

• A. $0.01148Sc{m}^{-1}$
• B. $0.00052S{m}^{-1}$
• C. $154.5Sc{m}^{-1}$
• D. $5.075S{m}^{-1}$

Answer 1

Answer: (A)

$1=50cm=0.5m$
$A=\pi r^2=3.14\times (0.5{)}^{2}c{m}^2$
$=0.785c{m}^2$
$=0.785\times 10^{-4}{m}^2$
$R=\rho \frac{l}{A}$ or $\rho =\frac{RA}{l}$
$=\frac{5.55\times 10^3\Omega \times 0.785c{m}^2}{50cm}$
$=87.135\Omega cm$
Conductivity $=K\frac{1}{\rho }=\left(\frac{1}{87.135}\right)Sc{m}^{-1}$
$=0.01148Sc{m}^{-1}$