A(g) → 2B(g) + C(g) is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be _________ mm Hg. (Nearest integer)

Solution

Chemistry ma’am · 4 steps

Pressure doubled in 10 min, so half of A is gone: 10 min is the half-life, and 30 min is three of them.

1. Track the pressures. Let the pressure of A fall by x. Then B rises by 2x and C by x. So p_A = 800 - x and the total is 800 - x + 2x + x = 800 + 2x.
2. Read the half-life. At 10 min, 800 + 2x = 1600, which gives x = 400 mm Hg. So p_A has dropped from 800 to 400 in 10 min. That makes t_(1/2) = 10 min.

   p_A(30 min) = 800 × (1/2)³ = 100 mm Hg

3. Pressure at 30 min. 30 min is 3 half-lives, so p_A = 100 mm Hg. That gives x = 800 - 100 = 700 mm Hg.
4. So. The total pressure is 800 + 2 × 700 = 2200 mm Hg, which is 2200.

The common slip: 3200. Assuming the pressure keeps rising by 800 mm Hg every 10 min gives 3200. A first order reaction slows down as A is used up, so each half-life adds less pressure.

The idea to keep. In a gas-phase first order reaction, write the total pressure in terms of x first. Only the reactant's own pressure halves every half-life. The total pressure never does.

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