If an acid ionizes completely, does that mean pH=0?

Question

Because I'm doing my homework, and one of the questions asked us to calculate the pH of H2SO4. The Ka1 of H2SO4 is very large, indicting that it ionizes completely. The answer is pH=0. Does this make sense?

The concentration of H2SO4 is 1.00mol/L. How does that affect the calculations? Because when I used 0.001mol/L for the concentration, I got pH=3. Why is it pH=0 when the concentration is 1.00mol/L though?

Answer 1

You have to know the concentration of H2SO4. For example, if H2SO4 is 0.001 M, and Ka1 is infinite, then [H+] = 0.001, Log[H+] = -3, and pH =3. This ignores the smaller Ka2 of H2SO4. The overall answer to your question is NO.