REACTION KINETICS

Introduction to Reaction Kinetics

Reaction kinetics is the branch of chemistry that deals with the study of the rates at
which chemical reactions occur and the factors that affect these rates. It involves
understanding the speed of a reaction, the mechanism through which reactants are
transformed into products, and how different conditions such as temperature,
concentration, and catalysts affect the reaction rate.

●​ Purpose: The goal of studying reaction kinetics is to understand the time

dependence of a chemical reaction, which can help in controlling reaction
conditions for various industrial applications, such as in the design of reactors or
in the production of chemicals.
●​ Important Concepts:
○​ Reaction rate: How fast a reactant is consumed or a product is formed.
○​ Factors influencing reaction rate: Concentration of reactants,
temperature, pressure, presence of catalysts, and nature of the reactants.

2. Rate of Reaction

The rate of reaction refers to the change in the concentration of reactants or products
per unit time. It is typically expressed as:

Rate of reaction=Change in concentration of reactant or productTime taken for the

change\text{Rate of reaction} = \frac{\text{Change in concentration of reactant or
product}}{\text{Time taken for the change}}Rate of reaction=Time taken for the
changeChange in concentration of reactant or product​

The rate of reaction depends on several factors, including:

●​ Concentration of reactants: Higher concentration generally leads to a faster

reaction rate.
●​ Temperature: Increasing temperature usually increases the reaction rate.
●​ Catalysts: Catalysts lower the activation energy, thereby increasing the rate.
●​ Surface area: Greater surface area of solid reactants results in more collisions
and a faster reaction.

The rate can be defined mathematically in terms of the concentration of reactants and
products:

Rate=k×[A]x×[B]y\text{Rate} = k \times [A]^x \times [B]^yRate=k×[A]x×[B]y

Where:

●​ kkk is the rate constant.

●​ [A][A][A] and [B][B][B] are the concentrations of reactants A and B, respectively.
●​ xxx and yyy are the orders of reaction with respect to A and B, which are
determined experimentally.

3. Instantaneous and Average Rate

Average Rate:

The average rate of reaction is the change in concentration of a reactant or product

over a time interval. It is calculated as:

Average rate=Change in concentrationChange in

time=[C]final−[C]initialtfinal−tinitial\text{Average rate} = \frac{\text{Change in
concentration}}{\text{Change in time}} = \frac{[C]_{\text{final}} -
[C]_{\text{initial}}}{t_{\text{final}} - t_{\text{initial}}}Average rate=Change in timeChange
in concentration​=tfinal​−tinitial​[C]final​−[C]initial​​

The average rate gives a general idea of the speed of a reaction over a given period of
time.

Instantaneous Rate:

The instantaneous rate refers to the rate of reaction at a specific moment in time. It is
determined by finding the slope of the concentration vs. time curve at that particular
point. Mathematically, the instantaneous rate can be expressed as the derivative of the
concentration with respect to time:

Instantaneous rate=d[A]dt\text{Instantaneous rate} = \frac{d[A]}{dt}Instantaneous

rate=dtd[A]​

Where:

●​ [A][A][A] is the concentration of a reactant at any given time.

●​ ttt is time.

The instantaneous rate gives a more precise measurement of how fast a reaction is
occurring at any given time and is usually used when the reaction rate changes over
time.

Example:
For a reaction where the concentration of reactant decreases over time, the
instantaneous rate at any point will give how fast the reactant is being consumed at that
exact moment, whereas the average rate gives an overall speed across a time interval.

4. Velocity Constant (Rate Constant)

The velocity constant (also known as the rate constant or reaction constant,
denoted as kkk) is a proportionality constant that relates the rate of reaction to the
concentrations of the reactants. It is specific to a given reaction and is dependent on
temperature.

The rate law for a reaction can be written as:

Rate=k×[A]x×[B]y\text{Rate} = k \times [A]^x \times [B]^yRate=k×[A]x×[B]y

Where:

●​ kkk is the rate constant.

●​ [A][A][A] and [B][B][B] are the concentrations of reactants A and B, respectively.
●​ xxx and yyy are the orders of reaction with respect to the respective reactants.

Factors Affecting the Rate Constant:

●​ Temperature: The rate constant typically increases with temperature. This is

described by the Arrhenius equation:​
k=A⋅e−EaRTk = A \cdot e^{-\frac{E_a}{RT}}k=A⋅e−RTEa​​
Where:
○​ kkk is the rate constant.
○​ AAA is the frequency factor (pre-exponential factor).
○​ EaE_aEa​is the activation energy.
○​ RRR is the universal gas constant.
○​ TTT is the temperature (in Kelvin).
●​ Activation Energy: A lower activation energy leads to a higher rate constant,
which means the reaction will proceed faster.
●​ Catalysts: Catalysts can increase the rate constant by lowering the activation
energy, thereby speeding up the reaction.

Unit of Rate Constant:

The unit of kkk depends on the order of the reaction. For example:

●​ For a first-order reaction, the unit of kkk is time−1\text{time}^{-1}time−1.

 ●​ For a second-order reaction, the unit of kkk is
concentration−1⋅time−1\text{concentration}^{-1} \cdot
\text{time}^{-1}concentration−1⋅time−1.
●​ For a zero-order reaction, the unit of kkk is
concentration⋅time−1\text{concentration} \cdot
\text{time}^{-1}concentration⋅time−1.

Applications of Reaction Kinetics:

1.​ Pharmaceutical Industry: Determining the rate of drug absorption and

degradation.
2.​ Industrial Chemical Reactions: Optimizing reaction conditions for maximum
product yield.
3.​ Environmental Chemistry: Studying pollutant degradation rates in the
environment.
4.​ Catalysis: Understanding how catalysts influence the rate of chemical reactions.

Order of Reaction

The order of reaction refers to the power to which the concentration of a reactant is
raised in the rate law equation. It gives an indication of how the rate of the reaction
depends on the concentration of reactants.

●​ Mathematically, for a reaction aA+bB→cC+dDaA + bB \rightarrow cC +

dDaA+bB→cC+dD, the rate law can be written as:​
Rate=k⋅[A]x⋅[B]y\text{Rate} = k \cdot [A]^x \cdot [B]^yRate=k⋅[A]x⋅[B]y​
Where:
○​ kkk is the rate constant,
○​ [A][A][A] and [B][B][B] are the concentrations of reactants,
○​ xxx and yyy are the orders of reaction with respect to AAA and BBB.
●​ The overall order of the reaction is the sum of the exponents:​
Overall order=x+y\text{Overall order} = x + yOverall order=x+y

Types of Reaction Orders:

●​ Zero-order reaction: The rate of reaction is independent of the concentration of

the reactant.
○​ Example: Rate=k\text{Rate} = kRate=k
●​ First-order reaction: The rate is directly proportional to the concentration of one
reactant.
○​ Example: Rate=k⋅[A]\text{Rate} = k \cdot [A]Rate=k⋅[A]
 ●​ Second-order reaction: The rate is proportional to the square of the
concentration of one reactant or the product of concentrations of two reactants.
○​ Example: Rate=k⋅[A]2\text{Rate} = k \cdot [A]^2Rate=k⋅[A]2 or
Rate=k⋅[A]⋅[B]\text{Rate} = k \cdot [A] \cdot [B]Rate=k⋅[A]⋅[B]

2. Half-Life Period

The half-life (t1/2t_{1/2}t1/2​) is the time required for the concentration of a reactant to
decrease to half of its initial value. The half-life is an important concept in reaction
kinetics as it is often used to characterize the speed of a reaction.

For Different Orders of Reaction:

●​ Zero-Order Reaction: The half-life is directly proportional to the initial

concentration.​
t1/2=[A]02kt_{1/2} = \frac{[A]_0}{2k}t1/2​=2k[A]0​​
Where:
○​ [A]0[A]_0[A]0​is the initial concentration of the reactant,
○​ kkk is the rate constant.
●​ First-Order Reaction: The half-life is independent of the initial concentration and
is constant.​
t1/2=0.693kt_{1/2} = \frac{0.693}{k}t1/2​=k0.693​​
Where:
○​ kkk is the rate constant.
●​ Second-Order Reaction: The half-life is inversely proportional to the initial
concentration.​
t1/2=1k⋅[A]0t_{1/2} = \frac{1}{k \cdot [A]_0}t1/2​=k⋅[A]0​1​
Where:
○​ [A]0[A]_0[A]0​is the initial concentration of the reactant.

In first-order reactions, the half-life is constant regardless of the starting concentration,

which makes it easy to determine the rate constant from the half-life.

3. Rate Determining Step

The rate-determining step (RDS) is the slowest step in a reaction mechanism that
determines the overall rate of the reaction. In a complex reaction with multiple steps, the
rate of the reaction is governed by the step that has the highest activation energy and
the slowest reaction rate.

●​ The RDS limits how fast the overall reaction can proceed. Even if other steps are
faster, the overall reaction rate will depend on the rate of the rate-determining
step.
●​ Example: In a reaction involving multiple steps:
○​ If Step 1 is slower than Step 2, then the overall reaction rate is determined
by Step 1.
○​ If Step 2 is the slowest, it becomes the rate-determining step.

The rate-determining step is typically studied to understand and control reaction rates in
industrial processes, such as the manufacture of chemicals and pharmaceuticals.

4. Determination of the Rate of a Chemical Reaction

The rate of a chemical reaction can be determined using both physical and chemical
methods. These methods help us understand the speed of the reaction and the factors
that influence it.

a) Physical Methods

Physical methods involve measuring changes in physical properties of the system that
occur as the reaction progresses. Some common physical methods are:

1.​ Change in Absorbance (Spectrophotometry):

○​ This method involves measuring the change in the absorbance of light at a
particular wavelength as the concentration of a colored reactant or product
changes over time.
○​ For example, if a reactant or product is colored, its absorbance can be
measured using a spectrophotometer.
2.​ Change in Pressure (for gas-phase reactions):
○​ In reactions where gases are produced or consumed, the pressure
change can be measured using a pressure sensor or manometer. For
example, in a reaction involving the decomposition of a gas, the pressure
decrease can give information about the rate of reaction.
3.​ Change in Volume:
○​ For reactions where gases are evolved, the volume of gas produced can
be measured at regular time intervals.
 ○​ For example, in the reaction of a solid with an acid to produce a gas, the
volume of gas can be measured to determine the rate.
4.​ Conductometric Method:
○​ This method involves measuring the change in electrical conductivity of a
solution as the reaction progresses, especially for ionic reactions.
5.​ Temperature Change (Calorimetry):
○​ The heat released or absorbed during a reaction can be measured using a
calorimeter to determine the rate.

b) Chemical Methods

Chemical methods involve directly measuring the concentration of reactants or products

at various time intervals using chemical reactions.

1.​ Titration:
○​ Regular sampling of the reaction mixture at different times can be titrated
to determine the concentration of a reactant or product. For example, if the
concentration of a reactant decreases over time, titration can be used to
measure how the concentration changes.
2.​ Colorimetry:
○​ For reactions involving colored species, the concentration of reactants or
products can be determined by measuring the color intensity at different
times using colorimetric analysis.
3.​ Gravimetric Method:
○​ This method is used when a solid product is formed in the reaction. The
change in mass of the system is measured at various time intervals to
determine the reaction rate.
4.​ Gas Volume Measurement:
○​ If the reaction produces a gas, the volume of gas evolved over time can
be measured to determine the reaction rate.
5.​ Manometry:
○​ This involves measuring the pressure changes during a reaction, which
can be used to determine the rate of gas-phase reactions.

1. Activation Energy (Ea)

Activation energy is the minimum energy required for a chemical reaction to occur. It
represents the energy barrier that must be overcome for reactants to transform into
products. The greater the activation energy, the slower the reaction, as fewer molecules
will have enough energy to react at a given temperature.
 ●​ Mathematically, the rate constant kkk is related to the activation energy
EaE_aEa​through the Arrhenius equation:

k=A⋅e−EaRTk = A \cdot e^{-\frac{E_a}{RT}}k=A⋅e−RTEa​​

Where:

●​ kkk is the rate constant,

●​ AAA is the frequency factor (pre-exponential factor),
●​ EaE_aEa​is the activation energy,
●​ RRR is the universal gas constant,
●​ TTT is the temperature in Kelvin.
●​ Graphical Representation: When the natural logarithm of the rate constant
(ln⁡k\ln klnk) is plotted against 1T\frac{1}{T}T1​(the inverse of temperature), the
slope of the line gives −EaR-\frac{E_a}{R}−REa​​. This allows determination of the
activation energy experimentally.
●​ Activation Energy and Temperature: As temperature increases, more
molecules have the required energy to overcome the activation barrier, resulting
in an increase in the reaction rate.

2. Finding the Order of Reaction

The order of reaction refers to the relationship between the rate of reaction and the
concentration of the reactants. There are various methods to determine the order of a
reaction, including the half-life method and the method of large excess.

a) Half-Life Method

The half-life method is based on observing how the half-life of a reactant changes as
the concentration changes during the reaction. The half-life is the time taken for the
concentration of a reactant to reduce to half of its initial value.

●​ Zero-Order Reactions:
○​ For a zero-order reaction, the rate is independent of the concentration of
the reactant.
○​ The half-life is directly proportional to the initial concentration.
○​ Formula: t1/2=[A]02kt_{1/2} = \frac{[A]_0}{2k}t1/2​=2k[A]0​​Where:
■​ [A]0[A]_0[A]0​is the initial concentration,
■​ kkk is the rate constant.
●​ First-Order Reactions:
○​ For a first-order reaction, the rate is directly proportional to the
concentration of one reactant.
 ○​ The half-life is independent of the initial concentration and is constant.
○​ Formula: t1/2=0.693kt_{1/2} = \frac{0.693}{k}t1/2​=k0.693​Where kkk is the
rate constant.
●​ Second-Order Reactions:
○​ For a second-order reaction, the rate depends on the square of the
concentration of one reactant.
○​ The half-life is inversely proportional to the initial concentration.
○​ Formula: t1/2=1k[A]0t_{1/2} = \frac{1}{k[A]_0}t1/2​=k[A]0​1​Where:
■​ [A]0[A]_0[A]0​is the initial concentration,
■​ kkk is the rate constant.

To find the order of the reaction, you can measure the half-life at different initial
concentrations and analyze how the half-life changes:

●​ If the half-life is constant, the reaction is first-order.

●​ If the half-life is inversely proportional to the initial concentration, the reaction is
second-order.
●​ If the half-life is proportional to the initial concentration, the reaction is
zero-order.

b) Method of Large Excess

The method of large excess involves carrying out the reaction with one reactant
present in a large excess compared to the other. This method helps simplify the rate law
by treating the excess reactant as if its concentration remains constant during the
course of the reaction.

●​ Steps:
○​ Excess Reactant: Take one reactant in large excess, so its concentration
effectively does not change during the reaction.
○​ Rate Law Simplification: For a reaction aA+bB→productsaA + bB
\rightarrow \text{products}aA+bB→products, if AAA is in excess, the rate
law simplifies to: Rate=k′[B]n\text{Rate} = k' [B]^nRate=k′[B]n Where k′k'k′
is the effective rate constant considering the excess concentration of AAA,
and nnn is the order of reaction with respect to BBB.
○​ Experimental Measurements: Measure the rate of reaction for different
concentrations of the limiting reactant BBB. Plot the rate against the
concentration of BBB and determine the order of reaction from the graph.
●​ Applications:
○​ This method is useful for reactions where one reactant is much more
concentrated than the others, allowing the reaction to behave as if it
depends only on the concentration of the limiting reactant.
 ○​ It is often used in reactions involving gases or large quantities of one
reactant.
●​ Example: In a reaction 2A+B→products2A + B \rightarrow
\text{products}2A+B→products, if reactant AAA is present in large excess, the
reaction rate can be written as:​
Rate=k′[B]n\text{Rate} = k' [B]^nRate=k′[B]n​
By varying [B][B][B] and measuring the rate, you can determine the order nnn
with respect to BBB.
●​ Applications:
1.​ Pharmaceutical Industry: Activation energy and reaction order can help in
determining how fast drugs are metabolized in the body.
2.​ Chemical Engineering: This method is used to optimize reaction rates in
industrial reactors.
3.​ Environmental Chemistry: Understanding reaction kinetics aids in studying
pollutant degradation and its effect on ecosystems.

Factors Affecting Rates of Reactions

The rate of a chemical reaction is influenced by several factors. These factors

determine how quickly reactants are converted into products. The main factors affecting
reaction rates are:

1. Concentration of Reactants

●​ Effect on Rate: For most reactions, an increase in the concentration of reactants

increases the rate of reaction. This is because more reactant molecules are
available to collide and react with each other.
●​ Why It Happens: Higher concentration means a greater number of molecules or
ions per unit volume, leading to more frequent collisions between them, which
increases the likelihood of effective collisions (collisions that lead to a reaction).
●​ Example: In the reaction between hydrochloric acid and sodium thiosulphate, the
rate of reaction increases when the concentration of hydrochloric acid is
increased.

2. Temperature

●​ Effect on Rate: An increase in temperature typically increases the rate of

reaction. This is because the kinetic energy of molecules increases with
temperature, leading to more frequent and energetic collisions between reactant
molecules.
 ●​ Why It Happens: Higher temperatures mean molecules move faster and have
more energy, which results in more collisions and a higher proportion of collisions
having enough energy to overcome the activation energy barrier.
●​ Example: In the decomposition of hydrogen peroxide, the rate increases
significantly with higher temperatures.

3. Presence of a Catalyst

●​ Effect on Rate: A catalyst speeds up the rate of reaction without being

consumed in the reaction. It provides an alternative reaction pathway with a
lower activation energy, which allows the reaction to occur faster.
●​ Why It Happens: Catalysts work by lowering the activation energy required for a
reaction. As a result, more reactant molecules have enough energy to overcome
the barrier, leading to an increased reaction rate.
●​ Example: In the catalytic conversion of carbon monoxide to carbon dioxide,
platinum acts as a catalyst to increase the rate of reaction.

4. Surface Area of Reactants

●​ Effect on Rate: The larger the surface area of reactants, the faster the reaction.
A larger surface area allows more particles to be exposed to other reactants,
leading to more collisions and a faster reaction.
●​ Why It Happens: A greater surface area means more area for collisions between
reactant molecules, which increases the frequency of successful collisions and,
consequently, the reaction rate.
●​ Example: A powdered solid reactant will react faster than a large chunk of the
same material because it has more exposed surface area.

5. Nature of Reactants

●​ Effect on Rate: The chemical nature of the reactants affects the rate of reaction.
Some substances react more readily than others. For example, ionic compounds
tend to react more quickly than covalent compounds.
●​ Why It Happens: The strength of bonds between atoms in molecules plays a
role in determining how easily reactants can form products. For example,
reactions involving ionic compounds are generally faster than those involving
covalent compounds because the bonds in ionic compounds are more easily
broken.
●​ Example: The reaction between sodium metal and water is much faster than the
reaction between magnesium metal and water due to the difference in reactivity
between the two metals.
6. Pressure (for Gas-phase Reactions)

●​ Effect on Rate: For reactions involving gases, increasing the pressure can
increase the rate of reaction. This is because increasing the pressure decreases
the volume, increasing the concentration of the gas molecules, which leads to
more frequent collisions.
●​ Why It Happens: At higher pressures, gas molecules are compressed into a
smaller volume, leading to more molecules in the same space and, therefore,
more collisions per unit time.
●​ Example: In the reaction between nitrogen and hydrogen to form ammonia (the
Haber process), increasing the pressure increases the rate of reaction.

7. Light (for Photochemical Reactions)

●​ Effect on Rate: Light, particularly ultraviolet (UV) light, can affect the rate of
certain reactions by providing energy to molecules, making them more reactive.
●​ Why It Happens: In photochemical reactions, light provides energy that can
break bonds or excite molecules to higher energy states, facilitating the reaction.
●​ Example: The decomposition of hydrogen halides (e.g., HCl) in the presence of
UV light is an example of a photochemical reaction.

8. Ionic Strength (for Reactions Involving Ions)

●​ Effect on Rate: The ionic strength of the solution (i.e., the concentration of ions)
can influence the rate of reactions involving ions. Higher ionic strength can
increase the rate of reactions by increasing the frequency of collisions between
reactants.
●​ Why It Happens: Higher ionic strength can reduce the repulsion between
charged species in the solution, facilitating collisions between oppositely charged
ions and increasing the reaction rate.
●​ Example: In reactions involving ionic compounds in solution, such as
precipitation reactions, increasing the ionic strength of the solution can speed up
the reaction.

Applications:

1.​ Chemical Industry: Control of reaction rates is vital in industrial processes, such
as in the production of chemicals, fertilizers (Haber process), and polymers.
2.​ Environmental Chemistry: Understanding how temperature, pressure, and
catalysts affect the rate of pollution breakdown is crucial for environmental
protection.
 3.​ Pharmaceuticals: In drug manufacturing, controlling the rate of reaction ensures
product consistency and efficiency.

Arrhenius Equation

The Arrhenius equation is a mathematical formula that describes how the rate
constant (kkk) of a chemical reaction depends on temperature. It provides insight into
the effect of temperature on the rate of reaction and the activation energy required for
the reaction to occur.

The equation is:

k=A⋅e−EaRTk = A \cdot e^{-\frac{E_a}{RT}}k=A⋅e−RTEa​​

Where:

●​ kkk = Rate constant of the reaction,

●​ AAA = Frequency factor or pre-exponential factor (represents the number of
collisions that result in a reaction),
●​ EaE_aEa​= Activation energy of the reaction (in joules per mole, J/mol),
●​ RRR = Universal gas constant (8.314 J/mol\cdotpK8.314 \,
\text{J/mol·K}8.314J/mol\cdotpK),
●​ TTT = Temperature in Kelvin (K).

Key Concepts

1.​ Activation Energy (Ea): The minimum energy that must be overcome for a
reaction to occur. Higher EaE_aEa​means slower reaction rates at a given
temperature.
2.​ Pre-exponential Factor (A): Also known as the frequency factor, this represents
the number of times reactants approach each other in the proper orientation to
react. It reflects the frequency of collisions and the probability that collisions will
result in a reaction.
3.​ Effect of Temperature: The rate constant kkk increases with an increase in
temperature because the exponential term e−EaRTe^{-\frac{E_a}{RT}}e−RTEa​​
becomes larger at higher temperatures.
4.​ Exponential Dependence: The exponential term
e−EaRTe^{-\frac{E_a}{RT}}e−RTEa​​suggests that as the temperature increases,
the rate constant increases exponentially because more molecules have
sufficient energy to overcome the activation energy barrier.

Logarithmic Form of the Arrhenius Equation

The Arrhenius equation can be linearized by taking the natural logarithm of both sides:

ln⁡k=ln⁡A−EaR⋅1T\ln k = \ln A - \frac{E_a}{R} \cdot \frac{1}{T}lnk=lnA−REa​​⋅T1​

This equation is useful for determining the activation energy EaE_aEa​from

experimental data. If the rate constant kkk is measured at different temperatures, you
can plot ln⁡k\ln klnk against 1T\frac{1}{T}T1​, and the slope of the resulting line will give
−EaR-\frac{E_a}{R}−REa​​.

Graphical Representation

●​ Plot: If you plot ln⁡k\ln klnk versus 1T\frac{1}{T}T1​(where TTT is in Kelvin), the
slope of the line will be −EaR-\frac{E_a}{R}−REa​​.
●​ Intercept: The y-intercept of the graph will be ln⁡A\ln AlnA.

How to Use the Arrhenius Equation

1.​ To Calculate Rate Constant at Different Temperatures:

○​ If you know EaE_aEa​and AAA, you can calculate the rate constant at any
given temperature using the Arrhenius equation.
2.​ To Determine Activation Energy (Ea):
○​ By measuring the rate constant at two or more temperatures, you can
rearrange the equation to find EaE_aEa​: ln⁡(k2k1)=EaR(1T1−1T2)\ln
\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} -
\frac{1}{T_2}\right)ln(k1​k2​​)=REa​​(T1​1​−T2​1​) Where k1k_1k1​and k2k_2k2​
are the rate constants at temperatures T1T_1T1​and T2T_2T2​,
respectively.

Example of Using the Arrhenius Equation

Suppose you have the rate constant of a reaction at two different temperatures:

●​ At T1=298 KT_1 = 298 \, KT1​=298K, k1=1.0×10−3 s−1k_1 = 1.0 \times 10^{-3} \,

\text{s}^{-1}k1​=1.0×10−3s−1.
●​ At T2=308 KT_2 = 308 \, KT2​=308K, k2=2.0×10−3 s−1k_2 = 2.0 \times 10^{-3} \,
\text{s}^{-1}k2​=2.0×10−3s−1.

You can use the Arrhenius equation to find the activation energy:

ln⁡(k2k1)=EaR(1T1−1T2)\ln \left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} -

\frac{1}{T_2}\right)ln(k1​k2​​)=REa​​(T1​1​−T2​1​)

Substitute the known values:

ln⁡(2.0×10−31.0×10−3)=Ea8.314(1298−1308)\ln \left(\frac{2.0 \times 10^{-3}}{1.0 \times
10^{-3}}\right) = \frac{E_a}{8.314} \left(\frac{1}{298} -
\frac{1}{308}\right)ln(1.0×10−32.0×10−3​)=8.314Ea​​(2981​−3081​)

Solve for EaE_aEa​.

Applications of the Arrhenius Equation

●​ Chemistry: Understanding how temperature affects reaction rates helps in

controlling reactions in industrial processes and laboratories.
●​ Pharmacology: In drug stability, temperature-dependent reactions of
medications can be modeled using this equation.
●​ Materials Science: The equation can help in understanding the rates of material
degradation at various temperatures.

Catalysis

Catalysis is the process of increasing the rate of a chemical reaction by adding a

substance called a catalyst. A catalyst works by lowering the activation energy of the
reaction, allowing the reaction to occur faster without being consumed in the process.

Types of Catalysis

Catalysis can be classified into two main types based on how the catalyst interacts with
the reactants:

1. Homogeneous Catalysis

●​ In homogeneous catalysis, the catalyst is in the same phase (state) as the

reactants. For example, a liquid catalyst used with liquid reactants or a gaseous
catalyst used with gaseous reactants.
●​ Example: The reaction between hydrogen and oxygen to form water, where a
platinum catalyst in the liquid phase can be used.

2. Heterogeneous Catalysis

●​ In heterogeneous catalysis, the catalyst is in a different phase from the

reactants. Typically, the catalyst is solid, and the reactants are in the liquid or gas
phase.
●​ Example: The catalytic converter in a car, where solid platinum and palladium
catalysts convert harmful gases (such as carbon monoxide) into less harmful
substances.
3. Autocatalysis

●​ Autocatalysis occurs when one of the products of the reaction itself acts as a
catalyst to accelerate the reaction.
●​ Example: The reaction between potassium permanganate and oxalic acid is
autocatalytic, where one of the products, manganese (II), acts as a catalyst for
the reaction.

Characteristics of Catalysts

●​ Change in Rate: Catalysts increase the rate of a reaction by lowering the

activation energy, without being consumed in the reaction.
●​ Reusability: A catalyst is not consumed during the reaction and can be reused
multiple times.
●​ Selectivity: Catalysts are often highly selective, meaning they can speed up
specific reactions without affecting others.
●​ Lower Activation Energy: A catalyst provides an alternative reaction pathway
with a lower activation energy.
●​ Reaction Mechanism: A catalyst often changes the mechanism of the reaction,
enabling it to occur through a different pathway.

Activation of a Catalyst

The activation of a catalyst involves a process where the catalyst interacts with the
reactants to form an intermediate complex that has a lower activation energy than the
uncatalyzed reaction. This complex then decomposes or reacts to give the final
products, regenerating the catalyst in the process.

●​ For Heterogeneous Catalysts: The reactants are adsorbed onto the surface of
the solid catalyst. The reaction takes place on the surface, where the activation
energy is lowered.
●​ For Homogeneous Catalysts: The catalyst is in the same phase as the
reactants, so it can easily collide and interact with them, facilitating the reaction.

Types of Catalysts

1. Positive Catalyst (Promoter)

●​ A positive catalyst accelerates the rate of reaction by lowering the activation

energy.
●​ Example: The use of platinum in the hydrogenation of alkenes, where platinum
serves as a positive catalyst.
2. Negative Catalyst (Inhibitor)

●​ A negative catalyst, also known as an inhibitor, slows down or decreases the

rate of a reaction by increasing the activation energy or interfering with the
reactants.
●​ Example: In the reaction of hydrogen peroxide decomposition, sodium fluoride
acts as a negative catalyst by slowing down the reaction.

3. Autocatalyst

●​ An autocatalyst is a product of the reaction that also catalyzes the reaction

itself. In this case, the reaction accelerates as more product is produced, which,
in turn, acts as a catalyst.
●​ Example: The reaction of oxidation of organic compounds, where the product
catalyzes its own further decomposition.

Enzyme Catalysis

Enzyme catalysis is a type of biological catalysis where enzymes (proteins that act as
catalysts) speed up biochemical reactions in living organisms. Enzymes are highly
specific and efficient catalysts.

Characteristics of Enzyme Catalysis:

1.​ Specificity:
○​ Enzymes are highly specific for their substrates (the molecules they act
upon). This specificity arises from the enzyme's three-dimensional shape,
which matches the substrate precisely.
○​ Example: Amylase is an enzyme that specifically catalyzes the
breakdown of starch into sugars.
2.​ Lower Activation Energy:
○​ Enzymes lower the activation energy required for biochemical reactions,
allowing reactions to proceed at the temperatures commonly found in
living organisms (body temperature, 37°C).
3.​ Efficiency:
○​ Enzymes are extremely efficient, with some enzymes being able to
catalyze thousands or even millions of reactions per second.
4.​ Regulation:
○​ Enzyme activity is often regulated, allowing cells to control metabolic
pathways. For example, the activity of enzymes can be regulated by the
presence of specific molecules called inhibitors or activators.
5.​ Reusability:
 ○​ Enzymes are not consumed in the reaction and can be reused repeatedly
to catalyze the same reaction.
6.​ Temperature and pH Sensitivity:
○​ Enzymes are sensitive to changes in temperature and pH. Most enzymes
function best within a specific temperature and pH range. For example,
human enzymes typically work best at 37°C and near neutral pH (around
pH 7).
7.​ Co-factors and Coenzymes:
○​ Some enzymes require non-protein molecules called co-factors or
coenzymes for their activity. Co-factors can be metal ions like zinc or iron,
and coenzymes are organic molecules, often vitamins or their derivatives.
○​ Example: Vitamin B12 acts as a coenzyme in enzyme catalysis.

Types of Enzyme Catalysis

1.​ Lock and Key Model:

○​ In this model, the substrate fits perfectly into the enzyme's active site, like
a key fitting into a lock. This theory explains the specificity of
enzyme-substrate interaction.
2.​ Induced Fit Model:
○​ In this model, the enzyme undergoes a conformational change when the
substrate binds, allowing a better fit between the enzyme and the
substrate. This model accounts for more flexibility in enzyme-substrate
binding.
3.​ Covalent Catalysis:
○​ Some enzymes use covalent bonds to temporarily form a reaction
intermediate, which accelerates the reaction.
4.​ Acid-Base Catalysis:
○​ Enzymes can donate or accept protons (H+ ions) during the reaction,
altering the charge of the substrate and facilitating the reaction.

Applications of Catalysis:

●​ Industrial Applications: Catalysis is crucial in industries such as

petrochemicals, pharmaceuticals, and food production. For example, catalytic
cracking is used to break down large hydrocarbons into gasoline in the
petroleum industry.
●​ Environmental Protection: Catalysts are used in devices like catalytic
converters in cars to reduce harmful emissions.
●​ Biological Processes: Enzymes are essential in digestion, metabolism, and
other biochemical reactions in living organisms.