Concentration of \( \mathrm{H_2SO_4} \) and \( \mathrm{Na_2SO_4} \) in a solution is \( 1 \, \text{M} \) and \( 1.8 \times 10^{-2} \, \text{M} \), respectively. Molar solubility of \( \mathrm{PbSO_4} \) in the same solution is \( X \times 10^{-Y} \, \text{M} \) (expressed in scientific notation). The value of \( Y \) is ________.
(Given: Solubility product of \( \mathrm{PbSO_4} \) \( (K_{sp}) = 1.6 \times 10^{-8} \). For \( \mathrm{H_2SO_4} \), \( K_{a_1} \) is very large and \( K_{a_2} = 1.2 \times 10^{-2} \))
At \( 25\,^{\circ}\mathrm{C} \), the concentration of \( \mathrm{H}^{+} \) ions in \( 1.00 \times 10^{-3} \) \( \mathrm{M} \) aqueous solution of a weak monobasic acid having acid dissociation constant \( (K_a) \) of \( 4.00 \times 10^{-11} \) is \( X \times 10^{-7} \) \( \mathrm{M} \). The value of \( X \) is __________.
Use: Ionic product of water \( K_w = 1.00 \times 10^{-14} \) at \( 25\,^{\circ}\mathrm{C} \)
