Resistance of ` 0.2 M` solution of an electrolue is ` 50 Omega`. The specific conductance of the solution is ` 1.4 S m^^(-1)`. The resistance of `0.5` M solution of the same electrolyte is `280. Omega`. The molar conducitivity of ` 0.5 M` solution of the electrolyte is ` S m^2 "mol"^(-1)` is.

Options

A. `5 xx 10^(2)`
B. `5 xx 10^(-4)`
C. `5 xx 10^(-3)`
D. `5 xx 10^(3)`

Answer

B

Explanation

For 0.2 M solution
`kappa = (1)/(R) xx (l)/(A) or 1.4 = (1)/(50) xx (l)/(A)`
or `(l)/(A) = 50 xx 1.4 = 70 m ^(-1) = 0.70 cm^(-1)`
For 0.5 M solution
`kappa = (1)/(R) xx (l)/(A) = (1)/(280) xx 0.70`
`= 2.5 xx 10^(-3) S cm^(-1)`
`Lambda_(m) = (kappa xx 1000)/("Molarity")`
`= (2.5 xx 10^(-3) xx 1000)/(0.5) = 5 S cm^(2) mol^(-1)`
`= 5 xx 10^(-4) S m^(2) mol^(-1)`