A sulfuric acid solution has a concentration of $5 \times 10^{-4} \text{ mol L}^{-1}$ - HSC - SSCE Chemistry - Question 8 - 2003 - Paper 1

To calculate the pH of the sulfuric acid solution, we must first determine the concentration of hydrogen ions ( ext{H}^+) produced by the complete ionization of the acid.

Step 1: Understanding Complete Ionization

Sulfuric acid (H₂SO₄) is a strong acid that dissociates completely in water:

H₂SO₄ → 2H⁺ + SO₄²⁻

Given the initial concentration of sulfuric acid is $5 \times 10^{-4} \text{ mol L}^{-1}$, for every mole of H₂SO₄ that ionizes, 2 moles of H⁺ ions are produced.

Step 2: Calculate [H⁺]

The concentration of H⁺ ions will therefore be:

[H⁺] = 2 \times (5 \times 10^{-4}) = 1.0 \times 10^{-3} \text{ mol L}^{-1}

Step 3: Calculate the pH

The pH is calculated using the formula:

pH = -\log_{10}([H⁺])

Substituting the value of [H⁺]:

pH = -\log_{10}(1.0 \times 10^{-3}) = 3.0

Conclusion

Thus, the pH of the sulfuric acid solution is 3.0.