The van der Waals equation for a real gas is given by $\left(P+\frac{a}{V^2}\right)(V-b)=R T$. What is the dimension of $\left(\frac{a}{b}\right)$ ?

$$ \text { The major product } P \text { of the following reaction is } $$

An aqueous solution contains 1.0 M of $\mathrm{X}^{2+}$ and 0.001 M of $\mathrm{Y}^2+$ ions at $25^{\circ} \mathrm{C} . \mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$ ions do not interact with each other. This solution is put in an electrolytic cell and the voltage is gradually increased till a current begins to flow through the cell. The voltage is maintained at this point and a deposit is observed on the cathode. What is the composition of the material deposited on the cathode?

(Given: Atomic weight of $X$ is 63 and $Y$ is 200.)

$$ \begin{aligned} & X^{2+}+2 e^{-} \rightarrow X, E^0=0.35 \\ & Y^{2+}+2 e^{-} \rightarrow Y, E^0=0.40 \mathrm{~V} \end{aligned} $$

( $E^0$ is the standard reduction potential.)

2 g of naphthoic acid (molecular weight $=172 \mathrm{~g} \mathrm{~mol}^{-} 1$ ) dissolved in 20 mL of benzene shows a freezing point depression of 2 K . For benzene, the freezing point depression constant, $K_f=5$ $\mathrm{K} \mathrm{kg} \mathrm{mol}{ }^{-1}$ and the density is $0.88 \mathrm{~g} \mathrm{~mL}^{-1}$. What is the magnitude of the van't Hoff factor?