For the following reaction

2NO2 -> 2NO +O2 is second order reaction. If the initial concentration of NO2 is 0.098M and the initial rate of disappearance is 2.72e-3 M/sec , what is the value of the rate constant?

rate = k(NO2)^2

rate is 1/2delta(NO2)/time

To determine the value of the rate constant for a second-order reaction, you can use the following equation derived from the integrated rate law:

Rate = k[NO2]^2

Where:
Rate = initial rate of disappearance (2.72e-3 M/sec)
k = rate constant (to be determined)
[NO2] = initial concentration of NO2 (0.098 M)

1. Rearrange the equation to solve for the rate constant (k):
k = Rate / [NO2]^2

2. Substitute the given values into the equation:
k = 2.72e-3 M/sec / (0.098 M)^2

3. Calculate the value of k:
k = 2.72e-3 M/sec / (0.098 M * 0.098 M)

k = 2.72e-3 M/sec / 0.009604 M²

k ≈ 0.283 M⁻¹sec⁻¹

Therefore, the value of the rate constant (k) is approximately 0.283 M⁻¹sec⁻¹.