At $298 \ K$,the conductivity of $KCl$ solutions of molarity $0.1 \ M, 0.01 \ M$ and $1.0 \ M$ are recorded as $X, Y$ and $Z \ S \ cm^{-1}$ respectively. The correct relation between $X, Y$ and $Z$ is

For an aqueous solution of $CaCl_2$ electrolyte,the graph between molar conductivity $(\lambda_m)$ and $(\text{concentration})^{1/2}$ is:

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: $Ba=137, S=32, O=16$)

The specific conductance of a saturated solution of silver bromide is $\kappa \ S \ cm^{-1}$. The limiting ionic conductances for $Ag^{+}$ and $Br^{-}$ are $x$ and $y$ $S \ cm^2 \ mol^{-1}$ respectively. Then the solubility of silver bromide (in $g/L$) will be $(Ag = 108, Br = 80)$.

$\Lambda_{m(HAc)}^0$ is equal to . . . . . . .

Calculate the molar conductivity of a solution having a concentration of $0.08 \ M$ and a resistivity of $5 \times 10^{-3} \ \Omega \ cm$.