The decomposition of N2O5 in the gas phase is first order in N2O5. How long would it take for N2O5 to drop from 0.200 M to 0.025

Question

The decomposition of N2O5 in the gas phase is first order in N2O5. If the concentration of N2O5 drops from 0.200 M to 0.100 M in 14.2 minutes, how long would it take for N2O5 to drop from 0.200 M to 0.025 M?

Answer 1

First order rate equation results in exponential decay for the integrated rate: C/C₀ = e^-kt where k is the reaction rate constant in time^-1 units. This is an exponential relationship, so it can also be given as

C/C₀ = 2^-t/τ where τ is the 1/2 life. This makes the problem a matter of inspection as 14.2 minutes is given as the half-life (C/C₀ = 1/2). To drop to .025 from .2 is a factor of 1/8 = (1/2)³ which will require 3 half-lives of 3 * 14.2 = 42.6 minutes.