The mechanism for the reaction of nitrogen dioxide with carbon monoxide to form nitric oxide and carbon dioxide is thought to be
NO2+NO2 > NO3+NO slow
NO3+CO > NO2+CO2 fast
Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction?
The order, and therefore the rate law, is dependent on the slowest step in a complex (multi-step) reaction.
The expected rate law for a reaction is
Rate = constant * (conc. of A)^n * (conc of B)^n
where A and B are reactants, and n and m are stochiometric coffecients
However, sometimes the powers are not equal to the stochiometric coefficients.
In this case, there is one reactant (NO2) and its coefficient is two.
Rate = k[NO2]^2
I agree with Arora for the rate law. The overall equation is the sum of the two steps.
Here is one of the best explanations of how to do these that I've seen.
https://courses.lumenlearning.com/boundless-chemistry/chapter/reaction-
This site clearly shows how to handle the rate law when the slow step is the first step in a multistep proposal as well as when it is not the first step. If you will be doing mechanisms I recommend you study this site thoroughly. It is VERY good in my opinion.
To determine the rate law expected for this mechanism, we need to analyze the individual steps and identify the rate-determining step.
Let's examine the first step: NO2 + NO2 → NO3 + NO (slow). This step is relatively slow compared to the second step, which is indicated by the "(slow)" notation. The coefficients in this step indicate that the reaction is second order overall (first order with respect to NO2 and first order with respect to NO).
Next, let's analyze the second step: NO3 + CO → NO2 + CO2 (fast). This step involves the reaction between NO3 and CO. The rate of this step depends on the concentrations of NO3 and CO, indicating a first-order dependence for each reactant.
Since the first step is the slowest step, it controls the overall rate of the reaction. Therefore, the rate law expected for this mechanism is determined by the rate-determining step, which is the first step:
Rate = k[NO2] * [NO2]
Now, let's balance the overall chemical equation. Combining the two steps, we have:
NO2 + NO2 + NO3 + CO → 2NO2 + NO + CO2
By canceling out common species on both sides, we obtain the balanced equation:
NO3 + CO → NO + CO2