2 CO (g) + O2 (g) --> 2 CO2 (g)
The mechanism below has been proposed for this reaction;
(slow) O2 + CO --> CO2 + O(fast) O + CO --> CO2
Based on this mechanism what is the rate law for this reaction?
To determine the rate law for the given reaction mechanism, we need to examine the overall reaction and the proposed elementary steps.
The overall balanced equation for the reaction is:
2 CO (g) + O2 (g) -> 2 CO2 (g)
According to the proposed mechanism, we have two elementary steps:
Step 1: O2 + CO -> CO2 + O (slow)
Step 2: O + CO -> CO2 (fast)
The rate-determining step is often the slowest step in the mechanism, which is Step 1 in this case.
In the rate law, the rate of the reaction is given by the rate-determining step. The rate-determining step involves O2 and CO, so the rate law can be written as:
Rate = k [O2]^[x] [CO]^[y]
To determine the values of x and y in the rate law, we look at the coefficients of O2 and CO in the rate-determining step.
From Step 1: O2 + CO -> CO2 + O
We can see that the coefficient of O2 is 1 and the coefficient of CO is also 1. Therefore, the rate law for this reaction would be:
Rate = k [O2]^[1] [CO]^[1]
Or simply:
Rate = k [O2] [CO]
Thus, the rate law for the given reaction is Rate = k [O2] [CO].
To determine the rate law for a given reaction, we need to first identify the rate-determining step (or slow step) in the proposed mechanism. In this case, the first step (O2 + CO -> CO2 + O) is the slow step.
The rate of the reaction is primarily determined by the rate of the slowest step. Therefore, we can write the rate law based on this slow step.
From the given mechanism, we see that the rate of the slow step is dependent on the concentrations of O2 and CO. We do not include O in the rate law because it is formed and consumed in the fast step, which does not appear in the overall rate equation.
The rate law expression based on the slow step can be written as:
Rate = k[O2][CO]
Here, k is the rate constant, and [O2] and [CO] represent the concentrations of O2 and CO, respectively.
Therefore, the rate law for this reaction, based on the proposed mechanism, is Rate = k[O2][CO].