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Reaction Kinetics: Reaction Mechanisms

Mechanisms of Chemical Reactions

Terms

Problems and Solutions

Properties of Mechanisms

Mechanisms describe in a stepwise manner the exact collisions and events that are required for the conversion of reactants into products. Mechanisms achieve that goal by breaking up the overall balanced chemical equation into a series of elementary steps. An elementary step is written to mean a single collision or molecular vibration that results in a chemical reaction. The following picture of an elementary step shows a single collision between water and boron trifluoride:

Figure %: Schematic representation of an elementary step

The molecularity of an elementary step describes the number of reactive partners in the elementary step. For example, the above elementary step is called bimolecular because two molecules collide. Commonly, elementary steps are mono-, bi-, or termolecular. The probability of four molecules colliding at exactly the same place and time is so small that we can safely assume that no reaction will ever be tetramolecular. Because take up a large amount of space, we will represent elementary steps in this SparkNote as normal reactions with molecular formula line equations. You will know from the context (i.e. talking about the steps of a mechanism) whether the reaction is an elementary step or an overall reaction.

To better understand mechanisms, let's consider the following mechanism for the decomposition of ozone, O3:

The above mechanism exhibits a property of all mechanisms: it is a series of elementary steps whose sum is the overall balanced reaction. Note the presence of the oxygen atom, O, intermediate in the above equation. It is an intermediate because it is both created and destroyed in the mechanism and does not appear in the net equation.

Another property of mechanisms is that they must predict the experimentally determined rate law. To calculate the rate law from a mechanism you need to first know the rate limiting step. The rate limiting step determines the rate of the reaction because it is the slowest step. You can rationalize that a reaction can only go so fast as its slowest step by thinking about what happens when you encounter an accident on the highway that closes all but one lane. You may have been able to race along at 65 m.p.h. (depending on your state's laws) before you reached the lane closure but the slow passage of cars past the accident limits your rate. You can only go as fast through that one lane as the slowest car in front of you.

In the above , the first reaction is labeled as "slow". This reaction is the rate determining step because it is the slowest step. As we have stated, that means that the rate of the overall reaction is equal to the rate of the rate determining step. The rate of an elementary step is the rate constant for that step multiplied by the concentrations of the reactants raised to their stoichiometric powers. Note that this rule only applies for elementary steps. The rate of an overall reaction is NOT the product of the concentrations of the reactants raised to their stoichiometric powers. The rate law for the first elementary step in the is rate = k [O3]. Because this step is the rate determining step, the rate law is also the rate law for the overall reaction. Using similar techniques we can calculate the rate law predicted by any mechanism. We then check the predicted rate law against the experimentally determined rate law to test the validity of the proposed mechanism.

Reaction Coordinate Diagrams

We can follow the progress of a reaction on its way from reactants to products by graphing the energy of the species versus the reaction coordinate. We will be vague in describing the reaction coordinate because its definition is a mess of other variables composed to best make sense of the progress of the reaction. The value of the reaction coordinate is between zero and one. Understanding the meaning of the reaction coordinate is not important, just know that small values of reaction coordinate (0-0.2) mean little reaction has taken place and large values (0.8-1.0) mean that the reaction is almost over. It is a kind of scale of the progress of a reaction. A typical reaction coordinate diagram for a mechanism with a single step is shown below:

Figure %: A reaction coordinate diagram for a single-step reaction

Note that the reactants are placed on the left and the products on the right. The choice of the energy levels of the reactants and products is dictated by their energies, those with higher energies are higher on the diagram and those with lower energies are lower on the diagram. The difference is energy between the reactants and the transition state is called the activation energy. The activation energy is the height of the energy barrier of the reaction. The transition state is the point of maximum energy on the diagram which represents a species possessing both reactant-like and product-like properties. Because it is so high in energy, the transition state is very reactive and can never be isolated due to its extremely short lifetime. The relative energy of the reactants and products, the ΔE on the diagram, determines whether the reaction is exothermic or endothermic. A reaction will be exothermic if the energy of the products is less than the energy of the reactants. A reaction is endothermic when the energy of the products is greater than the energy of the reactants. The is for an exothermic reaction. Below is a reaction coordinate diagram for an endothermic reaction.

Figure %: Reaction coordinate diagram for an endothermic reaction

If a reaction has n elementary steps in its mechanism, there will be n–1 minima between the products and reactants representing intermediates. There will also be n maxima representing the n transition states. For example, a reaction with three elementary steps could have the following reaction coordinate diagram.

Figure %: Reaction coordinate diagram for a three-step reaction

One confusing point about reaction coordinate diagrams is how to determine what the rate determining step is. Even experienced chemists consistently get this type of problem wrong. The rate determining step is not the one with the highest activation energy for the step. The rate determining step is the step whose transition state has the highest energy.

Activation Energy and the Arrhenius Equation

Intuitively, it makes sense that a reaction with a higher activation barrier will be slower. Think of how much harder you must roll a ball up a large hill than a smaller one. Let's consider chemical reactions more deeply to derive an equation which describes the relationship between the rate constant of a reaction and its activation barrier. To simplify our derivation, we will assume that the reaction has a one-step mechanism. This elementary step represents a collision as shown in . Therefore, the frequency of the collisions, f, will be important in our equation. Notice that only a certain orientation of the molecules will lead to a reaction. For example, the following collision will not lead to a reaction. The reagent molecules simply bounce off of one another:

Figure %: Only specific orientations during a collision will lead to a reaction.

Therefore, we will need to include an orientation factor (or steric factor), p, that takes into account the fact that only a certain fraction of collisions will lead to reaction due to the orientation of the molecules. Another factor we must consider is that only a certain fraction of the molecules colliding will have enough energy to overcome the activation barrier. The Boltzmann distribution is a thermodynamic equation that tells us what fraction of the molecules have a certain amount of energy. As you know, at higher temperatures the average kinetic energy of the molecules increases. Therefore, at higher temperatures more molecules have an energy greater than the activation energy--as shown in .

Figure %: Boltzmann distributions for T1 greater than T2

Combining the above considerations, we state the following relationship between the rate constant and the activation energy, called the Arrhenius equation:

The variable k is the rate constant, which is dependent on the frequency of the collisions f, orientation factor p, activation energy Ea, and temperature T. From the expression for the Arrhenius equation you should note that a small increase in activation energy leads to a large decrease in rate constant. Furthermore, temperature has a similarly exponential effect on the rate constant. An experimental rule of thumb is that a 10oC increase in temperature leads to a doubling of the rate constant.

One application of the Arrhenius equation that is useful is the determination of the activation energy for a reaction. Taking the natural log of the Arrhenius equation gives a linear equation:

A graph of ln k versus 1 / T should give a straight line whose slope is - Ea / R. By measuring the rate constant at a range of different temperatures, you can construct a graph to determine the activation energy of a reaction.

Catalysis

A catalyst speeds up a reaction without being explicit in the overall balanced equation. It does this by providing an alternate mechanism for the reaction that has a lower activation barrier than does the uncatalyzed pathway. Compare the catalytic and regular mechanisms for the hydrogenation of ethylene to ethane and their associated reaction coordinate diagrams in :

Figure %: Mechanisms of ethylene hydrogenation

As you can see, the catalyst changes the mechanism of the reaction and lowers the activation energy. The catalyst, because it does not appear in the overall balanced equation has absolutely no effect on the thermodynamics of the reaction.

There are two types of catalysts--heterogeneous catalysts and homogeneous catalysts. There is no fundamental difference in how these catalysts work. The difference lies in whether the catalyst is in the same phase (solid, liquid, or gas) as the reagents. A homogeneous catalyst is in the same phase as the reactants while a heterogeneous catalyst is not. An enzyme is a biological homogeneous catalyst.

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