Chemical Kinetics Class 12 Chemistry Chapter 3 Notes

Chemical Kinetics: Reaction Rates and Instantaneous Rates

Variability in Reaction Rates:

Chemical reactions exhibit a wide range of speeds, leading to different categories:
1. Very Fast Reactions: For example, the instantaneous precipitation of silver chloride when silver nitrate and sodium chloride solutions are mixed.
2. Very Slow Reactions: Such as the rusting of iron in the presence of air and moisture.
3. Moderate-Speed Reactions: Like the inversion of cane sugar and the hydrolysis of starch.

Rate of a Reaction:

Similar to measuring speed in terms of the change in position or distance over time for an automobile, the rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time.
It can be expressed as:
- Rate of disappearance of a reactant: ∆[R]/∆t
- Rate of appearance of a product: ∆[P]/∆t
- The square brackets denote molar concentration.

Average Rate of Reaction:

The average rate of a reaction (r_av) is determined by the change in concentration of reactants or products over a specified time interval.
It depends on the extent of change and the duration of time.
Average rate is used to describe the overall rate of reaction within a given time interval.

Units of Rate:

The units of rate are typically concentration per unit time (e.g., mol L⁻¹s⁻¹).
In gaseous reactions using partial pressures, the units may be expressed as atm s⁻¹.

Instantaneous Rate of Reaction:

The instantaneous rate of reaction (r_inst) is the rate at a particular moment in time.
It is calculated when the time interval (∆t) approaches zero.
Mathematically, it is expressed as:
- r_inst = -∆[R]/∆t = ∆[P]/∆t
- It can be determined graphically by drawing a tangent to the concentration vs. time curve at a specific time point.

Examples of Reaction Rates:

For a reaction like Hg(l) + Cl2(g) → HgCl2(s), where the stoichiometric coefficients are the same, the rate of disappearance of any reactant equals the rate of appearance of any product.
In reactions where stoichiometric coefficients differ, such as 2HI(g) → H2(g) + I2(g), the rate is expressed as ∆[HI]/2∆t = -∆[H2]/∆t = -∆[I2]/∆t.
For a complex reaction like 5Br⁻(aq) + BrO3⁻(aq) + 6H⁺(aq) → 3Br2(aq) + 3H2O(l), the rates are determined based on the stoichiometric coefficients, leading to various rate expressions.
In gaseous reactions, rate can also be expressed in terms of partial pressures.

Factors Influencing the Rate of a Reaction

The rate of a chemical reaction is influenced by several factors that impact the speed at which reactants are converted into products. These factors include:

Concentration
Rate Expression and Rate Constant
Order of a Reaction
Molecularity of a Reaction

Rate Law in Chemical Kinetics:

The rate law, also known as the rate equation or rate expression, is a mathematical representation of the relationship between the rate of a chemical reaction and the concentrations of its reactants. It describes how the rate of reaction changes with variations in reactant concentrations while keeping other factors such as temperature and pressure constant. Here are some key points about the rate law:

Dependence on Reactant Concentrations:
- The rate of a chemical reaction at a specific temperature is influenced by the concentrations of the reactants involved in the reaction.
- The rate law expresses how the rate of reaction is affected by changes in the concentrations of these reactants.
General Rate Law Form:
- The general form of a rate law for a reaction can be written as follows:
- Rate = k[A]^x[B]^y
- Where:
  - Rate is the rate of the reaction.
  - k is the rate constant, which depends on the specific reaction and temperature.
  - [A] and [B] are the concentrations of reactants A and B, respectively.
  - x and y are the reaction orders with respect to reactants A and B, respectively.
Reaction Order:
- The reaction order (exponent) x and y for each reactant in the rate law can be determined experimentally.
- The reaction order indicates how the rate of reaction is affected by changes in the concentration of a specific reactant.
- For example, if x is 1, it means that the rate of reaction is directly proportional to the concentration of reactant A. If x is 2, it means the rate is proportional to the square of [A].
- The overall reaction order is the sum of the individual reaction orders: Overall Order = x + y.
Rate Constant (k):
- The rate constant (k) is specific to each reaction and is determined experimentally at a given temperature.
- It represents the proportionality constant between the rate of the reaction and the product of the reactant concentrations raised to their respective reaction orders.
- k is temperature-dependent, and it usually increases with an increase in temperature.
Units of Rate Constant:
- The units of the rate constant (k) depend on the overall reaction order and the units of concentration.
- For a reaction with an overall order of n, the units of k are (concentration units)^(1-n) time^(-1).
Experimental Determination:
- The rate law is determined through experimental data, typically using the method of initial rates. By conducting experiments with varying reactant concentrations and measuring the initial reaction rates, scientists can deduce the values of x and y for each reactant and the rate constant k.
Specific Reaction:
- Each chemical reaction has its unique rate law, and the rate law provides crucial information about the reaction mechanism and how different reactants influence the rate.

Order of a Reaction

The order of a chemical reaction is a critical concept in chemical kinetics, and it is represented by the exponents (x and y) in the rate law expression:

Rate = k [A]^x [B]^y

Here are some key points regarding the order of a reaction:

Overall Order: The sum of the exponents (x + y) in the rate law expression gives the overall order of the reaction. This overall order indicates how the rate of the reaction depends on the concentrations of the reactants.
Possible Values: The order of a reaction can take various values, including 0, 1, 2, 3, or even fractional values. These values indicate how sensitive the rate of the reaction is to changes in the concentrations of the reactants.
Zero Order Reaction: A reaction is considered zero order with respect to a particular reactant if its rate is independent of the concentration of that reactant. In such cases, the rate law simplifies to Rate = k.
Elementary Reactions: Elementary reactions are single-step reactions that occur as written in a balanced chemical equation. The order of an elementary reaction is determined directly from its stoichiometry, matching the coefficients of the reactants.
Complex Reactions: Most real-world reactions are complex and involve multiple elementary steps. These sequences of elementary reactions are called reaction mechanisms. The order of the overall reaction may differ from the stoichiometric coefficients in the balanced equation due to the complexities of the mechanism.
Units of Rate Constant (k): The rate constant (k) has units that depend on the overall order (n) of the reaction. The units of k are determined by balancing the units in the rate law equation. The units are expressed as (concentration)^1-n time^(-1).

For example, if the overall order (n) of a reaction is 2, and the units of concentration are in mol L^(-1) and time is in seconds (s), then the units of the rate constant (k) would be L^(2-n) mol^(1-n) s^(-1).

Molecularity of a Reaction

Molecularity and the rate-determining step are important concepts in understanding chemical reactions, especially in the context of reaction mechanisms. Here are some key points regarding molecularity and the rate-determining step:

Molecularity: Molecularity refers to the number of reacting species (atoms, ions, or molecules) that must collide simultaneously in an elementary reaction to bring about a chemical reaction. It is a characteristic of elementary reactions, which are single-step reactions that occur as written in a balanced chemical equation.
- Unimolecular reactions involve the collision of one reacting species. Example: Decomposition of ammonium nitrite (NH4NO2). NH4NO2 → N2 + 2H2O
- Bimolecular reactions involve the simultaneous collision between two species. Example: Dissociation of hydrogen iodide (HI). 2HI → H2 + I2
- Trimolecular reactions involve the simultaneous collision between three reacting species. These reactions are relatively rare. Example: Formation of nitrogen dioxide (NO2) from nitrogen monoxide (NO) and oxygen (O2). 2NO + O2 → 2NO2
Complex Reactions: Most real-world reactions involve multiple elementary steps, making them complex reactions. These sequences of elementary reactions are called reaction mechanisms. Complex reactions can have varying orders, and the overall rate of the reaction is determined by the slowest step in the mechanism, which is known as the rate-determining step.
Rate-Determining Step: In a complex reaction mechanism, the rate-determining step is the slowest step that controls the overall rate of the reaction. It determines how fast the reaction proceeds. The order of the reaction is determined by the molecularity of the rate-determining step.
- For example, in the decomposition of hydrogen peroxide (H2O2) catalyzed by iodide ions (I–) in an alkaline medium, the reaction occurs in two steps. The first step is slower and involves the collision of H2O2 and I– to form an intermediate (IO–). The second step is faster. The rate of the overall reaction is determined by the rate of the slowest step, which is the rate-determining step.
- The rate equation for the reaction indicates that it is first order with respect to both H2O2 and I–, corresponding to the molecularity of the rate-determining step.
- Rate equation: Rate = k [H2O2] [I–]

Integrated Rate Equations

Integrated rate equations are mathematical expressions that relate the concentrations of reactants or products at different times to the rate constant and reaction order. These equations are derived by integrating the differential rate equation for a specific reaction order. Integrated rate equations are useful in understanding the kinetics of chemical reactions and can help determine reaction orders experimentally.

1. Zero Order Reactions

A zero-order reaction is a type of chemical reaction in which the rate of reaction is independent of the concentration of the reactants. In other words, the rate of a zero-order reaction remains constant over time, regardless of changes in reactant concentrations. The mathematical representation of a zero-order reaction is as follows:

Rate=k

Where:

Rate is the rate of the reaction.
k is the rate constant.

In this equation, the rate of the reaction is simply a constant value, k, which is characteristic of the specific reaction. Unlike first-order or second-order reactions, the concentration of reactants does not appear in the rate expression for a zero-order reaction.

To understand this concept further, let’s consider the integrated rate equation for a zero-order reaction:

[A]t=−kt+[A]0

Where:

[A]t is the concentration of the reactant at time t.
[A]0 is the initial concentration of the reactant.
k is the rate constant.
t is the time elapsed.

From this equation, it’s clear that the concentration of the reactant decreases linearly with time (t), and the slope of the concentration-time plot is equal to the negative rate constant (−k). The intercept of the plot is the initial concentration of the reactant [A]0).

Zero-order reactions are relatively rare but do occur in certain chemical systems. They often involve processes where the reaction rate is limited by factors other than reactant concentration, such as surface reactions on catalysts or enzyme-catalyzed reactions. A well-known example of a zero-order reaction is the thermal decomposition of gaseous ammonia (NH3) on a platinum catalyst surface at high pressure. In this case, the reaction rate remains constant because the catalyst surface becomes saturated with ammonia molecules, and further increases in ammonia concentration do not affect the reaction rate.

Zero-order reactions are an important concept in chemical kinetics, and their rate expressions and behavior are distinct from those of first-order and second-order reactions.

2. First-order reaction

A first-order reaction is a type of chemical reaction in which the rate of the reaction is directly proportional to the concentration of one of the reactants. Mathematically, a first-order reaction is represented as follows:

Rate=k[A]

Where:

Rate is the rate of the reaction.
k is the rate constant.
[A] is the concentration of the reactant.

In a first-order reaction, the rate of the reaction is directly proportional to the concentration of the reactant [A], which means that as the concentration of [A] decreases over time, the rate of the reaction also decreases proportionally.

The integrated rate equation for a first-order reaction is as follows:

ln([A]0/[A])=−kt

Where:

[A] is the concentration of the reactant at time t.
[A]0 is the initial concentration of the reactant.
k is the rate constant.
t is the time elapsed.

From this equation, it is evident that the natural logarithm of the ratio of [A] at time t to the initial concentration [A]0 is directly proportional to time t. The slope of the plot of ln([A]/[A]0) against t is equal to −k, and the intercept is equal to ln([A]0).

Another way to express the rate equation for a first-order reaction is in terms of the common logarithm (base 10):

log([A]/[A]0)=2.303kt

In this equation, the ratio [A]0/[A] is directly proportional to time t, and the slope of the plot of log([A]0/[A]) against t is equal to 2.303k.

Examples of first-order reactions include the radioactive decay of unstable nuclei, the hydrogenation of ethene, and the decomposition of certain chemical compounds like N2O5.

First-order reactions are important in chemical kinetics, and their rate expressions are characterized by their dependence on the concentration of a single reactant. The rate constant k is specific to each reaction and can be determined experimentally.

Half Life Of A Reaction

The concept of half-life (t1/2) is a fundamental parameter used to describe the kinetics of a chemical reaction. It represents the time it takes for the concentration of a reactant to decrease to half of its initial value. The expression for half-life varies depending on the reaction order (zero order, first order, etc.).

1. Half Life Of A Zero Order Reaction

In chemistry, the half-life (t1/2) of a reaction is a crucial parameter. It represents the time required for the concentration of a reactant to decrease to half of its initial value. In the case of a zero-order reaction, the rate of the reaction is independent of the initial concentration of the reactant.

Here’s how to calculate the half-life (t1/2) for a zero-order reaction:

Start with the zero-order rate equation: Rate=k, where RateRate is the rate of the reaction, and k is the rate constant.
Use the following formula to determine the half-life (t1/2):

t1/2=[A]0/2k

In this formula:

t1/2 represents the half-life of the reaction.
[A]0 is the initial concentration of the reactant.
k is the rate constant.

It’s important to note that the half-life of a zero-order reaction is not a fixed constant like it is in first-order reactions. Instead, it depends on both the initial concentration of the reactant and the rate constant. Specifically:

If you double the initial concentration of the reactant ([A]0[A]0), the half-life (t1/2) will also double.
If you decrease the rate constant (k), the half-life (t1/2) will increase.

Understanding the half-life of a zero-order reaction is valuable in various chemical processes, as it helps predict how long it takes for reactants to be consumed or products to be formed in reactions where the rate remains constant regardless of initial concentrations.

2. Half Life Of A First Order Reaction

The half-life of a first-order reaction is a fundamental concept in chemistry. It represents the time required for the concentration of a reactant to decrease to half of its initial value in a reaction where the rate is directly proportional to the concentration of the reactant. Here’s how to calculate the half-life (�1/2t1/2) for a first-order reaction:

Start with the first-order rate equation: R=k⋅[A], where:
- R is the rate of the reaction.
- k is the rate constant.
- [A] is the concentration of the reactant.
Express the rate constant k as ln(2)/t1/2, where ln(2) is the natural logarithm of 2.
Set the initial concentration of the reactant [A]0 to half of its initial value, which is [A]0/2, and substitute it into the first-order rate equation:

Rate=k⋅([A]0/2)

Solve for t1/2:

(k⋅[A]0)/2=ln(2)/t1/2

Rearrange the equation to solve for �1/2t1/2:

t1/2=0.693/k

In this formula:

t1/2 represents the half-life of the reaction.
k is the rate constant for the first-order reaction.

It’s important to note that the half-life of a first-order reaction is a constant value and is independent of the initial concentration of the reactant. This means that no matter how much reactant you start with, it will always take the same amount of time for half of it to react.

Understanding the half-life of a first-order reaction is crucial in various fields of chemistry, such as pharmacology (for drug elimination), nuclear chemistry (for radioactive decay), and chemical kinetics (for reaction rate analysis).

Pseudo First Order Reactions

Pseudo-first-order reactions, also known as pseudo-first-order kinetics, refer to chemical reactions that can be treated as first-order reactions under certain conditions, even though they might involve higher-order kinetics. In a true first-order reaction, the rate of the reaction is directly proportional to the concentration of a single reactant. However, in some cases, reactions that are inherently second-order or higher-order can appear to be first-order under specific conditions.

Here are some common situations and examples of pseudo-first-order reactions:

Excess Reactant Conditions: Pseudo-first-order kinetics often occur when one reactant is present in a large excess compared to the others. In such cases, the concentration of the reactant in excess remains relatively constant throughout the reaction, allowing the rate of the reaction to depend mainly on the concentration of the limiting reactant.Example: The hydrolysis of an ester (like ethyl acetate) in the presence of excess water. Although this reaction is second order with respect to both ester and water, the concentration of water remains constant, making the reaction effectively first order with respect to the ester.
Catalyzed Reactions: Some reactions involve intermediates or catalysts that are consumed in small quantities compared to the main reactants. When the concentration of the catalyst remains nearly constant, the reaction can be approximated as first order.Example: The catalytic hydrogenation of a compound using a transition metal catalyst, where the catalyst concentration remains constant.
Dilute Solutions: In dilute solutions, the reactions can often be approximated as pseudo-first-order reactions because the concentrations of most reactants are much lower than the solvent.Example: The hydrolysis of sucrose (table sugar) in dilute aqueous solutions.
Radioactive Decay: Many nuclear decay processes, such as the decay of radioactive isotopes, follow pseudo-first-order kinetics because the number of radioactive nuclei present in a sample decreases over time. For example the decay of carbon-14 (C-14) in archaeological dating.

To analyze pseudo-first-order reactions, scientists typically use integrated rate equations and experimental data to determine rate constants and half-lives. These reactions are valuable in various fields of chemistry, including chemical kinetics, biochemistry, and environmental chemistry, as they simplify reaction rate calculations and provide insights into reaction mechanisms.

Temperature Dependence of the Rate of a Reaction

The Arrhenius equation is a fundamental concept in chemical kinetics that explains how the rate of a chemical reaction depends on temperature. It’s a powerful tool for understanding the relationship between temperature, activation energy, and reaction rate. Let’s break down the key components of the Arrhenius equation:

Rate Constant (k): This is a measure of how quickly a reaction proceeds. It quantifies the rate at which reactants are transformed into products. The rate constant is temperature-dependent and varies with different reactions.
Arrhenius Factor (A): Also known as the pre-exponential factor, the Arrhenius factor represents the frequency of successful collisions between reactant molecules. It is specific to a particular reaction and typically remains constant unless the reaction conditions change significantly.
Gas Constant (R): The gas constant is a universal constant used in thermodynamics and is approximately equal to 8.314 J/(mol·K) when expressed in SI units. It relates the temperature (in Kelvin) to energy.
Activation Energy (Ea): Activation energy is the energy barrier that reactant molecules must overcome to form products. It represents the minimum energy required for a successful reaction to occur.

The Arrhenius equation is given as follows:

k=A⋅e^*(−Ea/RT)

Where:

k is the rate constant.
A is the Arrhenius factor (pre-exponential factor).
Ea is the activation energy (in joules per mole, J/mol).
R is the gas constant (8.314 J/(mol·K)).
T is the absolute temperature (in Kelvin, K).

Here’s a breakdown of how temperature affects reaction rates according to the Arrhenius equation:

Increasing Temperature: When temperature rises, the exponential term e^(−Ea/RT) decreases because the denominator (RT) becomes larger. As a result, the rate constant (k) increases, and the reaction rate accelerates. Higher temperatures provide reactant molecules with more kinetic energy, increasing the likelihood of successful collisions with energy exceeding the activation energy.
Decreasing Temperature: Lowering the temperature decreases the rate constant (k), slowing down the reaction. At lower temperatures, fewer reactant molecules possess the necessary energy to overcome the activation energy barrier. Consequently, the reaction rate decreases.
Activation Energy (Ea): A higher activation energy means that reactants need more energy to initiate the reaction. As Ea increases, the reaction becomes more temperature-sensitive, and even small changes in temperature can have a significant impact on the rate.

Scientists use the Arrhenius equation to study the temperature dependence of reaction rates experimentally. By measuring reaction rates at different temperatures, they can calculate the activation energy (Ea) and the Arrhenius factor (A) for a given reaction. This information helps in understanding the mechanism and kinetics of chemical reactions, as well as optimizing reaction conditions in various industrial processes.

Effect of Catalyst

A catalyst is a substance that plays a crucial role in increasing the rate of a chemical reaction without itself undergoing any permanent chemical change. Catalysts are essential in various industrial and laboratory processes because they enable reactions to occur at a faster rate, often under milder conditions, which can save time, energy, and resources.

Here are some key points about catalysts:

Rate Enhancement: Catalysts function by providing an alternative reaction pathway with a lower activation energy (Ea) compared to the uncatalyzed reaction. This lower activation energy allows reactant molecules to overcome the energy barrier more easily and, thus, accelerate the reaction rate.
Intermediate Complex Theory: According to this theory, a catalyst participates in the reaction by forming temporary bonds with the reactants, leading to the creation of an intermediate complex. This complex has a transitory existence and eventually decomposes to yield the products and regenerate the catalyst.
Activation Energy: Catalysts reduce the activation energy required for a reaction to proceed. By lowering the potential energy barrier between reactants and products (as depicted in Fig. 3.11), catalysts enable a more significant fraction of reactant molecules to have the necessary energy to initiate the reaction.
No Permanent Change: Importantly, catalysts themselves are not consumed in the reaction, and they return to their original state after facilitating the reaction. This means that a small amount of catalyst can catalyze a large amount of reactants, making them highly efficient.
Equilibrium and Gibbs Energy: Catalysts do not alter the Gibbs free energy (∆G) of a reaction. They catalyze spontaneous reactions but do not influence non-spontaneous reactions. Catalysts also do not change the equilibrium constant (K) of a reaction. However, they help reactions reach equilibrium faster by catalyzing both the forward and reverse reactions to the same extent.

Collision Theory of Chemical Reactions

Collision theory provides valuable insights into the energetic and mechanistic aspects of chemical reactions, especially when it comes to understanding reaction rates. Developed by Max Trautz and William Lewis in the early 20th century, this theory is based on the kinetic theory of gases and assumes that reactant molecules behave as hard spheres. According to this theory, chemical reactions occur when these molecules collide with each other.

Here are some key points about collision theory:

Collision Frequency (Z): The number of collisions per second per unit volume of the reaction mixture is known as collision frequency (Z). It represents how often reactant molecules collide with each other.
Activation Energy (Ea): Activation energy (Ea) is a critical factor affecting reaction rates. It represents the minimum amount of kinetic energy that colliding molecules must possess to overcome the energy barrier and react. Reactant molecules need to have sufficient kinetic energy to break existing bonds and form new ones during a collision.
Rate Expression: For a bimolecular elementary reaction involving reactants A and B, the rate of the reaction can be expressed using collision theory as shown in equation (3.23). Here, ZAB represents the collision frequency of A and B, and e^(-Ea/RT) represents the fraction of molecules with energies equal to or greater than Ea.
Steric Factor (P): To account for the fact that not all collisions result in product formation, a steric factor (P) is introduced. The steric factor considers the probability of proper molecular orientation during a collision. Effective collisions occur when molecules collide with sufficient kinetic energy and the correct orientation for bonds to break and new bonds to form.
Effective Collisions: Effective collisions are those in which reactant molecules collide with the necessary kinetic energy and proper orientation to facilitate bond breaking and product formation. Ineffective collisions occur when molecules collide but lack the required energy or orientation, leading to no product formation.
Limitations: Collision theory simplifies molecular behavior by treating molecules as hard spheres and overlooking their structural complexities. While it provides valuable insights for reactions involving atomic species or simple molecules, it may not fully capture the behavior of complex molecules.