On decreasing the \( \mathrm{pH} \) from \( 7 \) to \( 2 \), the solubility of a sparingly soluble salt \( (\mathrm{MX}) \) of a weak acid \( (\mathrm{HX}) \) increased from \( 10^{-4} \, \mathrm{mol \, L^{-1}} \) to \( 10^{-3} \, \mathrm{mol \, L^{-1}} \). The \( \mathrm{p}K_a \) of \( \mathrm{HX} \) is:
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 \( 25\,^{\circ}\mathrm{C} \)
