Chapter 14 - Chemical Kinetics

Reaction Rates Rate Laws

Rate Constants Effect of Concentration on Reaction Rate

Kinetics

The study of the factors that affect the speed of a reaction and the mechanism by which a reaction proceeds

Why Study Kinetics ?

RateHow much a quantity changes in a given period of time

Rate of a Chemical Reaction

How much the concentration of a reactant decreases in a given

period of time

Defining Rate

•  rate is how much a quantity changes in a given

period of time

•  the speed you drive your car is a rate – the distance

your car travels (miles) in a given period of time (1

hour)

 so the rate of your car has units of mi/hr

How much the concentration of a product increases in a given

period of time

Defining Reaction Rate

•  the rate of a chemical reaction is generally measured in

terms of how much the concentration of a reactant

decreases in a given period of time

 or product concentration increases

•  for reactants, a negative sign is placed in front of the

definition

Defining Reaction Rate

•  the rate of a chemical reaction is generally measured in

terms of how much the concentration of a reactant

decreases in a given period of time

 or product concentration increases

•  for reactants, a negative sign is placed in front of the

definition

Reaction Rate Over Time

As time passes, the reaction rate generally slows down because the concentration of the reactants decreases.

At some time the reaction stops either because the reactants run out or the reaction reaches equilibrium.

Reaction Rates and Stoichiometry

In most reactions, the coefficients in the balanced equation are not the same:

The change in concentration of one substance is a multiple of the concentration of another. Rate of a

reaction, therefore, can be described in terms of reactants or products:

Reaction Rate and Stoichiometry •  in most reactions, the coefficients of the balanced

equation are not all the same

H2 (g) + I2 (g) → 2 HI(g)

•  for these reactions, the change in the number of molecules of one substance is a multiple of the change in the number of molecules of another

 for the above reaction, for every 1 mole of H2 used, 1 mole of I2 will also be used and 2 moles of HI made

 therefore the rate of change will be different

•  in order to be consistent, the change in the concentration of each substance is multiplied by 1/coefficient

Reaction Rate and Stoichiometry •  in most reactions, the coefficients of the balanced

equation are not all the same

H2 (g) + I2 (g) → 2 HI(g)

•  for these reactions, the change in the number of molecules of one substance is a multiple of the change in the number of molecules of another

 for the above reaction, for every 1 mole of H2 used, 1 mole of I2 will also be used and 2 moles of HI made

 therefore the rate of change will be different

•  in order to be consistent, the change in the concentration of each substance is multiplied by 1/coefficient

Average RateThe average rate is the change in measured concentration

in a particular time period.

Instantaneous RateThe instantaneous rate is the change in concentration at

any one particular time.

Avg. Rate, M/s Avg. Rate, M/s

Time (s) [H2], M [HI], M -Δ[H2]/Δt 1/2 Δ[HI]/Δt

0.000 1.000 0.000

10.000 0.819 0.362 0.0181 0.0181

20.000 0.670 0.660 0.0149 0.0149

30.000 0.549 0.902 0.0121 0.0121

40.000 0.449 1.102 0.0100 0.0100

50.000 0.368 1.264 0.0081 0.0081

60.000 0.301 1.398 0.0067 0.0067

70.000 0.247 1.506 0.0054 0.0054

80.000 0.202 1.596 0.0045 0.0045

90.000 0.165 1.670 0.0037 0.0037

100.000 0.135 1.730 0.0030 0.0030

Average RateReaction Rate and Stoichiometry •  in most reactions, the coefficients of the balanced

equation are not all the same

H2 (g) + I2 (g) → 2 HI(g)

•  for these reactions, the change in the number of molecules of one substance is a multiple of the change in the number of molecules of another

 for the above reaction, for every 1 mole of H2 used, 1 mole of I2 will also be used and 2 moles of HI made

 therefore the rate of change will be different

•  in order to be consistent, the change in the concentration of each substance is multiplied by 1/coefficient

H2 (g) + I2 (g) → 2 HI (g) Using [H2], the

instantaneous rate at

50 s is:

Using [HI], the

instantaneous rate at

50 s is:

H2 (g) + I2 (g) → 2 HI (g) Using [H2], the

instantaneous rate at

50 s is:

Using [HI], the

instantaneous rate at

50 s is:

H2 (g) + I2 (g) → 2 HI (g) Using [H2], the

instantaneous rate at

50 s is:

Using [HI], the

instantaneous rate at

50 s is:

H2 (g) + I2 (g) → 2 HI (g) Using [H2], the

instantaneous rate at

50 s is:

Using [HI], the

instantaneous rate at

50 s is:

Instantaneous Rate

Measuring Reaction Rates

Continuous Monitoring (for short periods of time) Periodic Sampling

Factors Affecting Reaction Rates

Nature of Reactants

Small vs large molecules Gases vs liquids vs solids

Powders vs solid blocks of substance Reduction/Oxidation potentials

Ions vs molecules

Temperature of Reaction

Catalysts

Reactant Concentration

Rate LawThe mathematical relationship between the rate of the

reaction and the concentration of reactants

The rate of a reaction is directly proportional to concentrations of the reactant raised to a power.

For the reaction aA + bB→ products

Rate = k[A]n[B]m

Rate constantReaction order for

each reactant

Reaction Order

The sum of the exponents on the reactants

For the reaction 2 NO (g) + O2 (g) → 2NO2 (g)

Rate = k[NO]2[O2]

The reaction is second order with respect to [NO], first order with respect to [O2]

and third order overall.

The rate law is determined experimentally and is not related to the coefficients in the

balanced equation !!!

Sample Rate LawsSample Rate Laws

The reaction is autocatalytic, because a product affects the rate.

Hg2+ is a negative catalyst, increasing its concentration slows the reaction.

Graphical Representation of Kinetic Data

Zero Order Reaction

First Order Reaction

Second Order Reaction

Deriving a Rate Law from Initial Rate Data

The method involves observing the effect on the initial rate of a reaction when the initial concentration of only

one reactant is changed.

For zero order reactions, changing the concentration has no effect on the rate.

For 1st order reactions, the rate changes by the same factor as the concentration (i.e., Doubling the initial

concentration doubles the rate.).

For 2nd order reactions, the rate changes by the square of the factor the concentration changes (i.e., Doubling

the initial concentration quadruples the rate.).

1) Determine the rate law and rate constant for the reaction: NH4+ + NO2-1 → N2 + 2 H2O given the data below.

Expt.Number

1.

2.

3.

4.

0.0200

0.0600

0.200

0.200

0.200

0.200

0.0202

0.0404

10.8

32.3

10.8

21.6

Initial [NH4+], M

Initial [NO2-], M

Initial Rate, (x 10-7), M/s

Rate = k [NH4+][NO2-]

Reaction is 1st order with respect to NH4+

Reaction is 1st order with respect to NO2—

1) Determine the rate law and rate constant for the reaction: NH4+ + NO2-1 → N2 + 2 H2O given the data below.

Expt.Number

1.

2.

3.

4.

0.0200

0.0600

0.200

0.200

0.200

0.200

0.0202

0.0404

10.8

32.3

10.8

21.6

Initial [NH4+], M

Initial [NO2-], M

Initial Rate, (x 10-7), M/s

Rate = k[NH4+][NO2-]

10.8 x 10-7 M/s = k(0.0200 M)(0.200 M)

k = 10.8 x 10-7 M/s (0.0200 M)(0.200 M)

= 2.70 x 10-4 M-1·s-1

21.6 x 10-7 M/s = k(0.200 M)(0.0404 M)

k = 21.6 x 10-7 M/s (0.200 M)(0.0404 M)

= 2.70 x 10-4 M-1·s-1

2) Determine the rate law and rate constant for the reaction: NO2 + CO → NO + CO2 given the data below.

Expt.Number

1.

2.

3.

4.

0.100

0.200

0.200

0.400

0.100

0.100

0.200

0.100

0.0021

0.0082

0.0083

0.033

Initial [NO2], M

Initial [CO], M

Initial Rate, M/s

Rate = k [NO2]2[CO]0

Reaction is 2nd order with respect to NO2

Reaction is 0 order with respect to CO

2) Determine the rate law and rate constant for the reaction: NO2 + CO → NO + CO2 given the data below.

Expt.Number

1.

2.

3.

4.

0.100

0.200

0.200

0.400

0.100

0.100

0.200

0.100

0.0021

0.0082

0.0083

0.033

Initial [NO2], M

Initial [CO], M

Initial Rate, M/s

Rate = k [NO2]2[CO]0

Rate = k [NO2]2

0.0021 M/s = k[NO2]2

0.0021 M/s = k(0.10 M)2

k = 0.0021 M/s (0.10 M)2 = 0.21 M-1·s-1

0.033 M/s = k[NO2]2

0.033 M/s = k(0.400 M)2

k = 0.033 M/s (0.40 M)2 = 0.21 M-1·s-1

3) Determine the rate law and rate constant for the reaction: O2 + 2 NO → 2 NO2 given the data below.

Expt.Number

1.

2.

3.

4.

5.

1.10 x 10-2

2.20 x 10-2

1.10 x 10-2

3.30 x 10-2

1.10 x 10-2

1.30 x 10-2

1.30 x 10-2

2.60 x 10-2

1.30 x 10-2

3.90 x 10-2

3.21 x 10-3

6.40 x 10-3

12.8 x 10-3

9.60x 10-3

28.8 x 10-3

Initial [O2], M

Initial [NO], M

Initial Rate, M/s

Rate = k [O2][NO]2

Reaction is 1st order with respect to O2

Reaction is 2nd order with respect to NO

9.6 x10-3 M/s = k[O2][NO]2

9.6 x10-3 M/s = k(3.30 x 10-2)(1.30 x 10-2)2

k = 9.60 x10-3 M/s (3.30 x 10-2 M)(1.30 x 10-2 M)2 = 1.72 x 103 M-2·s-1

Deriving a Rate Law Alternative Method for Partial Reaction Order

Rate = k[A]n[B]m Rate1 Rate2 ( )[B]1

[B]2

n=

( )[B]1 [B]2

n=( )log logRate1 Rate2

n =Rate1 Rate2( )log

( )[B]1 [B]2

log

Deriving a Rate Law Alternative Method for Partial Reaction Order

4) Determine the rate law and rate constant for the reaction: NO + NO3 → 2 NO2

given the data below.

Expt.Number

Initial [NO], M

Initial [NO3], M

Initial Rate, M/s

1.

2.

3.

1.25 x 10-3

1.50 x 10-3

1.50 x 10-3

1.25 x 10-3

1.25 x 10-3

2.00 x 10-3

2.45 x 104

2.94 x 104

4.71 x 104

n=1Reaction is 1st order with respect to NO

Reaction is 1st order with respect to NO3