The generic equilibrium reaction for a weak acid is
HA_((aq)) rightleftharpoons H_((aq))^(-) + A_((aq))^(-)HA(aq)⇌H−(aq)+A−(aq)
Start from the pH of the solution. You can use the pH to determine the concentration of H^(+)H+ in solution by
[H^(+)] = 10^(-pH_"sol") = 10^-3.22 = "0.0006026 M"[H+]=10−pHsol=10−3.22=0.0006026 M
Calculate percent ionization by dividing the concentration of hydrogen ions produced in solution by the initial concentration of the weak acid, and multiplying by 100
"% ionization" = ([H^(+)])/([HA]) * 100% ionization=[H+][HA]⋅100
"% ionization" = (0.0006026cancel("M"))/(0.2cancel("M")) * 100 = color(green)("0.3%")
The acid dissociation constant is determined by using the equilibrium concentrations of all the species involved in the reaction.
Since you have 1:1 mole ratios between all the species, you can say that the concentration of HA decreased by the same amount as the concentrations of H^(+) and A^(-) increased.
This means that the equilibrium concentrations for all three species will be
[H^(+)] = [A^(-)] = "0.0006020 M"
[HA] = [HA]_0 - [H^(+)] = 0.2 - 0.0006026 = "0.19940 M"
By definition, K_a will be
K_a = ([H^(+)] * [A^(-)])/([HA])
K_a = (0.0006026 * 0.0006026)/(0.19940) = color(green)(1.82 * 10^(-6))
Calculate pK_a by using
pK_a = -log(K_a) = -log(1.82 * 10^(-6)) = color(green)(5.74)
