Chemical Kinetics Class 12 – Notes, NCERT Solutions, Formulas & CBSE PYQs | Unit 4 Chemistry

Chemical kinetics is a fundamental branch of chemistry focused on understanding the speed of chemical reactions and their underlying mechanisms. It investigates how substances with defined properties are transformed into other substances with different properties through chemical reactions.

Unit 4 – Chemical Kinetics

4.1 Rate of a Chemical Reaction

4.2 Factors Influencing Rate of a Reaction

4.3 Integrated Rate Equations

4.4 Temperature Dependence of the Rate of a Reaction

4.5 Collision Theory of Chemical Reactions

I. What is Chemical Kinetics?

Chemistry is inherently concerned with change, specifically how chemical reactions convert substances. To fully understand any chemical reaction, chemists aim to determine:

• Feasibility: Whether a reaction can occur, which is predicted by thermodynamics (a reaction is feasible if Gibbs energy, ΔG, is less than 0 at constant temperature and pressure).
• Extent: To what degree a reaction will proceed, determined by chemical equilibrium.
• Speed (Rate): The time a reaction takes to reach equilibrium. This is where chemical kinetics comes in, as it specifically studies reaction rates and their mechanisms. The term "kinetics" originates from the Greek word "kinesis," meaning movement.

It's crucial to understand that thermodynamics only indicates a reaction's feasibility, not its rate. For example, thermodynamics suggests diamond should convert to graphite, but this conversion is so slow it's imperceptible, leading to the saying "diamond is forever". Chemical kinetics provides insights into how rapidly processes like food spoilage occur, how to design fast-setting dental materials, or what controls fuel burn rates in engines.

II. Objectives of Studying Chemical Kinetics

By studying chemical kinetics, you can learn to:

• Define average and instantaneous rates of a reaction.
• Express reaction rates in terms of changes in concentration of reactants or products over time.
• Distinguish between elementary and complex reactions.
• Differentiate between the molecularity and order of a reaction.
• Define the rate constant.
• Discuss how factors like concentration, temperature, and catalysts influence reaction rates.
• Derive and determine integrated rate equations and rate constants for zero and first-order reactions.
• Describe collision theory.

III. Rate of a Chemical Reaction

The rate of a chemical reaction, similar to the speed of an automobile, is defined as the change in concentration of a reactant or product per unit time. It can be expressed in two ways:

• Rate of decrease in concentration of any one of the reactants: Since reactant concentration decreases, the change (Δ[R]) is negative. To make the rate a positive quantity, it is multiplied by -1.
• Rate of increase in concentration of any one of the products: The change (Δ[P]) is positive as product concentration increases.

Chemical reactions can vary greatly in their speed:

• Very fast reactions: Like the precipitation of silver chloride from silver nitrate and sodium chloride solutions, which occurs instantaneously.
• Very slow reactions: Such as the rusting of iron in the presence of air and moisture.
• Reactions with moderate speed: Examples include the inversion of cane sugar and the hydrolysis of starch.

A. Average vs. Instantaneous Rate

• Average Rate ($r_{av}$): This is the rate measured over a significant period of time, depending on the change in concentration of reactants or products and the time taken for that change. For a hypothetical reaction R → P, if volume is constant:
  • Rate of disappearance of R = $-\frac{\Delta[R]}{\Delta t}$
  • Rate of appearance of P = $+\frac{\Delta[P]}{\Delta t}$
  • The average rate is typically represented by these expressions.
• Instantaneous Rate ($r_{inst}$): This is the rate of reaction at a specific moment in time. It is calculated as the change in concentration over an infinitesimally small time interval ($dt$). Mathematically, it is given by:
  • $r_{inst} = -\frac{d[R]}{dt} = +\frac{d[P]}{dt}$.
  • The instantaneous rate can be determined graphically by drawing a tangent to the concentration vs. time curve at a specific time and calculating its slope.

B. Units of Rate of a Reaction

The standard units for the rate of a reaction are concentration per unit time.

• If concentration is in mol L⁻¹ and time in seconds, the units are mol L⁻¹s⁻¹.
• For gaseous reactions where concentration is expressed as partial pressures, the units will be atm s⁻¹.

C. Rate Expression with Stoichiometric Coefficients

For a general reaction where stoichiometric coefficients are not all unity, the rate of reaction must be normalized. For example, in the reaction $2HI(g) \rightarrow H_2(g) + I_2(g)$, the rate of disappearance of HI is divided by its stoichiometric coefficient (2) to make it comparable to the rate of formation of products. Rate of reaction = $-\frac{1}{2}\frac{\Delta[HI]}{\Delta t} = \frac{\Delta[H_2]}{\Delta t} = \frac{\Delta[I_2]}{\Delta t}$.

IV. Factors Influencing Rate of a Reaction

The rate of a chemical reaction is influenced by several experimental conditions, including:

• Concentration of reactants (or pressure in the case of gases).
• Temperature.
• Catalyst.

A. Dependence of Rate on Concentration (Rate Law and Order of Reaction)

• Rate Law / Rate Equation / Rate Expression: This is an experimental representation of the reaction rate in terms of the concentrations of reactants and sometimes products. It cannot be predicted by merely looking at the balanced chemical equation; it must be determined experimentally.
  • Generally, reaction rates decrease as reactant concentrations decrease over time. Conversely, rates typically increase when reactant concentrations are increased. This shows that the rate of a reaction depends on the concentration of reactants.
  • For a generic reaction, $aA + bB \rightarrow cC + dD$, the rate law is typically written as: Rate = $k[A]^x[B]^y$.
    • Here, $k$ is the rate constant (a proportionality factor).
    • $x$ and $y$ are the exponents (often integers, but can be zero or even fractions) that indicate how sensitive the rate is to changes in the concentrations of A and B, respectively.
• Order of a Reaction: The sum of the exponents (powers) of the concentration terms in the rate law expression is called the overall order of that chemical reaction. The individual exponents ($x$ and $y$) represent the order with respect to specific reactants (A and B).
  • The order of a reaction can be 0, 1, 2, 3, or even a fraction.
  • A zero-order reaction means the rate of reaction is independent of the concentration of reactants.
  • Examples:
    • If Rate = $k[A]^{1/2}[B]^{3/2}$, the order is $1/2 + 3/2 = 2$ (second order).
    • If Rate = $k[A]^{3/2}[B]^{-1}$, the order is $3/2 + (-1) = 1/2$ (half order).
    • The decomposition of N₂O ($2N_2O(g) \rightarrow 2N_2(g) + O_2(g)$) has a rate law $Rate = k[N_2O]$ which is first order.
    • The hydrolysis of ethyl acetate ($CH_3COOC_2H_5 + H_2O \rightarrow CH_3COOH + C_2H_5OH$) in reality is a second order reaction, but when water is in large excess, it behaves as a first order reaction, with Rate = $k[CH_3COOC_2H_5]^1[H_2O]^0$ (or just $k[CH_3COOC_2H_5]$).

B. Elementary vs. Complex Reactions

• Elementary Reactions: Reactions that take place in a single step.
• Complex Reactions: Reactions that occur through a sequence of elementary reactions (known as the mechanism) to produce the final products. Examples include oxidation of ethane, which involves intermediate steps, and nitration of phenol, yielding multiple products.
• Rate-Determining Step: In a complex reaction, the overall rate of the reaction is controlled by the slowest step in its mechanism. This slowest step is called the rate-determining step, analogous to the slowest person in a relay race determining the team's chances of winning.

C. Molecularity of a Reaction

Molecularity is a property defined only for an elementary reaction. It refers to the number of reacting species (atoms, ions, or molecules) that must collide simultaneously to bring about a chemical reaction.

• Molecularity values are typically limited from 1 to 3 (unimolecular, bimolecular, termolecular).
• Reactions with molecularity higher than three are very rare because the probability of more than three molecules colliding simultaneously is very small.
• Molecularity and the order of an elementary reaction are the same. However, for complex reactions, molecularity has no meaning, and the overall reaction order must be determined experimentally. For instance, a reaction like $KClO_3 + 6FeSO_4 + 3H_2SO_4 \rightarrow KCl + 3Fe_2(SO_4)_3 + 3H_2O$ appears to be tenth order based on stoichiometry, but it is actually a second-order reaction, indicating it proceeds in multiple steps.

D. Effect of Temperature

It is commonly observed that for many chemical reactions, a rise in temperature of 10°C (or 10K) approximately doubles the rate constant. The quantitative relationship between temperature and the rate constant is accurately explained by the Arrhenius Equation: $k = A e^{-E_a/RT}$ Where:

• $k$ is the rate constant.
• $A$ is the Arrhenius factor (also known as the frequency factor or pre-exponential factor). It is a constant specific to a particular reaction.
• $E_a$ is the activation energy, measured in Joules/mole (J mol⁻¹). This is the energy required to form an unstable intermediate called an activated complex.
• $R$ is the gas constant.
• $T$ is the temperature in Kelvin.

The Arrhenius equation indicates that increasing the temperature or decreasing the activation energy will result in an increase in the rate of the reaction and an exponential increase in the rate constant. The relationship can be visualized by plotting $\ln k$ against $1/T$, which yields a straight line. The slope of this line is $-E_a/R$, and the intercept is $\ln A$.

The Maxwell-Boltzmann distribution curve helps explain the effect of temperature. This curve plots the fraction of molecules with a given kinetic energy against kinetic energy.

• The peak represents the most probable kinetic energy for the maximum fraction of molecules.
• Molecules need a minimum kinetic energy, activation energy ($E_a$), to react effectively upon collision.
• Increasing the temperature shifts the distribution curve, leading to a larger fraction of molecules possessing energy equal to or greater than the activation energy, thereby increasing the reaction rate.

E. Effect of Catalyst

A catalyst is a substance that increases the rate of a reaction without undergoing any permanent chemical change itself. For instance, MnO₂ catalyzes the decomposition of KClO₃.

• Conversely, a substance that reduces the rate of a reaction is called an inhibitor.
• The action of a catalyst is explained by the intermediate complex theory. According to this theory, the catalyst forms temporary bonds with reactants, creating an intermediate complex. This complex is short-lived and breaks down to yield products and regenerate the catalyst.
• The primary role of a catalyst is to provide an alternate reaction pathway or mechanism that has a lower activation energy. By lowering the potential energy barrier between reactants and products, the catalyst speeds up the reaction.
• A small amount of catalyst can affect a large quantity of reactants.
• Crucially, a catalyst does not alter the Gibbs energy (ΔG) of a reaction. It can only catalyze spontaneous reactions (ΔG < 0) and cannot initiate non-spontaneous reactions.

V. Integrated Rate Equations

Integrated rate equations relate the concentration of reactants (or products) to time. They are derived from differential rate equations and are essential for determining rate constants and understanding reaction progress.

A. Zero-Order Reactions

• Definition: The rate of reaction is proportional to the zero power of the concentration of reactants. This means the rate is independent of the reactant concentration.
• Differential Rate Law: Rate = $-\frac{d[R]}{dt} = k[R]^0 = k$.
• Integrated Rate Law: $[R] = -kt + [R]_0$.
  • Where $[R]_0$ is the initial concentration of the reactant at $t=0$, and $[R]$ is the concentration at time $t$.
  • Alternatively, the rate constant $k$ can be expressed as: $k = \frac{[R]_0 - [R]}{t}$.
• Half-Life ($t_{1/2}$): The time required for the concentration of the reactant to be reduced to half of its initial concentration. For a zero-order reaction:
  • $t_{1/2} = \frac{[R]_0}{2k}$.
  • This shows that the half-life for a zero-order reaction is directly proportional to the initial concentration of the reactants and inversely proportional to the rate constant.
• Examples: Zero-order reactions are relatively uncommon but can occur under specific conditions, such as:
  • Some enzyme-catalyzed reactions.
  • Reactions occurring on metal surfaces.
  • The decomposition of gaseous ammonia on a hot platinum surface at high pressure: $2NH_3(g) \xrightarrow{Pt catalyst, 1130K} N_2(g) + 3H_2(g)$, where $Rate = k[NH_3]^0 = k$.

B. First-Order Reactions

• Definition: The rate of reaction is proportional to the first power of the concentration of reactants.
• Differential Rate Law: Rate = $-\frac{d[R]}{dt} = k[R]^1 = k[R]$.
• Integrated Rate Law:
  • $\ln[R] = -kt + \ln[R]_0$.
  • Or, $k = \frac{2.303}{t} \log \frac{[R]_0}{[R]}$.
• Half-Life ($t_{1/2}$): For a first-order reaction:
  • $t_{1/2} = \frac{0.693}{k}$.
  • The half-life period for a first-order reaction is constant and independent of the initial concentration of the reacting species.
• Examples:
  • Hydrogenation of ethene: $C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)$, Rate = $k[C_2H_4]$.
  • All natural and artificial radioactive decay of unstable nuclei follow first-order kinetics.
  • Decomposition of N₂O₅ and N₂O are also examples.

C. Pseudo First-Order Reactions

These are reactions that appear to be of the first order but are actually higher-order reactions. This happens when one of the reactants is present in such a large excess that its concentration remains almost constant throughout the reaction.

• Example 1: Hydrolysis of Ethyl Acetate $CH_3COOC_2H_5 + H_2O \xrightarrow{H^+} CH_3COOH + C_2H_5OH$
  • This is intrinsically a second-order reaction involving both ethyl acetate and water.
  • However, if water is used in a large excess (e.g., 10 mol of water for 0.01 mol of ethyl acetate), the change in water concentration is negligible (from 10 mol to 9.99 mol).
  • Therefore, the reaction rate is primarily affected only by the concentration of ethyl acetate, making it behave like a first-order reaction. Its rate law becomes $Rate = k[CH_3COOC_2H_5]^1[H_2O]^0 = k'[CH_3COOC_2H_5]$ where $k'$ effectively includes the constant water concentration.
• Example 2: Inversion of Cane Sugar $C_{12}H_{22}O_{11} + H_2O \xrightarrow{H^+} C_6H_{12}O_6 + C_6H_{12}O_6$ (Glucose + Fructose)
  • This is another pseudo first-order reaction because water is typically present in vast excess.
  • The rate law is $Rate = k[C_{12}H_{22}O_{11}]$.

D. Summary of Integrated Rate Laws (Table 3.4)

Order	Reaction Type	Differential Rate Law	Integrated Rate Law	Straight Line Plot	Half-Life ($t_{1/2}$)	Units of $k$
0	R $\rightarrow$ P	$d[R]/dt = -k$	$kt = [R]_0 - [R]$	$[R]$ vs $t$	$[R]_0 / 2k$	mol L⁻¹s⁻¹
1	R $\rightarrow$ P	$d[R]/dt = -k[R]$	$kt = \ln([R]_0/[R])$	$\ln[R]$ vs $t$	$0.693 / k$	s⁻¹

VI. Collision Theory of Chemical Reactions

Collision theory provides a molecular-level explanation for how reactions occur. It postulates that reactions happen when molecules collide with each other, treating them as hard spheres.

• Collision Frequency (Z): The number of collisions per second per unit volume of the reaction mixture.
• For a bimolecular elementary reaction, A + B $\rightarrow$ Products, the rate can be expressed as: Rate = $Z_{AB} e^{-E_a/RT}$
  • $Z_{AB}$ represents the collision frequency between reactants A and B.
  • $e^{-E_a/RT}$ represents the fraction of molecules that have kinetic energy equal to or greater than the activation energy ($E_a$).

However, this initial model has limitations:

• It predicts rate constants fairly accurately for reactions involving simple atomic species or molecules but shows significant deviations for complex molecules.
• The main reason for these deviations is that not all collisions lead to the formation of products.

To account for this, the concept of effective collisions was introduced:

• Effective Collisions: These are collisions in which molecules meet with sufficient kinetic energy (known as threshold energy) and proper orientation.
  • Threshold Energy: This is the minimum energy required for a collision to be effective. It is equal to the activation energy plus the energy already possessed by the reacting species.
  • Proper Orientation: Molecules must align correctly during collision to facilitate the breaking of old bonds and the formation of new ones. For example, the formation of methanol from bromoethane requires specific orientations of the reactant molecules; improper orientation causes them to simply bounce back.
• Probability or Steric Factor (P): To incorporate the requirement of proper orientation, a factor 'P' is added to the rate equation. Rate = $P Z_{AB} e^{-E_a/RT}$

Thus, collision theory, in its refined form, states that both activation energy and the proper orientation of molecules are crucial criteria for an effective collision and, consequently, for determining the rate of a chemical reaction.

Despite its utility, collision theory still has drawbacks, primarily because it simplifies atoms and molecules as hard spheres, ignoring their complex structural aspects.

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To think of chemical kinetics is like considering a race.

• Thermodynamics tells you if the race can be run (is it physically possible?), and how far you will get (the finish line).
• Chemical Kinetics tells you how fast you run the race. It investigates your speed (rate of reaction), what factors slow you down or speed you up (concentration, temperature, catalyst), and the specific steps you take to get there (reaction mechanism).
• The activation energy is like the hurdle you need to jump over to start running effectively; if it's too high, you might not even try, or you'll be very slow.
• A catalyst is like a shortcut or a clear path over the hurdle, making it easier and faster to jump.
• Collision theory is the idea that you actually have to bump into other runners in the right way and with enough energy to exchange places or achieve your goal. If you just gently touch or run past each other without proper engagement, nothing changes.

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