The gas-phase decomposition of NO₂, 2 NO₂

Question

The gas-phase decomposition of NO₂, 2 NO₂(g) → 2 NO(g) + O₂(g), is studied at 383°C, giving the following data:

Time (s) [NO₂] (M)

0.0 0.100

5.0 0.017

10.0 0.0090

15.0 0.0062

20.0 0.0047

(a) Is the reaction first order or second order with respect to the concentration of NO₂?

(c) Predict the reaction rates at the beginning of the reaction for initial concentrations of 0.200 M, 0.100 M, and 0.050 M NO₂.

Accepted Answer

Identify the rate law for the reaction. Since the reaction is 2 $$NO_2$$ \rightarrow 2 NO + $$O_2$$, it is likely a second-order reaction with respect to $$NO_2.. $$Use the integrated rate law for a second-order reaction: $$ \frac{1}{[A]} = kt + \frac{1}{[A]_0} $$, where $$[A] is $$the concentration of $$NO_2 at $$time $$t$$, $$[A]_0 is $$the initial concentration, and $$k is $$the rate constant.. Calculate the rate constant $$k$$ using the given data. Choose two data points, for example, $$[NO_2]_0 = 0.100\, M at$$ $$t = 0\, s$$ and $$[NO_2] = 0.017\, M at$$ $$t = 5.0\, s$$, and substitute into the integrated rate law to solve for $$k.. $$Once $$k is $$determined, use the rate law $$rate = k[NO_2]^2 to $$calculate the initial reaction rates for the given initial concentrations: 0.200 M, 0.100 M, and 0.050 M.. Substitute each initial concentration into the rate law to find the initial rate for each concentration. Remember, the rate is dependent on the square of the concentration for a second-order reaction.

Verified video answer for a similar problem:

Key Concepts

Reaction Rate

Rate Law

Concentration and Its Effect on Reaction Rate