Question

100 mL of 0.1M $HCl$ and 100 mL of 0.05 M $H_{2}SO_{4}$ are mixed and the solution is diluted to 2.0 L by adding water. The pH of the resulting solution is

• A. 1
• B. 3
• C. 2
• D. 4

Hint:

Don't forget that $H_{2}SO_{4}$ is diprotic—it gives two $H^{+}$ ions per molecule!

Answer 1

The Correct Option is C

Step 1: Concept
pH is the negative logarithm of the $H^{+}$ ion concentration.

Step 2: Meaning
Calculate total millimoles of $H^{+}$ ions: From $HCl$: $100 \times 0.1 = 10$ mmol. From $H_{2}SO_{4}$: $100 \times 0.05 \times 2 = 10$ mmol. Total $H^{+}$ = $20$ mmol = $0.02$ moles.

Step 3: Analysis
Final concentration $[H^{+}]$ = Moles Volume (L) = $0.02 / 2.0 = 0.01$ M = $10^{-2}$ M. pH = $-\log[10^{-2}] = 2$.

Step 4: Conclusion
The pH of the resulting solution is 2.
Final Answer: (C)