Determine the rate law and the value of k for the following reaction using the data provided.
NO2(g) + O3(g) → NO3(g) + O2(g)
[NO2(g)] (M) [O3(g)] (M) Initial Rate
0.10 0.33 1.42
0.10 0.66 2.84
0.25 0.66 7.10
To determine the rate law and the value of k, we can use the method of initial rates and compare the initial rates for different sets of concentrations.
First, we can compare the initial rates when the concentration of NO2(g) is kept constant and the concentration of O3(g) is doubled. From the data, we have:
[NO2(g)] = 0.10 M [O3(g)] = 0.33 M Initial Rate = 1.42
[NO2(g)] = 0.10 M [O3(g)] = 0.66 M Initial Rate = 2.84
Since the concentration of NO2(g) is kept constant, any change in the initial rate must be due to the change in the concentration of O3(g). When the concentration of O3(g) is doubled, the initial rate also doubles. This indicates that the reaction is first order with respect to O3(g).
Next, we can compare the initial rates when the concentration of O3(g) is kept constant and the concentration of NO2(g) is doubled. From the data, we have:
[NO2(g)] = 0.10 M [O3(g)] = 0.66 M Initial Rate = 2.84
[NO2(g)] = 0.25 M [O3(g)] = 0.66 M Initial Rate = 7.10
Since the concentration of O3(g) is kept constant, any change in the initial rate must be due to the change in the concentration of NO2(g). When the concentration of NO2(g) is doubled, the initial rate increases by a factor of 2.5 (7.10/2.84). This indicates that the reaction is approximately second order with respect to NO2(g).
Combining the information, we can write the rate law as:
Rate = k[NO2(g)]^2[O3(g)]
Finally, to determine the value of k, we can use any set of data. Let's use the first set:
[NO2(g)] = 0.10 M [O3(g)] = 0.33 M Initial Rate = 1.42
Using the rate law equation, we have:
1.42 = k(0.10)^2(0.33)
Solving for k, we find:
k ≈ 12.97
Therefore, the rate law for the reaction is:
Rate = 12.97[NO2(g)]^2[O3(g)] and the value of k is approximately 12.97.