Sulfuric acid (H₂SO₄) is a strong diprotic acid, meaning it can donate two protons (H⁺) per molecule. When it dissolves in water, it dissociates completely in two steps:
1. \( \text{H}_2\text{SO}_4 \rightarrow \text{H}^+ + \text{HSO}_4^- \)
2. \( \text{HSO}_4^- \rightarrow \text{H}^+ + \text{SO}_4^{2-} \)
Initially, every mole of H₂SO₄ produces one mole of H⁺ and one mole of HSO₄⁻.
The second dissociation of HSO₄⁻ is also complete for the purpose of initial concentration calculations, so it produces an additional mole of H⁺ for every mole of H₃SO₄⁻ ionized.
Thus, for an initial concentration of 0.82 M H₂SO₄, each molecule produces a total of 2 moles of H⁺:
\[
[\text{H}^+] = 0.82 \, \text{M} \times 2 = 1.64 \, \text{M}
\]
So, the concentration of protons (H⁺) in the solution would be 1.64 M.