Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

2.7 Temperature dependence of rate coefficients 35
2.7 Temperature dependence of rate coefficients
2.7.1 Arrhenius equation
I Arrhenius: 20 Svante Arrhenius (Arrhenius 1889) found the following empirical relation
describing the temperature dependence of the reaction rate constant:
ln
(1 ) = −
(2.156)
I
Definition 2.4: is called the Arrhenius activation energy of the reaction:
= − ln
(1 )
(2.157)
I
It is very important to keep in mind the following points:
• Eq. 2.156 is nothing else but a simple and very convenient way to describe the
empirical temperature dependence of reaction rate constants!
• Eq. 2.156 says that, within experimental error, a plot of ln vs. 1 should give
a straight line. We will see later, however, that this is rarely exactly true. The
study and the understanding of non-Arrhenius behavior is in fact an important
topicinmodernkinetics.
• as determined by Eqs. 2.156 and 2.157 is therefore a purely empirical quantity!
• We will use Eq. 2.157 simply as the definition and recipy for determining from
experimental data and to relate theoretical models to the experimental data!
I The rationale behind the Arrhenius equation (2.156): The rationale for the
Arrhenius equation is that molecules need additional energy so that chemical bonds can
be broken, atoms can rearrange, and new bonds can be formed (Fig. 2.14).
Van’t Hoff’s equation:
∆ = 2 ln
= 2 ln −→
= 2 ln −→ ←−
− 2 ln ←−
(2.158)
(2.159)
= −→ − ←− (2.160)
Thus we can write
ln
=
2 (2.161)
20 Arrhenius is generally regarded as one of the founders of physical chemistry (together with Faraday,
van’t Hoff, andOstwald).