Introduction to Chemical Kinetics

Introduction

Why do chemical reactions occur?

Reactant molecules will rearrange to form more stable (lower energy) products.

Physical analogy: A car on a hill with no brake will roll to the bottom.

Chemical examples:

    CH_4(g) + 2 O_2(g) CO_2(g) + 2 H₂O_(l) + energy (heat)

    2 Fe_(s) + 3/2 O_2(g) + 3 H₂O_(l) 2 Fe(OH)_{3 (s)} + energy (heat)

(formation of Fe(OH)_{3 (s)} is the first step in the rusting of iron and steel)

Activation Energy Diagram

Is a balloon filled with H₂ and O₂ stable?

A model for reactions:

        ^
        |                     ________
Energy  |                    /        \
        |        reactants  /    Ea    \
        |        __________/     __     \
        |                                \
        |                                 \
        |                        H        \
        |                                    \  products
        |                        __           \_________
        |
        |

E_a is the activation energy and H is the heat of reaction (in kJ/mol).

To answer the question about a mixture of H₂ and O₂:
The reaction:
    H_{2 (g)} + 1/2 O_{2 (g)} H₂O_(l) + energy (heat)
is not stable thermodynamically, but we can say that it is stable kinetically. It is not an equilibrium situation.

Really Big Concepts in Chemistry

Kinetics describes how quickly or slowly a reaction occurs.

Thermodynamics describes the changes in the form of energy when a reaction occurs, for example, converting chemical energy to heat.

Equilibrium describes reactions in which the reactants and products coexist.

Reaction Rates

Definition: Chemical kinetics is the study of the rate at which chemical reactions occur.

The rate of a chemical reaction, or simply the reaction rate, is the change in concentration of the reactants or products as a function of time.

Example:  R  P

               |
               X
               |
               |X
               | X
               |  X
 Concentration |   X 
     of R      |    X
               |      X
               |        X
               |           X
               |               X
               |                     X
               |____________________________________X______
                               time


       -{[R]t2 - [R]t1}        [P]t2 - [P]t1
rate = ----------------   =   -------------
            (t2-t1)               (t2-t1)

       -[R]      [P]
rate = -----   =   -----
        t         t

[R]_t2 is the concentration of R at time t₂.
can be read as "the change in". For very small changes we use the differential symbol "d".
the negative sign is present because the reactants, R, decrease with time.

From the plot you can see that the rate depends on the particular values of t₂ and t₁, and is called the "instantaneous rate." [R] and [P] change rapidly at early time, and change more slowly at later time.

The "average rate" can be found by using the end of the reaction as t₂ and time=0 as t₁.

A more complicated example considering stoichiometry:

N_2(g) + 3 H_2(g) 2 NH_3(g) + energy (heat)

         -[N2]         -[H2]         [NH3]
rate =  ---------   =   --------   =   ---------
         1 t           3 t           2 t

Rate Expressions and Rate Constants

Why does reaction rate decrease as the reaction progresses?

In general, what experimental variables affect the reaction rate?

To a first approximation, the reaction rate depends on how frequently the reactants collide. Reactant collisions increase when we raise (1) temperature or (2) reactant concentration.

We can write rate expressions (a.k.a. rate laws) for reactions.

In general, for:

aA + bB products

rate = k [A]^m [B]ⁿ

where
m is the order of the reaction with respect to A
n is the order of the reaction with respect to B
and the overall order of the reaction is m+n

The reaction order depends on the mechanism of the reaction and NOT on the stoichiometry.

Example:

CO_(g) + NO_2(g) CO_2(g) + NO_(g)

To study the kinetics of this reaction prepare a series of mixtures of CO and NO₂ and measure the reaction rate immediately after mixing the reactants.

[CO]	[NO2]	TEMP	Initial Rate
0.2 M	0.2 M	600 K	0.48 mol/L/min
0.2 M	0.1 M	600 K	0.24 mol/L/min
0.1 M	0.1 M	600 K	0.12 mol/L/min
0.1 M	0.1 M	660 K	0.93 mol/L/min

From the above data we see that the reaction rate is directly proportional to both [CO] and [NO₂]

therefore rate = k [CO][NO₂]

where k is a temperature dependent rate constant.

The units of k varies for each particular expression. Since reaction rate has units of mol/L/min, do a dimensional analysis to find the units of k.

Integrated Rate Expressions

We can convert the rate expressions to new expressions that relate reactant concentration to time.

Zero-order reaction: A products

        -[A]
rate  =  --------  =  k[A]0  =  k
         t

integrating gives:

[A] = [A]_o - kt

First-order reaction: A products
(Figures 16.2 and 16.3 in Rubinson & Rubinson show typical plots for a 1st-order reaction.)

         -[A]
rate  =  -------  =  k[A]
           t

-ln([A]_t/[A]_o) = kt

where [A]_o is the initial concentration of A
and [A]_t is the concentration of A at time t.

Rearranging: ln[A] = ln[A]_o - kt

So a plot of ln[A] vs. time will be a straight line.

Second-order reaction: A products

        -[A]
rate  =  --------  =  k[A]2
         t

1/[A] - 1/[A]_o = kt

To summarize:

order     linear plot
  0        [A] vs. t
  1      ln[A] vs. t
  2      1/[A] vs. t

Why is the order important?
    provides clues to the reaction mechanism
    allows optimization of chemical processes

Kinetics Key Concepts

1. activation energy, E_a, model
2. rate of reaction definition
3. writing rate expressions
   • rate constants
   • reaction order
4. integrated rate expressions