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