Ionic Equilibrium · Chemistry · JEE Advanced

Solubility product constants (K$$_{sp}$$) of salts of types MX, MX$$_2$$ and M$$_3$$X at temperature T are 4.0 $$\times$$ 10$$^{-8}$$, 3.2 $$\times$$ 10$$^{-14}$$ and 2.7 $$\times$$ 10$$^{-15}$$, respectively. Solubilities (mol dm$$^{-3}$$) of the salts at temperature 'T' are in the order:

2.5 mL of $$\frac{2}{5}$$M weak monoacidic base (K$$_b$$ = 1 $$\times$$ 10$$^{-12}$$ at 25$$^\circ$$C) is titrated with $$\frac{2}{15}$$M HCl in water at 25$$^\circ$$C. The concentration of H$$^+$$ at equivalence point is (K$$_w$$ = 1 $$\times$$ 10$$^{-14}$$ at 25$$^\circ$$C).

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 $\left.K_{a 2}=1.2 \times 10^{-2}\right]$

A solution is prepared by mixing $0.01 \mathrm{~mol}$ each of $\mathrm{H}_{2} \mathrm{CO}_{3}, \mathrm{NaHCO}_{3}, \mathrm{Na}_{2} \mathrm{CO}_{3}$, and $\mathrm{NaOH}$ in $100 \mathrm{~mL}$ of water. $p \mathrm{H}$ of the resulting solution is _________.

[Given: $p \mathrm{~K}_{\mathrm{a} 1}$ and $p \mathrm{~K}_{\mathrm{a} 2}$ of $\mathrm{H}_{2} \mathrm{CO}_{3}$ are $6.37$ and 10.32, respectively; $\log 2=0.30$ ]

The dissociation constant of a substituted benzoic acid at 25$$^\circ$$C is 1.0 $$\times$$ 10$$^{-4}$$. The pH of a 0.01 M solution of its sodium salt is __________.