Chapter 18: Kinetics

Learning Outcomes

  • Identify catalysts in a reaction mechanism
  • Describe the impact of catalysts on reaction rates

Among the factors affecting chemical reaction rates discussed earlier in this chapter was the presence of a catalyst, a substance that can increase the reaction rate without being consumed in the reaction. The concepts introduced in the previous section on reaction mechanisms provide the basis for understanding how catalysts are able to accomplish this very important function.

Figure 18.7.1 shows reaction diagrams for a chemical process in the absence and presence of a catalyst. Inspection of the diagrams reveals several traits of these reactions. Consistent with the fact that the two diagrams represent the same overall reaction, both curves begin and end at the same energies (in this case, because products are more energetic than reactants, the reaction is endothermic). The reaction mechanisms, however, are clearly different. The uncatalyzed reaction proceeds via a one-step mechanism (one transition state observed), whereas the catalyzed reaction follows a two-step mechanism (two transition states observed) with a notably lesser activation energy. This difference illustrates the means by which a catalyst functions to accelerate reactions, namely, by providing an alternative reaction mechanism with a lower activation energy. Although the catalyzed reaction mechanism for a reaction needn’t necessarily involve a different number of steps than the uncatalyzed mechanism, it must provide a reaction path whose rate determining step is faster (lower Ea).

A graph is shown with the label, “Extent of reaction,” appearing in a right pointing arrow below the x-axis and the label, “Energy,” in an upward pointing arrow just left of the y-axis. Approximately one-fifth of the way up the y-axis, a very short, somewhat flattened portion of both a red and a blue curve are shown. This region is labeled “Reactants.” A red concave down curve extends upward to reach a maximum near the height of the y-axis. From the peak, the curve continues downward to a second horizontally flattened region at a height of about one-third the height of the y-axis. This flattened region is labeled, “Products.” A second curve is drawn in blue with the same flattened regions at the start and end of the curve. The height of this curve is about two-thirds the height of the first curve and just right of its maximum, the curve dips low, then rises back and continues a downward trend at a lower height, but similar to that of the red curve. A horizontal dashed straight line extends from the point where both curves start in the “Reactants” region. A double sided arrow extends from the “Products” region at the end of both curves to this horizontal dashed line. This is labeled “capital delta H.” A double sided arrow extends from the dashed horizontal line to the peak of the red concave down curve. This arrow is labeled “E subscript a.” Another double sided arrow extends from the dashed horizontal line to the peak of the blue curve. This arrow is labeled “E subscript a.”
Figure 18.7.1. Reaction diagrams for an endothermic process in the absence (red curve) and presence (blue curve) of a catalyst. The catalyzed pathway involves a two-step mechanism (note the presence of two transition states) and an intermediate species (represented by the valley between the two transitions states).

Example 18.7.1: Using Reaction Diagrams to Compare Catalyzed Reactions

The two reaction diagrams here represent the same reaction: one without a catalyst and one with a catalyst. Estimate the activation energy for each process, and identify which one involves a catalyst.

In this figure, two graphs are shown. The x-axes are labeled, “Extent of reaction,” and the y-axes are labeled, “Energy ( k J ).” The y-axes are marked off from 0 to 50 in intervals of five. In a, a blue curve is shown. It begins with a horizontal segment at about 6. The curve then rises sharply near the middle to reach a maximum of about 32 and similarly falls to another horizontal segment at about 10. In b, the curve begins and ends similarly, but the maximum reached near the center of the graph is only 20.

[reveal-answer q=”151291″]Show Solution[/reveal-answer]
[hidden-answer a=”151291″]

Activation energies are calculated by subtracting the reactant energy from the transition state energy.

[latex]\text{diagram (a): }{E}_{\text{a}}=32\text{kJ}-6\text{kJ}=26\text{kJ}[/latex]

[latex]\text{diagram (b): }{E}_{\text{a}}=20\text{kJ}-6\text{kJ}=14\text{kJ}[/latex]

The catalyzed reaction is the one with lesser activation energy, in this case represented by diagram (b).

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Check Your Learning

Homogeneous Catalysts

A homogeneous catalyst is present in the same phase as the reactants. It interacts with a reactant to form an intermediate substance, which then decomposes or reacts with another reactant in one or more steps to regenerate the original catalyst and form product.

As an important illustration of homogeneous catalysis, consider the earth’s ozone layer. Ozone in the upper atmosphere, which protects the earth from ultraviolet radiation, is formed when oxygen molecules absorb ultraviolet light and undergo the reaction:

[latex]\ce{3O2}(g)\stackrel{hv}{\longrightarrow }\ce{2O3}(g)[/latex]

Ozone is a relatively unstable molecule that decomposes to yield diatomic oxygen by the reverse of this equation. This decomposition reaction is consistent with the following mechanism:

[latex]\begin{array}{l}\\ {\ce{O}}_{3}\rightarrow{\ce{O}}_{2}+\ce{O}\\ \ce{O}+{\ce{O}}_{3}\rightarrow 2{\ce{O}}_{2}\end{array}[/latex]

A number of substances can catalyze the decomposition of ozone. For example, the nitric oxide–catalyzed decomposition of ozone is believed to occur via the following three-step mechanism:

[latex]\begin{array}{l}\ce{NO(}g\text{)}+{\ce{O}}_{3}\text{(}g\text{)}\rightarrow{\ce{NO}}_{2}\text{(}g\text{)}+{\ce{O}}_{2}\text{(}g\text{)}\\ {\ce{O}}_{3}\left(g\right)\rightarrow{\ce{O}}_{2}\left(g\right)+\{O}\left(g\right)\\ {\ce{NO}}_{2}\left(g\right)+\ce{O}\left(g\right)\rightarrow\ce{NO}\left(g\right)+{\ce{O}}_{2}\left(g\right)\end{array}[/latex]

As required, the overall reaction is the same for both the two-step uncatalyzed mechanism and the three-step NO-catalyzed mechanism:

[latex]\ce{2O3}(g)\rightarrow \ce{3O2}(g)[/latex]

Notice that NO is a reactant in the first step of the mechanism and a product in the last step. This is another characteristic trait of a catalyst: Though it participates in the chemical reaction, it is not consumed by the reaction.

Heterogeneous Catalysts

A heterogeneous catalyst is a catalyst that is present in a different phase (usually a solid) than the reactants. Such catalysts generally function by furnishing an active surface upon which a reaction can occur. Gas and liquid phase reactions catalyzed by heterogeneous catalysts occur on the surface of the catalyst rather than within the gas or liquid phase.

Heterogeneous catalysis has at least four steps:

  1. Adsorption of the reactant onto the surface of the catalyst
  2. Activation of the adsorbed reactant
  3. Reaction of the adsorbed reactant
  4. Diffusion of the product from the surface into the gas or liquid phase (desorption).

Any one of these steps may be slow and thus may serve as the rate determining step. In general, however, in the presence of the catalyst, the overall rate of the reaction is faster than it would be if the reactants were in the gas or liquid phase.

Figure 18.7.2. illustrates the steps that chemists believe to occur in the reaction of compounds containing a carbon–carbon double bond with hydrogen on a nickel catalyst. Nickel is the catalyst used in the hydrogenation of polyunsaturated fats and oils (which contain several carbon–carbon double bonds) to produce saturated fats and oils (which contain only carbon–carbon single bonds).

In this figure, four diagrams labeled a through d are shown. In each, a green square surface is shown in perspective to provide a three-dimensional appearance. In a, the label “N i surface” is placed above with a line segment extending to the green square. At the lower left and upper right, pairs of white spheres bonded tougher together appear as well as white spheres on the green surface. Black arrows are drawn from each of the white spheres above the surface to the white sphere on the green surface. In b, the white spheres are still present on the green surface. Near the center of this surface is a molecule with two central black spheres with a double bond indicated by two horizontal black rods between them. Above and below to the left and right, a total of four white spheres are connected to the black spheres with white rods. A line segment extends from this structure to the label, “Ethylene absorbed on surface breaking pi bonds.” Just above this is a nearly identical structure greyed out with three downward pointing arrows to the black and white structure to indicate downward motion. The label “Ethylene” at the top of the diagram is connected to the greyed out structure with a line segment. In c, the diagram is very similar to b except that the greyed out structure and labels are gone and one of the white spheres near the black and white structure in each pair on the green surface is greyed out. Arrows point from the greyed out white spheres to the double bond between the two black spheres. In d, only a single white sphere remains from each pair in the green surface. A curved arrow points from the middle of the green surface to a model above with two central black spheres with a single black rod indicating a single bond between them. Each of the black rods has three small white spheres bonded as indicated by white rods between the black spheres and the small white spheres. The four bonds around each black sphere are evenly distributed about the black spheres.
Figure 18.7.2. Mechanism for the Ni-catalyzed reaction [latex]\ce{C2H4}+\ce{H2}\longrightarrow\ce{C2H6}[/latex] (a) Hydrogen is adsorbed on the surface, breaking the H–H bonds and forming Ni–H bonds. (b) Ethylene is adsorbed on the surface, breaking the [latex]\ce{C-C}[/latex] π-bond and forming [latex]\ce{Ni-C}[/latex] bonds. (c) Atoms diffuse across the surface and form new [latex]\ce{C-H}[/latex] bonds when they collide. (d) [latex]\ce{C2H6}[/latex] molecules desorb from the Ni surface.

Many important chemical products are prepared via industrial processes that use heterogeneous catalysts, including ammonia, nitric acid, sulfuric acid, and methanol. Heterogeneous catalysts are also used in the catalytic converters found on most gasoline-powered automobiles Figure 18.7.3.

Key Concepts and Summary

Catalysts affect the rate of a chemical reaction by altering its mechanism to provide a lower activation energy. Catalysts can be homogenous (in the same phase as the reactants) or heterogeneous (a different phase than the reactants).

Try It

  1. Consider this scenario and answer the following questions: Chlorine atoms resulting from decomposition of chlorofluoromethanes, such as [latex]\ce{CCl2F2}[/latex], catalyze the decomposition of ozone in the atmosphere. One simplified mechanism for the decomposition is:
    [latex]\begin{array}{l}{\ce{O}}_{3}\stackrel{\text{sunlight}}{\longrightarrow }{\ce{O}}_{2}+\ce{O}\\ {\ce{O}}_{3}+\ce{Cl}\rightarrow{\ce{O}}_{2}+\ce{ClO}\\ \ce{ClO}+\ce{O}\rightarrow\ce{Cl}+{\ce{O}}_{2}\end{array}[/latex]

      1. Explain why chlorine atoms are catalysts in the gas-phase transformation:
        [latex]\ce{2O3}\rightarrow \ce{3O2}[/latex]
      2. Nitric oxide is also involved in the decomposition of ozone by the mechanism:
          1. [latex]\begin{array}{l} {\ce{O}}_{3}\stackrel{\text{sunlight}}{\longrightarrow }{\ce{O}}_{2}+\ce{O}\\ {\ce{O}}_{3}+\ce{NO}\rightarrow{\ce{NO}}_{2}+{\ce{O}}_{2}\\ {\ce{NO}}_{2}+\ce{O}\rightarrow\ce{NO}+{\ce{O}}_{2}\end{array}[/latex]
      3. Is [latex]\ce{NO}[/latex] a catalyst for the decomposition? Explain your answer.

For each of the following pairs of reaction diagrams, identify which of the pair is catalyzed:Two graphs showing the extent of reaction and energy. Graph A starts at about 12 kJ, peaks at 25 kJ, then plateaus at 5 kJ. Graph B starts at about 12 kJ, peaks at 20 kJ, then plateaus at 5 kJ.Two graphs showing the extent of reaction and energy. Graph A starts at about 2 kJ, peaks at about 43 kJ, then plateaus at 15 kJ. Graph B starts at about 2 kJ, peaks at about 32 kJ, then plateaus at 15 kJ.

 

[reveal-answer q=”354631″]Show Selected Solutions[/reveal-answer]
[hidden-answer a=”354631″]

  1. The answers are as follows:
    1. Chlorine atoms are a catalyst because they react in the second step but are regenerated in the third step. Thus, they are not used up, which is a characteristic of catalysts.
    2. NO is a catalyst for the same reason as in part (a).

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Glossary

heterogeneous catalyst: catalyst present in a different phase from the reactants, furnishing a surface at which a reaction can occur

homogeneous catalyst: catalyst present in the same phase as the reactants

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