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?

The rate law for a reaction determines how the rate of the reaction depends on the concentrations of the reactants. To determine the rate law for this reaction based on the proposed mechanism, we need to examine the rate-determining step, which is typically the slowest step in a reaction mechanism.

From the proposed mechanism, we see that the slow step is:
O2 + CO --> CO2 + O

The stoichiometry of this slow step shows that one molecule of O2 reacts with one molecule of CO to produce one molecule of CO2 and one molecule of O. Therefore, the rate of this step will depend on the concentrations of O2 and CO as follows:

Rate = k1 [O2] [CO]

Now, let's look at the overall balanced reaction:
2 CO (g) + O2 (g) --> 2 CO2 (g)

The stoichiometry of the overall reaction shows that for every two molecules of CO consumed, one molecule of O2 is consumed, and two molecules of CO2 are produced. This means that the rate of the overall reaction must be twice the rate of the slow step to account for the stoichiometry. Therefore, the rate law for the overall reaction is:

Rate = 2k1 [O2] [CO]

Thus, the rate law for this reaction based on the proposed mechanism is rate = 2k1 [O2] [CO].

To determine the rate law for the given reaction mechanism, we need to examine the rate-determining step, which is the slowest step in the mechanism. The rate law for the overall reaction will be determined by the reactants involved in this step.

According to the proposed mechanism:
(slow) O2 + CO --> CO2 + O
(fast) O + CO --> CO2

Since the slow step involves the reaction between O2 and CO, we can assume that the rate-determining step involves these two reactants. Therefore, the rate law for the overall reaction can be expressed as:

Rate = k[O2][CO]

Here, [O2] and [CO] represent the concentrations of O2 and CO, respectively, and k is the rate constant which combines all the factors that affect the reaction rate except concentrations.

Therefore, based on the proposed mechanism, the rate law for this reaction is Rate = k[O2][CO].