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Hydronium ion (H3O+) is sometimes better shortened to hydrogen ion (H+). Let acetic acid be abbreviated HOAc. Let acetate ion be abbreviated OAc-.
HOAc <===> H+ + OAc-
Ka = [H+][OAc-]/[HOAc] = 1.85 x 10^-5
The problem is to find [H+]. We know [HOAc], because that's 1.5M. It's true that a certain amount of the 1.5M ionizes, but it's so small that we can say that [HOAc] = 1.5M. Also, [OAc-] from ionization of HOAc is so small, that it is swamped by the 0.20M NaOAc that was added. So [OAc-] = 0.20M. Then:
Ka = [H+](0.20)/(1.5) = 1.85 x 10^-5
[H+] = (1.5)(1.85x10^-5)/(0.20) = 1.4 x 10^-4M to ywo significant figures