(c) $0.0100 \space M \space HC_2H_3O_2$ has the greatest percent ionization, and (b) 0.500 M $HC_2H_3O_2$ has the lowest pH.
Work Step by Step
According to Le Chatelier's principle, the percent ionization increases as the initial concentration of the reactant (the acid) decreases. Thus, the solution with the lowest acid concentration is the one with the greatest percent ionization. The concentration of $H_3O^+$ at equilibrium increases as the initial concentration of acid increases. Therefore, the solution with greatest concentration is the one with greatest hydronium ion concentration and thus the one with lowest pH.