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For polyprotic acids, the K for the reactions are different for each time, so you would only write the conjugate acid in the specific reaction you are looking at to find the equilibrium constant.
you have to write out each equation separate as though the two reactions are independent, making two different ice tables, however with the second ice table, you have to be sure to add the hydronium or h+ ions that were created in the first reaction so the initial concentration of hydronium in the second ice table will not be zero
For polyprotics you have multiple Ka values depending on the number of hydrogens. Each ka after the initial one is smaller (because its hard to separate a H+ from a negatively charged ion). Sulfuric acid is a strong acid during its initial deprotonation. Afterwards, its a weak acid. Other acids (unlike sulfuric) are weak upon their initial deprotonation, and each subsequent deprotonation is weaker. Check the book section on polyprotics for more information.
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