Consider the following first order gas phase reaction at constant temperature A(g) → 2 B( g)+C(g)
If the total pressure of the gases is found to be 200 torr after 23 sec. and 300 torr upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is ________ × 10⁻² s⁻¹ (nearest integer)
[Given : log ₁₀(2)=0.301]

Solution

Chemistry ma’am · 4 steps

Use the final pressure to find where A started, and you will see 23 s is exactly one half-life.

1. Pressure bookkeeping. Let A start at P₀ and let x of it react. Then A is P₀ - x, B is 2x and C is x, so the total pressure is P₀ + 2x.
2. Find P0 and x. At the end all of A has gone, so x = P₀ and the total is 3P₀ = 300 torr, giving P₀ = 100 torr. At 23 s, 100 + 2x = 200, so x = 50 torr and A left is 50 torr.

   k = 2.303/t log p_(A,0)/p_A = 2.303/23 log 100/50

3. Put in numbers. k = (2.303 × 0.301)/23 = 0.693/23 = 3.01 × 10⁻² s⁻¹. A has halved, so 23 s is the half-life.
4. So. The rate constant is about 3 × 10⁻² s⁻¹, so the answer is 3.

The common slip: 1. Using log 2 without the factor 2.303 gives 1.3 × 10⁻² s⁻¹, which rounds to 1.

The idea to keep. For gas-phase decompositions, write each species in terms of x and add them up. The pressure after a very long time tells you the starting pressure of the reactant.

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