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# Activation Energy and Catalysts for AP Chemistry

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By McGraw-Hill Professional
Updated on Feb 9, 2011

Practice problems for these concepts can be found at:

### Activation Energy

A change in the temperature at which a reaction is taking place affects the rate constant k. As the temperature increases, the value of the rate constant increases and the reaction is faster. The Swedish scientist Arrhenius derived a relationship in 1889 that related the rate constant and temperature. The Arrhenius equation has the form: k = Ae–Ea /RT where k is the rate constant, A is a term called the frequency factor that accounts for molecular orientation, e is the natural logarithm base, R is the universal gas constant 8.314 J mol K–1, T is the Kelvin temperature, and Ea is the activation energy, the minimum amount of energy that is needed to initiate or start a chemical reaction.

The Arrhenius equation is most commonly used to calculate the activation energy of a reaction. One way this can be done is to plot the ln k versus 1/T. This gives a straight line whose slope is –Ea /R. Knowing the value of R allows the calculation of the value of Ea.

Normally, high activation energies are associated with slow reactions. Anything that can be done to lower the activation energy of a reaction will tend to speed up the reaction.

A catalyst is a substance that speeds up the rate of reaction without being consumed in the reaction. A catalyst may take part in the reaction and even be changed during the reaction, but at the end of the reaction it is at least theoretically recoverable in its original form. It will not produce more of the product, but it allows the reaction to proceed more quickly. In equilibrium reactions (see the chapter on Equilibrium), the catalyst speeds up both the forward and reverse reactions. Catalysts speed up the rates of reaction by providing a different mechanism that has a lower activation energy. The higher the activation energy of a reaction, the slower the reaction will proceed. Catalysts provide an alternate pathway that has a lower activation energy and thus will be faster. In general, there are two distinct types of catalyst.

### Homogeneous Catalysts

Homogeneous catalysts are catalysts that are in the same phase or state of matter as the reactants. They provide an alternate reaction pathway (mechanism) with a lower activation energy.

The decomposition of hydrogen peroxide is a slow, one–step reaction, especially if the solution is kept cool and in a dark bottle:

2 H2O2 → 2 H2O + O2

However, if ferric ion is added, the reaction speeds up tremendously. The proposed reaction sequence for this new reaction is:

2 Fe3+ + H2O2 → 2 Fe2+ + O2 + 2 H+
2 Fe2+ + H2O2 + 2 H+ → 2 Fe3+ + 2 H2O

Notice that in the reaction the catalyst, Fe3+, was reduced to the ferrous ion, Fe2+, in the first step of the mechanism, but in the second step it was oxidized back to the ferric ion. Overall, the catalyst remained unchanged. Notice also that although the catalyzed reaction is a two–step reaction, it is significantly faster than the original uncatalyzed one–step reaction.

### Heterogeneous Catalysts

A heterogeneous catalyst is in a different phase or state of matter from the reactants. Most commonly, the catalyst is a solid and the reactants are liquids or gases. These catalysts lower the activation energy for the reaction by providing a surface for the reaction, and also by providing a better orientation of one reactant so its reactive site is more easily hit by the other reactant. Many times these heterogeneous catalysts are finely divided metals. The Haber process, by which nitrogen and hydrogen gases are converted into ammonia, depends upon an iron catalyst, while the hydrogenation of vegetable oil to margarine uses a nickel catalyst.

Practice problems for these concepts can be found at:

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