The reaction
3NO → N₂O + NO₂
Is found to obey the rate law Rate = k[NO]². If the first half-life of the reaction is found to be 3.5 s, what is the length of the fourth half-life?

Question

The reaction 3NO → N₂O + NO₂ Is found to obey the rate law Rate = k[NO]². If the first half-life of the reaction is found to be 3.5 s, what is the length of the fourth half-life?

Quizplus · Accepted Answer

The half-life of a first-order reaction is given by t1/2 = 0.693/k. Since the first half-life of the reaction is 3.5 s, we can calculate the rate constant k as follows:
t1/2 = 0.693/k
3.5 s = 0.693/k
k = 0.198 s^-1
The length of the fourth half-life can be calculated as follows:
t4 = 4*t1/2
t4 = 4*(0.693/k)
t4 = 4*(0.693/0.198)
t4 = 13.9 s
Rounding to the nearest whole number gives the answer of 14 s. Therefore, the correct answer is (C).

The Reaction 3NO → N2O + NO2

The Reaction 3NO → N₂O + NO₂