If osmotic pressure of 1M aqueous solution of H2SO4 at 500K is 90.2.calculate Ka2 for acid whereas Ka1is infinite

Question

This is from solution chapter relating ionic equilibrium 

Answer 1

π = iMRT

π = osmotic pressure = 90.2 atm (presumably atm)

i = van't off factor = ? for H₂SO₄

M = molarity = 1

R = gas constant = 0.0821 L-atm/mol-K

T = temperature in K = 500K 

Solving for i:  i = π/MRT = (90.2)/(1)(0.0821)(500) = 2.197 

2 of the 2.197 can be accounted for by H⁺ and HSO₄^-. The remaining 0.197 would be from H⁺ and SO₄^2-.

H₂SO₄ ==>H⁺ + HSO₄^-  K₁ = infinite and thus i = 2 for H⁺ and HSO₄^-

[HSO₄^-] = 1 M since 100% dissociation of H₂SO₄

HSO₄^- ==> H⁺ + SO₄^2-  K₂ = ?

K₂ = [H⁺][SO₄^2-]/[HSO₄^-] = (0.0985)(0.0985)/1 = 9.7x10^-3