Concentration of $\mathrm{H}_{2} \mathrm{SO}_{4}$ and $\mathrm{Na}_{2} \mathrm{SO}_{4}$ in a solution is $1 \mathrm{M}$ and $1.8 \times 10^{-2} \mathrm{M}$, respectively. Molar solubility of $\mathrm{PbSO}_{4}$ in the same solution is $\mathrm{X} \times 10^{-\mathrm{Y}} \mathrm{M}$ (expressed in scientific notation). The value of $Y$ is ________.

[Given: Solubility product of $\mathrm{PbSO}_{4}\left(K_{s p}\right)=1.6 \times 10^{-8}$. For $\mathrm{H}_{2} \mathrm{SO}_{4}, K_{a l}$ is very large and $\left.K_{a 2}=1.2 \times 10^{-2}\right]$

An aqueous solution is prepared by dissolving $0.1 \mathrm{~mol}$ of an ionic salt in $1.8 \mathrm{~kg}$ of water at $35^{\circ} \mathrm{C}$. The salt remains $90 \%$ dissociated in the solution. The vapour pressure of the solution is $59.724 \mathrm{~mm}$ of Hg. Vapor pressure of water at $35{ }^{\circ} \mathrm{C}$ is $60.000 \mathrm{~mm}$ of $\mathrm{Hg}$. The number of ions present per formula unit of the ionic salt is _________.

Consider the strong electrolytes $Z_{m} X_{n}, U_{m} Y_{p}$ and $V_{m} X_{n}$. Limiting molar conductivity ( $\Lambda^{0}$ ) of $\mathrm{U}_{\mathrm{m}} \mathrm{Y}_{\mathrm{p}}$ and $\mathrm{V}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}}$ are 250 and $440 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$, respectively. The value of $(\mathrm{m}+\mathrm{n}+\mathrm{p})$ is

Given:

Ion	$\mathrm{Z}^{\mathrm{n}+}$	$\mathrm{U}^{\mathrm{p}+}$	$\mathrm{V}^{\mathrm{n}+}$	$\mathrm{X}^{\mathrm{m}-}$	$\mathrm{Y}^{\mathrm{m}-}$
$\lambda^{0}\left(\mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\right)$	$50.0$	$25.0$	$100.0$	$80.0$	$100.0$

$\lambda^{0}$ is the limiting molar conductivity of ions

The plot of molar conductivity ( $\Lambda$ ) of $\mathrm{Z}_{\mathrm{m}} \mathrm{X}_{\mathrm{n}} v s\, \mathrm{c}^{1 / 2}$ is given below.

The reaction of $\mathrm{Xe}$ and $\mathrm{O}_{2}{F}_{2}$ gives a $\mathrm{Xe}$ compound $\mathbf{P}$. The number of moles of $\mathrm{HF}$ produced by the complete hydrolysis of $1 \mathrm{~mol}$ of $\mathbf{P}$ is __________.