Polyprotic acid vs base dissociation

[Arya Bhalla 1H]

When H2SO4 dissociates do we assume that it loses both H+ at once or that it loses 1 H+ and then HSO4- later loses another H+. I'm asking because for the bases like BaOH2, it loses both OH- at the same time. How come H2SO4 only loses 1 H+ as a strong acid and then functions as a weak acid when it loses the second H+ but BaOH2 loses both OH- at once as a strong base?

[Alison King 3L]

I think that we treat the first dissociation as a strong acid, so it completely loses the first H+, but for the second dissociation we treat it as a weak acid and use an ICE table and the Ka to calculate the second H+, then add the two H+ concentrations from the two dissociations to get the total [H+]

[Kaira Shibata 1E]

H2SO4 is a special case because it can lose the first H+ and become HSO4- which is amphiprotic. In this case, you would assume that it is a strong acid when it dissociates to become H+ and HSO4-.