6E.1 Question

[Laila Alkhouri 3H]

In the table it says the value is from Ka2 which is 1.2 * 10^-2. I tried to just plug that in for the Ka value and solve and I got a pH of 1 something. However, the answer is 0.8. There have been a few examples where the numerator is not x^2 and it has been like in this particular example (0.15+x)*x and I was wondering why we do this and when we know to do this to solve for the x value before getting the pH.

[Elena Liu 2J]

For the specific problem you're referring to, the acid is H2SO4, which is special because the the first protonation goes until completion, aka H2SO4 is a strong acid. Therefore, you know the value of HSO4- (it's just the concentration of H2SO4 since stoichiometric ratio is 1:1), and you incorporate that into the second protonation equation.