The mechanism for the reaction described by
No2+CO--->CO2+NO
is suggested to be
(1)2NO2--->NO3+NO
(2)NO3+CO--->NO2+CO2
Assuming that [NO3] is governed by steady-state conditions, derive the rate law for the production of CO2(g) and enter it in the space below.
rate of CO2 production=
To derive the rate law for the production of CO2 in the given reaction, we need to use the suggested mechanism and apply the steady-state approximation. The steady-state approximation assumes that the rate of formation and consumption of an intermediate species (in this case, NO3) are equal.
Let's assume that the rate of the forward reaction (2NO2 --> NO3 + NO) is k1 and the rate of the reverse reaction (NO3 + NO --> 2NO2) is k-1. Additionally, let's denote the rate of the reaction (NO3 + CO --> NO2 + CO2) as k2.
According to the steady-state approximation, the rate of formation of NO3 is equal to its rate of consumption. Therefore, we can write:
Rate of formation of NO3 = Rate of consumption of NO3
Using the rate constants, we can write the above expression as follows:
k1[NO2]^2 = k-1[NO3][NO]
Now, let's consider the overall stoichiometry of the reaction:
2NO2 + CO --> CO2 + NO
From the balanced equation, we can see that the rate of formation of CO2 is equal to twice the rate of formation of NO. Thus, we have:
Rate of CO2 production = 2 * Rate of formation of NO
Substituting the expression for the rate of formation of NO from the steady-state approximation, we get:
Rate of CO2 production = 2 * k1[NO2]^2 / k-1[NO3]
Therefore, the rate law for the production of CO2 is:
Rate of CO2 production = (2k1 / k-1) * [NO2]^2 / [NO3]
Please note that the rate constants (k1, k-1) need to be provided in order to fully determine the rate law for this reaction.