The molar conductance of NaCl varies with the concentration as shown in the following table and all values follows the equation.
`lambda_(m)^(c)=lambda_(m)^(oo)-bsqrt(C)` where `lambda_(m)^(c)`= molar specific conductance `lambda_(m)^(oo)=` molar specific conductance at infinite dilution C=molar concentration

When a certain conductivity cell (C) was filled with 25`xx10^(-4)(M) NaCl` solution, the resistance of the cell was found to be 1000 ohm. At infinite dilution, conductance of `Cl^(-)` and `SO_(4)^(2-)` are `80ohm^(-1) cm^(2) "mole"^(-1)` and `160ohm^(-1) cm^(2) "mole"^(-1)` respectively.
What is the cell constant of the conductivity cell (C)?

Options

A. `0.385cm^(-1)`
B. `3.86cm^(-1)`
C. `38.5cm^(-1)`
D. `0.1925cm^(-1)`

Answer

D

Explanation

For `25xx10^(-4)` (M) NaCl solution ltbr `lamda_(m)=lamda_(m)^(infty)-bsqrt(C)`
`lamda_(m)=127-10^(3)(25xx10^(-4))^(1//2)`
`lamda_(m)=127-10^(3)xx5xx10^(-2)`
`lamda_(m)=77`
but `lamda_(m)=(Kxx1000)/(M)`:`K=((l)/(a))xx(1)/(R))`
`lamda_(m)=((l)/(a))xx(1)/(R)xx(1000)/(M)`
`lamda_(m)=`[cell constant] `xx(1000)/(RxxM)implies77=`[cell constanta]`xx(1000)/(1000xx25xx10^(-4))`
Cell constant `=77xx25xx10^(-4)=0.1925cm^(-1)`