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Chemical Kinetics

Chapter 13

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Chemical Kinetics• Kinetics is the study of how fast chemical reactions

occur and how they occur.• There are 4 important factors which affect rates of

reactions:– reactant concentration– temperature– catalyst– surface area

• Goal: to understand chemical reactions at the molecular level.

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Reaction Rates• Speed of a reaction (rxn) is measured by the change in

concentration with time.• For a rxn A → B

• Suppose A reacts to form B. Let us begin with 1.00 mol A (and no B).

Average rate =change in the number of moles of B

change in time

=Δ moles of B( )

Δt =

final mol B - initial mol BΔt

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Reaction Rates–At t = 0 (time zero) there is 1.00 mol A (100

red spheres) and no B present.–At t = 20 min, there is 0.54 mol A and 0.46

mol B.–At t = 40 min, there is 0.30 mol A and 0.70

mol B.–Eventually, there will be no more A left, and

only B will be present.

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Reaction Rates

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Reaction Rates

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Reaction Rates• We can use this data to find the average

rate:( )

( ) ( )

mol/min 026.0min 0 - min 10mol 0 - mol 26.0

min 0 - min 100at B of moles10at B of moles

B of molesrate Average

==

=−==

ΔΔ

=

ttt

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Chemical KineticsReaction Rates• For the rxn A →B there are two ways of measuring

rate:– the speed at which the products appear (i.e. change in

moles of B per unit time), or– the speed at which the reactants disappear (i.e. the

change in moles of A per unit time).

– Note the minus sign! This reminds us that the rate is being expressed as the disappearance of a reactant.

Ave rate = -Δ(mol A)

Δt

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Rates in Terms of Concentrations• Most of the time, we will determine the rate of a rxn

by monitoring a change in concentration of a reactant or product.

• Molarity is the most useful unit for rxn rates although pressure is used for gases. Since volume is usually constant, molarity (or pressure) and moles are directly proportional.

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Rates in Terms of Concentrations• Consider:

C4H9Cl(aq) + H2O(l) →C4H9OH(aq) + HCl(aq)

• We can calculate the average rate in terms of the disappearance of C4H9Cl.

• The units for average rate are mol/L•s or M/s.• The average rate decreases with time as C4H9Cl

disappears.

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Rates in Terms of ConcentrationsC4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)

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Rates in Terms of Concentrations• We now plot [C4H9Cl] versus time.

• The rate at any instant in time is called the instantaneous rate.

• The instantaneous rate is the slope of the straight line tangent to the curve at that instant.

• Instantaneous rate is different from average rate.• Note: The instantaneous rate is usually just called the

rate, unless otherwise specified.

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Rates in Terms of Concentrations

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Reaction Rates and Stoichiometry• For the rxn

C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)

we know

• What if the stoichiometric relationships aren’t 1:1?

2HI(g) → H2(g) + I2(g)

• The HI:H2 ratio and the HI:I2 ratio are both 2:1!

[ ] [ ]t

OHHC

t

ClHCRate 9494

Δ

Δ=

Δ

Δ−=

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Reaction Rates and Stoichiometry2HI(g) →H2(g) + I2(g)

• It should be clear that as HI is consumed (or disappears), only half as much H2 (and I2) is produced or appears.

• So the rate of disappearance of HI is twice the rate of appearance of H2 (and I2).

rateHI = 2rateH2 OR

rateH2 = 0.5rateHI

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Reaction Rates and Stoichiometry• We now have 2 different rates for the same rxn.• These rates are related by the balanced equation

stoichiometry.• We commonly talk in terms of the rxn rate, or the rate

of the rxn, not just in terms of the rate of appearance of a product or the rate of disappearance of a product.

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Reaction Rates and Stoichiometry• The rxn rate, or called just the rate, may be expressed

as:

• Or we can write it more generally as:

raterxn = rateH2 = rateI2 = 0.5rateHI

rate = -1

2

Δ HI[ ]Δt

= Δ H2[ ]Δt

= Δ I2[ ]Δt

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Reaction Rates and Stoichiometry• In general for the rxn:

aA + bB → cC + dD• The overall rxn rate may be expressed as:

• Or in nonmathematical terms:

[ ] [ ] [ ] [ ]tD1

tC1

tB1

tA1

RateΔ

Δ=

ΔΔ

=Δ

Δ−=

ΔΔ

−=dcba

rate = 1

arateA =

1

brateB =

1

crateC =

1

drateD

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Reaction Rates and Stoichiometry• Be careful!• Experiments are conducted in terms of the rates of

appearance/disappearance of a product/reactant.• These rates may then be converted to rxn rates using

the balanced equation.• Read problems carefully so you know what you are

given!• If it is not specified, it is by default a rxn rate.

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The Dependence of Rate on Concentration• In general, rates:

– Increase when reactant [ ] are increased.– Decrease when product [ ] are increased.

• We often examine the effects of concentration on a rxn rate by measuring how the rxn rate at the beginning of a rxn depends on concentration.

• The instantaneous rxn rate at the start of a rxn is called the initial rate.

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The Dependence of Rate on Concentration• Let’s look at the following rxn: NH4

+(aq) + NO2-(aq) →N2(g) + 2H2O(l)

• The initial rate is the instantaneous rate at t = 0. (You get the initial rate from a graph.)

• We find the initial rate for various initial concentrations of each reactant; for this rxn, NH4

+

and NO2-.

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Finding Initial Rate

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The Dependence of Rate on Concentration

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The Dependence of Rate on Concentration

• As [NH4+] doubles, with [NO2

-] constant, the rate doubles.

• So the rate is proportional to [NH4+]

• As [NO2-] doubles, with [NH4

+] constant, the rate doubles.

• So the rate is proportional to [NO2-]

• We conclude that the rate [NH∝ 4+] and to

[NO2-].

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The Dependence of Rate on Concentration• The overall concentration dependence of the

rxn rate is given in a rate law or rate expression.

• For this example, the rate law is:

Rate = k[NH4+][ NO2

-]

• k is the rate constant and is constant except for a change in temperature.

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The Dependence of Rate on Concentration• So what is a rate law?• It is a mathematical description of how the

concentration of a reactant affects the rate of the rxn.

• After we determine the rate law and k for a rxn, we can then use this info to calculate initial rates or concentrations for any initial reactant concentrations.

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Reaction Order• For a general reaction with rate law

Rate = k[reactant 1]m[reactant 2]n,

we say the reaction is mth order in reactant 1 and nth order in reactant 2.

• The overall rxn order is m + n + ….• The rxn orders (values of the exponents) must be

determined experimentally. They are not necessarily related to stoichiometry.

• Rxn orders of 0, 1, and 2 are common (0th, 1st, and 2nd orders).

• But negative and fractional rxn orders are possible.

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Reaction Order• For the rxn: NH4

+(aq) + NO2-(aq) → N2(g) + 2H2O(l)

• The rxn has been experimentally found to be 1st order in NH4

+ and 1st in NO2-.

• The overall rxn order is 2.• So, the rate law is:

Rate = k[NH4+][ NO2

-].

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Units of k, the Rate Constant• The units of the rate constant, k, depend on

the overall rxn order.• For example, for a rxn with a rxn order of 2,

the k units are:

Units of rate = (units of rate constant)(units of concentration)2

• Or:rate constant units =

units of rate

units of concentration( )2

rate constant units = M

sM2 =

1M • s

= M -1s-1

The time unit s could be any other time unit, depends on rxn

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Using Initial Rates to Determine Rate Laws• To determine the rate law, we observe the

effect of changing initial concentrations.• For the general rxn:

aA + bB → cC + dD• The rate law is:

Rate = k[A]m[B]n

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Using Initial Rates to Determine Rate Laws• Mathematically, we compare the rates of 2 or more

experiments, which are conducted at different reactant concentrations.

• Solving this gives us the exponents, which gives us the rxn order.

• Once the exponents are known, k may be calculated.• We then know the complete rate law!

rate2

rate1 =

k A[ ]2m B[ ]2

n

k A[ ]1m B[ ]1

n = A[ ]2

m B[ ]2n

A[ ]1m B[ ]1

n = A[ ]2A[ ]1

⎛

⎝⎜

⎞

⎠⎟

mB[ ]2B[ ]1

⎛

⎝⎜

⎞

⎠⎟

n

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Using Initial Rates to Determine Rate Laws• A rxn is zero order in a reactant if the change in

concentration of that reactant produces no effect.• A rxn is first order if doubling the concentration

causes the rate to double.• A rxn is second order if doubling the concentration

results in a 22 increase in rate. • A rxn is nth order if doubling the concentration

causes an 2n increase in rate.• Note that the rate, not the rate constant, depends on

concentration.

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• Example for rxn A + B → C:

Exp # [A] [B] Initial rate (M/s)

1 0.100 0.100 4.0x10-5

2 0.100 0.200 4.0x10-5

3 0.200 0.100 16.0x10-5

4 0.400 0.400

5 0.100 2.0x10-5

• Find a) rate law; b) k; and c) fill in the blanks.