The conductivity of a centimolar solution of $KCl$ at $25^{\circ} C$ is $0.0210 \, \Omega^{-1} cm^{-1}$ and the resistance of the cell containing the solution at $25^{\circ} C$ is $60 \, \Omega$. The value of the cell constant is $......... \, cm^{-1}$.

What is the concentration of an electrolyte solution to have molar conductivity of $101 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ and conductivity of $1.01 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$ at $298 \ K$ (in $M$)?

The equivalent conductance of a monobasic acid at infinite dilution is $348 \ ohm^{-1} \ cm^2 \ eq^{-1}$. If the resistivity of the solution containing $15 \ g$ of the acid (molecular weight $49$) in $1 \ L$ is $18.5 \ ohm \ cm$,what is the degree of dissociation of the acid? (Answer in percentage)

What is the molar conductivity at zero concentration in $\Omega^{-1} \ cm^2 \ mol^{-1}$ for aluminium sulphate,if the molar ionic conductivities at zero concentration of $Al^{3+}$ and $SO_4^{2-}$ are $189 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ and $50.1 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively?

If the conductivity of a $0.5 \ M \ KCl$ solution at $298 \ K$ is $0.024 \ S \ cm^{-1}$,then the molar conductivity of the solution would be $S \ cm^2 \ mol^{-1}$.

The ionisation constant of a weak acid $(HA)$ in terms of $\Lambda _m^\infty$ and $\Lambda _m$ is: