Confused about calculating pH?

Question

Take 0.10M H2SO4.

It's an acid, its diprotic. (I'm assuming I got this bit right..)

[H3O+] = 2x[acid] = 2 x 0.1 = 0.2

pH = -log(0.2) = 0.699 (which is not the answer of 1).

I know the answer is 1, but because its diprotic, don't I need to o the 2x[acid] at the front?

I hope my working out is clear and shows where I've gone wrong or my misunderstanding.

Thanks a lot for any help!

Answer 1

First look at an easy acid to understand, such as HCl. You have a 0.1M solution of HCl. You reasoning is quite correct, that because the HCl ionises completely you will produce 0.1mol/litre H+ ions.

pH = -log [H+]

pH = -log 0.1

pH = 1.00

Now consider H2SO4. If it ionises completely, it will produce 0.2mol/litre H+ions. You will see that it has produced double the number of H+ ions as the HCl did for the same molarity. This is because H2SO4 is diprotic. Therefore, because if the increased concentration of H+ ions, the pH must be lower. You have correctly calculated this as pH = 0.669.

Note: this is only true if you assume that H2SO4 ionises completely to produce 2mol H+ ions per mol of H2SO4. This is not correct in practice, but for your question, and I guess your level of chemical study you can work with this assumption.