CHEMICAL REACTION ENGINEERING

Chapter 1: Chemical Reaction Kinetics

Prepared By: Engr. Carlos Miguel C. Dacaimat

Introduction:
What is Chemical Kinetics & Chemical
Topic Outline
Reaction Engineering?
• Introduction: What is Chemical Chemical Kinetics
Kinetics & Chemical Reaction - the area of chemistry concerned with the speeds, or
Engineering? rates, at which a chemical reaction occurs (Chang,
• Chemical Kinetics and Chemical 2010).
Reaction Engineering - the study of reaction rates which might depend on
• Classifications of Chemical variables that can be controlled, such as
Reactions pressure, temperature, or presence of a catalyst that
• Rate of a Chemical Reaction can optimize the reaction rate by appropriate
choice of conditions.
• Rate Equation (Rate Law)
- the branch of physical chemistry that deals with
• Concentration-Dependent Term of quantitative studies of the rates at which chemical
a Rate Equation processes occur, the factors on which these rates
• Elementary Reaction depend, and the molecular acts involved in reaction
• Nonelementary Reaction processes (Hill, 2014).
• Testing Kinetic Models - the study of chemical reaction rates and reaction
• Temperature-Dependent Term of a mechanisms (Fogler, 2022)
Rate Equation
Chemical Reaction
- a process in which a substance(s) is/are changed
into one or more new substances. (Chang, 2010).

Chemical Equation
- a representation using chemical symbols to show what happens during a chemical
reaction. (Chang, 2010).

Example: H2 + O2 → 2 H2O
C3H8 + O2 → 3 CO2 + H2O
NaOH + KCl → NaCl + KOH

Chemical Reaction Engineering

- the study of chemical kinetics associated with the reactors in which the chemical
reactions occur (Fogler, 2022).
- The synthesis of thermodynamics, chemical kinetics, fluid mechanics, heat transfer, mass
transfer and economics with the aim of properly designing a chemical reactor
(Levenspiel, 1999).
- It is used to accomplish the task of describing how to choose size, optimal operating
conditions for a reactor whose purpose is to produce a certain amount of substance.
(Davis & Davis, 2003)

Chemical Kinetics and Chemical Reaction Engineering

- the study of chemical kinetics will determine what a chemical reactor should be able to do
in which the data from the said study will be the basis for the reactor design for scaling
up to larger units (Levenspiel, 1999).

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

- For a chemically reacting system (that will be utilized for chemical reactor design), it give
answers to what changes are expected to occur and how fast they will occur (Davis &
Davis, 2003)
- Chemical engineers have traditionally approached kinetics studies with the goal of
describing the behavior of reacting systems in terms of macroscopically
observable quantities (Hill, 2014).

Classification of Chemical Reactions

According to Phases
1. Homogeneous Reactions – a chemical reaction that takes place within a single phase
only.

Example: H2(g) + Cl2(g) → 2 HCl(g)

C3H8 (g) + 5 O2(g) → 3 CO2 (g) + 4 H2O (g)
NaOH (aq) + HCl (l) → NaCl (aq) + H2O (l)

2. Heterogeneous Reactions - a chemical reaction at which the reactants and products

are in two or more phases.

Example: CaCO3 (s) → CaO (g) + CO2 (g)

CH4 (g) + 2 O2(g) → CO2 (g) +2 H2O (l)

According to Direction
1. Irreversible Reactions – a chemical reaction that occurs at a single direction only.

Example: H2(g) + Cl2(g) → 2 HCl(g)

NaOH (aq) + HCl (l) → NaCl (aq) + H2O (l)
2. Reversible Reactions - a chemical reaction at that occurs at forward and backward
directions.

Example: N2(g) + O2 (g) ⇌ 2 NO (g)

HSO4- ⇌ H+ + SO42-

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

3. Multiple Reactions - a chemical reaction that occur at multiple directions (series or

parallel reaction).

According to Catalyst

Catalyst
- a substance that influences the rate or the direction of a chemical reaction without being
appreciably consumed (Hill, 2014).
- a substance that affects the rate of a reaction but emerges from the process unchanged.
(Fogler, 2022)
- a substance that lowers the activation energy of a chemical reaction. (Fogler, 2022)

1. Catalytic Reactions – a chemical reaction that uses a catalyst.

Example: Hydrogenation of ethylene using a nickel catalyst

Oxidation of sulfur dioxide to sulfur trioxide using vanadium pentoxide

2. Noncatalytic Reactions - a chemical reaction without using a catalyst.

Example: Oxidation of NO to NO2

Combustion of Methane

According to Molecularity

Molecularity of a Chemical Reaction

- For an elementary reaction, it is the number of molecules involved in the chemical
reaction (Levenspiel, 1999).
- It is the number of chemical species involved in a single elementary reaction (Hill,
2014).
- It is the number of atoms, ions or molecules involved (colliding) in a single step
(reaction) (Fogler, 2022).

1. Unimolecular Reaction – a chemical reaction which one molecule of reactant

involved. [A → P]
2. Bimolecular Reaction – a chemical reaction which two molecules of reactant are
involved. [A + B → P ; A + A → P]
3. Termolecular Reaction – a chemical reaction which three molecules of reactant are
involved. [A + B + C → P]

Examples: H2O + CO2 → H2CO3 (Bimolecular)

2 H2 + O2 → 2 H2O (Termolecular)

According to Stoichiometry and Rate Correspondence

1. Elementary Reactions
– the reaction in which the molecules react exactly as the stoichiometric equation written
for a chemical equation.

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

– the reaction which are carried out in a single step.

– the reaction for which the order of the reaction matches the stoichiometric coefficient
in a given single chemical reaction.
– the reaction for which the stoichiometry and rate have direct correspondence.

2. Nonelementary Reactions
– the reaction which is carried out in several elementary reactions whose resultant
reaction may not be elementary.
– the reaction in which the rate equation does not obey the rate law for an elementary
reaction.
– the reaction for which the stoichiometry and rate have no direct
correspondence.

According to Heat Effects

Heats of Chemical Reaction

- refers to the change in enthalpy of the system for the chemical reaction to proceed at
constant temperature.

1. Exothermic Reaction
- a process or chemical reaction that gives off heat or transfers thermal energy to the
surroundings for the reaction to proceed.
[Recall: “-“ is sign convention for giving off heat from system to surroundings]

Example: CO (g) + ½ O2 (g) → CO2 (g) ΔHo = - 283.0 kJ/mol

2. Endothermic Reaction
- a process or chemical reaction that absorbs heat or transfers thermal energy to the
system for the reaction to proceed.
[Recall: “+“ is sign convention for absorbing heat from surroundings to system]

Example: CaCO3 (s) → CaO (g) + CO2 (g) ΔHo = + 177.8 kJ/mol

Rate of a Chemical Reaction

Rate of Chemical Reaction

- refers to the speed at which the reactants converted into products.
- It refers to the rate of formation of products or rate or disappearance of reactant
per unit of volume.

Definitions of Rate of Reaction (Levenspiel, 1999)

Definitions Rate of Reaction

1 𝑑𝑁𝑖 𝑚𝑜𝑙𝑒𝑠 𝑖 𝑓𝑜𝑟𝑚𝑒𝑑
Based on unit volume of reacting fluid 𝑟𝑖 = =
𝑉 𝑑𝑡 (𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑)(𝑡𝑖𝑚𝑒)

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

Definitions Rate of Reaction

Based on unit mass of solid in fluid-solid 1 𝑑𝑁𝑖 𝑚𝑜𝑙𝑒𝑠 𝑖 𝑓𝑜𝑟𝑚𝑒𝑑
𝑟𝑖 ′ = =
systems 𝑊 𝑑𝑡 (𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑)(𝑡𝑖𝑚𝑒)
Based on unit interfacial surface in two-fluid 1 𝑑𝑁𝑖 𝑚𝑜𝑙𝑒𝑠 𝑖 𝑓𝑜𝑟𝑚𝑒𝑑
systems or based on unit surface of solid in 𝑟𝑖 ′′ = =
𝑆 𝑑𝑡 (𝑠𝑢𝑟𝑓𝑎𝑐𝑒)(𝑡𝑖𝑚𝑒)
gas-solid systems
Based on unit volume of solid in gas-solid 1 𝑑𝑁𝑖 𝑚𝑜𝑙𝑒𝑠 𝑖 𝑓𝑜𝑟𝑚𝑒𝑑
𝑟𝑖 ′′′ = =
systems 𝑉𝑠 𝑑𝑡 (𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑)(𝑡𝑖𝑚𝑒)
1 𝑑𝑁𝑖 𝑚𝑜𝑙𝑒𝑠 𝑖 𝑓𝑜𝑟𝑚𝑒𝑑
Based on unit volume of reactor 𝑟𝑖 ′′′′ = =
𝑉𝑟 𝑑𝑡 (𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑜𝑟)(𝑡𝑖𝑚𝑒)

Reaction Rate Relations 𝑉𝑟𝑖 = 𝑊𝑟𝑖 ′ = 𝑆𝑟𝑖 ′′ = 𝑉𝑠 𝑟𝑖 ′′′ = 𝑉𝑟 𝑟𝑖 ′′′′

Factors Affecting the Rate of Reaction

1. Nature of Reactants and Products
2. Concentration of Reactants
3. Temperature of a System
4. Pressure of a System
5. Nature of Catalyst
6. Surface Area of Reactants
7. Heat and Mass Transfer Rates

Rate Equation (Rate Law)

- expresses the relationship of the rate of a reaction to the rate constant and the
concentrations of the reactants raised to some powers (Chang, 2010).
- equations that give the rate of reaction as a function of the reacting species
concentrations and of temperature in a specific reaction (Fogler, 2022).

Relative Rates of Reaction

- it tells how fast one species is disappearing or appearing relative to the other species in
the given reaction (Fogler, 2022).

1. Rate of Formation (+r or r) – refers to the speed at which products from a chemical
equation are formed during reaction.

2. Rate of Disappearance (-r) – refers to the speed at which reactants from a chemical
equation is disappeared during reaction.

Consider the stoichiometric equation:

aA + bB → cC + dD

a, b, c, d = stoichiometric coefficients
A, B, C, D = molecules (A, B are reactants and C, D are products)

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

𝒓𝑨 𝒓𝑩 𝒓𝑪 𝒓𝑫
Relative Rates of Reaction: − =− = =
𝒂 𝒃 𝒄 𝒅
Example: Given the following chemical reaction:

2 NO(g) + O2(g) → 2 NO2(g)

If NO2 is formed at a rate of 4 mol m-3 s-1, what are the rates of disappearance of
NO and O2 molecules?

Solution:
𝒓𝑨 𝒓𝑩 𝒓𝑪 𝒓𝑫
− =− = =
𝒂 𝒃 𝒄 𝒅

Rewrite the equation in terms of NO, O2 and NO2:

𝑟𝑁𝑂 𝑟𝑂 𝑟𝑁𝑂2
− =− 2=
2 1 2
𝑟𝑁𝑂 𝑟𝑁𝑂2
− = −𝑟𝑂2 =
2 2
Solving for the rates of disappearance of NO and O2:

𝑚𝑜𝑙
𝑟𝑁𝑂2 4 𝑚3 − 𝑠 𝒎𝒐𝒍
−𝑟𝑂2 = = = 𝟐 𝟑
2 2 𝒎 −𝒔
𝑟𝑁𝑂
− = −𝑟𝑂2
2
𝑚𝑜𝑙 𝒎𝒐𝒍
−𝑟𝑁𝑂 = 2(−𝑟𝑂2 ) = 2 (2 3 )= 𝟒 𝟑
𝑚 −𝑠 𝒎 −𝒔
Net Rates
- for a formation of a given species, it is the sum of the rate of reactions of A in all the
reactions in which A is either a reactant or product in the system. (Fogler, 2022).

Concentration-Dependent Term of a Rate Equation

For various chemical reactions, the rate of reaction with respect to a reactant (usually limiting
reactant) can be written as a function of a rate constant and function of concentrations of
various chemical species involved in the reaction:

rate of disappearance of 𝐴 = −𝑟𝐴 = 𝑘𝐴 𝑓(𝐶𝐴 , 𝐶𝐵 , … )

kA = rate constant
CA, CB, … = concentration of reactants A, B, …

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

Elementary Reactions
– the reaction for which the stoichiometry and rate have direct correspondence.
– the reaction in which the molecules react exactly as the stoichiometric equation written
for a reaction.

When to say that a chemical reaction is an elementary reaction?

- the reaction which are carried out in a single step.
- the reaction for which the order of the reaction matches the stoichiometric
coefficient in a given single chemical reaction.

Molecularity and Order of Reaction

Molecularity of a Chemical Reaction

- It is the number of chemical species involved in a single elementary reaction (Hill,
2014).
- The molecularity of a chemical reaction can be (most of the time) unimolecular,
bimolecular, or trimolecular.

Order of Reaction
- in a rate equation of an elementary reaction, it is the powers (or exponents) to which the
concentrations are raised.

What is the difference between molecularity and order?

- Molecularity is a theoretical quantity only, whereas the order can be either a
theoretical and/or experimental quantity.
- Molecularity of a reaction must be a whole number and never be zero or a fraction,
whereas the order of a reaction may be whole number, zero or a fraction.

Overall Order of Reaction

- in a rate equation of an elementary reaction, it is the sum of powers (or order).
(n = a + b + c + …)

Consider the stoichiometric equation:

aA + bB + … → rR

a, b, r = stoichiometric coefficients
A, B, R = molecules (A, B are reactants and R are products)

Rate Equation: −𝒓𝑨 = 𝒌𝑪𝒂𝑨 𝑪𝒃𝑩 … = 𝒌[𝑨]𝒂 [𝑩]𝒃 …

a th order with respect to A
Order of the Reaction: b th order with respect to B
n th (or a+b)th (overall order)

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

Example: Given the following chemical reaction:

H2(g) + Br2(g) → 2 HBr(g)

a) What is the molecularity of the chemical reaction?

b) Write the relative rates of formation and disappearance.
c) Write the rate equation with respect to reactant Br2?
d) Identify the order of the reaction with respect to each reactant.
e) What is the overall order of the reaction?

Solution:
a) Since there are two (2) molecules of chemical species involved, the chemical
reaction is bimolecular.
b) The relative rate of the chemical reaction can be written as:

𝑟𝐴 𝑟𝐵 𝑟𝐶 𝑟𝐷
− =− = =
𝑎 𝑏 𝑐 𝑑
Writing the relative rate based on the given reactant and stoichiometric
coefficient:

𝑟𝐻2 𝑟𝐵𝑟 𝑟𝐻𝐵𝑟

− =− 2 =
1 1 2
𝒓𝑯𝑩𝒓
−𝒓𝑯𝟐 = −𝒓𝑩𝒓𝟐 =
𝟐
c) The rate equation can be written as:

−𝒓𝑯𝟐 = −𝒓𝑩𝒓𝟐 = 𝒌𝑪𝑯𝟐 𝑪𝑩𝒓𝟐 = 𝒌[𝑯𝟐 ][𝑩𝒓𝟐 ]

d) The chemical reaction is first order with respect to H2, first order with
respect to Br2
e) Since both stoichiometric coefficients are equal to one (1), then the overall
order is (1+1=2). Hence, the overall reaction order is 2nd order.

Rate Constant (k)

– A measure of the rate of chemical reaction when all the reactants are at unit
concentration.

Unit(s) of a Rate Constant

for an nth order reaction: 𝒌 = (𝒕𝒊𝒎𝒆)−𝟏 (𝒄𝒐𝒏𝒄𝒆𝒏𝒕𝒓𝒂𝒕𝒊𝒐𝒏)𝟏−𝒏

Kinetic Models for Elementary Reactions

Given an elementary reaction, with a schematic chemical reaction and its stoichiometry as
[A → P], the following rate equation can be written as follows:

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

Order n Rate Equation Rate Constant Units

Zero 0 −𝑟𝐴 = 𝑘 (time)−1 (concentration)1
One 1 −𝑟𝐴 = 𝑘[𝐴] (time)−1
Two 2 −𝑟𝐴 = 𝑘[𝐴]2 (time) (concentration)−1
−1

Third 3 −𝑟𝐴 = 𝑘[𝐴]3 (time)−1 (concentration)−2

nth n −𝑟𝐴 = 𝑘[𝐴]𝑛 (time)−1 (concentration)1−n

For other elementary reaction schemes, the following rate equation can be written as follows:

Stoichiometry Rate Equation

A+B→P −𝑟𝐴 = 𝑘[𝐴][𝐵]
A + 2B → P −𝑟𝐴 = 𝑘[𝐴][𝐵]2
A + 2B + 3C→ P −𝑟𝐴 = 𝑘[𝐴][𝐵]2 [𝐶]3

Nonelementary Reactions
– the reaction for which the stoichiometry (order of the reaction) and rate have no
direct correspondence.
– the reaction may follow series of elementary reaction in which some chemical
species may act as an intermediate.
– the stoichiometric equation for non-elementary reaction reflects only the initial and
states of the reaction system involved and failed to describe the mechanism of a
reaction in details.
– the key to identify the connection between the rate and stoichiometry is the
identification of reaction mechanism that will lead to the net stoichiometry or
chemical equation.

Example:
Stoichiometry: CO(g) + Cl2(g) → COCl2(g)
3
Rate: −𝑟𝐶𝑂 = 𝑘[𝐶𝑂][𝐶𝑙2 ]2
Rate (if elementary): −𝑟𝐶𝑂 = 𝑘[𝐶𝑂][𝐶𝑙2 ]

If NO2 is formed at a rate of 4 mol m-3 s-1, what are the rates of disappearance of
NO and O2 molecules?

Kinetic Models for Nonelementary Reactions

– It is assumed that the overall reaction is the result of a series of elementary or
nonelementary reactions that involve in the formation and subsequent reaction of
intermediate chemical species.
– The intermediates are present in very short span of time and thus undetected.
– To determine the kinetic models, a series of reaction is proposed through reaction
mechanism, determine its correspondence to the experimental model, otherwise
develop an alternative kinetic model.
– the reaction may follow series of elementary reaction in which some chemical
species may act as an intermediate.

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

– the stoichiometric equation for non-elementary reaction reflects only the initial and
states of the reaction system involved and failed to describe the mechanism of a
reaction in details.
– the key to identify the connection between the rate and stoichiometry is the
identification of reaction mechanism that will lead to the net stoichiometry or
chemical equation.

Reaction Mechanism
– it refers to the step or series of steps by which the initial reactants interact in the
process of forming products.

Intermediates
– it is the transient species within a multistep reaction that is produced in the
preceding step and consumed in a subsequent step for the formation of product in the
given chemical equation.
– it is chemical species that has zero net formation in a multistep reaction.

Types of Intermediates

1. Free Radicals
– it is the free atoms or larger fragments of stable molecules that contain one or
more unpaired electrons.
– these are molecules that are known to be unstable and highly reactive.
2. Ions and Polar Substances
– Electrically charged atoms, molecules or fragment of molecules.
3. Molecules
– it is the chemical species that is highly reactive, that is presence is very short or
its concentration is relatively negligible to measure.
– it is considered as a stable but a reactive intermediate.
4. Transition Complexes
– it refers to the unstable forms of molecules due to possible numerous collisions
and wide distribution of energies among individual molecules that lead to various
unstable association of molecules which decompose to give products or by further
collision return to the molecule in the normal and stable form.

Reaction Mechanism Schemes

1. Nonchain Reactions
– the reaction in which the intermediate is formed in the first reaction and then
disappears as it reacts further to form the final product.
2. Chain Reactions
– the reaction in which the reactants form an intermediate through an initiation step,
then the intermediate combines with the reactant producing more intermediate and
product through a propagation step, then the intermediate disappear through the
termination step.

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

Non-Chain Reaction Chain Reaction

Net Stoichiometry R→P R→P

R → I*
R → I*
Reaction Mechanism R + I* → I* + P
I* → P
I* → P

where R is reactant, I* is an intermediate and P is product

Testing Kinetic Models for Nonelementary Reactions

– to test the correspondence between experiment and a proposed reaction mechanism
scheme, it is important that each reaction step in the said scheme must have an
appropriate rate equation based on the rate law determined for an elementary
reaction.
– In matching the proposed reaction mechanism with the nonelementary rate equation,
the following rules shall be as follows:
1. If any chemical species take part in more than one reaction then its net rate of
change is equal to the sum of the rates of change of component of that
corresponding chemical species in each of the elementary reactions in which it is
participated.

𝑟𝑖 (𝑛𝑒𝑡) = ∑ 𝑟𝑖 (participated reactions)

2. Since intermediates (I*) are highly reactive and present in a very short span of
time or its concentration is almost negligible, the net rate of formation of an
intermediate is assumed to be zero. (Steady-State Approximation)

rate of formation of 𝐼 ∗ = 𝑟𝐼∗ ≅ 0

Hypothesized Elementary Reaction for Intermediates

1. Type 1
– an unseen and unmeasured intermediate X* usually present at such small
concentration that its rate of change in the mixture can be taken to be zero.

𝑑[𝑋 ∗ ]
[𝑋 ∗ ] ≪ 0; ≅0
𝑑𝑡
2. Type 2
– Whenever a homogeneous catalyst with initial concentration C0 is present in two forms
– (1) as a free catalyst C and (2) in combination with reactant to form active
intermediate X*, an accounting for the catalyst gives:

[𝐶0 ] = [𝐶] + [𝑋]

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
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– It is also assumed that the intermediate is in equilibrium or its rate of formation is zero

𝐴+𝐶 ⇌ 𝑋*
where
𝑑[𝑋 ∗ ]
=0
𝑑𝑡
and
𝑘1 [𝑋]
𝐾= =
𝑘2 [𝐴][𝐶]

Guidelines in Determining the Feasibility of a Proposed Reaction Mechanism

(Hill, 2014)
1. The most fundamental basis for mechanistic speculation is a complete analysis of the
reaction products.
2. The atomic and electronic structure of the reactants and products may provide important
clues as to the nature of possible intermediate species.
3. All of the elementary reactions involved in a mechanistic sequence must be feasible with
respect to bond energies.
4. A number of elementary reactions sufficient to provide a complete path for the formation
of all observed products must be employed.
5. All of the intermediates produced by the elementary reactions must be consumed by other
elementary reactions so that there will be no net production of intermediate species.
6. The great majority of known elementary steps are bimolecular, the remainder being
unimolecular or termolecular.
7. A mechanism postulated for a reaction in the forward direction must also hold for the
reverse reaction.
8. Transitory intermediates (highly reactive species) do not react preferentially with one
another to the exclusion of their reaction with stable species.
9. When the overall order of a reaction is greater than 3, the mechanism probably has one
or more equilibria yielding intermediates prior to the rate-determining step.
10. Inverse (negative) orders arise from rapid equilibria prior to the rate-determining step.
11. Whenever a rate law contains non-integer orders, there are intermediates present in the
reaction sequence.
12. If the magnitude of the stoichiometric coefficient of a reactant exceeds the order of the
reaction with respect to that species, there are one or more intermediates and reactions
after the rate-determining step.
13. If the order of a reaction with respect to one or more species increases as the
concentration of that species increases, this is an indication that the reaction may be
proceeding by two or more parallel paths.
14. If there is a decrease in the order of a reaction with respect to a particular substance as
the concentration of that species increases, the dominant form of that species in solution
may be undergoing a change brought about by the change in concentration.

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
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Sample Problem: Given the chemical reaction and rate equation, prove the rate equation
by proposing a series/sequence of reactions.

A + B → AB rAB = k[B]2

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

Temperature-Dependent Term of a Rate Equation

- For various chemical reactions, the rate of reaction at different temperature varies.
- The rate constant k is the typical parameter that varies the reaction rate at different
temperatures.
- The rate constant generally varies with the absolute temperature T of the system
according to Arrhenius Law:
k = 𝐴𝑒 −𝐸/𝑅𝑇
k = rate constant
A = frequency factor
e = exponential number (2.71828…)
E = Activation Energy (kJ/mol)
R = Ideal Gas Constant (8.314 J/mol - K)
T = Absolute Temperature (in Kelvin, K)

- At the same concentration but at two different temperatures, Arrhenius’ Law can be
written as:
𝑘2 𝐸 1 1
ln = ( − )
𝑘1 𝑅 𝑇1 𝑇2

k1 = rate constant at absolute temperature 1, T1

k2 = rate constant at absolute temperature 2, T2

Activation Energy
- The minimum amount of energy which the colliding molecules must have in order to
bring a reaction.
- It is the minimum amount energy that must be possessed by reacting molecules before
the reaction will occur for converting it into products.

Activation Energy and Temperature Dependency

- From Arrhenius’ Law, there is linear relationship between ln k and 1/T whose slope
are large slope corresponds for large E and small slope corresponds for small E.
- Reactions with high activation energies are very temperature sensitive and
reactions with low activation energies are very temperature insensitive.

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 CHEMICAL REACTION ENGINEERING
Chapter 1: Chemical Reaction Kinetics
Prepared By: Engr. Carlos Miguel C. Dacaimat

References

Chang, R. M. (2010). Chemistry (10th ed.). McGraw-Hill

Davis, M. E., & Davis, R. J. (2003). Fundamentals of Chemical Reaction Engineering (1st ed.).
McGraw-Hill

Fogler, H. S. (2022). Elements of Chemical Reaction Engineering (6th ed.). Prentice-Hall

Hill, C. G. Jr., & Root, T. W. (2014). Introduction to Chemical Engineering Kinetics & Reactor
Design (2nd ed.). Wiley.

Levenspiel, O. (1999). Chemical Reaction Engineering (3rd ed.). John Wiley & Sons, Inc.

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