$0.2\% (w/v)$ solution of $NaOH$ is measured to have resistivity $870.0 \ m\Omega \ m$. The molar conductivity of the solution will be $........ \times 10^2 \ mS \ dm^2 \ mol^{-1}$. $(Nearest \ integer)$

What is the expression for the ionisation constant $(K_a)$ of a weak acid $(HA)$ in terms of molar conductivity at infinite dilution $(\Lambda_m^\infty)$ and molar conductivity at a given concentration $(\Lambda_m)$?

If the values of $\Lambda_{\infty}$ of $NH_4Cl$,$NaOH$ and $NaCl$ are $130$,$217$ and $109 \ ohm^{-1} \ cm^2 \ equiv^{-1}$ respectively,the $\Lambda_{\infty}$ of $NH_4OH$ in $ohm^{-1} \ cm^2 \ equiv^{-1}$ is:

$\Lambda_{m}^0$ for $NaCl$,$HCl$ and $NaAc$ are $126.4 \ S \ cm^2 \ mol^{-1}$,$425.9 \ S \ cm^2 \ mol^{-1}$ and $91.0 \ S \ cm^2 \ mol^{-1}$ respectively. Calculate $\Lambda^0$ for $HAc$.

The resistance of a conductivity cell filled with $0.1 \ M$ electrolyte solution is $100 \ \Omega$. The conductivity of this solution is $1.29 \ S \ m^{-1}$. If the resistance of the same cell filled with $0.02 \ M$ solution is $520 \ \Omega$,what is the molar conductivity of the $0.02 \ M$ solution?

In an aqueous solution,how does specific conductivity of electrolytes change with the addition of water?