The generic equilibrium reaction for a weak acid is
#HA_((aq)) rightleftharpoons H_((aq))^(-) + A_((aq))^(-)#
Start from the pH of the solution. You can use the pH to determine the concentration of #H^(+)# in solution by
#[H^(+)] = 10^(-pH_"sol") = 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" = (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)#
