Relative lowering of vapour pressure of a dilute solution is 0.5 . What is the mole fraction of the non-volatile solute?

The solubility product of a sparingly soluble $A B_2$ salt is $2.56 \times 10^{-4} \mathrm{M}^3$ at $25^{\circ} \mathrm{C}$. The $K_f$ of water is 1.8 K kg mol ${ }^{-1}$. The depression in freezing point of a standard solution of $A B_2$ is

$\mathrm{Mg}^{2+}$ displaces hydrogen from acids but copper does not. A galvanic cell prepared by combining $\mathrm{Cu} / \mathrm{Cu}^{2+}$ and $\mathrm{Mg} / \mathrm{Mg}^{2+}$ has an EMF of 2.71 V at 298 K . If the potential of copper electrode is 0.34 V , what is the reduction potential of Mg electrode?

For a reversible reaction $A \rightleftharpoons B$, pre-exponential factor is same for both the forward and backward reactions and has value of $20 \mathrm{~S}^{-1}$. If the enthalpy change along the forward reaction is $-41.5 \mathrm{~kJ} / \mathrm{mol}$, the value of equilibrium constant at 500 K is