If the resistance of a $0.01 \, M$ electrolyte in a cell is $40 \, \Omega$ and the cell constant is $0.4 \, \text{cm}^{-1}$,what is the molar conductivity in $\Omega^{-1} \, \text{cm}^2 \, \text{mol}^{-1}$?

If the molar conductivity of a solution is $1.26 \times 10^{2} \ \Omega^{-1} \ cm^{2} \ mol^{-1}$ and its molarity is $0.01 \ M$,what will be its specific conductivity?

Molar conductivities $(\Lambda ^o_m)$ at infinite dilution of $NaCl$,$HCl$ and $CH_3COONa$ are $126.4$,$425.9$ and $91.0 \ S \ cm^2 \ mol^{-1}$ respectively. $(\Lambda ^o_m)$ for $CH_3COOH$ will be .......... $S \ cm^2 \ mol^{-1}$.

Equivalent conductances of $BaCl_2$,$H_2SO_4$ and $HCl$ at infinite dilution are $\Lambda_1^\infty$,$\Lambda_2^\infty$ and $\Lambda_3^\infty$ respectively. Then,the equivalent conductance of $BaSO_4$ at infinite dilution will be:

$A$ conductivity cell has been calibrated with $0.01 \ M$ $1:1$ electrolyte solution (specific conductance,$k = 1.25 \times 10^{-3} \ S \ cm^{-1}$) in the cell and the measured resistance was $800 \ \Omega$ at $25^{\circ}C$. The cell constant will be (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).