12: Chapter Chemical Kinetics, Part 3
The Arrhenius Equation Arrhenius discovered that most reaction-rate data obeyed an equation based on three factors: The number of collisions per unit time. The fraction of collisions that occur with the correct orientation. The fraction of the colliding molecules that have energy equal to or greater than Ea. From these observations Arrhenius developed the Arrhenius equation:
Where k is the rate constant, Ea is the activation energy, R is the ideal-gas constant (8.314 J/Kmol), and T is the temperature in K. A is called the frequency factor. It is related to the frequency of collisions and the probability that a collision will have a favorable orientation. It is also related to molecular size and shape. Both A and Ea are specific to a given reaction.
Ea and A may be determined experimentally. If we have data from 2 different temperatures we can find Ea mathematically. We use the Arrhenius equation:
If we have data from 3 or more different temperatures, we can find Ea and A graphically. We can do this because of the second way of representing the Arrhenius Equation:
If we graph lnk vs. 1/T, we obtain a straight line, with a slope of Ea/R and a y-intercept of ln(A).
Reaction Mechanisms
The balanced chemical equation provides information about substances present at the beginning and end of the reaction. But it doesn't tell you the path or the steps of the rxn. The reaction mechanism is the process by which the reaction occurs. Mechanisms provide a picture of which bonds are broken and formed during the course of a reaction. They also tell you the individual steps in a chemical rxns.
Elementary Steps Elementary steps are any processes that occur in a single step. The number of molecules present in an elementary step gives the molecularity of that elementary step. Unimolecular: one molecule in the elementary step.
Bimolecular: two molecules in the elementary step.
Termolecular: three molecules in the elementary step.
It is not common to see termolecular processes (statistically improbable). A multistep mechanism consists of a sequence of elementary steps. The elementary steps must add to give the balanced chemical equation. Some multistep mechanisms will include intermediates. These are species that appear in an elementary step but are neither a reactant nor product. Intermediates are formed in one elementary step and consumed in another. They are not found in the balanced equation for the overall reaction.
Rate Laws of Elementary Steps The rate laws of the elementary steps determine the overall rate law of the reaction. The rate law of an elementary step is determined by its molecularity. For elementary steps, the coefficients of the reactants determine the rate law. Note that this is only true for elementary steps, so you need to be careful! Unimolecular processes are first order.
Bimolecular processes are second order.
Termolecular processes are third order.
Rate Laws of Multistep Mechanisms Most reactions occur by mechanisms with more than one elementary step. Often one step is much slower than the others. The slow step limits the overall reaction rate. This is called the rate-determining step of the reaction. This step governs the overall rate law for the overall reaction. Consider the reaction: NO2(g) + CO(g) NO(g) + CO2(g)
The experimentally derived rate law is: Rate = k[NO2]2. We propose a mechanism for the reaction: Step 1: NO2(g) + NO2(g) Step 2: NO3(g) + CO(g)
k1 k2
NO3(g) + NO(g) NO2(g) + CO2(g)
slow step fast step
Note that NO3 is an intermediate. If k2 >> k1, then the overall reaction rate will depend on the first step (the rate-determining step).
This theoretical rate law is in agreement with the experimental rate law. This supports (but does not prove) our mechanism.
Mechanisms with an Initial Fast Step Consider the reaction: 2NO(g) + Br2(g) The experimentally determined rate law is:
2NOBr(g)
Consider the following proposed mechanism: Step 1: NO(g) + Br2(g)
k1 k
1
NOBr2(g)
fast step
Step 2:
NOBr2(g) + NO(g)
k2
2NOBr(g)
slow step
The theoretical rate law for this mechanism is based on the rate-determining step, step 2:
Problem: This rate law depends on the concentration of an intermediate species. Intermediates are usually unstable, have low/unknown concentrations, and so are difficult to measure.
We need to find a way to remove this term from our rate law. We can express the concentration of [NOBr2] in terms of NOBr and Br2 by assuming that NOBr2 is unstable and doesn't accumulate. This means that NOBr2 breaks apart as soon as it forms. It can do this by reacting with NO to produce the product NOBr. But this is a slow step, so this happens to a very small extent. NOBr2 may also fall apart into NO and Br2 by the reverse of Step 1, the equilibrium fast step. In a dynamic equilibrium, forward the rate equals the reverse rate. Therefore, by definition of equilibrium we get:
Rearranging we get:
Therefore, the overall rate law becomes
Note that the final rate law is consistent with the experimentally observed rate law.
Catalysis
A catalyst is a substance that changes the rate of a chemical reaction without itself undergoing a permanent chemical change in the process. There are two types of catalysts. Homogeneous. Heterogeneous. Catalysts are common in the body, in the environment, and in the chemistry lab!
Homogeneous Catalysis A homogeneous catalyst is one that is present in the same phase as the reacting molecules. For example, hydrogen peroxide decomposes very slowly in the absence of a catalyst: 2H2O2(aq) 2H2O(l) + O2(g)
In the presence of bromide ion, the decomposition occurs rapidly in acidic solution: 2Br(aq) + H2O2(aq) + 2H+(aq) Br2(aq) + H2O2(aq) Br2(aq) + 2H2O(l)
2Br(aq) + 2H+(aq) + O2(g)
Br is a catalyst because it is regenerated at the end of the reaction. The net reaction is still: 2H2O2(aq) 2H2O(l) + O2(g)
How do catalysts increase reaction rates? In general, catalysts operate by lowering the activation energy for a reaction. However, catalysts can operate by increasing the number of effective collisions.
That is, from the Arrhenius equation: Catalysts increase k by increasing A or decreasing Ea.
A catalyst usually provides a completely different mechanism for the reaction. In the preceding peroxide decomposition example, in the absence of a catalyst, H2O2 decomposes directly to water and oxygen. In the presence of Br, Br2(aq) is generated as an intermediate. When a catalyst adds an intermediate, the activation energies for both steps must be lower than the activation energy for the uncatalyzed reaction.
The above diagrams are called reaction coordinate diagrams.
Heterogeneous Catalysis A heterogeneous catalyst exists in a different phase than the reactants. Often we encounter a situation involving a solid catalyst in contact with gaseous reactants and gaseous products (example: catalytic converters in cars) or with reactants in a liquid. Many industrial catalysts are heterogeneous. How do they do their job? First step is adsorption (the binding of reactant molecules to the catalyst surface). Adsorption occurs due to the high reactivity of atoms or ions on the surface of the solid. Molecules are adsorbed onto active sites on the catalyst surface. The number of active sites on a given amount of catalyst depends on factors such as: The nature of the catalyst. How the catalyst was prepared. How the catalyst was treated prior to use. For example, consider the hydrogenation of ethylene to form ethane: C2H4(g) + H2(g) C2H6(g) H = 137 kJ/mol
The reaction is slow in the absence of a catalyst. In the presence of a finely divided metal catalyst (Ni, Pt, or Pd) the reaction occurs quickly at room temperature. First, the ethylene and hydrogen molecules are adsorbed onto active sites on the metal surface. The HH bond breaks and the H atoms migrate about the metal surface. When an H atom collides with an ethylene molecule on the surface, the CC bond breaks and a CH bond forms. An ethyl group, C2H5, is weakly bonded to the metal surface with a metal-carbon bond. When C2H6 forms, it desorbs from the surface. When ethylene and hydrogen are adsorbed onto a surface, less energy is required to break their bonds. The activation energy for the reaction is lowered. Thus the reaction rate is increased.
Enzymes Enzymes are biological catalysts. Most enzymes are large protein molecules. Molecular masses are in the range of 10,000 to 106 amu. Enzymes are capable of catalyzing very specific reactions. For example, catalase is an enzyme found in blood and liver cells. It catalyzes the decomposition of hydrogen peroxide: 2H2O2(aq) 2H2O(l) + O2(g)
This reaction is important in removing peroxide, a potentially harmful oxidizing agent. The enzyme catalyzes the reaction at its active site. The substances that undergo reaction at the active site on enzymes are called substrates. A simple view of enzyme specificity is the lock-and-key model. Here, a substrate is pictured as fitting into the active site of an enzyme in a manner similar to a specific key fitting into a lock. This gives an enzyme-substrate (ES) complex. Only substrates that fit into the enzyme lock can be converted to product. A reaction occurs very quickly once substrate is bound. Products depart from the active site at the end of the reaction. This allows new substrate molecules to bind to the enzyme. If a molecule binds so tightly to an enzyme that substrate molecules cannot displace it, then the active site is blocked and the catalyst is inhibited. Such molecules are called enzyme inhibitors. Many poisons act by binding to the active site: blocking the binding of substrates.