At $298 \text{ K}$, the specific conductance $(\kappa)$ of a $0.0020 \text{ M } NaCl$ solution is $2.50 \times 10^{-4} \text{ S cm}^{-1}$. Calculate the molar conductivity $(\Lambda_m)$ of the solution in $\text{S cm}^2 \text{mol}^{-1}$.

$0.0129 \ S \ cm^{-1}$ is equivalent to how many $S \ m^{-1}$ (in $S \ m^{-1}$)?

Resistance of a cell containing $0.02 \ M \ KCl$ solution is $164 \ \Omega$. If the cell is filled with $0.05 \ M \ AgNO_3$,the resistance becomes $75.8 \ \Omega$. Calculate the following: [Conductivity of $0.02 \ M \ KCl = 2.768 \times 10^{-3} \ \Omega^{-1} \ cm^{-1}$] $(i)$ Conductivity of $0.05 \ M \ AgNO_3$ (ii) Molar conductivity of $AgNO_3$ solution.

Given the following molar conductivities at $25\,\text{}^{\circ}C$: $HCl = 426\,\Omega^{-1}\,cm^{2}\,mol^{-1}$,$NaCl = 126\,\Omega^{-1}\,cm^{2}\,mol^{-1}$,and sodium crotonate $(NaC)$ = $83\,\Omega^{-1}\,cm^{2}\,mol^{-1}$. Calculate the ionization constant $(K_{a})$ of crotonic acid $(HC)$ if the conductivity of a $0.001\,M$ crotonic acid solution is $3.83 \times 10^{-5}\,\Omega^{-1}\,cm^{-1}$.

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185 \ S \ cm^2 \ mol^{-1}$ and the ionic conductance of hydroxyl and chloride ions are $170$ and $70 \ S \ cm^2 \ mol^{-1}$,respectively. If molar conductance of $0.02 \ M$ solution of ammonium hydroxide is $85.5 \ S \ cm^2 \ mol^{-1}$,its degree of dissociation is given by $x \times 10^{-1}$. The value of $x$ is $...........$ $(Nearest \ integer)$

What is the $SI$ unit of conductivity?