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what is the [H3O+] in a solution made by adding 0.020 moles of nitric acid to 500.0ml of water?

Nitric acid is a strong acid, so it completely dissociates in water. The molarity of the acid is the molarity of the H3O+ ion.

Molarity = moles/liters = (0.02 mol)/(0.5 L) = 0.04 M

Your answer is 0.04 M.

Incidentally, if you wanted the pH, you could take the negative log of 0.04 and you would have a pH of 1.40