Consider the 2-step reaction mechanism
fast 2NO + H2 $ N2O+H2O
slow N2O+H2 ! N2+H2O
net 2NO + 2H2 ! N2 + 2H2O
Which of the following rate laws is cor-
rect for the given mechanism? Note that the
constant k may represent a combination of
elementary reaction rate constants.
The rate law for the given mechanism can be determined by considering the slow step of the reaction mechanism. The slow step is:
N2O + H2 → N2 + H2O
The rate of this reaction depends on the concentration of N2O and H2. Therefore, the rate law for this mechanism is:
Rate = k[N2O][H2]
To determine the correct rate law for the given mechanism, we need to examine the rate-determining (slow) step of the reaction. In this case, the slow step is "N2O + H2 → N2 + H2O".
In general, the rate law for a reaction is determined by the slowest step (also known as the rate-determining step) because it is the step that limits the overall rate of the reaction.
Looking at the balanced equation for the slow step, we see that the coefficients of N2O and H2 are both 1. Therefore, the rate law for this step can be written as:
Rate = k[N2O][H2]
Since the slow step is the rate-determining step, the overall rate law for the reaction will be the same as the rate law for the slow step. Therefore, the correct rate law for the given mechanism is:
Rate = k[N2O][H2]
To determine the rate law for a reaction mechanism, we need to examine the overall stoichiometry of the reaction and the rate-determining step.
Looking at the given mechanism, we can see that the rate-determining step is the slow step, which is the second step: N2O + H2 → N2 + H2O.
The coefficients of the reactants in the rate-determining step represent the order of the reaction. In this case, the coefficient of H2 is 1, indicating that the reaction is first order with respect to H2. Therefore, the rate law for the rate-determining step is rate = k[H2].
Since the given mechanism shows that the overall reaction is the sum of the two steps, we can write the rate law for the overall reaction by multiplying the rate laws of the individual steps:
rate = k1[NO][H2] (for the first step) * k2[N2O][H2] (for the second step)
Simplifying this equation gives us:
rate = k1k2[NO][N2O][H2]^2
Therefore, the correct rate law for the given mechanism is rate = k1k2[NO][N2O][H2]^2.