What is the concentration of H^+ ions in a 0.010 M aqueous solution of sulfuric acid (H_2SO_4), assuming complete dissociation?

• A. 0.010 M
• B. 0.0050 M
• C. 0.020 M
• D. 0.015 M

Answer: (C)

Verified step by step guidance

1. Recognize that sulfuric acid (H_2SO_4) is a strong acid that dissociates completely in water in two steps: the first dissociation is complete, producing one H^+ ion and one HSO_4^- ion, and the second dissociation partially dissociates HSO_4^- to produce another H^+ ion and SO_4^{2-}. However, for this problem, we assume complete dissociation of both protons.
2. Write the dissociation reactions for sulfuric acid: \[\text{H}_2\text{SO}_4 \rightarrow \text{H}^+ + \text{HSO}_4^-\] \[\text{HSO}_4^- \rightarrow \text{H}^+ + \text{SO}_4^{2-}\]
3. Since the initial concentration of H_2SO_4 is 0.010 M and both protons dissociate completely, each mole of H_2SO_4 produces 2 moles of H^+ ions. Therefore, calculate the concentration of H^+ ions by multiplying the initial concentration by 2: \[[\text{H}^+] = 2 \times 0.010\, \text{M}\]
4. Express the final concentration of H^+ ions as the product from the previous step, which represents the total concentration of hydrogen ions in solution after complete dissociation.
5. Confirm that this concentration matches the expected answer choice, understanding that complete dissociation of both protons doubles the initial acid concentration in terms of H^+ ion concentration.