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. `0.385 cm^(-1)`
B. `3.85 cm^(-1)`
C. `38.5 cm^(-1)`
D. `0.1925 cm^(-1)`

Answer

D

Explanation

For `25xx10^(-4)(M)` NaCl solution
`lambda_m=lambda_m^oo-bsqrtC`
`lambda_m=127-10^3(25xx10^(-4))^(1//2)`
`lambda_m=127-10^3xx5xx10^(-2)`
`lambda_m=77`
`lambda=(1000.G.sigma)/M` so, `sigma=(Mlambda)/(1000 G)=(Mlambda)/(1000 G)=(25xx10^(-4)xx77xx1000)/1000=0.1925 cm^(-1)`