Integrated rate law equation for a first order gas phase reaction is given by (where Pᵢ is initial pressure and Pₜ is total pressure at time t)

Solution

Chemistry ma’am · 4 steps

Write pressure of A in terms of total pressure, then use initial over remaining inside the log.

1. Set up the reaction. Take the standard gas phase case A(g) → B(g) + C(g). At t = 0 only A is present at pressure Pᵢ. If its pressure falls by x at time t, then B and C each reach x.
2. Use total pressure. Total pressure is Pₜ = (Pᵢ - x) + x + x = Pᵢ + x, so x = Pₜ - Pᵢ. The pressure of A left is Pᵢ - x = 2Pᵢ - Pₜ.
3. First order law. Pressure of A is proportional to its concentration. So in k = 2.303/t log[A]₀/[A] you put Pᵢ on top and 2Pᵢ - Pₜ below.

   k = 2.303/t log Pᵢ/(2Pᵢ - Pₜ)

4. So. The integrated rate law is option (a).

The idea to keep. In gas phase kinetics, always convert total pressure into the pressure of the reactant left. The log then holds initial reactant over remaining reactant, never total pressures.

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