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

kis the rate constant for the reactionE

_{a}is the activation energyR 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 = –E_{a}/R

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) H_{2}(g) + I_{2}(g)

The following data was measured:

k(M ^{–1}s^{–1}) |
T ( ^{o}C) |

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
E_{a}, but is computationally quicker.

Find the activation energy for the following reaction:

CO(

g) + NO_{2}(g) CO_{2}(g) + NO(g)

The rate constants were found to be 0.028 M^{–1}s^{–1}
at 327 ^{o}C and 23 M^{–1}s^{–1} at 527 ^{o}C.

*k*_{1} = 0.028 M^{–1}s^{-1}
T_{1} = 327 + 273 = 600 K

*k*_{2} = 23 M^{–1}s^{–1}
T_{2} = 527 + 273 = 800 K

E_{a} = 133800 J/mol = 130 kJ/mol

What is the total order of reaction?

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.