Page 186 - Instant notes

Physical chemistry 172

Arrhenius equation

The rate constant, k, and hence the rate of a chemical reaction, are usually observed to
vary with temperature, T. For the majority of chemical reactions the rate constant
increases with temperature. The temperature dependence is summarized mathematically
in the Arrhenius equation:

The two parameters A and E a are together known as the Arrhenius parameters and are
characteristic to each reaction. The parameter A has the same units as k and is called the
pre-exponential or Arrhenius factor, and E a is called the activation energy. (R is the
universal gas constant.) The Arrhenius equation can also be written in the form:

Therefore, a plot of lnk against 1/T produces a straight line with slope equal to −E a/R and
intercept equal to lnA.
Reaction rate increases with temperature when E a is positive (which is generally the
case). The larger the activation energy the greater is the sensitivity of the reaction to
changes in temperature. A reaction with an activation energy close to zero has a rate that
is largely independent of temperature. Most reactions have an activation energy
−1
somewhere in the range of a few tens to a few hundreds of kJ mol and a useful rule of
−1
thumb is that reactions with E a in the range 50–60 kJ mol have rate constants that
approximately double for each 10 K rise in temperature at around room temperature.
A reaction with a negative activation energy (corresponding to the observation of a
decrease in rate with increase in temperature) usually indicates that the observed rate
constant is a composite of rate constants of elementary reactions contributing to a
complex mechanism. For example, if k=k 1k 2/k 3 and k 3 increases more rapidly with
temperature than the product k 1k 2 then k will decrease overall (see Topic F4).

Collision theory
Collision theory is a theoretical framework to explain the origin of the Arrhenius
equation. The fundamental assumption of collision theory is that reaction occurs when
two molecules collide with one another in a bimolecular reaction. As in the kinetic
theory of gases (see Topic A2) collision theory makes the assumption that molecules are
hard, structureless spheres (like billiard balls) which do not interact until they come into
direct contact. It is further assumed that reaction only occurs when molecules collide with
a kinetic energy greater than some threshold value.