A(g)⇌ 2 B(g)+C(g)
For the given reaction, if the initial pressure is 450 mm Hg and the pressure at time t is 720 mm Hg at a constant temperature T and constant volume V. The fraction of A(g) decomposed under these conditions is x× 10⁻¹. The value of x is ___________ (nearest integer)

Solution

Chemistry ma’am · 4 steps

Each A that splits leaves 3 gas molecules, so the pressure rise is twice the pressure of A lost.

1. Pressure tracks moles. At constant T and V, the partial pressure of each gas is proportional to its moles. So you can do the whole stoichiometry in mm Hg.
2. Set up the table. Let p be the pressure of A that has decomposed by time t. Then A is 450 - p, B is 2p and C is p.

   Pₜₒₜₐₗ = (450 - p) + 2p + p = 450 + 2p = 720

3. Solve for p. 2p = 270, so p = 135 mm Hg. The fraction of A decomposed is 135/450 = 0.3.
4. So. 0.3 = 3 × 10⁻¹, so x = 3.

The common slip: 6. Taking the whole pressure rise of 270 mm Hg as the A decomposed gives 270/450 = 0.6, so 6. One A makes 3 molecules, so the rise is 2p, not p.

The idea to keep. For gas reactions at fixed T and V, write each partial pressure in terms of p. The total rises by Δ n_g × p, not by p.

Answer from the NTA final answer key. Solution by PrepWiser.