The number of hydrogen ions in 1.0dm$^3$ of a 0.25 mole tetraoxosulphate(Vl) acid solution is [Avogadro constant = 6.02 x 10$^{23}$]

Analyze the question: We need the number of H⁺ ions in 1.0 dm³ of a solution containing 0.25 mol of H₂SO₄ (tetraoxosulphate(VI) acid).

Concept: H₂SO₄ is a strong dibasic acid, so each mole gives 2 moles of H⁺:

H₂SO₄ → 2H⁺ + SO₄²⁻

Number of ions = moles of ions × Avogadro constant

Solution:

1. Moles of H₂SO₄ = 0.25 mol (1.0 dm³ × 0.25 mol/dm³)
2. Moles of H⁺ = 2 × 0.25 = 0.50 mol
3. Number of H⁺ ions = 0.50 × 6.02 × 10²³ = 3.01 × 10²³

This is approximately 3.00 × 10²³, which matches option C.

Check: Option B (1.50 × 10²³) would be the answer if you forgot the factor of 2 (0.25 × 6.02 × 10²³ ≈ 1.5 × 10²³). That is the common trap.

Tip: For acid questions, always check the basicity (number of replaceable H atoms): HCl = 1, H₂SO₄ = 2, H₃PO₄ = 3. Multiply the moles of acid by this number to get the moles of H⁺ before multiplying by Avogadro's number.