Calculate the molar conductivity of $NH_4OH$ at infinite dilution,given that the molar conductivities of $Ba(OH)_2$,$BaCl_2$,and $NH_4Cl$ are $523.28$,$280.0$,and $129.8 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively.

The resistance of a decimolar solution of $NaCl$ is $30 \ \Omega$. Calculate the conductivity of the solution if the cell constant is $0.33 \ cm^{-1}$.

The conductivity of $0.005 \ M$ $NaI$ solution at $25^{\circ} C$ is $6.07 \times 10^{-4} \ \Omega^{-1} \ cm^{-1}$. Calculate its molar conductivity.

The resistance of a conductivity cell containing $0.01 \, M \, KCl$ solution at $298 \, K$ is $1750 \, \Omega$. If the conductivity of $0.01 \, M \, KCl$ solution at $298 \, K$ is $0.152 \times 10^{-3} \, S \, cm^{-1}$,then the cell constant of the conductivity cell is $.......... \, \times 10^{-3} \, cm^{-1}$.

At $298 \text{ K}$,the molar conductivity of $x\% \text{ (w/w)}$ $MX$ solution (aqueous) is $123.5 \text{ S cm}^2 \text{ mol}^{-1}$. The conductance of the same solution is $1.9 \times 10^{-3} \text{ S}$. The value of $x$ is . . . . . . $\times 10^{-2}$. (Given: cell constant = $1.3 \text{ cm}^{-1}$; molar mass of $MX$ is $75 \text{ g mol}^{-1}$,density of aqueous solution of $MX$ at $298 \text{ K}$ is $1.0 \text{ g mL}^{-1}$)

The molar conductivities of $KCl$,$NaCl$,and $KNO_3$ are $152$,$128$,and $111 \ S \ cm^2 \ mol^{-1}$ respectively. The molar conductivity of $NaNO_3$ is ............. $S \ cm^2 \ mol^{-1}$.