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Sulphuric acid dissociates completely (H2SO4 -> HSO4⁻ + H⁺).
Its product HSO4⁻ has a pKa of 1.92 which should then dissociate partially into SO4²⁻ and H⁺.

I was trying to find out the pH of a 0.05M H2SO4 solution and used the Common Ion Effect to shift the reaction towards the reactants, getting a pH of 1.23. The professor's solution does not take into account the hydrogen ions produced during the first dissociation and calculates a pH of 1.16. The CIE only applies to weak acids which according to the definition I have should be anything with a pKa > 0 (approx).

Could you tell me which solution is correct and maybe why I shouldn't be taking into account the H⁺ produced during the first step?

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  • $\begingroup$ Any solution is correct if it respects 1/ mass and charge balances, 2/ equations of equilibrium 3/ proper usage of justified strong inequalities for equation simplification. $\endgroup$
    – Poutnik
    Commented Jan 30 at 14:37
  • $\begingroup$ @Poutnik And am I being too bold if I ask which if not both (or non) of the solutions satisfies your propositions? $\endgroup$
    – David
    Commented Jan 30 at 14:46
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    $\begingroup$ Why do not you check it? BTW they are not propositions, but mandatory requirements // Take the equilibrium equation for K_a2 and try to express [HSO4-] and [SO4^2-] using [H+] variable. $\endgroup$
    – Poutnik
    Commented Jan 30 at 14:59
  • $\begingroup$ @Poutnik Yes, you are right they aren't propositions. My bad. Yes, they satisfy those requirements the only difference is how I define [H⁺] 1) = [SO4²⁻] + 0.05 (mine) 2) = [SO4²⁻] (professor's). My TA said that the professor was right from a thermo point of view but no clue why $\endgroup$
    – David
    Commented Jan 30 at 15:08
  • $\begingroup$ H+ from the 1st dissociation cannot be ignored, forming majority of H+. // $K_\text{a2} = \dfrac{[\ce{H+}][\ce{SO4^2-}]}{[\ce{HSO4-}]} \approx \dfrac{[\ce{H+}]([\ce{H+}] - \pu{0.05 M})}{\pu{0.1 M} - [\ce{H+}] }$, with neglection of water autodissociation. $\endgroup$
    – Poutnik
    Commented Jan 30 at 15:26

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