Verified answer

So you have two ionizations for sulfuric acid. The first is complete (H2SO4 is a strong acid). So momentarily ignoring the second ionization gives:

[H2SO4] = 0

[HSO4-] = 0.12 M (but this will change) and

[H+] = 0.12 M (so will this)

Now, consider Ka2:

Ka2 = [H+][SO42-]/[HSO4-] = 1.3X10^-2

From the starting condition, let x = [SO42-]. Then, [H+] = 0.12 + x, and [HSO4-] = 0.12 - x. Plugging those into the expression for Ka2 gives:

1.3X10^-2 = (0.12 +x) (x) / (0.12-x)

1.56X10^-3 - 1.3X10^-2x = 0.12x + x^2

x^2 + 0.133x - 1.56X10^-3 = 0

x = 0.01084

So, [SO42-] = 0.011 M

[HSO4-] = 0.12 - 0.011 = 0.11 M

[H+] = 0.12 + 0.011 = 0.13 M

[H2SO4] = 0

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