Chemical KineticsBy

Dr. Amr Ibrahim

© Dr. Amr Ibrahim, 2010, all rights reserved. The commercial use of these slides withoutpermission is strictly prohibited.

What is chemical kinetics?

Chemical kinetics is the part of chemical science dealing with thestudy of the rates of chemical reactions and the factors which affectthe reaction rates.

Why studying chemical kinetics can be important for mechanicaland automotive engineers?

• combustion is a major chemical reaction which takes place ininternal combustion engines

• the combustion process greatly affects both engine performanceand emissions

• studying chemical kinetics can help in predicting major engineemissions such as CO & NOx emissions

• computer engine simulation (also called engine modeling) are usedto predict engine performance and emissions during engine designstage

• computer engine simulation is important in order to optimize theengine design parameters to reduce the emissions and improveengine performance

• the combustion is a very complicated process and it can not beaccurately simulated

Chemical reactions can be classified according to the speed ofreaction into:

• explosive reactions (very fast reactions)

• non explosive reactions

Chemical reactions can be classified according to the physical stateof the reacting substances into:

• gas phase reactions

• liquid phase reactions

• solid phase reactions

• heterogeneous reactions which occur at the interfaces of twosubstances of different faces such as gas-solid interfaces

The rate of chemical reaction depend on main factors which include:

• concentrations of chemical compounds

• temperature

• pressure

• presence of a catalyst or inhibitor

• The concentration of a substance for example A is usually given a symbol of [A] or CA

• concentration has units of mole/cm3

• concentration rate (e.g. ) has units of mole/cm3 s dtAd

Kinetic Theory of Gases:

A simple model for matter in the gas phase developed using kinetic theory of the microscopic world assumes that:

• Matter exists as discrete particles or molecules.

• Molecules can be treated ideally as small spheres of diameter σ.

• Mean distance between molecules >> σ.

• Molecules are in continuous three-dimensional motion.

• Each molecule moves in a random direction through space at a different speed.

•No appreciable inter-atomic forces exist between gas molecules except when they collide

Collision Theory and Chemical Reactions

Consider the reaction between A and B to form the products C and D:

• The molecules (or atoms) of A and B are assumed to be inert until theyapproach each other (collide)

• at that moment, re-arrangement of the molecular structure occurs leadingto new species C and D

• after C and D are formed, they separate from the molecular conversion siteand remain stable until they come into close contact with additionalmolecules

Elemental chemical reactions:

• Reaction equations that describe actual molecular activity occurring on the microscopic level are called elemental reactions

• an overall (or net or global) reaction equation, however, is not an example of an elemental reaction

• for example, the overall reaction of water production is

OHOH 222 22

• detailed studies show that the production of H2O from H2 and O2 is not produced by a single collision between the molecules of H2 and O2

• the production of H2O may be described by 38 elemental reactions including the following 2 elemental reactions:

OH+H2 → H2O+H

H+O2→ OH+O

• many reactive intermediates like H, O, and OH are formed during thisreaction

• most of chemical reactions are not one-step reactions, however, theycan be described by a group of elemental reactions

• chemical reactions which occur during the combustion process may bedescribed by hundreds of elemental chemical reactions

The activation energy:

• The activation energy (Ea) is the minimum energy required for thereaction to occur

• the colliding molecules must have a total kinetic energy equal to orgreater than Ea in order for the chemical reaction to start

• only those molecules which possess energy equal to or greater thanthe activation energy will react and these high energy active moleculeslead to products

The activated complex

• when the reacting molecules collide, they form a temporary(transitory) chemical species which is called the activated complex

• the activated complex is formed by the reacting colliding molecules asa result of the collision before they form the products

• consider the reaction between A and B to form C and D. The formationof the products is preceded by the production of the activated complex(X):

A+B → X → C+D

• the activated complex has a much higher reactivity than normal atoms

Example

Consider the reaction between NO2 and CO to form NO and CO2

NO2+CO→NO2CO→NO+CO2

• when the reacting molecules of NO2 and CO collide, they form atemporary molecule of NO2CO which is called the activated complex

• NO2CO is then converted to the products of NO and CO2

A+B

C+D

X

A+B

C+DX

An exothermic reaction

An endothermic reaction

E is the activation energy

RH is the energy release observed thermodynamically

• The activated complex (X) islocated at the point of highestenergy on the reaction path

• The activation energy is requiredto form X

Rprodreact HEE

Rprodreact HEE

• An external heat source such as aspark or a flame may be requiredto increase the reactants energy bythe activation energy so that thereaction starts

The stoichiometric coefficients

Consider the decomposition of nitrogen dioxide:

2NO2 → 2NO + O2

• the stoichiometric coefficient of the reactants is given the symbol

• the stoichiometric coefficient of the products is given the symbol

For the reactants: 22NO

For the products: 2NO 12O

The law of mass action:

The law of mass action, which is confirmed experimentally, states thatfor an elementary chemical reaction, the rate of reaction (RR) isproportional to the product of the concentrations of the reactingchemical species, where each concentration is raised to a power equalto the corresponding stoichiometric coefficient

Consider the previous example: 2NO2 → 2NO + O2

22NORR

22NOkRR

Where k is called the specific reaction rate constant and depends only on the temperature of the reaction

• The net rate of change of concentration of a chemical component A can be calculated by:

RR ννdtAd

AA

Consider the previous example: 2NO2 → 2NO + O2

22NO0

2NO

222 NOk 20

dtNOd

2NO 0NO

For NO2

For NO

22NOk 02dtNOd

For O2 12O 0

2O

222 NOk 01

dtOd

Concentration versus time for a decomposition reaction:

• The overall order of reaction is defined as

Example

Consider the reaction: H+O2 → OH+ O

Determine the reaction rate and the net rate of change of theconcentration of reactants and products. What are the units of k? whatis the order of the reaction?

RR = k [H] [O2]

For H: 0H 1H

2OHk 10dtHd

H+O2 → OH+ O

For O2: 02O 1

2O

22 OHk 10

dtOd

For OH: 1OH 0OH

2OHk 01dtOHd

For O: 1O 0O

2OHk 01dtOd

The units of the specific reaction rate constant, k, differ according to the type of reaction.

• The units of k: 2OHk dtOd

333 sec cmmole

cmmolek

cmmole

sec molecm3

The units of k are

• The overall order of reaction = 2112

OH

The reaction is a second order reaction

Equation of Arrhenius

)TR

Eexp(A ku

a

Where:

k = the specific reaction rate constant

A = a pre-exponential factor

Ea = the activation energy (J/mole)

Ru = the universal gas constant= 8.314 J/mole K

T = the temperature (K)

Note that the concentrations of the reactants and products can bemeasured at different times, and hence, k can be determinedexperimentally.

From Arrhenius equation:

TREAku

a lnln

The specific reaction rate constant, k, can be determined experimentallyat different temperatures. Hence, the activation energy can bedetermined by plotting (lnk) versus (1/T)

u

Note that the reaction rate constant depends on the temperature as well as the temperature range

Low temperature data

High temperaturedata

Opposing reactions

Generally, chemical reactions can proceed in both the forward direction(reactants forming products) and the reverse direction (products reforming thereactants) at the same time. For example:

322fk

bk2NH H3N

• Initially, N2 and H2 are mixed together, so the reaction proceeds only in theforward direction

• as time goes on, the ammonia is formed and some of it begins to breakdown to form N2 and H2

• overtime, as N2 and H2 are used up to form NH3, the rate of forwardreaction slows down. At the same time, the amount of NH3 gets larger andthe rate of backward reaction becomes greater.

•When the forward and backward reaction rates will be equal to eachother, there will be no net change in mixture chemical composition,and the mixture is said to be at chemical equilibrium

• At chemical equilibrium, the rate constants kf and kb are relatedthrough the equilibrium constant Kc

b

fc k

kK

Competitive reactions

A competitive reaction occurs when two or more sets of products are produced from the same set of reactants:

ABBA k 1

FEBA k 2

Consecutive reactions

In consecutive reactions, the products of one reaction undergo further reaction to give other products:

DCABBA kk 21

Chain reactions

• Chain reactions are the most common type of chemical reactions

• Chain reactions consist of a series of consecutive, competitive, andopposing reaction steps with different reaction rate constants

• These complex chemical reactions occur in all combustion processes