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 $KCl$.

(N/A) The Kohlrausch equation is given by $\Lambda_m = \Lambda_m^o - A c^{1/2}$.
To verify this,we calculate the square root of the concentration $(c^{1/2})$:

$c^{1/2} / (mol \, L^{-1})^{1/2}$	$\Lambda_m / S \, cm^2 \, mol^{-1}$
$0.01407$	$148.61$
$0.01758$	$148.29$
$0.02283$	$147.81$
$0.03145$	$147.09$

$A$ plot of $\Lambda_m$ ($y$-axis) versus $c^{1/2}$ ($x$-axis) yields a straight line.
By extrapolating the line to $c^{1/2} = 0$,we find the intercept $\Lambda_m^o = 150.0 \, S \, cm^2 \, mol^{-1}$.
The slope of the line is given by $A = - \text{slope} = - \frac{147.09 - 148.61}{0.03145 - 0.01407} \approx 87.46 \, S \, cm^2 \, mol^{-1} / (mol \, L^{-1})^{1/2}$.