The reaction 2 NO2(g)--> 2NO(g)+O2(g) is postulated to occur via the mechanism below:
NO2)g)+ NO2(g)-->NO(g)+NO3(g) ;K1,slow NO3(g)--+O2(g);K2 , fast
What is the rate law for this mechanism
The rate law for the slowest step (which is the rate-determining step) will give us the overall rate law.
The slow step is: NO2(g) + NO2(g) --> NO(g) + NO3(g)
The rate law for this step can be written as:
rate = k1[NO2][NO2]
The fast step is: NO3(g) + O2(g) --> NO2(g) + O3(g)
The rate law for this step can be written as:
rate = k2[NO3][O2]
Now, we need to eliminate NO3 from the rate law of the overall reaction. We can do this by using the fast step to express [NO3] in terms of [NO2] and [O2]:
k2[NO3][O2] = rate of NO3 consumption = k1[NO2][NO2]
[NO3] = (k1/k2)[NO2]^2[O2]
Substituting this expression for [NO3] into the rate law for the fast step:
rate = k2[(k1/k2)[NO2]^2[O2]][O2] = k1k2[NO2]^2[O2]^2
Therefore, the rate law for the overall reaction is:
rate = k1k2[NO2]^2[O2]^2
To determine the rate law for this mechanism, we need to examine the slowest step, known as the rate-determining step. In this case, the slow step is the first step:
NO2(g) + NO2(g) → NO(g) + NO3(g)
From this step, we can see that the rate of the reaction depends on the concentration of NO2(g) squared.
Therefore, the rate law for this mechanism is:
Rate = k[NO2(g)]^2
Where k is the rate constant.
To determine the rate law for this mechanism, we need to first write the overall balanced equation for the reaction.
The given reaction is: 2 NO2(g) --> 2 NO(g) + O2(g)
Now, let's consider the individual steps of the mechanism:
Step 1: NO2(g) + NO2(g) --> NO(g) + NO3(g) (K1, slow)
Step 2: NO3(g) --> O2(g) (K2, fast)
The first step is the slowest step in this mechanism, so we can assume it is the rate-determining step. The rate law for the overall reaction will then be determined by the rate of this slow step.
In the slow step, we can see that the reactants are NO2(g) and NO2(g), so we can write the rate expression as:
Rate = k1[NO2(g)][NO2(g)]
Here, k1 is the rate constant for the slow step.
However, we notice that the stoichiometric coefficient in the balanced equation for the slow step is 1:1 for NO2(g) to NO(g). So, we can rewrite the rate expression as:
Rate = k1[NO2(g)]^2
Therefore, the rate law for this mechanism is Rate = k1[NO2(g)]^2.