Resistance of `0.2 M` solution of an electrolyte is `50 ohm`. 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 conductivity of `0.5 M` solution of the electrolyte in `S m^(2) mol^(-1)` id

Options

A. `5xx10^(2)`
B. `5xx10^(-4)`
C. `5xx10^(-3)`
D. `5xx10^(3)`

Answer

B

Explanation

(b) In first case : `k=(1)/(R )xx(1)/(a)`
`(l)/(a)=kxxR=(1.40" ohm"^(-1)m^(-1))xx(50" ohm")`
`=70 m^(-1)`
In second case : `k=(1)/(R )xx(l)/(a)`
`=(1)/((282" ohm"))xx(70 m^(-1))=0.25" ohm"^(-1)m^(-1)`
`^^_(m)=(k)/(Mx1000)`
`C=0.5 M =(0.5 mol)/(1L)=(0.5 mol)/(m^(3))=0.5 mol m^(-3)`
`^^_(m)=((0.25" ohm"^(-1)m^(-1)))/((10^(3)xx0.5 mol m^(-3)))=5xx10^(-4)" ohm"^(-1) m^(2) mol^(-1)`