The iron-catalyzed exchange reaction NH3( g)+D2( g) ⟶NH2 D(g)+HD(g) obeys the rate law v=(k[D2]^

The iron-catalyzed exchange reaction NH3( g)+D2( g) ⟶NH2...

The iron-catalyzed exchange reaction $$ \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{D}_{2}(\mathrm{~g}) \longrightarrow \mathrm{NH}_{2} \mathrm{D}(\mathrm{g})+\mathrm{HD}(\mathrm{g}) $$ obeys the rate law $$ v=\frac{k\left[\mathrm{D}_{2}\right]^{1 / 2}\left[\mathrm{NH}_{3}\right]}{\left(1+K\left[\mathrm{NH}_{3}\right]\right)^{2}} $$ Is this rate law consistent with either the Eley-Rideal or Langmuir-Hinshelwood mechanisms? How are $k$ and $K$ related to the rate constants of the individual steps of the mechanism you chose? What does the rate law tell you about the relative adsorption of $\mathrm{D}_{2}(\mathrm{~g})$ and $\mathrm{NH}_{3}(\mathrm{~g})$ to the iron surface?

The iron-catalyzed exchange reaction
$$
\mathrm{NH}_{3}(\mathrm{~g})+\mathrm{D}_{2}(\mathrm{~g}) \longrightarrow \mathrm{NH}_{2} \mathrm{D}(\mathrm{g})+\mathrm{HD}(\mathrm{g})
$$
obeys the rate law
$$
v=\frac{k\left[\mathrm{D}_{2}\right]^{1 / 2}\left[\mathrm{NH}_{3}\right]}{\left(1+K\left[\mathrm{NH}_{3}\right]\right)^{2}}
$$
Is this rate law consistent with either the Eley-Rideal or Langmuir-Hinshelwood mechanisms? How are $k$ and $K$ related to the rate constants of the individual steps of the mechanism you chose? What does the rate law tell you about the relative adsorption of $\mathrm{D}_{2}(\mathrm{~g})$ and $\mathrm{NH}_{3}(\mathrm{~g})$ to the iron surface?

Key Concepts

Eley-Rideal Mechanism

This mechanism involves one reactant being adsorbed on the catalyst surface while the other remains in the gas (or solution) phase and reacts directly with the adsorbed species. It is typically characterized by simpler rate expressions that depend linearly on the concentration of the gas?phase species. However, since the rate law in the question shows a fractional order dependence and a complex denominator, the Eley-Rideal mechanism is not consistent with the observed behavior.

Langmuir-Hinshelwood Mechanism

In the Langmuir-Hinshelwood mechanism, both reactants adsorb on the catalyst surface and the reaction occurs via an interaction between adsorbed species. This mechanism often yields rate laws that include adsorption equilibrium terms and can give rise to fractional reaction orders when one of the adsorbed species, especially if its adsorption is dissociative, contributes nonlinearly. The given rate law, with its ([NH3]) term in the numerator and an adsorption term (1 + K[NH3])² in the denominator along with a fractional order in D2, aligns well with a Langmuir-Hinshelwood type behavior.

Surface Adsorption Equilibrium

Catalytic reactions on solid surfaces are governed by adsorption equilibria where reactants bind to active sites. The adsorption equilibrium constant (K) reflects the strength and extent of adsorption. In heterogeneous catalysis, competing adsorption among different molecules can influence the availability of surface sites, and this is illustrated by the denominator term in the rate law. The form (1 + K[NH3])² indicates that the adsorption of NH3 strongly affects site occupancy, thereby modulating the overall reaction rate.

Rate Law Derivation in Heterogeneous Catalysis

Deriving rate laws for surface-catalyzed reactions involves combining the kinetics of adsorption/desorption and the surface reaction steps. The overall rate constant (k) in the reported rate law is typically a composite constant that includes the intrinsic rate constant for the surface reaction and factors arising from the adsorption equilibria. Similarly, the adsorption equilibrium constant (K) directly relates to the forward and reverse rate constants for the adsorption of reactants. Analyzing the form of the rate law sheds light on which steps are rate determining and how the reaction dynamics are influenced by the adsorption of different reactants on the catalyst surface.

Transcript

00:01 For these types of questions, we first of all, you have to write the balanced chemical equation of the rate law.

00:07 Who's a rate law we want to determine? so we've got c -o -b -r -n -h -3 -5.

00:14 This is a complex ion 2 -plus that is dissolving or reacting with o -h -ions to form c -o -n -h -3 -5, o -h -2 -plus and br -i.

00:29 So looking at this, when we are looking at the rate, by definition, let's just call this a, b, c and d.

00:38 When we are looking at the rate of reaction, the rate of reaction is we are saying, how fast is a being consumed? which is also equal to how fast is b being consumed or how fast is c being produced or formed or how fast is d being produced? so what we've been given here is data that relates to the rate of formation and we've been given information to the concentrations of b and the concentrations of a.

01:13 So what we want to do here is we want to look and analyze the data that we've been given.

01:19 If we are looking at first run and the second run, what has happened here is we are studying the effect of varying the concentration of a because we have kept the concentration of b constant.

01:33 So if we do that, if we double the concentration of a, it results in the doubling of the rate of reaction.

01:43 So what this means is the rate is directly proportional to the concentration of a.

01:49 This information we got from the first and the second one.

01:54 Then if we look at run one and three, looking at this, if we increase the concentration of b by a factor of 3, what happens to the rate of reaction is it also increases by a factor of 3...

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