2NO(g) + O2(g) --> 2NO2(g)
Derive the theoretical rate law and indicate whether or not this is a possible mechanism for the above reaction:
(1) 2NO(g) <-->* N2O2(g) (fast)
(2) N2O2(g) + O2(g) --> 2NO2(g) (slow)
Extra Info: This reaction is third order overall. NO is second order, and O2 is first order.
* indicates equilibrium arrows
Thank you!
To derive the theoretical rate law for the given reaction, we need to determine the rate-determining step. The rate-determining step is the slowest step in a reaction and it determines the overall rate of the reaction.
From the given mechanism, we can see that the second step (2) is the slow step because it is the only step that includes the reactant N2O2. The first step (1) is a fast equilibrium step, which means its rate is much faster compared to the second step.
Now, let's analyze the stoichiometry of the slow step (2):
N2O2(g) + O2(g) --> 2NO2(g)
According to the balanced equation, the stoichiometric coefficients in the slow step represent the reaction order. The coefficient of N2O2 is 1, and since it appears once on the reactant side, it is the first order. The coefficient of O2 is also 1, so it is also first order.
Based on the information given, we know that the overall reaction is third order. This implies that there must be another reactant that contributes to the overall reaction rate. In this case, NO is the other reactant.
If we assume that the rate law for the overall reaction is given by:
Rate = k[NO]^x[O2]^y
From the given information, we know that NO is second order overall and O2 is first order overall. Therefore, we can assign values to x and y as follows:
x = 2 (because NO is second order)
y = 1 (because O2 is first order)
So, the theoretical rate law for the given reaction is:
Rate = k[NO]^2[O2]
Now, let's determine whether this is a possible mechanism for the reaction. To do this, we need to verify if the rate law obtained from the mechanism matches the experimentally determined rate law. If they match, then the mechanism is possible.
Since the given rate law is consistent with the experimentally determined rate law, we can conclude that this is a possible mechanism for the reaction.
Hope this helps!