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Chemical Kinetics
Chapter 14
Summary of the Kinetics Reactions
Order Rate LawConcentration-Time
Equation Half-Life
0
1
2
rate = k
rate = k [A]
rate = k [A]2
ln[A] = ln[A]o - kt
1[A]
=1
[A]o
+ kt
[A] = [A]o - kt
t½ln 2k
=
t½ =[A]o
2k
t½ =1
k[A]o
rate = k [A][B] t½ =1
k[A]o
2
Generally, as T increases, so does the reaction rate
k is temperature dependent
Fig 14.11 Temperature affectsthe rate of chemiluminescenceIn light sticks
Fig 14.12 Dependence of rate constant on temperature
In a chemical rxn, bonds are broken and new bonds are formed
Molecules can only react if they collide with each other
Furthermore, molecules must collide with the correct orientation and with enough energy
Fig 14.13
Cl + NOCl Cl2 + NO
Activation Energy
Fig 14.14 An energy barrier
Reactant
Activated complexor
Transition state
Product
Activation energy (Ea) ≡ minimum amount of energy required to initiate a chemical reaction
Fig 14.15
Activated complex (transition state) ≡ very short-lived and cannot be removed from reaction mixture
methyl isonitrile acetonitrile
Sample Exercise 14.10 Rank the following series of reactionsfrom slowest to fastest
• The lower the Ea the faster the reaction
• Slowest to fastest: (2) < (3) < (1)
ExothermicExothermic Endothermic
How does a molecule acquire sufficient energyto overcome the activation barrier?
Fig 14.16 Effect of temperature on distribution of kinetic energies
f = e-Ea
RT
Fraction ofmolecules with
E ≥ Ea
R = 8.314 J/(mol ∙ K)T = kelvin temperature
Maxwell–Boltzmann Distributions
f = e-Ea
RTFraction of molecules with E ≥ Ea
R = 8.314 J/(mol ∙ K)T = kelvin temperature
e.g., suppose Ea = 100 kJ/mol at T = 300 K:
f = e-Ea
RT = 3.9 x 10-18 (implies very few energetic molecules)
at T = 300 K: f = 1.4 x 10-17 (about 3.6 times more molecules)
Temperature Dependence of the Rate ConstantTemperature Dependence of the Rate Constant
k = A • exp(− Ea/RT )
Ea ≡ activation energy (J/mol)
R ≡ gas constant (8.314 J/K•mol)
T ≡ kelvin temperature
A ≡ frequency factor
ln k = −Ea
R1T
+ ln A
(Arrhenius equation)
y = mx +b
Fig 14.12
k1 = A • exp(−Ea/RT1)
The Arrehenius equation can be used to relate
rate constants k1 and k2 at temperatures T1 and T2.
21
21a
2
1
TTTT
RE
kk
ln
k2 = A • exp(−Ea/RT2)combine to give:
Plot of ln k vs 1/T
Slope = −Ea/R
ln k =− Ea
R1T
+ ln A
Fig 14.17 Graphical determination of activation energy
y = m x + b
Arrhenius Equation
Sample Exercise 14.11 The following table shows the rate constants for the rearrangement of methyl isonitrile at various temperatures:
(a) From these data, calculate the activation energy for the reaction.
(b) What is the value of the rate constant at 430.0 K?
Solution
Analyze: We are given rate constants, k, measured at several temperatures and asked to determine the activation energy, Ea, and the rate constant, k, at a particular temperature.
Plan: We can obtain Ea from the slope of a graph of ln k versus 1/T and the rate constant, k, at a particular temperature. Once we know Ea, we can use Equation 14.21 together with the given rate data to calculate the rate constant at 430.0 K.
Solve: (a) We must first convert the temperatures from degrees Celsius to kelvins. We then take the inverse of each temperature, 1/T, and the natural log of each rate constant, ln k.
A graph of ln k versus 1/T results in a straight line, as shown in Figure 14.17:
slope = − Ea/R = − 1.9 x 104
We use the value for the molar gas constant R in units of J/mol-K (Table 10.2). We thus obtain
(b) To determine the rate constant, k1, at T1 = 430.0 K, we can use Equation 14.21 with Ea = 160 kJ/mol, and one of the rate constants and temperatures from the given data, such as:
k2 = 2.52 × 10–5 s–1 and T2 = 462.9 K:
Thus,
Note that the units of k1 are the same as those of k2.
Practice Exercise
The first-order rate constant for the reaction of
methyl chloride with water to produce methanol and
hydrochloric acid is 3.32 x 10-10 s-1 at 25 °C. Calculate
the rate constant at 40 °C if the activation energy is
116 kJ/mol.
21
21a
2
1
TTTT
RE
kk
ln
k2 = 0.349 s-1
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