Question

What is the molarity of \(\text{H}_2\text{SO}_4\) solution having \(\text{pH} = 4\) ?

• A. \(4\times 10^{-1} \text{M}\)
• B. \(4\times 10^{-2} \text{M}\)
• C. \(5\times 10^{-5} \text{M}\)
• D. \(1\times 10^{-4} \text{M}\)

Hint:

Find [H+] from pH, then divide by two because each H2SO4 gives two H+ ions.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
pH is \(-\log[\text{H}^+]\). Sulphuric acid is a strong acid that gives two \(\text{H}^+\) ions per molecule in dilute solution.

Step 2: Key Formula or Approach:
1. \([\text{H}^+] = 10^{-\text{pH}}\).
2. \(\text{H}_2\text{SO}_4 \to 2\text{H}^+ + \text{SO}_4^{2-}\), so \([\text{H}_2\text{SO}_4] = \frac{[\text{H}^+]}{2}\).

Step 3: Detailed Explanation:
\([\text{H}^+] = 10^{-4}\) M.
\[ [\text{H}_2\text{SO}_4] = \frac{10^{-4}}{2} = 5 \times 10^{-5}\ \text{M} \]
Option D (\(1 \times 10^{-4}\) M) forgets that one molecule gives two protons. Options A and B are many times larger and would give a pH far below 4.

Final Answer:
The molarity is \(5 \times 10^{-5}\) M, option (C). \[ \boxed{5 \times 10^{-5}\ \text{M}} \]