Resistivity of $0.5 \ M$ electrolytic solution is $10 \ \Omega \ cm$. Find the molar conductivity of the solution.

The specific conductance of a solution containing $1.0 \ g$ of anhydrous $BaCl_2$ in $200 \ cm^3$ of solution is $0.0058 \ S \ cm^{-1}$. Calculate the molar and equivalent conductivity of the solution. (Molar mass of $BaCl_2 = 208 \ g \ mol^{-1}$)

The resistance of $0.05\, M$ solution of oxalic acid is $200\, \Omega$ and the cell constant is $2.0\, cm^{-1}$. The equivalent conductance in $S\, cm^2\, eq^{-1}$ will be:

What is the cell constant of $\frac{N}{10}$ $KCl$ solution at $25^{\circ} C$,if conductivity and resistance of a solution is $0.0112 \ \Omega^{-1} cm^{-1}$ and $55.0 \ \Omega$ respectively (in $cm^{-1}$)?

Two solutions of electrolytes $X$ and $Y$ are taken in two beakers and diluted by adding $500 \ mL$ of water. The molar conductivity $(\Lambda_m)$ of $X$ increases by $1.5$ times,while that of $Y$ increases by $20$ times. What could be the electrolytes $X$ and $Y$?

Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.