Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...
Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ... Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...
2.1 Definitions and conventions 9 • Convenient units for gas phase reactions: — molar units: [] = mol cm 3 s (2.8) — molecular units: 14 [] =molecules cm 3 s ⇒ cm −3 s −1 (2.9) — We prefer to use molar units for rate constants, because rate constants are inherently quantities that are “averages” of some other quantity, e.g., a molecular cross section weighted by the relevant statistical distribution function (usually the Boltzmann distribution). Rate constants are thus properties of an ensemble of molecules, they are not original molecular quantities. • Convenient units for liquid phase reactions: [] = mol ls=M s (2.10) 2.1.2 Rate laws and rate coefficients I Therateequation(ratelaw): Experiments show that the reaction rate generally depends on the concentrations of the reactants. The functional dependence is expressed by the rate equation (also called rate law), 15 e.g. for reaction 2.3. = − 1 [B 1 ] = | 1 | (2.11) = ([B 1 ] [B 2 ] [B ] [B +1 ] ) (2.12) Theratelawsofcomplexreactions(i.e.,the ([B 1 ] , [B 2 ] , , [B ] , [B +1 ] , )) are often rather complicated; only rarely (as in the case of elementary reactions) are they simple and intuitive. Often (but not always), ([B 1 ] , [B 2 ] , , [B ] , [B +1 ] , ) can be written as a product of a rate coefficient and some power series of the concentrations, for example = − 1 [B 1 ] = [B 1 ] [B 2 ] ... (2.13) | 1 | Note that the exponents . . . are not usually equal to 1 2 ... I Therateconstant(ratecoefficient): The rate constant (also called rate coefficient) 16 usually depends on temperature ( = ( )) and sometimes also on pressure ( = ()), but not on the concentrations ( 6= ()). 14 IUPAC has decided that “molecules” is not a unit; see (Mills 1989) or (Homann 1995). 15 Rate law = Geschwindigkeits- oder Zeitgesetz. 16 Rate constant = Geschwindigkeitskonstante. Es wird manchmal auch die Übersetzung “Ratenkonstante” verwendet (aber bitte nicht “Ratekonstante”).
2.1 Definitions and conventions 10 I Rate laws for first-order and second-order reactions: Simple rate laws describe first-order and second-order reactions: • Example of a first-order reaction: CH 3 NC → CH 3 CN = − [CH 3NC] =+ [CH 3CN] = [CH 3 NC] (2.14) • Example of a second-order reaction: C 4 H 9 +C 4 H 9 → C 8 H 18 = − 1 2 [C 4 H 9 ] =+ [C 8H 18 ] = [C 4 H 9 ] 2 (2.15) I Question: How can we determine reaction rates and rate constants ? I Figure 2.1: The easiest — and always applicable — method for determining the reaction rate and rate coefficient is the tangent method. To determine , yousimplytake the slope of a plot of () at time ; then follows via Eq. 2.13. We’ll learn about better methods for determining for elementary reactions (first-order and second-order reactions) further below. 2.1.3 The order of a reaction I Definition 2.2: The order of a reaction is defined as the sum of the exponents in the rate law (Eq. 2.13).
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2.1 Definitions and conventions 9<br />
• Convenient units for gas phase reactions:<br />
<strong>—</strong> molar units:<br />
[] = mol cm 3 s (2.8)<br />
<strong>—</strong> molecular units: 14 [] =molecules cm 3 s ⇒ cm −3 s −1 (2.9)<br />
<strong>—</strong> We prefer to use molar units for rate constants, because rate constants are<br />
inherently quantities that are “averages” of some other quantity, e.g., a molecular<br />
cross section weighted by the relevant statistical distribution function<br />
(usually the Boltzmann distribution). Rate constants are thus properties of<br />
an ensemble of molecules, they are not original molecular quantities.<br />
• Convenient units for liquid phase reactions:<br />
[] = mol ls=M s (2.10)<br />
2.1.2 Rate laws and rate coefficients<br />
I Therateequation(ratelaw): Experiments show that the reaction rate generally<br />
depends on the concentrations of the reactants. The functional dependence is expressed<br />
by the rate equation (also called rate law), 15 e.g.<br />
for reaction 2.3.<br />
= − 1 [B 1 ]<br />
= <br />
| 1 | <br />
(2.11)<br />
= ([B 1 ] [B 2 ] [B ] [B +1 ] ) (2.12)<br />
Theratelawsofcomplexreactions(i.e.,the ([B 1 ] , [B 2 ] , , [B ] , [B +1 ] , ))<br />
are often rather complicated; only rarely (as in the case of elementary reactions) are<br />
they simple and intuitive.<br />
Often (but not always), ([B 1 ] , [B 2 ] , , [B ] , [B +1 ] , ) can be written as a<br />
product of a rate coefficient and some power series of the concentrations, for<br />
example<br />
= − 1 [B 1 ]<br />
= [B 1 ] [B 2 ] ... (2.13)<br />
| 1 | <br />
Note that the exponents . . . are not usually equal to 1 2 ...<br />
I Therateconstant(ratecoefficient): The rate constant (also called rate coefficient)<br />
16 usually depends on temperature ( = ( )) and sometimes also on pressure<br />
( = ()), but not on the concentrations ( 6= ()).<br />
14 IUPAC has decided that “molecules” is not a unit; see (Mills 1989) or (Homann 1995).<br />
15 Rate law = Geschwindigkeits- oder Zeitgesetz.<br />
16 Rate constant = Geschwindigkeitskonstante. Es wird manchmal auch die Übersetzung “Ratenkonstante”<br />
verwendet (aber bitte nicht “Ratekonstante”).