Question

Conductivity of a solution of an electrolyte of concentration $0.1M$ filled in conductivity cell is $2.5S{m}^{-1}$. Resistance of this conductivity cell is $100ohm$. Resistance of the same cell when filled with $0.3M$ of the same solution is $800ohm$. The molar conductivity of $0.3M$ solution of the electrolyte will be:

• A. $450\times {10}^{-6}S{m}^{2}mo{l}^{-1}$
• B. $483\times {10}^{-5}S{m}^{2}mo{l}^{-1}$
• C. $150\times {10}^{-3}S{m}^{2}mo{l}^{-1}$
• D. $104\times {10}^{-5}S{m}^{2}mo{l}^{-1}$

Answer 1

The correct option is D $104\times {10}^{-5}S{m}^{2}mo{l}^{-1}$

Cell constant is same for a particular cell. It is a constant.

We know,
$\text{Conductivity,}\kappa =\frac{1}{R}\times \text{Cell constant}$
For $0.1M$ solution,

$\text{Resistance,}\left(R\right)=100\Omega$
$\text{Conductivity,}\kappa =2.5S{m}^{-1}$

$\kappa =\frac{1}{R}\times \frac{l}{A}$

$2.5=\frac{1}{100}\times \frac{l}{A}$

$\text{Cell constant,}\frac{l}{A}=250m^{-1}$

For $0.3M$ solution,
$\text{Resistance,}\left(R\right)=800\Omega$
$\text{Conductivity,}\kappa =\frac{1}{R}\times \text{Cell constant}$
$\text{Conductivity,}\kappa =\frac{1}{800}\times 250$
$\text{Conductivity,}\kappa =0.3125S{m}^{-1}$

${\Lambda }_m=\frac{\kappa }{C}$
Also, we know
$1L={10}^{-3}{m}^3$
$1L^{-1}={10}^3{m}^{-3}$
$\text{Molar concentration,}\left(C\right)=0.3\times {10}^{3}mol{m}^{-3}$
${\Lambda }_m=\frac{0.3125}{0.3\times {10}^3}$

${\Lambda }_m=104.1\times {10}^{-5}S{m}^{2}mo{l}^{-1}$