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)
* indicates equilibrium arrows
Thank you!
To derive the theoretical rate law for the given reaction, we need to determine the rate-determining step (also known as the slowest step). In this case, the second step ((2) N2O2(g) + O2(g) --> 2NO2(g)) is the slow step.
In the rate-determining step, the rate of the reaction depends on the reactant concentrations, which we can express using the stoichiometric coefficients of the balanced equation. From the balanced equation, we see that the stoichiometric coefficient of N2O2 is 1, and the stoichiometric coefficient of O2 is also 1.
Therefore, the rate law for the reaction is given by:
Rate = k [N2O2][O2]
Now let's determine whether or not the proposed mechanism is possible for the given reaction. A mechanism is considered plausible if the overall balanced reaction matches the given reaction, and the elementary steps of the mechanism sum up to the overall reaction.
Let's analyze the proposed mechanism:
(1) 2NO(g) <-->* N2O2(g) (fast)
(2) N2O2(g) + O2(g) --> 2NO2(g) (slow)
The first step suggests the formation of N2O2 from 2NO, and it is in equilibrium with NO. Therefore, the forward direction represents the formation of N2O2, while the reverse direction represents the dissociation of N2O2 to NO.
If we sum up the two steps, we get:
2NO(g) + O2(g) --> 2NO2(g), which matches the overall given reaction.
Hence, the proposed mechanism is possible for the given reaction.