kinetics-lecture6.pdf
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This document discusses key concepts relating to reaction rates: - The half-life of a first-order reaction does not depend on initial concentration, while half-lives of second and zero-order reactions do depend on initial concentration. - Reaction rates increase with higher concentrations because there are more collisions between reactant particles. - Temperature also affects reaction rates because it increases the kinetic energy of particles, resulting in more frequent collisions exceeding the activation energy. - The Arrhenius equation quantifies the exponential relationship between temperature and the rate constant.
![Half-life Equations
For a first-order reaction, t1/2 does not depend on the
initial concentration.
For a second-order reaction, t1/2 is inversely proportional
to the initial concentration:
=
1
k[A]0
t1/2 (second order process; rate = k[A]2)
For a zero-order reaction, t1/2 is directly proportional to
the initial concentration:
[A]0
2k0
1/2
t = (zero order process; rate = k)
Dr. N. Singh](https://image.slidesharecdn.com/kinetics-lecture6-220901050557-25b5c82f/85/kinetics-lecture6-pdf-1-320.jpg)
![Table 5 An Overview of Zero-Order, First-Order, and
Simple Second-Order Reactions
Zero Order First Order Second Order
Rate law
Units for k
Half-life
rate = k
mol/L·
s [A]0
Integrated rate law
in straight-line form
Plot for straight line
2k
[A]t = -kt +[A]0
t
[A] vs.t t
ln[A] vs.t 1 vs. t
Slope, y intercept
Graph
-k, [A]0 -k, ln[A]0
[A]t
k, 1
[A]0
rate = k[A]
1/s
ln 2
k
ln[A]t = -kt +ln[A]0
rate = k[A]2
L/mol·s
1
k[A]0
1
= kt +
1
[A]t [A]0
Dr. N. Singh](https://image.slidesharecdn.com/kinetics-lecture6-220901050557-25b5c82f/85/kinetics-lecture6-pdf-2-320.jpg)
![Figure 14 Increase of the rate constant with temperature for
the hydrolysis of an ester
Expt [Ester] [H2O] T (K) Rate
(mol/L·s)
k
(L/mol·s)
1 0.100 0.200 288 1.04x10-3 0.0521
2 0.100 0.200 298 2.20x10-3 0101
3 0.100 0.200 308 3.68x10-3 0.184
4 0.100 0.200 318 6.64x10-3 0.332
Reaction rate and k increase exponentially as T increases.
Dr. N. Singh](https://image.slidesharecdn.com/kinetics-lecture6-220901050557-25b5c82f/85/kinetics-lecture6-pdf-7-320.jpg)
kinetics-lecture6.pdf
- 1. Half-life Equations For a first-order reaction, t1/2 does not depend on the initial concentration. For a second-order reaction, t1/2 is inversely proportional to the initial concentration: = 1 k[A]0 t1/2 (second order process; rate = k[A]2) For a zero-order reaction, t1/2 is directly proportional to the initial concentration: [A]0 2k0 1/2 t = (zero order process; rate = k) Dr. N. Singh
- 2. Table 5 An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions Zero Order First Order Second Order Rate law Units for k Half-life rate = k mol/L· s [A]0 Integrated rate law in straight-line form Plot for straight line 2k [A]t = -kt +[A]0 t [A] vs.t t ln[A] vs.t 1 vs. t Slope, y intercept Graph -k, [A]0 -k, ln[A]0 [A]t k, 1 [A]0 rate = k[A] 1/s ln 2 k ln[A]t = -kt +ln[A]0 rate = k[A]2 L/mol·s 1 k[A]0 1 = kt + 1 [A]t [A]0 Dr. N. Singh
- 3. Theories of Chemical Kinetics Reaction Mechanisms: The Steps from Reactant to Product Dr. N. Singh
- 4. Collision Theory and Concentration The basic principle of collision theory is that particles must collide in order to react. An increase in the concentration of a reactant leads to a larger number of collisions, hence increasing reaction rate. The number of collisions depends on the product of the numbers of reactant particles, not their sum. Concentrations are multiplied in the rate law, not added. Dr. N. Singh
- 5. Figure 13 The number of possible collisions is the product, not the sum, of reactant concentrations. 4 collisions 6 collisions 9 collisions add another add another Dr. N. Singh
- 6. Temperature and the Rate Constant Temperature has a dramatic effect on reaction rate. For many reactions, an increase of 10°C will double or triple the rate. Experimental data shows that k increases exponentially as T increases. This is expressed in the Arrhenius equation: Higher T increased rate larger k k = Ae-Ea/RT k = rate constant A = frequency factor Ea = activation energy Dr. N. Singh
- 7. Figure 14 Increase of the rate constant with temperature for the hydrolysis of an ester Expt [Ester] [H2O] T (K) Rate (mol/L·s) k (L/mol·s) 1 0.100 0.200 288 1.04x10-3 0.0521 2 0.100 0.200 298 2.20x10-3 0101 3 0.100 0.200 308 3.68x10-3 0.184 4 0.100 0.200 318 6.64x10-3 0.332 Reaction rate and k increase exponentially as T increases. Dr. N. Singh
- 8. Activation Energy In order to be effective, collisions between particles must exceed a certain energy threshold. When particles collide effectively, they reach an activated state. The energy difference between the reactants and the activated state is the activation energy (Ea) for the reaction. The lower the activation energy, the faster the reaction. Smaller Ea larger f larger k increased rate Dr. N. Singh
- 9. Energy-level diagram for a reaction. Collisions must occur with sufficient energy to reach an activated state. This particular reaction is reversible and is exothermic in the forward direction. Dr. N. Singh High jump
- 10. Temperature and Collision Energy An increase in temperature causes an increase in the kinetic energy of the particles. This leads to more frequent collisions and reaction rate increases. At a higher temperature, the fraction of collisions with sufficient energy equal to or greater than Ea increases. Reaction rate therefore increases. Dr. N. Singh
- 11. The effect of temperature on the distribution of collision energies. Dr. N. Singh