I know the equation
2NO + O2 --> 2NO2
A mechanism would be
2NO --> N2O2 (1) FAST
N2O2 + O2 --> 2NO2 (2) SLOW
How would i derive the rate equation with respect to [NO2]
I've been trying but keep getting confused..
To derive the rate equation with respect to [NO2], we need to examine the rate-determining step of the reaction mechanism. The rate-determining step is the slowest step in the mechanism and determines the overall rate of the reaction.
In this case, the rate-determining step is the second step, which is the slow step: N2O2 + O2 --> 2NO2 (2).
The rate of this step can be determined by the concentration of reactants involved in the slow step. Based on the stoichiometry of the reaction, the rate of the formation of NO2 is directly proportional to the rate of disappearance of N2O2. Therefore, we can write the rate equation for this step as:
Rate2 = k2[N2O2][O2],
where k2 is the rate constant for the second step.
Now, to find the rate equation with respect to [NO2], we need to express [N2O2] in terms of [NO2]. Looking at the first step of the mechanism, we can see that 2 moles of NO react to form 1 mole of N2O2. Therefore, the concentration of N2O2 can be expressed as:
[N2O2] = (2/2) × [NO2] = [NO2].
Substituting this expression into the rate equation for the second step, we get:
Rate2 = k2[NO2][O2].
Hence, the rate equation with respect to [NO2] for the overall reaction is:
Rate_overall = k2[NO2][O2],
where k2 is the rate constant for the second step of the mechanism, and [O2] represents the concentration of O2.