Chemical Kinetics Lesson 18 by Owen Borville 11.1.2025
Chemical kinetics is the study of the rate of chemical reactions, which can vary significantly depending on the chemicals involved. Increasing the rate of a reaction is important to many industrial processes and therefore it is beneficial to mankind.
Most reactions occur faster at higher temperature. Chemical reactions usually occur as a result of collisions between reacting molecules.
Collision theory of chemical kinetics: the reaction rate is directly proportional to the number of molecular collisions per second:
Rate ∝ number of collisions/second
Effective collisions are collisions that result in a chemical reaction.
Activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction. Molecules must also be oriented in a way that favors reaction.
Ineffective collisions are collisions that do not result in a chemical reaction.
Activated complex (or transition state) is formed by molecules when they collide in an effective collision.
In graphical representation of collisions of kinetic energy and number of molecules, the blue curve line represents a collection of molecules at a lower temperature. The red curve line represents a collection of molecules at a higher temperature. At the higher temperature more molecules have enough energy to exceed the activation energy and undergo efficient collisions.
Chemical kinetics is the study of how fast reactions take place, or the rate of chemical reactions over a certain time period. Rate is always a positive quantity.
A => B
Rate = -Δ[A]/Δt ([A] decreases)
Rate = Δ[B]/Δt
The average reaction rate of two different molecules can be plotted on a graph featuring number of molecules on the y axis and time on the x axis. As the number of molecules increases, time also increases. As the number of molecules decreases, time also decreases.
Average reaction rate is =
-Δ[A]/Δt=
-([A]final - [A] initial)/(t(final) - t(initial))
Average reaction rate can also be shown on a graphical plot of absorption versus wavelength (nm) of different rate time curves. Reaction rates are recorded in table form at a certain temperature and various time intervals, showing the concentration available at each time interval and the rate at each time interval.
A graphical plot can also show the rate increase as the concentration of a substance increases.
The instantaneous rate is the rate of reaction for a specific instant in time. The rate of reaction can also be calculated for a particular time interval, such as 50 seconds or 100 seconds by measuring the concentration of a substance during the time interval.
The rate constant (k) for substance A is notated as
rate ∝ [A] or
rate = k[A]
k = rate/[A] at a particular time interval
rate = Δ[A]/Δt = (1/RT)(ΔPA/Δt)
Stoichiometry and Reaction Rate:
aA + bB => cC + dD (lowercase letter represents number of moles or stochiometric coefficient, uppercase letter represents the substance)
rate = -Δ[A]/aΔt = -Δ[B]/bΔt = Δ[C]/cΔt = Δ[D]/dΔt
The Rate Law: Dependence of Reaction Rate on Reactant Concentration: The rate law is an equation that relates the rate of reaction to the concentrations of reactants.
aA + bB =>cC + dD
rate = 𝑘[A]^x[B]^y
k = the rate constant (determined experimentally)
x = order with respect to A (determined experimentally)
y = order with respect to B (determined experimentally)
x + y is the overall reaction order
The initial rate is the instantaneous rate at the beginning of the reaction.
Reaction order is the exponent to which a reactant's concentration is raised in the rate law, indicating how that reactant's concentration affects the reaction rate. The overall reaction order is the sum of all individual reaction orders in the rate law. A reaction that is first-order in a reactant will have a rate that doubles if the reactant's concentration is doubled.
Between the reaction of two substances, if the concentration of one substance is doubled while the concentration of the other substance is the same but the reaction rate doubles, the reaction is first order, x = 1 If the concentration is quadrupled, the rate will also quadruple in a first-order reaction, so it is directly proportional.
In a second order reaction, x = 2, the rate is proportional to the square of the concentration of that reactant, so doubling the concentration will quadruple the rate.
The units of a rate constant depend on the overall order of the reaction.
Reaction order 0, rate = k, units = M * s-1
Reaction order 1, rate = k[A] or k[B], units = s-1
Reaction order 2, rate = k[A]^2, k[B]^2, or k[A][B], units = M-1*s-1
Reaction order 3, rate = k[A]^2[B] or rate = k[A][B]^2, units = M-2*s-1
Rate Law: (1) The exponents in a rate law must be determined from a table of experimental data. (2) Comparing changes in individual reactant concentrations with changes in rate shows how the rate depends on each reactant concentration. (3) Reaction order is always defined in terms of reactant concentrations, never on product concentrations.
Dependence of Reactant Concentration on Time: The rate law can be used to determine the rate of a reaction using the rate constant and the reactant concentrations:
rate = k[A]^x[B]^y A rate law can also be used to determine the concentration of a reactant at a specific time during a reaction.
First order reaction: is a reaction whose rate depends on the concentration of one of the reactants raised to the first power. rate = k[A].
In a first-order reaction of the type A => products,
The rate can be expressed as the rate of change in reactant concentration, rate = -Δ[A]/Δt
as well as in the form of the rate law, rate = k[A]
Setting these two expressions equal to each other gives -Δ[A]/Δt = k[A]
Using calculus, it is possible to show that:
ln([A]t/[A]0) = -kt (integrated rate law for a first order reaction)
ln is the natural logarithm
[A]0 and [A]t refer to the concentration of A at times 0 and t
Rearrangement of the first-order integrated rate law gives:
ln[[A]t/[A]0) = -kt
ln[A]t = -kt + ln[A]0 (This is the form of the linear equation y=mx + b)
Slope = -k
Y-Intercept = ln[A]0
Half-life (t1/2) is the time required for the reactant concentration to drop to half its original value.
ln([A]t/[A]0) = -kt rearranges to t = (1/k)ln([A]0/[A]t)
t = t1/2 when [A]t = 1/2[A]0
t1/2 = (1/k)ln[A]0/([A]0/2) simplifies to t1/2 = 0.693/k
The half life (t1/2) is the time required for the reactant concentration to drop to half its original value. t1/2 = 0.693/k
Second-order reaction is a reaction whose rate depends on the concentration of one reactant raised to the second power or on the product of the concentrations of two different reactants (first order in each).
Second order integrated rate law:
1/[A]t = kt + 1/[A]0
Second order half-life:
t1/2 = 1/k[A]0
The rate of a zero-order reaction is a constant.
[A]t = -kt + [A]0 integrated rate law for Zero-th order
t1/2 = [A]0/2k for Zero-th order
Third order and higher are rare.
Dependence of Reaction Rate on Temperature: The Arrhenius Equation: The dependence of the rate constant on temperature can be expressed by the Arrhenius equation.
k = Ae^-Ea/RT
A is the collision frequency (frequency factor)
Ea is the activation energy (in kJ/mol)
R is the gas constant (8.314 j/mol*K)
T is the absolute temperature
e is the base of the natural logarithm
Taking the natural log of both sides, the Arrhenius equation may be written as:
lnk = lnA - Ea/RT
Rearrangement gives the linear form of the Arrhenius equation:
lnk = (-Ea/R)(1/T) + lnA
Two point form of the Arrhenius equation is:
ln(k1/k2) = (Ea/R)[1/T2)-(1/T1)]
If the rate constants at two different temperatures are known, it is possible to calculate the activation energy. If the activation energy and rate constant at one temperature are known, it is possible to determine the rate constant at any other temperature.
Reaction Mechanisms: A balanced chemical equation does not indicate how a reaction actually takes place. Reaction mechanisms are the sequence of steps that sum to give the overall reaction.
Step 1: A + B => C
Step 2: C + B => D (C's cancel out)
Overall Reaction: A + 2B =>D
Intermediates are chemical species that appear in the reaction mechanism, but not in the overall chemical reaction.
Step 1: AB + AB => A2B2
Step 2: A2B2 + B2 => 2AB2
Overall Reaction: 2AB + A2 => 2AB2
A2B2 is an intermediate.
Elementary Reactions: Each step in a reaction mechanism represents an elementary reaction, one that occurs in a single collision of the reactant molecules. The molecularity of an elementary reaction is essentially the number of reactant molecules involved in the collision.
unimolecular (one reactant molecule)
A => products
rate = k[A]
first order
bimolecular (two reactant molecules)
A + B => products
rate = k[A][B]
second order
A + A => products
rate = k[A]^2
second order
termolecular (three reactant molecules)
Rate-determining Step: gives the rate law for the overall process in a reaction mechanism consisting of more than the elementary step. The rate-determining step is the slowest step in the sequence. A proposed mechanism must satisfy two requirements: (1) The sum of the elementary reaction must be the overall balanced equation for the reaction. (2) The rate-determining step must have the same rate law as that determined from the experimental data.
Mechanisms with a Fast First Step: Not all reactions have a single rate-determining step, however.
Experimental Support for Reaction Mechanisms: It is not possible to prove that a mechanism is correct using rate data alone. To determine whether or not a proposed reaction mechanism is actually correct, we must conduct other experiments.
Catalysts are substances that increase the rate of a chemical reaction without itself being consumed. A catalyst speeds up a reaction by providing a set of elementary steps with more favorable kinetics than those that exist in its absence. A catalyst usually speeds up a reaction by lowering the activation energy.
Catalytic rate constant: When there is a catalyst in a reaction, the rate constant is kc, called the catalytic rate constant.
Heterogenous catalysis occurs when the reactants and the catalysts are in different phases.
Homogeneous catalysis occurs when the reactants and the catalysts are dispersed in a single phase, usually liquid. Advantages of this are reactions can be carried out under atmospheric conditions, can be designed to function selectively, and are generally cheaper.
Enzymes are biological catalysts. The mathematical treatment of enzyme kinetics is complex, but can be simplified to:
E + S (k1) ⇌ (k-1) ES
ES (k2) => E + P
Generally the rate of an enzyme catalyzed reaction is given by the equation:
rate = Δ[P]/Δt = k[ES]
This equation produces a mathematical curve when plotted on a graph of [S] concentration versus rate of product formation. This is a rapidly increasing curve that flattens out near horizontally.
Chemical kinetics is the study of the rate of chemical reactions, which can vary significantly depending on the chemicals involved. Increasing the rate of a reaction is important to many industrial processes and therefore it is beneficial to mankind.
Most reactions occur faster at higher temperature. Chemical reactions usually occur as a result of collisions between reacting molecules.
Collision theory of chemical kinetics: the reaction rate is directly proportional to the number of molecular collisions per second:
Rate ∝ number of collisions/second
Effective collisions are collisions that result in a chemical reaction.
Activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction. Molecules must also be oriented in a way that favors reaction.
Ineffective collisions are collisions that do not result in a chemical reaction.
Activated complex (or transition state) is formed by molecules when they collide in an effective collision.
In graphical representation of collisions of kinetic energy and number of molecules, the blue curve line represents a collection of molecules at a lower temperature. The red curve line represents a collection of molecules at a higher temperature. At the higher temperature more molecules have enough energy to exceed the activation energy and undergo efficient collisions.
Chemical kinetics is the study of how fast reactions take place, or the rate of chemical reactions over a certain time period. Rate is always a positive quantity.
A => B
Rate = -Δ[A]/Δt ([A] decreases)
Rate = Δ[B]/Δt
The average reaction rate of two different molecules can be plotted on a graph featuring number of molecules on the y axis and time on the x axis. As the number of molecules increases, time also increases. As the number of molecules decreases, time also decreases.
Average reaction rate is =
-Δ[A]/Δt=
-([A]final - [A] initial)/(t(final) - t(initial))
Average reaction rate can also be shown on a graphical plot of absorption versus wavelength (nm) of different rate time curves. Reaction rates are recorded in table form at a certain temperature and various time intervals, showing the concentration available at each time interval and the rate at each time interval.
A graphical plot can also show the rate increase as the concentration of a substance increases.
The instantaneous rate is the rate of reaction for a specific instant in time. The rate of reaction can also be calculated for a particular time interval, such as 50 seconds or 100 seconds by measuring the concentration of a substance during the time interval.
The rate constant (k) for substance A is notated as
rate ∝ [A] or
rate = k[A]
k = rate/[A] at a particular time interval
rate = Δ[A]/Δt = (1/RT)(ΔPA/Δt)
Stoichiometry and Reaction Rate:
aA + bB => cC + dD (lowercase letter represents number of moles or stochiometric coefficient, uppercase letter represents the substance)
rate = -Δ[A]/aΔt = -Δ[B]/bΔt = Δ[C]/cΔt = Δ[D]/dΔt
The Rate Law: Dependence of Reaction Rate on Reactant Concentration: The rate law is an equation that relates the rate of reaction to the concentrations of reactants.
aA + bB =>cC + dD
rate = 𝑘[A]^x[B]^y
k = the rate constant (determined experimentally)
x = order with respect to A (determined experimentally)
y = order with respect to B (determined experimentally)
x + y is the overall reaction order
The initial rate is the instantaneous rate at the beginning of the reaction.
Reaction order is the exponent to which a reactant's concentration is raised in the rate law, indicating how that reactant's concentration affects the reaction rate. The overall reaction order is the sum of all individual reaction orders in the rate law. A reaction that is first-order in a reactant will have a rate that doubles if the reactant's concentration is doubled.
Between the reaction of two substances, if the concentration of one substance is doubled while the concentration of the other substance is the same but the reaction rate doubles, the reaction is first order, x = 1 If the concentration is quadrupled, the rate will also quadruple in a first-order reaction, so it is directly proportional.
In a second order reaction, x = 2, the rate is proportional to the square of the concentration of that reactant, so doubling the concentration will quadruple the rate.
The units of a rate constant depend on the overall order of the reaction.
Reaction order 0, rate = k, units = M * s-1
Reaction order 1, rate = k[A] or k[B], units = s-1
Reaction order 2, rate = k[A]^2, k[B]^2, or k[A][B], units = M-1*s-1
Reaction order 3, rate = k[A]^2[B] or rate = k[A][B]^2, units = M-2*s-1
Rate Law: (1) The exponents in a rate law must be determined from a table of experimental data. (2) Comparing changes in individual reactant concentrations with changes in rate shows how the rate depends on each reactant concentration. (3) Reaction order is always defined in terms of reactant concentrations, never on product concentrations.
Dependence of Reactant Concentration on Time: The rate law can be used to determine the rate of a reaction using the rate constant and the reactant concentrations:
rate = k[A]^x[B]^y A rate law can also be used to determine the concentration of a reactant at a specific time during a reaction.
First order reaction: is a reaction whose rate depends on the concentration of one of the reactants raised to the first power. rate = k[A].
In a first-order reaction of the type A => products,
The rate can be expressed as the rate of change in reactant concentration, rate = -Δ[A]/Δt
as well as in the form of the rate law, rate = k[A]
Setting these two expressions equal to each other gives -Δ[A]/Δt = k[A]
Using calculus, it is possible to show that:
ln([A]t/[A]0) = -kt (integrated rate law for a first order reaction)
ln is the natural logarithm
[A]0 and [A]t refer to the concentration of A at times 0 and t
Rearrangement of the first-order integrated rate law gives:
ln[[A]t/[A]0) = -kt
ln[A]t = -kt + ln[A]0 (This is the form of the linear equation y=mx + b)
Slope = -k
Y-Intercept = ln[A]0
Half-life (t1/2) is the time required for the reactant concentration to drop to half its original value.
ln([A]t/[A]0) = -kt rearranges to t = (1/k)ln([A]0/[A]t)
t = t1/2 when [A]t = 1/2[A]0
t1/2 = (1/k)ln[A]0/([A]0/2) simplifies to t1/2 = 0.693/k
The half life (t1/2) is the time required for the reactant concentration to drop to half its original value. t1/2 = 0.693/k
Second-order reaction is a reaction whose rate depends on the concentration of one reactant raised to the second power or on the product of the concentrations of two different reactants (first order in each).
Second order integrated rate law:
1/[A]t = kt + 1/[A]0
Second order half-life:
t1/2 = 1/k[A]0
The rate of a zero-order reaction is a constant.
[A]t = -kt + [A]0 integrated rate law for Zero-th order
t1/2 = [A]0/2k for Zero-th order
Third order and higher are rare.
Dependence of Reaction Rate on Temperature: The Arrhenius Equation: The dependence of the rate constant on temperature can be expressed by the Arrhenius equation.
k = Ae^-Ea/RT
A is the collision frequency (frequency factor)
Ea is the activation energy (in kJ/mol)
R is the gas constant (8.314 j/mol*K)
T is the absolute temperature
e is the base of the natural logarithm
Taking the natural log of both sides, the Arrhenius equation may be written as:
lnk = lnA - Ea/RT
Rearrangement gives the linear form of the Arrhenius equation:
lnk = (-Ea/R)(1/T) + lnA
Two point form of the Arrhenius equation is:
ln(k1/k2) = (Ea/R)[1/T2)-(1/T1)]
If the rate constants at two different temperatures are known, it is possible to calculate the activation energy. If the activation energy and rate constant at one temperature are known, it is possible to determine the rate constant at any other temperature.
Reaction Mechanisms: A balanced chemical equation does not indicate how a reaction actually takes place. Reaction mechanisms are the sequence of steps that sum to give the overall reaction.
Step 1: A + B => C
Step 2: C + B => D (C's cancel out)
Overall Reaction: A + 2B =>D
Intermediates are chemical species that appear in the reaction mechanism, but not in the overall chemical reaction.
Step 1: AB + AB => A2B2
Step 2: A2B2 + B2 => 2AB2
Overall Reaction: 2AB + A2 => 2AB2
A2B2 is an intermediate.
Elementary Reactions: Each step in a reaction mechanism represents an elementary reaction, one that occurs in a single collision of the reactant molecules. The molecularity of an elementary reaction is essentially the number of reactant molecules involved in the collision.
unimolecular (one reactant molecule)
A => products
rate = k[A]
first order
bimolecular (two reactant molecules)
A + B => products
rate = k[A][B]
second order
A + A => products
rate = k[A]^2
second order
termolecular (three reactant molecules)
Rate-determining Step: gives the rate law for the overall process in a reaction mechanism consisting of more than the elementary step. The rate-determining step is the slowest step in the sequence. A proposed mechanism must satisfy two requirements: (1) The sum of the elementary reaction must be the overall balanced equation for the reaction. (2) The rate-determining step must have the same rate law as that determined from the experimental data.
Mechanisms with a Fast First Step: Not all reactions have a single rate-determining step, however.
Experimental Support for Reaction Mechanisms: It is not possible to prove that a mechanism is correct using rate data alone. To determine whether or not a proposed reaction mechanism is actually correct, we must conduct other experiments.
Catalysts are substances that increase the rate of a chemical reaction without itself being consumed. A catalyst speeds up a reaction by providing a set of elementary steps with more favorable kinetics than those that exist in its absence. A catalyst usually speeds up a reaction by lowering the activation energy.
Catalytic rate constant: When there is a catalyst in a reaction, the rate constant is kc, called the catalytic rate constant.
Heterogenous catalysis occurs when the reactants and the catalysts are in different phases.
Homogeneous catalysis occurs when the reactants and the catalysts are dispersed in a single phase, usually liquid. Advantages of this are reactions can be carried out under atmospheric conditions, can be designed to function selectively, and are generally cheaper.
Enzymes are biological catalysts. The mathematical treatment of enzyme kinetics is complex, but can be simplified to:
E + S (k1) ⇌ (k-1) ES
ES (k2) => E + P
Generally the rate of an enzyme catalyzed reaction is given by the equation:
rate = Δ[P]/Δt = k[ES]
This equation produces a mathematical curve when plotted on a graph of [S] concentration versus rate of product formation. This is a rapidly increasing curve that flattens out near horizontally.