The reaction 2 NO+2 H2 ⟶N2+2 H2 O is second order in [NO]...

The reaction $2 \mathrm{NO}+2 \mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O} \quad$ is second order in [NO] and first order in $\left[\mathrm{H}_{2}\right] .$ A three step mechanism has been proposed. The first, fast step is the elementary process given as equation (20.25) on page $953 .$ The third step, also fast, is $\mathrm{N}_{2} \mathrm{O}+$ $\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O} .$ Propose an entire three-step mechanism, and show that it conforms to the experimentally determined reaction order.

The reaction $2 \mathrm{NO}+2 \mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+2 \mathrm{H}_{2} \mathrm{O} \quad$ is second order in [NO] and first order in $\left[\mathrm{H}_{2}\right] .$ A three step mechanism has been proposed. The first, fast step is the elementary process given as equation (20.25) on page $953 .$ The third step, also fast, is $\mathrm{N}_{2} \mathrm{O}+$ $\mathrm{H}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O} .$ Propose an entire three-step
mechanism, and show that it conforms to the experimentally determined reaction order.

Key Concepts

Reaction Intermediates

Reaction intermediates are species that are produced and consumed during the course of a multi-step reaction and do not appear in the overall balanced equation. These intermediates can provide insight into the detailed pathway of the reaction by linking the sequence of elementary steps, and they often play a role in transmitting the effect of the fast pre-equilibrium or other rapid steps to the slow, rate-determining step.

Rate-Determining Step

The rate-determining step (RDS) is the slowest step in a multi-step reaction mechanism, acting as a bottleneck that limits the overall reaction rate. Since the overall reaction kinetics are governed by the RDS, the rate law of this step is primarily responsible for the experimentally observed reaction order. Identifying the RDS is crucial in ensuring that the proposed mechanism matches kinetic observations.

Steady-State/Pre-Equilibrium Approximation

The steady-state and pre-equilibrium approximations are techniques used to simplify the kinetic analysis of reaction mechanisms involving intermediates by assuming that the concentration of these intermediates remains relatively constant (steady-state) or rapidly reaches equilibrium with the reactants (pre-equilibrium). These assumptions allow for the derivation of an overall rate law that depends solely on the concentrations of the stable reactants, thus aligning with the observed kinetics.

Reaction Order

Reaction order refers to the exponent of the concentration term of a reactant in the rate law, which indicates how the rate of reaction changes with respect to changes in concentration. In the context of reaction mechanisms, the observed overall reaction order serves as a critical constraint that any proposed sequence of elementary steps must satisfy, ensuring that the derived rate law from the mechanism is consistent with experimental kinetic data.

Elementary Reaction Steps

Elementary reaction steps are the simplest processes that occur in a reaction mechanism and describe the molecular events in a single collision or a simple rearrangement. They obey their own intrinsic rate laws, which are typically easy to predict based on molecularity. Proposing a series of elementary steps allows chemists to break down a complex reaction into manageable parts that collectively account for the overall reaction stoichiometry and kinetics.

Mechanism Consistency with Rate Law

A proposed reaction mechanism must produce an overall rate law that is consistent with the experimentally determined kinetics. In this context, constructing a multi-step mechanism involves ensuring that the contributions from each step, especially the rate-determining step and the equilibria of rapid steps, combine to yield the correct orders with respect to each reactant. This consistency check links the macroscopic kinetic observations with the microscopic sequence of elementary processes.

Transcript

00:01 Hey guys, so in this question, we're given the reaction between nitrogen monoxide and hydrogen gas, and it's forming nitrogen gas and water.

00:11 We're given that the order with respect to nitrogen monoxide is second order, and we're given that the order with respect to hydrogen gas is first order, given by this rate law right here.

00:24 And we're asked to find a three -step mechanism.

00:28 And we're given the first two steps, which are both fast steps, and these two first steps are according to the information from the textbook.

00:36 And we have to try to find the second step for this three -step mechanism to complete this question.

00:44 So we have to make sure that our order with respect to the rates or the reactants is the same.

00:53 So the first thing i'm going to do is i'm going to make sure that's so.

01:00 For nitrogen or nitrogen monoxide, the order is two.

01:05 So that means that we have to have a coefficient of two in front of that in our reactants and a coefficient of one in front of hydrogen gas.

01:19 So that we'll just write that as h2.

01:21 And we know that this step has to be the slow step.

01:26 And we can say that the coefficients of this are equal to the order because this is the slowest step, and the slowest step we know is the rate determining step.

01:35 So the orders are going to be the same as our molecularity here.

01:41 The next thing i'm going to do is i'm going to look at my intermediates.

01:46 So i have an intermediate of n2ho2, and that doesn't appear in any of the reactants here on steps 2 and 3.

01:55 So i'm going to go ahead and add it to step two.

02:00 And we do this because we want our intermediates to cancel out.

02:04 So we are left with only the reactants and the products given in the overall reaction.

02:10 So i have that here.

02:13 And i'm going to go ahead and do the same thing for my other intermediate...