Nitrogen dioxide reacts with carbon monoxide to produce nitrogen monoxide and carbon dioxide in the reaction, . The first step in the reaction is proposed to be two NO2 molecules colliding to form NO3 and NO. The NO3 intermediate then reacts with CO to form CO2. What is the rate law for this proposed mechanism?
Rate law = k[NO2]^2[CO]
To determine the rate law for the proposed mechanism, we need to look at the rate-determining step, which is the slowest step in the reaction and determines the overall rate of the reaction.
Based on the proposed mechanism, the rate-determining step is the reaction between NO3 and CO to form CO2. Let's assume the rate of this step is given by the following rate law:
Rate = k[NO3][CO]
where k is the rate constant and [NO3] and [CO] represent the concentrations of NO3 and CO, respectively.
However, we also need to consider the stoichiometry of the reaction to relate the concentrations of reactants and products. From the balanced chemical equation:
2NO2 + 2CO -> 2NO + 2CO2
we can see that the stoichiometric coefficient of NO3 is 2, meaning that two NO3 molecules are formed for every two NO2 molecules reacting.
Therefore, we can modify the rate law by substituting [NO3] with [NO2]:
Rate = k[NO2]^2[CO]
So, the rate law for the proposed mechanism is:
Rate = k[NO2]^2[CO]
The rate law for a proposed mechanism can be determined by examining the slowest step, also known as the rate-determining step. In this case, the step that involves the formation of NO3 intermediate is proposed to be the slowest step.
The balanced chemical equation for this step is:
2 NO2 → NO3 + NO
Let's assume that the rate of this step is proportional to the concentration of NO2 raised to the power of x (x is the reaction order for NO2) and the concentration of NO raised to the power of y (y is the reaction order for NO). The rate expression for this step can be written as:
rate = k1 [NO2]^x [NO]^y
Now, let's consider the step involving the reaction of NO3 with CO:
NO3 + CO → CO2 + NO
Since NO3 is an intermediate, its concentration does not appear in the overall rate law. Therefore, the rate expression for this step can be written as:
rate = k2 [NO3] [CO]
Combining these two rate expressions, we can write the overall rate law for the proposed mechanism as:
rate = k1 k2 [NO2]^x [NO]^y [NO3] [CO]
Thus, the rate law for this proposed mechanism is:
rate = k1 k2 [NO2]^x [NO]^y [NO3] [CO]