Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...
Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ... 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).
2.7 Temperature dependence of rate coefficients 36 or 21 ln (1 ) = − (2.164) I Figure 2.14: Derivation of the Arrhenius equation. I Experimental determination of E (see Fig. 2.14): Aplotofln vs. 1 gives a straight line with slope − I Integration of Eq. 2.156: Assuming that is independent of ,Eq.2.156canbe integrated: ln = (2.165) 2 y ln = − + (2.166) y ( )= − (2.167) Equation 2.167 is used to represent ( ) over a limited -range using the two parameters and : • = Arrhenius activation energy (measure for the energy barrier of the reaction) • = pre-exponential factor (frequency factor, collision frequency). 21 y (1 ) = − 1 2 (2.162) = − 2 (1 ) (2.163)
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- Page 3 and 4: iii 2.7 Temperature dependence of r
- Page 5 and 6: v 7.1.2 Formal kinetic model 149 7.
- Page 7 and 8: vii 12 Photochemical reactions 241
- Page 9 and 10: ix Preface This scriptum contains l
- Page 11 and 12: xi Disclaimer Use of this text is e
- Page 13 and 14: xiii I Figure 2: Organisational mat
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- Page 17 and 18: 1.2 Time scales for chemical reacti
- Page 19 and 20: 1.2 Time scales for chemical reacti
- Page 21 and 22: 1.3 Historical events 6 I Empirical
- Page 23 and 24: 1.4 References 8 2. Formal kinetics
- Page 25 and 26: 2.1 Definitions and conventions 10
- Page 27 and 28: 2.1 Definitions and conventions 12
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- Page 31 and 32: 2.2 Kinetics of irreversible first-
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- Page 57 and 58: 3.1 Determination of the order of a
- Page 59 and 60: 3.2 Application of the steady-state
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2.7 Temperature dependence of rate coefficients 35<br />
2.7 Temperature dependence of rate coefficients<br />
2.7.1 Arrhenius equation<br />
I Arrhenius: 20 Svante Arrhenius (Arrhenius 1889) found the following empirical relation<br />
describing the temperature dependence of the reaction rate constant:<br />
ln <br />
(1 ) = − <br />
<br />
(2.156)<br />
I<br />
Definition 2.4: is called the Arrhenius activation energy of the reaction:<br />
= − ln <br />
(1 )<br />
(2.157)<br />
I<br />
It is very important to keep in mind the following points:<br />
• Eq. 2.156 is nothing else but a simple and very convenient way to describe the<br />
empirical temperature dependence of reaction rate constants!<br />
• Eq. 2.156 says that, within experimental error, a plot of ln vs. 1 should give<br />
a straight line. We will see later, however, that this is rarely exactly true. The<br />
study and the understanding of non-Arrhenius behavior is in fact an important<br />
topicinmodernkinetics.<br />
• as determined by Eqs. 2.156 and 2.157 is therefore a purely empirical quantity!<br />
• We will use Eq. 2.157 simply as the definition and recipy for determining from<br />
experimental data and to relate theoretical models to the experimental data!<br />
I The rationale behind the Arrhenius equation (2.156): The rationale for the<br />
Arrhenius equation is that molecules need additional energy so that chemical bonds can<br />
be broken, atoms can rearrange, and new bonds can be formed (Fig. 2.14).<br />
Van’t Hoff’s equation:<br />
∆ = 2 ln <br />
<br />
= 2 ln −→ <br />
<br />
= 2 ln −→ ←− <br />
<br />
− 2 ln ←− <br />
<br />
(2.158)<br />
(2.159)<br />
= −→ − ←− (2.160)<br />
Thus we can write<br />
ln <br />
<br />
= <br />
2 (2.161)<br />
20 Arrhenius is generally regarded as one of the founders of physical chemistry (together with Faraday,<br />
van’t Hoff, andOstwald).