When the molar conductivity of a weak electrolyte is plotted against the square root of its concentration $(\sqrt{C})$,which of the following is observed?

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).

Resistance and conductivity of a cell containing $0.1 \ M \ KCl$ solution at $298 \ K$ are $115 \ \Omega$ and $1.90 \times 10^{-6} \ S \ cm^{-1}$ respectively. What is the value of cell constant (in $cm^{-1}$)?

The resistance of $0.01 \ M$ $KCl$ solution at $298 \ K$ is $1500 \ \Omega$. If the conductivity of $0.01 \ M$ $KCl$ solution at $298 \ K$ is $0.1466 \times 10^{-3} \ S \ cm^{-1}$,the cell constant of the conductivity cell in $cm^{-1}$ is:

Find out the ionisation constant of a weak acid $(HA)$ in terms of $\Lambda_m^o$ and $\Lambda_m^c$. (Given $\alpha$ cannot be ignored with respect to $1$)

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. . . . . .