Chemistry Chapter 3 Notes of CBSE Class 12

Chemical Kinetics is a branch of chemistry that studies the rate of chemical reactions, the factors affecting them, and their mechanisms . While thermodynamics predicts the feasibility and extent of a reaction, kinetics focuses on how fast it proceeds. The rate of a reaction is measured by the change in concentration of reactants or products over time. Key concepts include average and instantaneous rates, rate laws, reaction order, molecularity, and the distinction between elementary and complex reactions. Factors like concentration, temperature, pressure (for gases), and catalysts significantly influence reaction rates. Integrated rate laws relate concentration to time, while the Arrhenius equation describes temperature dependence and the role of activation energy. Collision theory provides insight into molecular requirements (energy and orientation) for effective reactions.

1. Introduction

• Chemistry deals with change, where substances are converted into others via chemical reactions.
• For any reaction, chemists study:
  • Feasibility: Predictable by thermodynamics (DG < 0 for feasible reactions at constant T, P).
  • Extent: Determined by chemical equilibrium.
  • Speed (Rate): Time taken to reach equilibrium, studied by chemical kinetics.
• Chemical Kinetics is the branch of chemistry that studies reaction rates and their mechanisms .
• Kinetics tells us about the rate of a reaction, whereas thermodynamics tells us about its feasibility . A thermodynamically feasible reaction might be kinetically very slow (e.g., diamond converting to graphite).

2. Rate of a Chemical Reaction

• The rate (or speed) of a reaction is defined as the change in concentration of a reactant or product per unit time.
• It can be expressed as:
  • Rate of decrease in concentration of any reactant [6(i)].
  • Rate of increase in concentration of any product [6(ii)].
• Concentration is typically expressed in molarity (mol L⁻¹).
• For a simple reaction R ® P:
  • Rate of disappearance of R = - D[R] / Dt
  • Rate of appearance of P = + D[P] / Dt
  • The negative sign for reactants makes the rate a positive quantity.
• Average Rate (r_av): Rate calculated over a specific time interval (Dt). It depends on the change in concentration and the time taken. The average rate decreases over time as reactant concentrations decrease.
• Instantaneous Rate (r_inst): The rate at a particular moment in time. It is the average rate over an infinitesimally small time interval (dt), where Dt approaches zero.
  • Mathematically: r_inst = - d[R]/dt = + d[P]/dt.
  • Graphically: Determined by the slope of the tangent to the concentration vs. time curve at a specific time 't'.
• Units of Rate: Concentration time⁻¹. Examples: mol L⁻¹s⁻¹ or atm s⁻¹ (for gaseous reactions using partial pressures).
• Expressing Rate for Reactions with Stoichiometry: For reactions where stoichiometric coefficients are not one:
  • The rate of disappearance/appearance of each species is divided by its respective stoichiometric coefficient to equate them.
  • For a reaction aA + bB ® cC + dD: Rate = - (1/a) d[A]/dt = - (1/b) d[B]/dt = (1/c) d[C]/dt = (1/d) d[D]/dt.

3. Factors Influencing Rate of a Reaction

• Reaction rate depends on experimental conditions:
  • Concentration of reactants (pressure in case of gases).
  • Temperature .
  • Catalyst .
• Rate generally increases when reactant concentrations increase.

4. Rate Expression and Rate Constant

• Rate Law (or Rate Equation/Expression): Represents the rate of reaction in terms of the concentration of reactants.
• For a general reaction aA + bB ® cC + dD:
  • Rate µ [A]ˣ [B]ʸ
  • Rate = k [A]ˣ [B]ʸ
  • This is the differential rate equation.
• k: The proportionality constant, called the rate constant . It is specific to a particular reaction under specific conditions (like temperature).
• Important Note: The exponents x and y in the rate law may or may not be equal to the stoichiometric coefficients (a and b) of the reactants. The rate law must be determined experimentally .

5. Order of a Reaction

• Order with respect to a reactant: The power to which the concentration of that reactant is raised in the rate law expression (e.g., x is the order with respect to A, y is the order with respect to B).
• Overall Order of a reaction: The sum of the powers of the concentration terms in the rate law expression (x + y).
• Order is an experimental quantity .
• Order can be 0, 1, 2, 3, and even a fraction .
• Zero Order Reaction: Rate is independent of the concentration of reactants (Rate = k [R]⁰ = k).

6. Molecularity

• Molecularity: Defined only for an elementary reaction .
• It is the number of reacting species (atoms, ions, or molecules) that collide simultaneously in an elementary reaction to bring about the reaction.
• Molecularity is always an integer .
• • Unimolecular: One reacting species involved (e.g., decomposition of NH₄NO₂).
  • Bimolecular: Simultaneous collision between two species (e.g., dissociation of 2HI).
  • Trimolecular (Termolecular): Simultaneous collision between three species (e.g., 2NO + O₂).
• Reactions with molecularity greater than three are very rare and slow due to the low probability of simultaneous collision.

7. Elementary and Complex Reactions

• Elementary Reactions: Reactions that take place in one single step .
• Complex Reactions: Reactions that occur in a sequence of elementary steps , called a mechanism .
• For complex reactions, the slowest step in the mechanism is the rate-determining step .
• The molecularity of the slowest (rate-determining) step in a complex reaction is the same as the overall order of the reaction.
• Intermediate species are formed during the mechanism but do not appear in the overall balanced equation.

8. Molecularity vs. Order

9. Units of Rate Constant (k)

• The units of the rate constant depend on the overall order of the reaction.
• For a reaction with overall order 'n', the units of k are generally (concentration)¹⁻ⁿ (time)⁻¹.
• Using mol L⁻¹ for concentration and s for time:
  • Zero Order (n=0): mol L⁻¹ s⁻¹.
  • First Order (n=1): s⁻¹.
  • Second Order (n=2): L mol⁻¹ s⁻¹.

10. Integrated Rate Equations

• Used to relate reactant concentrations at different times to the rate constant, avoiding graphical determination of instantaneous rate from tangents.
• Integrated rate equations are specific to the order of the reaction.
• For Zero Order Reaction (R ® P) :
  • Differential rate law: Rate = -d[R]/dt = k.
  • Integrated rate law: [R] = -kt + [R]₀ or k = ([R]₀ - [R])/t .
    • [R]₀ is the initial concentration at t=0.
  • Plot: [R] vs. t gives a straight line with slope = -k and intercept = [R]₀.
  • Half-life (t₁/₂): Time for [R] to become [R]₀/2. t₁/₂ = [R]₀ / 2k . Half-life is directly proportional to initial concentration .
  • Examples: Decomposition of NH₃ on hot platinum at high pressure.
• For First Order Reaction (R ® P) :
  • Differential rate law: Rate = -d[R]/dt = k[R].
  • Integrated rate laws:
    • ln [R] = -kt + ln [R]₀
    • kt = ln([R]₀/[R])
    • k = (2.303/t) log([R]₀/[R])
    • [R] = [R]₀ e ⁻ ᵏᵗ
    • [R]₀ is the initial concentration at t=0.
  • Plots:
    • ln [R] vs. t gives a straight line with slope = -k and intercept = ln [R]₀.
    • log([R]₀/[R]) vs. t gives a straight line with slope = k/2.303 .
  • Half-life (t₁/₂): Time for [R] to become [R]₀/2. t₁/₂ = 0.693/k . Half-life is constant and independent of initial concentration .
  • Examples: Radioactive decay of unstable nuclei, decomposition of N₂O₅, hydrogenation of ethene.
  • Pseudo First Order Reactions: Reactions that are higher order in reality (e.g., second order) but behave like first order under specific conditions (e.g., one reactant is in large excess, like solvent). Examples: Hydrolysis of ethyl acetate in excess water, inversion of cane sugar. The rate depends only on the concentration of the reactant not in excess.

11. Temperature Dependence of the Rate of a Reaction

• Reaction rates increase with temperature .
• Rate constant nearly doubles for every 10°C rise in temperature.
• Explained by the Arrhenius Equation :
  • k = A e ⁻ ᴱᵃ/ ᴿᵀ
  • k: Rate constant.
  • A: Arrhenius factor (or frequency factor, pre-exponential factor). It is a constant specific to a reaction. Related to collision frequency.
  • E ₐ: Activation Energy . Measured in J mol⁻¹.
  • R: Gas constant.
  • T: Absolute temperature (in Kelvin).
  • The term e⁻ᴱᵃ/ᴿᵀ represents the fraction of molecules having kinetic energy greater than Eₐ.
• Activation Energy (E ₐ): The energy required to form an unstable intermediate called the activated complex . The activated complex exists for a very short time and then forms products. Eₐ is the energy difference between the activated complex and reactants.
• Arrhenius Plot: Plotting ln k vs. 1/T gives a straight line.
  • From ln k = -Eₐ/RT + ln A, the slope is -E ₐ/R and the intercept is ln A .
• Equation for rate constants at two different temperatures (T₁ and T₂):
  • log(k₂/k₁) = (E ₐ / 2.303R) * [(T ₂ - T ₁) / (T ₁T ₂)] .
• Increasing temperature or decreasing activation energy leads to an increase in the rate constant and thus the reaction rate.

12. Effect of Catalyst

• A catalyst is a substance that increases the rate of a reaction without undergoing any permanent chemical change itself.
• A substance that reduces the rate is called an inhibitor .
• Action of a catalyst: Provides an alternate reaction pathway (mechanism) with a lower activation energy . This lowers the potential energy barrier.
• A small amount of catalyst can affect a large amount of reactants.
• A catalyst does not alter the Gibbs energy (ΔG) of a reaction.
• A catalyst does not change the equilibrium constant .
• It helps in attaining equilibrium faster by catalyzing the forward and backward reactions to the same extent.

13. Collision Theory

• Developed by Max Trautz and William Lewis.
• Based on the kinetic theory of gases.
• Assumptions: Reactant molecules are hard spheres, reactions occur when molecules collide.
• Collision Frequency (Z): Number of collisions per second per unit volume of the reaction mixture.
• Initial rate expression based on collisions: Rate = Z e⁻ᴱᵃ/ᴿᵀ. This compares A (from Arrhenius equation) to collision frequency (Z).
• Limitations: This simple model predicts rate constants well for simple molecules but less so for complex ones. Not all collisions lead to products.
• Effective Collisions: Collisions that result in the formation of products. Effective collisions require two conditions:
  • Sufficient kinetic energy: The colliding molecules must have energy equal to or greater than the threshold energy . Threshold energy = Activation Energy + energy possessed by reacting species [73 footnote].
  • Proper Orientation: Molecules must collide with the correct orientation to facilitate breaking old bonds and forming new ones. Improper orientation leads to molecules bouncing back.
• Steric Factor (P): Introduced to account for the requirement of proper orientation. It's also called the probability factor.
• Modified collision theory equation: Rate = P Z e ⁻ ᴱᵃ/ ᴿᵀ .
• Therefore, activation energy (energy requirement) and proper orientation (orientation requirement) together determine effective collisions and reaction rate.
• Drawback: Still considers molecules as hard spheres, ignoring structural aspects.

Frequently Asked Questions:

1. What is the difference between order and molecularity of a reaction?
   
   
   • Order is determined experimentally from the rate law and can be an integer, zero, or fraction for any type of reaction.
   • Molecularity is the number of simultaneously colliding species in an elementary step and is always an integer (1, 2, or 3) defined only for elementary reactions.
   • For complex reactions, the overall order equals the molecularity of the slowest step, but molecularity has no meaning for the overall reaction itself.
2. How does a catalyst affect the rate of a reaction?
   
   
   • A catalyst increases the rate of a reaction by providing an alternative reaction pathway.
   • This new pathway has a lower activation energy compared to the uncatalyzed reaction.
   • A catalyst does not change the overall thermodynamics (ΔG) or the equilibrium constant of the reaction.
3. What is activation energy and its significance according to Arrhenius equation?
   
   
   • Activation energy (Eₐ) is the minimum energy required to form the activated complex, an unstable intermediate, from the reactants.
   • The Arrhenius equation (k = A e⁻ᴱᵃ/ᴿᵀ) shows that a lower activation energy leads to a larger rate constant (k).
   • This means reactions with lower activation barriers proceed faster.