The first and second ionization constants of H₂X are $2.5 \times 10^{-8}$ and $1.0 \times 10^{-13}$ respectively.

The concentration of ${X^{2-}}$ in $0.1\ \mathrm{M}$ H₂X solution is ______ $\times 10^{-15}\ \mathrm{M}$. (Nearest Integer)

A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol⁻¹) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is ______ × 10⁻². (nearest integer)

[Given: K_b of the solvent = 5.0 K kg mol⁻¹]

Assume the solution to be dilute and no association or dissociation of X takes place in solution.

MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K.

$\mathrm{MX}(\mathrm{s}) \rightleftharpoons \mathrm{M}^{+}(\mathrm{aq})+\mathrm{X}^{-}(\mathrm{aq}) ; \quad \mathrm{K}_{\mathrm{sp}}=10^{-10}$

If the standard reduction potential for M⁺ (aq) + e⁻ → M(s) is
$\left(\mathrm{E}_{\mathrm{M}^{+} / \mathrm{M}}^{\ominus}\right)=0.79 \mathrm{~V}$, then the value of the standard reduction potential for the metal/metal insoluble salt electrode $\mathrm{E}_{\mathrm{X}^{-} / \mathrm{MX}(\mathrm{s}) / \mathrm{M}}^{\ominus}$ is ______ mV. (nearest integer)

[Given: $ \dfrac{2.303 RT}{F} = 0.059\ \text{V} $]

If the line $\alpha x+4 y=\sqrt{7}$, where $\alpha \in \mathbf{R}$, touches the ellipse $3 x^2+4 y^2=1$ at the point P in the first quadrant, then one of the focal distances of $P$ is :