Question

The elementary reaction

2NO2(g) → 2 NO(g) + O2(g)
is second order in NO2 and the rate constant at 720 K is 2.88 × 10^1 M^-1 s^-1. The reaction half-life at this temperature when [NO2]0 = 0.45 M is ________ s.
a) 0.0048
b) 0.024
c) 0.048
d) 0.24
e) none of these

Answer 1

The half-life for a second-order reaction, calculated using the formula t1/2 = 1 / (k [A]0), with given rate constant of 2.88 × 10^1 M^-1 s^-1 and [NO2]0 of 0.45 M, results in 0.0772 s, which is not one of the provided options. the correct answer is none of these, which aligns with option (e).

Step-by-step explanation:

The half-life for a second-order reaction can be calculated using the formula t1/2 = 1 / (k [A]0), where t1/2 is the half-life, k is the rate constant, and [A]0 is the initial concentration of the reactant A. In the given reaction 2NO2(g) → 2NO(g) + O2(g), the rate constant at 720 K is 2.88 × 10^1 M^-1 s^-1, and the initial concentration of NO2, [NO2]0, is 0.45 M.

To calculate the half-life (t1/2), we substitute the given values into the formula:

t1/2 = 1 / (2.88 × 10^1 M^-1 s^-1 × 0.45 M) = 1 / (12.96 s^-1) = 0.0772 s.

Since the result is not listed in the options provided, the correct answer is none of these, which aligns with option (e).