The conductivity of a $0.05 \, M$ solution of a weak monobasic acid is $10^{-3} \, S \, cm^{-1}$. If $\lambda_{m}^{\infty}$ for the weak acid is $500 \, S \, cm^{2} \, mol^{-1}$,calculate the $K_{a}$ of the weak monobasic acid.

At $291 \ K$,a saturated solution of $BaSO_4$ was found to have a specific conductivity of $3.648 \times 10^{-6} \ \Omega^{-1} \ cm^{-1}$ and that of the water used is $1.25 \times 10^{-6} \ \Omega^{-1} \ cm^{-1}$. If the ionic conductances of $Ba^{2+}$ and $SO_4^{2-}$ are $110$ and $136.6 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively,the solubility of $BaSO_4$ at $291 \ K$ will be (Atomic masses: $Ba=137, S=32, O=16$)

Write a note on the difficulties associated with the measurement of resistivity of an ionic solution.

Conductivity of a saturated solution of a sparingly soluble salt $AB$ at $298 \ K$ is $1.85 \times 10^{-5} \ S \ m^{-1}$. Solubility product of the salt $AB$ at $298 \ K$ is. Given $\Lambda_{m}^{\circ}(AB) = 140 \times 10^{-4} \ S \ m^{2} \ mol^{-1}$.

Which one of the following graphs between molar conductivity $(\Lambda_m)$ versus $\sqrt{C}$ is correct?

The molar conductivity of $KCl$ solutions at different concentrations at $298 \, K$ are given below:

$c^{1/2} / (mol \, L^{-1})^{1/2}$	$\Lambda_m / S \, cm^2 \, mol^{-1}$
$0.000198$	$148.61$
$0.000309$	$148.29$
$0.000521$	$147.81$
$0.000989$	$147.09$

Show that a plot between $\Lambda_m$ and $c^{1/2}$ is a straight line. Determine the values of $\Lambda_m^o$ and $A$ for $KCl$.