If the distance between two $Pt$ electrodes is $2 \, cm$,the cross-sectional area is $4.0 \, cm^2$,and the resistance is $25 \, \Omega$,find the molar conductivity of a $0.5 \, M$ solution.

The resistance of a conductivity cell of $0.1 \ M$ $KCl$ solution is $120 \ \Omega$ and conductivity is $1.64 \times 10^{-4} \ S \ cm^{-1}$. What is the value of cell constant (in $cm^{-1}$)?

Conductivity of $0.001 \ M$ aqueous solution of $Na_2SO_4$ is found to be $2.6 \times 10^{-3} \ S \ cm^{-1}$ at $25 \ ^oC$. If limiting molar conductance of $Na^+$ is $50 \ S \ cm^2 \ mol^{-1}$,then limiting molar conductance of $SO_4^{2-}$ will be .............. $S \ cm^2 \ mol^{-1}$ (neglect conductivity of water).

The resistance of a conductivity cell with cell constant $1.14 \, cm^{-1}$,containing $0.001 \, M \, KCl$ at $298 \, K$ is $1500 \, \Omega$. The molar conductivity of $0.001 \, M \, KCl$ solution at $298 \, K$ in $S \, cm^{2} \, mol^{-1}$ is ...... . (Integer answer)

When a solution of an electrolyte is heated,the conductance of the solution:

At $298 \ K$,the limiting molar conductivity of a weak monobasic acid is $4 \times 10^2 \ S \ cm^2 \ mol^{-1}$. At $298 \ K$,for an aqueous solution of the acid,the degree of dissociation is $\alpha$ and the molar conductivity is $y \times 10^2 \ S \ cm^2 \ mol^{-1}$. At $298 \ K$,upon $20$ times dilution with water,the molar conductivity of the solution becomes $3y \times 10^2 \ S \ cm^2 \ mol^{-1}$. $(1)$ The value of $\alpha$ is. . . . . . $(2)$ The value of $y$ is. . . . . .