Chemistry 112

## Arrhenius Theory

Since the formation of the activated complex is the most important feature in determining the rate of a reaction, the temperature dependence of the collision frequency is often ignored. Then, the rate constant can be written as

k is the rate constant for the reaction

Ea is the activation energy

R is the gas constant in energy units = 8.314 J/mol•K

T is the absolute temperature

A is the pre-exponential factor.

The Arrhenius equation is often written in the logarithmic form:

This is (yet another) straight line equation: if ln k is plotted against 1/T, a straight line is found. The slope of the line gives the activation energy:

slope = –Ea/R

#### Using the Arrhenius Equation:

To obtain activation energies, the rate constant is measured at several different temperatures. These are then plotted as ln k vs. 1/T and the slope of the straight line gives the activation energy.

Consider the reaction:

2 HI(g) H2(g) + I2(g)

The following data was measured:

 k (M–1s–1) T (oC) 3.52×10–7 283 3.02×10–5 356 2.19×10–4 393 1.16×10–3 427 3.95×10–2 508

If there is a limited amount of data, the two-point form of the Arrhenius equation can be used:

If we know the rate constants at two temperatures, then the activation energy can be found. This gives less accurate values for Ea, but is computationally quicker.

### Example

Find the activation energy for the following reaction:

CO(g) + NO2(g) CO2(g) + NO(g)

The rate constants were found to be 0.028 M–1s–1 at 327 oC and 23 M–1s–1 at 527 oC.

k1 = 0.028 M–1s-1 T1 = 327 + 273 = 600 K

k2 = 23 M–1s–1 T2 = 527 + 273 = 800 K

Ea = 133800 J/mol = 130 kJ/mol

## Chemical Reactions at the Molecular Level:

Reactions are caused by collisions between molecules. Thus, we should be able to describe every reaction, no matter how complicated, by a series of collisions. This is called a reaction mechanism.

An elementary reaction is a reaction that describes a physical collision at the microscopic level.

The sequence of elementary reactions that lead to a macroscopic reaction is called the reaction mechanism.

Reaction mechanisms are just a list of elementary reactions in the correct order.

Elementary reactions are special because the rate law can be found from the stoichiometric coefficients: the order of reaction in each reactant is equal to its stoichiometric coefficient.

Remember that this is true only for elementary reactions.