1

REACTION KINETICS

In order for a reaction to take place, reactants must collide with sufficient energy to overcome

activation energy and with the correct orientation that can lead to rearrangement of the

atoms.

Only effective collisions lead to chemical reactions.

Rate of reaction depends on the collision frequency and the proportion of the collisions that

have sufficient energy to overcome activation energy.

The activation energy of a reaction (Ea) is the minimum energy which the reacting particles must

possess in order to overcome the energy barrier before becoming products.

Magnitude of Ea does not depend on ΔH.

It is always positive as bonds are first broken and then formed during a reaction.

Kinetically favourable reactions have low Ea because large portion of the molecules have the

necessary energy to overcome energy barrier.

Reactions with high Ea Reactions with low Ea

Ions of similar charge Ions of opposite charge

Bonds are broken to form free radicals Between 2 radicals

A transition state/activated complex is the arrangement of atomic nuclei and bonding

electrons at the maximum potential energy.

It can either be broken up to form the products or converted back into original reactant

molecules.

It cannot be isolated as a compound due to its high instability.

Ea is measured from the energy level of the reactants to the energy level of the activated

complex.

The change in concentration of a reactant/product per unit time.

aA + bB → cC + dD

rate = −𝟏

𝒂

𝒅 [𝑨]

𝒅𝒕 = −

𝟏

𝒃

𝒅 [𝑩]

𝒅𝒕 =

𝟏

𝒄

𝒅 [𝑪]

𝒅𝒕 =

𝟏

𝒅

𝒅 [𝑫]

𝒅𝒕

Rate of reaction is always positive.

Since [reactant] decreases during a reaction, 𝑑 [𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡]

𝑑𝑡 is negative. Hence −

𝑑 [𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡]

𝑑𝑡 is

COLLISION THEORY

ACTIVATION ENERGY

REACTION PATHWAYS

RATE OF REACTION

2

positive.

Stoichiometric coefficients expresses the quantitative relationship between rate of change of

concentration of different reactants/products.

The rate equation is an experimentally determined equation that relates rate of reaction to the

concentrations of the reactants raised to appropriate powers.

Rate = k [A]m [B]n…

Power of the reactants is the order of reaction with respect to the reactant.

Sum of all the powers of the reactants is the overall order of the reaction.

K is the rate constant. Its value is constant throughout the reactions but changes with

temperature or presence of a catalyst.

When a reactant does not appear in the rate equation, the reaction is of zero order with

respect to that reactant.

All components in the rate equation are determined experimentally and are not related to the

stoichiometry ratio.

Orders of reaction can be a fraction or negative.

The rate constant, k, is the proportionality constant in the experimentally determined rate equation

and is a constant at a given temperature.

Arrhenius equation:

k = Ae-Ea/RT

A = pre-exponential factor/frequency factor

Ea = activation energy

R = molar gas constant

T = absolute temperature

e-Ea/RT = fraction of particles with minimum energy to react

The larger the rate constant, the faster the rate of reaction.

Units of k = (mol dm-3)1-N s-1

N is the overall order of reaction.

Time component can be either in s, min or h.

RATE CONSTANT

RATE EQUATION

3

The order of reaction with respect to a reactant is the power on its concentration term in the rate

equation and it must be determined experimentally.

The overall order of reaction is the sum of the individual orders.

1. Comparing Initial Rates

This is used for reactions involving more than 1 reactant.

EITHER

Comparing experiments ___ and ___, [__] and [__] are constant, when [X] is increased/decreased

_____ times, initial rate increased/decreased ____ times. Hence rate ∝ [X], the reaction is of

_____ order with respect to X.

OR

Let rate equation be: rate = k [A]x[B]y[C]z and compare the rate ratio and concentration ratio.

2. Graph Analysis

Half-life, t1/2 of a reaction is the time taken for the concentration of a reactant to decrease to half

of its initial value.

For an overall first-order reaction:

T1/2 = 𝒍𝒏 𝟐

𝒌

k is the rate constant

Half-life of an overall first order reaction is independent of reactant concentration.

It has a unit of time.

Overall first-order reactions have a constant half-life. To confirm that a reaction is first order,

consecutive half-lives can be shown to be the same on a [reactant]-time graph or [product]-time

graph.

For reactions with an order greater than 1, the successive half-lives become longer.

ORDER OF REACTION

4

Order of reaction 0 1 2

Graph

Explanation Gradient of a concentration-time graph at any point of time represents the instantaneous rate of reaction at t.

[A] decreases at a constant rate and

reaches 0 when reaction is completed.

Decrease in [A] has no effect on rate

since gradient is constant. Rate

remains constant at value of k

throughout.

[A] decreases exponentially with time

and with a constant half-life.

Rate decreases as [A] falls and gradient

of graph becomes less steep over time.

Successive half-lives are not constant.

Gradient at any point in time would be

gentler than that of a first order

reaction, provided value k in the rate

equation is the same.

Same decrease in [A] slows down the

reactions more in second order reaction

than that of a first order.

CONCENTRATION-TIME GRAPHS

5

[Reactant]-time & [Product]-time Graphs

[A]I is the intial concentration of reactant A.

First half-life ([A]i to 1

2[A]I) is same as second

half-life (1

2[A]I to

1

4[A]I).

[B]f is the final concentration of product, B. It

can be calculated from stoichiometry.

First half-life (0 to 1

2[B]f) is same as second

half-life (1

2[B]f to

3

4[B]f).

6

Order of reaction 0 1 2

Graph

Explanation The data can be obtained in the following ways:

Measuring the gradient at various points in the concentration-time graph and plotting these against their corresponding reactant

concentrations.

Carrying out the reaction a few times with different initial [A] and determining the initial rate in each case by obtaining gradient at t =0

from concentration-time graph.

Rate is constant as [A] changes. Rate increases as [A] increases.

Rate = k [A]

y = mx

A straight line with gradient k

passes through origin.

Rate increases at a faster rate as [A] increases.

Rate = k [A]2

y = mx2

A parabola starting from origin.

Graph of rate against [A]2 produces a straight line

passing through origin (confirms it is a second order

reaction) .

RATE-REACTION GRAPHS

7

To obtain a rate-time graph, gradient of different points on the concentration-time graph was found

and rate at each timing was determined. It is not usually used to determine the order of a reaction.

Order of reaction Graphs

0

Rate remains constant during the

reaction until reaction is

completed.

1

Rate decreases exponentially

with time.

2

Rate decreases exponentially

with time.

For the same value of k, rate

decreases faster than that of a

first order reaction.

RATE-TIME GRAPHS

8

aA + bB → cC + dD

rate = k [A]m[B]n

when B is in large excess (10× larger than reactant isolated), then:

rate = k’ [A]m, where k’ = k[B]n

The reaction actually has an overall order of m + n but appears to have an order of m in this

case. The reaction is said to be a pseudo-mth-order reaction in this case.

Reaction with respect to [B] will be pseudo-zero.

1. Presence of a Large Excess of a Reactant

Some reactants are added in large excess so that a particular reactant can be isolated to study

the rate of reaction with respect to it.

2. Solvent is a Reactant

Amount of solvent reacted is negligible compared to the total amount of solvent present.

3. Presence of a Catalyst

Concentration of catalyst is regarded as constant throughout the reaction.

The reaction mechanism of a reaction is a collection of elementary steps in the proper sequence

showing how reactant particles are converted into products.

Elementary Steps

A reaction occurs in a series of elementary steps.

Reaction mechanism refers to the sequence of the elementary steps.

The elementary step that has higher activation energy is the rate-determining step and it

determines the overall rate of the reaction.

It is also the slowest step in a multi-step reaction mechanism.

Molecularity

It counts the number of particles (molecules, ions, or atoms) that must collide to produce the

reaction indicated in an elementary step.

Unimolecular (1 reactant), bimolecular (2 reactants) and termolecular (3 reactants)

Molecularity only applies to elementary steps and cannot be assigned to an overall reaction.

PSEUDO-ORDER REACTIONS

REACTION MECHANISMS

9

Intermediates

An intermediate is a special species produced in an early step of a mechanism and consumed in

a later step.

They do not appear in the overall balanced equation, nor in the overall rate equation.

Proposed Reaction Mechanisms

1. Elementary steps must add up to the overall balanced equation.

2. The elementary steps must be physically reasonable. E.g. collisions between 3 particles and

between ions of like charges are rare.

3. The mechanism must be consistent with the experimentally-determined rate equation.

Order of reaction with respect to each reactant can be deduced from the molecularity of the

rate-determining step.

The coefficients in the rate-determining step are used as the order with respect to each

reactant.

Molecularity of the rate-determining step is equal to the overall order of the reaction.

Consists of only 1 elementary step.

This step will determine rate of reaction.

The reaction mechanism is identical to the stoichiometric equation for the reaction

Rate equation can be deduced directly from stoichiometric equation.

Elementary Reaction Reaction Mechanism Molecularity Rate Equation

A → 2R A → 2R Unimolecular Rate = k [A]

2A → P2 2A → P2 Bimolecular Rate = k [A]2

A + B → C + D A + B → C + D Bimolecular Rate = k [A] [B]

2A + B → C + D 2A + B → C + D Termolecular Rate = k [A]2 [B]

For a multi-step reaction, the rate equation is derived directly from the stoichiometry of the

slowest step, i.e. the rate-determining step.

Reactant species that react before or in the rate-determining step will appear in the rate

equation.

Reactant species that react after the rate-determining step will not appear

REACTION MECHANISMS & RATE EQUATION

SINGLE-STEP REACTION MECHANISM

MULTI-STEP REACTION MECHANISM

10

Rate-Determining Step is the First Step

Reaction 2N2O → 2N2 + O2

Reaction Mechanism Step 1: N2O → N2 + O slow

Step 2: N2O + O → N2 + O2 fast

Overall Equation 2N2O → 2N2 + O2

The rate equation for the overall reaction

can be deduced starting from the slow step.

The reactants that participate in the slow

step are those reactants that appear in the

rate equation.

The order of reaction with respect to a

reactant X is the number of X particles that

participates in the slow step.

N2O is the reactant that appears in the slow

step. Hence it must appear in the rate

equation.

There is only one N2O molecule reacting in

the slow step. Hence order of reaction with

respect to N2O = 1.

Another N2O molecule participants in the

fast step after the slow step and hence does

not appear in the rate equation.

i.e. rate ≠ [N2O]2

O is an intermediate and does not appear in

the overall equation nor the rate equation.

Rate-Determining Step is NOT the First Step

An intermediate would be involved if the rate-determining step is not the first step.

Since intermediates do not appear in the rate equation, the reactants producing them should

appear in the rate equation instead.

Perform substitution based on the elementary steps that occur before the rate-determining

step.

Reaction 2NO + O2 → 2NO2

Reaction Mechanism Step 1: NO + O2 NO3 fast & reversible

Step 2: NO3 + NO → 2NO2 slow

Overall Equation 2NO + O2 → 2NO2

11

From step 2,

Rate = k1 [NO3] [NO]

NO3 is an intermediate and should NOT appear in the rate equation and chemical equation.

From step 1,

Kc = [𝑵𝑶𝟑]

[𝑵𝑶][𝑶𝟐]

[NO3] = Kc [NO][O2]

Substituting [NO3],

Rate = k1kc [NO][O2][NO] = k1kc [NO]2[O2]

Rate = k [NO]2[O2] where k = k1kc

The graphs shown above are for a two-step reaction. There is one intermediate the 2 transition

states. In (a), the first step is determining in (b), the second step is rate-determining.

A transition state is different from an intermediate.

Transition State Intermediate

Occurs at energy maximum (top of energy

curve).

Occurs at an energy minimum, but as it is a

relatively reactive species, it has higher

energy than the reactants or products.

12

A transition state has no permanent

lifetime of its own and exists for only a few

femtoseconds when the molecules are in

contact with each other.

An intermediate is a definite chemical

species that exists for a finite length of

time.

A reactive intermediates has a lifetime of

only a microsecond, still has a longer

lifetime in comparison with the time that

colliding particles are in contact.

Rate of reaction depends on the collision frequency and the proportion of the collisions that

have sufficient energy to overcome activation energy (effective collisions).

Usually, rate of reaction increases when the reactant concentration is increased.

Answering technique:

At a higher concentration, there are more reactant particles per unit volume, hence, (reacting

particles A) and (reacting particles B) are closer together. ( ) and ( ) collide

more frequently. Thus, number of effective collisions increases and rate of reaction increases.

The rate of reaction will increase only if the concentration of reactants that appear in the rate

equation is increased. Otherwise, it will not increase if the rate of reaction is of 0 order with

respect to the reactant not shown in the rate equation.

Same effect is observed if pressure is increases for a gaseous reaction.

Change in pressure has virtually no effect on the rate for solid/liquid phase reactions. Volume

of a solid or liquid changes very little when put under pressure.

If the solid reactant is in a more finely divided state, the surface area over which the solid can

come into contact with liquid or gaseous reactants is larger.

As a result, the frequency of collision among the (reacting particles) at the surface of

the solid reactant increases, leading to the increase of frequency of effective collision

(between reacting particles), speeding up the rate of reaction.

As the temperature increases, there will be higher proportion of collisions having sufficient

energy to overcome the activation energy barrier, and the number of effective collision

increases. The reactants also move faster as they now have higher kinetic energies and collide

more frequently.

FACTORS AFFECTING RATE OF REACTION

EFFECT OF CONCENTRATION OR PRESSURE

EFFECT OF STATE OF DIVISION (SOLID REACTANTS)

EFFECT OF TEMPERATURE

13

Gauge of effect of increase in temperature: a 10 °C increase in temperature doubles the rate of

reaction.

Relatively large increase in reaction rate with temperature cannot be explained simply by

stating that increase in collision frequency associated with an increase in the average kinetic

energy of the reactant particles.

Boltzmann Distribution Diagram

At higher temperature, the proportion of molecules with kinetic energy greater than or equal

to the activation energy increases. Frequency of effective collision increases and rate of

reaction increases.

Checklist for drawing Boltzmann Distribution diagram:

Labelling of axes, origin must start at 0

Curve shifts right and peak is lowered at higher temperature

Labelling of curves with appropriate temperatures

Shaded area corresponds to description for proportion of molecules having KE greater or

equals to Ea

Arrhenius Equation

k = Ae-Ea/RT

K increases when T increases.

When T increases,

Ea/RT decreases

- Ea/RT increases

e-Ea/RT increases

k increases

14

A catalyst is a substance that speeds up a chemical reaction by providing an alternative reaction

pathway of lower activation energy, while remaining chemically unchanged at the end of the

reaction.

Note: catalysts lowers Ea, not ΔHr.

Boltzmann Distribution Diagram

A catalyst provides an alternative reaction pathway which requires a lower activation energy

(Ea’). There is an increase in the fraction of reactant particles that have kinetic energy geater

EFFECT OF CATALYSTS

15

than or equal to activation energy Ea’. Frequency of effective collision increases and rate of

reaction increases.

Checklist for Boltzmann Distribution Diagram:

Labelling of axes, origin starts at 0

Lower Ea with catalyst present

Shaded area corresponds to description for proportion of molecules have KE greater or

equals to Ea and Ea’ respectively

Arrhenius Equation

k = Ae-Ea/RT

K is larger of Ea is smaller.

When catalyst is added, alternative pathway has lower Ea.

Ea/RT decreases

- Ea/RT increases

e-Ea/RT increases

k increases

Photochemical reactions

When reactant molecules absorb light energy, the average kinetic energy of the particles

increases hence increasing the fraction of reacting particles with enough energy to overcome

the activation energy barrier.

Type of catalysis is determined by the phase in which the catalyst and the reactants are in.

Phase refers to a physically distinctive form of matter, e.g. solid, liquid, gas, or plasma.

A phase of matter is characterized by having relatively uniform chemical and physicals

properties.

Phases are different from states of matter.

The states of matter are phases (e.g. solids, liquids, gases), but matter can exist in different

phase yet the same state of matter. E.g. liquid mixtures can exist in multiple phases, like oil

phase and an aqueous phase.

EFFECT OF LIGHT

CATALYSIS

16

Related Terms

Inhibitor An inhibitor is a substance which decreases the rate of a chemical

reaction.

E.g. presence of dilute acids or glycerine retards the decomposition of

hydrogen peroxide.

Promoter A promoter is a substance which enhances the efficiency of a catalyst

E.g. In the Haber Process, small amounts of Al2O3 and K2O are added to

promote the efficiency of the iron catalyst.

Catalyst Poison A catalyst poison is a substance that inhibits the effectiveness of a

catalyst.

E.g. Lead poisons the platinum-rhodium surface in car exhaust catalytic

converters, hence the need for un-leaded petrol.

Examples of Catalysts

A homogeneous catalysts acts in the same phase as reactants and is uniformly mixed with them.

HOMOGENOUS CATALYSIS

17

It involves the formation of an intermediate between the catalyst and one of the reactants.

Catalyst is then regenerated in the next step of the reaction.

Catalyzed reaction may involve 2 or more steps, each of which must has a lower activation

energy than the unanalyzed equation.

A homogenous catalyst must be involved in the rate-determining step in order for it to affect

the rate of reaction.

Concentration of the homogeneous catalyst usually appears in the rate equation for the

catalyzed pathway. It does not appear in the overall balanced equation.

Transition Metals as Effective Homogeneous Catalysts

They are effective because

They can exist in different oxidation states and

They can undergo conversion from one oxidation sate to another oxidation state relatively

easily.

These features facilitate the formation of, and decomposition of, the intermediate formed from the

transition metal ion catalyst and the reactants.

Reaction between Peroxodisulfate Ions and Iodide Ions Catalysed by Fe2+ or Fe3+

Uncatalysed Reaction S2O82- (aq) + 2I- (aq) → 2SO4

2- (aq) + I2 (aq)

In the uncatalysed reaction, there is a direct reaction between two

similarly charged ions.

The electrostatic repulsion between the two negatively charged

ions partly causes the reaction to have a high activation energy

18

and hence to proceed slowly.

Reaction catalysed by Fe2+ Step 1: 2Fe2+ (aq) + S2O82- (aq) → 2Fe3+(aq) + 2SO4

2-(aq)

Step 2: 2Fe3+(aq) + 2I- (aq) → 2Fe2+ (aq) + I2 (aq)

Each step involved a reaction between oppositely charged ions

which have a natural tendency to attract each other. This lowers

the activation energy and catalyzes the reaction.

Reaction catalysed by Fe3+ Step 1: 2Fe3+ (aq) + 2I- (aq) → 2Fe2+(aq) + I2 (aq)

Step 2: 2Fe2+(aq) + S2O82- (aq) → 2Fe3+ (aq) + 2SO4

2- (aq)

Catalytic Oxidation of Atmospheric Sulfur Dioxide by Atmospheric Oxides of Nitrogen

Uncatalysed Reaction SO2 (g) + ½ O2 (aq) → SO3 (g)

Atmospheric SO2 can be oxidized to SO3 by O2 but the reaction is

slow without a catalyst.

Reaction catalysed by NO2 In the presence of NO2, the rate of oxidation of SO2 is increased.

Step 1: SO2 (g) + NO2 (g) → SO3 (g) + NO (g)

Step 2: NO(g) + ½ O2 (g) → NO2 (g)

Overall: SO2 (g) + ½ O2 (aq) → SO3 (g)

In step 1, NO2 (from car exhaust fumes) can oxidize atmospheric

SO2 (from burning of fossil fuels) to SO3.

In step 2, NO2 is regenerated.

Remarks The SO3 (a secondary pollutant) formed then reacts with rain water

to form sulfuric acid.

SO3 (g) + H2O (l) → H2SO4 (aq)

A heterogeneous catalyst acts in a different physical state or phase from the reactants.

Usually involves a solid interacting with gaseous/liquid reactants.

Heterogeneous catalysts do not appear in the rate equation.

Their effect is included in the value of rate constant, k.

HETEROGENEOUS CATALYSIS

19

For a heterogeneous catalysis to occur, the reactant molecules need to be readily adsorbed onto

the catalyst surface. The heterogeneous catalyst provided active sites on its surface which there

can be formation of weak bonds between reactant molecules and the surface catalyst atoms.

The adsorption of the reactant molecules at the catalyst surface (i.e. weak bonds between

catalyst surface and reactant molecules) increases the rate of reaction.

1. The adsorption weakens the covalent bonds within the reactant molecules, thereby reducing the

activation energy for the reaction.

2. The adsorption increases the concentration of the reactant molecules at the catalyst surface and

allows the reactant molecules to come into close contact with proper orientation for the reaction.

Mode of Action of Heterogeneous Catalysts

Reaction: Haber Process

1. Diffusion

N2 and H2 diffuse towards the surface of

the Fe catalyst.

2. Adsorption

They are adsorbed onto the active sites

at the surface. Weak attraction forces are

formed. This increases the local

concentration of reactants and also

weakens the covalent bonds in the

molecules.

3. Reaction

Adjacent reactant molecules react to

form products. (This reaction has lower

activation energy than the uncatalysed

reaction.)

20

Catalytic Removal of Oxides of Nitrogen in the Exhaust Gases from Car Engines

A three-way catalytic converter consists of a ceramic honeycomb structure made from

alumina (Al2O3) coated with platinum (Pt), palladium (pd) and rhodium (Rh) which acts as

catalysts. A honeycomb structure is used to maximize the surface area on which the

heterogeneously catalyzed reactions take place.

The 3 catalysts are selective in the reactions they catalyzed.

1 Rhodium as catalyst

2NO (g) + 2CO(g) → 2CO2(g) + N2 (g)

NO2 (g) + 2CO (g) → 2CO2(g) + ½ N2 (g)

2 Palladium/Platinum as catalyst

2CO (g) + O2 (g) → 2CO2 (g)

3 Palladium/Platinum as catalyst

CxHy (g) + (x+𝑦

4) O2 (g) →

𝑦

2 H2O (g) + x CO2 (g)

4. Desorption

Product molecule, NH3, desorbs and

diffuses away from the catalyst surface.

The vacant active sites are now available

for adsorbing other reactant molecules.

The rate of reaction is controlled by how

fast the gaseous reactants are absorbed

and how fast the products are desorbed.

When the catalyst is saturated, there is

no increase in reaction rate even if the

pressure of the system increased.

Order of reaction with respect to reactant

molecules at saturation point is 0.

21

Autocatalysis is a type of catalytic reaction whereby the product of a reaction acts as a catalyst for

the reaction.

A reaction in which a product as a catalyst is said to be autocatalytic.

Mn2+ ions catalyst the reaction between manganite (VII) ions and ethanedioate ions:

2MnO4- (aq) + 16H+ (aq) + 5C2O4

2- (aq) → 2Mn2+ (aq) + 10CO2 (g) + 8H2O (l)

Hydrolysis of an ester produces ethanoic acid, which ionises slightly in aqueous mixture to give

H+ ion which acts as a catalyst for the reaction itself:

CH3CO2CH3 + H2O ⇌ CH3CO2H + C2H5OH

Graph of [reactant] Against Time for an Autocatalytic Reaction

Graph of Rate Against Time for an Autocatalytic Reaction

AUTOCATALYSIS

22

Biological catalysts that speed up reactions in living systems while remaining unchanged at the

end of reaction.

They are specific in their action.

They are proteins.

An enzyme has features of both a homogenous and a heterogeneous catalyst.

A substrate binds to the enzyme’s active site through intermolecular attractions like hydrogen

bonds or van der Waal’s forces.

It has no fixed order of reaction.

Mechanism of Enzyme Action

Enzyme + substrate ⇌ enzyme-substrate complex (fast)

Enzyme-substrate complex → enzyme + products (slow, rate-determining)

[Substrate] & Rate of an Enzyme-Catalysed Reaction

At low [substrate], enzyme concentration is greater than substrate concentration, rate of

reaction increases proportionally with increasing substrate concentration. Reaction is of first

order with respect to substrate.

At high [substrate], all the active sites are filled with substrate molecules and saturation point is

reached. Any further increase [substrate] does not affect rate of reaction. Reaction is of zero

order with respect to substrate.

To overcome such saturation point, increase [enzyme].

pH & Temperate on Enzyme Activity

At a high temperature, the attraction forces holding the specific three-dimensional shape of

the enzyme molecules are overcome, the enzyme is denatured. The denatured enzyme has a

random structure and the active site has been irreversibly distorted.

ENZYMES

23