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Class 12 Chemistry Notes Chapter 4 (Chemical Kinetics) – Examplar Problems Book

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Philoid

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Examplar Problems
Detailed Notes with MCQs of Chapter 4: Chemical Kinetics from your NCERT Exemplar. This chapter is crucial for understanding the rates and mechanisms of chemical reactions, and frequently appears in various government exams. Pay close attention to the definitions, formulas, and graphical interpretations.

Chemical Kinetics: Detailed Notes for Exam Preparation

1. Introduction:

  • Chemical Kinetics is the branch of chemistry dealing with the study of the speed or rate at which chemical reactions occur, the factors influencing these rates, and the mechanism by which reactions proceed.

2. Rate of a Chemical Reaction:

  • Definition: The change in concentration of any one of the reactants or products per unit time.
  • Average Rate: The rate measured over a significant time interval (Δt).
    • For a reaction: R → P
    • Average Rate = -Δ[R]/Δt = +Δ[P]/Δt
    • Negative sign indicates decrease in reactant concentration.
    • Positive sign indicates increase in product concentration.
  • Instantaneous Rate: The rate at a specific instant in time (dt → 0).
    • Instantaneous Rate = -d[R]/dt = +d[P]/dt
    • It is the slope of the tangent drawn to the concentration vs. time curve at that specific instant.
  • Units of Rate: Concentration time⁻¹ (e.g., mol L⁻¹ s⁻¹, mol L⁻¹ min⁻¹, atm s⁻¹ for gaseous reactions).
  • Expressing Rate for a General Reaction:
    • For 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
    • Remember to divide by the stoichiometric coefficients.

3. Factors Influencing Rate of Reaction:

  • Concentration of Reactants: Generally, the rate increases with increasing concentration of reactants (more collisions).
  • Temperature: Rate usually increases significantly with increasing temperature (more energetic collisions, more molecules crossing the energy barrier). Typically, the rate doubles for every 10°C rise.
  • Nature of Reactants and Products: Bond strengths, physical state, and complexity of molecules affect the rate. Reactions involving ionic species are usually faster than those involving covalent molecules.
  • Presence of a Catalyst: A catalyst alters the rate (usually increases it) without being consumed in the reaction. It provides an alternative reaction pathway with lower activation energy.
  • Surface Area of Reactants: For heterogeneous reactions (reactants in different phases), a larger surface area leads to a faster rate (more contact points).
  • Exposure to Radiation: Some reactions (photochemical reactions) are initiated or accelerated by absorbing photons of suitable wavelength (e.g., H₂(g) + Cl₂(g) --(hv)--> 2HCl(g)).

4. Rate Law and Rate Constant:

  • Rate Law (or Rate Equation): An experimentally determined expression that relates the rate of reaction to the molar concentrations of reactants, each raised to some power.
    • For aA + bB → Products
    • Rate = k [A]ˣ [B]ʸ
    • Here, 'x' is the order of reaction with respect to A, and 'y' is the order with respect to B.
    • x and y are determined experimentally and may or may not be equal to the stoichiometric coefficients (a and b).
  • Rate Constant (k):
    • The proportionality constant in the rate law.
    • Defined as the rate of reaction when the concentration of each reactant is unity.
    • Also called specific reaction rate.
    • Value depends only on temperature and the presence of a catalyst. It is independent of reactant concentrations.
    • Units of k depend on the overall order of the reaction: (Concentration)¹⁻ⁿ Time⁻¹, where n = overall order.
      • Zero order: mol L⁻¹ s⁻¹
      • First order: s⁻¹
      • Second order: L mol⁻¹ s⁻¹

5. Order of Reaction:

  • Definition: The sum of the powers of the concentration terms of the reactants in the experimentally determined rate law expression.
    • Overall Order (n) = x + y (from the rate law above).
  • It can be 0, 1, 2, 3, or even a fraction.
  • It is an experimental quantity.
  • Zero-Order Reaction: Rate is independent of reactant concentration. Rate = k.
  • First-Order Reaction: Rate is directly proportional to the concentration of one reactant. Rate = k[A]¹.
  • Second-Order Reaction: Rate is proportional to the product of concentrations of two reactants or the square of the concentration of one reactant. Rate = k[A]² or Rate = k[A][B].
  • Pseudo-First Order Reaction: Reactions which are bimolecular but behave as first order. This happens when one reactant is present in large excess, and its concentration remains practically constant during the reaction. Example: Acid hydrolysis of ester (Water is in large excess). Rate = k'[Ester].

6. Molecularity of a Reaction:

  • Definition: The number of reacting species (atoms, ions, or molecules) that must collide simultaneously in an elementary reaction (a reaction occurring in a single step) to bring about a chemical change.
  • It is a theoretical concept applicable only to elementary reactions.
  • It must be a whole number (1, 2, or 3). It cannot be zero or fractional.
  • For complex reactions (multi-step), molecularity has no meaning for the overall reaction. The slowest step (rate-determining step) determines the overall rate, and its molecularity is important.
  • Difference between Order and Molecularity:
    • Order: Experimental, sum of powers in rate law, can be zero/fractional, applies to overall reaction.
    • Molecularity: Theoretical, number of colliding species in an elementary step, always whole number, applies only to elementary steps.

7. Integrated Rate Equations: (Important for calculations)

  • Relate concentration to time directly.
  • Zero-Order Reaction:
    • Rate = k
    • Integrated Rate Law: k = ([R]₀ - [R]) / t or [R] = [R]₀ - kt
    • [R]₀ = Initial concentration, [R] = Concentration at time t.
    • Plot of [R] vs t is a straight line with slope = -k and intercept = [R]₀.
    • Half-life (t₁/₂): Time taken for concentration to reduce to half its initial value.
    • t₁/₂ = [R]₀ / 2k (Half-life is directly proportional to initial concentration).
  • First-Order Reaction:
    • Rate = k[R]
    • Integrated Rate Law (two common forms):
      • k = (2.303 / t) log₁₀ ([R]₀ / [R])
      • ln[R] = ln[R]₀ - kt or [R] = [R]₀ e⁻ᵏᵗ
    • Plot of ln[R] vs t is a straight line with slope = -k and intercept = ln[R]₀.
    • Plot of log₁₀[R] vs t is a straight line with slope = -k/2.303 and intercept = log₁₀[R]₀.
    • Half-life (t₁/₂):
    • t₁/₂ = 0.693 / k (Half-life is independent of initial concentration). This is a key characteristic used for identification.
    • For gaseous reactions, concentration can be replaced by partial pressure. k = (2.303 / t) log₁₀ (P₀ / Pₜ)

8. Temperature Dependence - Arrhenius Equation:

  • Relates the rate constant (k) to temperature (T) and activation energy (Ea).
  • Arrhenius Equation: k = A e⁻ᴱᵃ/ᴿᵀ
    • k = Rate constant
    • A = Arrhenius factor or Frequency factor or Pre-exponential factor. It relates to the frequency of collisions and the orientation factor. Units are the same as k.
    • Ea = Activation Energy: The minimum extra energy that reacting molecules must possess (above their average energy) to overcome the energy barrier and form products. Units: J mol⁻¹ or kJ mol⁻¹.
    • R = Gas constant (8.314 J K⁻¹ mol⁻¹)
    • T = Absolute temperature (in Kelvin).
  • Logarithmic Form: ln k = ln A - Ea / RT or log₁₀ k = log₁₀ A - Ea / (2.303 RT)
  • Graphical Determination: A plot of ln k vs 1/T gives a straight line with:
    • Slope = -Ea / R
    • Intercept = ln A
  • Calculating Ea from rate constants at two temperatures (T₁ and T₂):
    • log₁₀ (k₂ / k₁) = (Ea / 2.303 R) [ (T₂ - T₁) / (T₁ T₂) ]

9. Collision Theory of Reaction Rates:

  • Based on the kinetic theory of gases.
  • Postulates:
    • For a reaction to occur, reactant molecules must collide.
    • Not all collisions lead to product formation. Only effective collisions do.
    • Effective Collisions: Collisions where molecules possess sufficient kinetic energy (≥ Threshold Energy) and proper orientation.
  • Threshold Energy: The minimum total energy that colliding molecules must possess for the collision to be effective.
  • Activation Energy (Ea): Threshold Energy - Average Kinetic Energy of Reactants.
  • Rate = Z<0xE2><0x82><0x9AB> * P * e⁻ᴱᵃ/ᴿᵀ
    • Z<0xE2><0x82><0x9AB> = Collision frequency (number of collisions per second per unit volume between reactants A and B).
    • P = Probability or Steric factor (accounts for proper orientation).
    • e⁻ᴱᵃ/ᴿᵀ = Fraction of molecules having energy equal to or greater than Ea.
  • The Arrhenius factor A = Z<0xE2><0x82><0x9AB> * P.
  • Limitations: Assumes molecules are hard spheres, doesn't fully account for structural aspects.

10. Effect of Catalyst:

  • Definition: A substance that increases the rate of a chemical reaction without itself undergoing any permanent chemical change.
  • Mechanism: Provides an alternative reaction pathway or mechanism with a lower activation energy (Ea).
  • It does not alter the Gibbs energy change (ΔG) or equilibrium constant (K) of the reaction. It helps attain equilibrium faster.
  • Forms temporary bonds with reactants, forming an intermediate complex.
  • Characteristics: Required in small quantities, specific in action, remain unchanged chemically at the end (though physical state might change).
  • Inhibitors: Substances that decrease the reaction rate (sometimes called negative catalysts).

Multiple Choice Questions (MCQs):

  1. The unit of rate constant for a zero-order reaction is:
    a) s⁻¹
    b) L mol⁻¹ s⁻¹
    c) mol L⁻¹ s⁻¹
    d) L² mol⁻² s⁻¹

  2. For a first-order reaction A → Products, the half-life (t₁/₂) is:
    a) Directly proportional to the initial concentration [A]₀
    b) Inversely proportional to the initial concentration [A]₀
    c) Independent of the initial concentration [A]₀
    d) Proportional to the square of the initial concentration [A]₀

  3. The role of a catalyst is to change the:
    a) Gibbs energy of reaction
    b) Enthalpy of reaction
    c) Activation energy of reaction
    d) Equilibrium constant

  4. According to the Arrhenius equation, the rate constant (k) increases with:
    a) Increasing activation energy (Ea) and decreasing temperature (T)
    b) Decreasing activation energy (Ea) and decreasing temperature (T)
    c) Decreasing activation energy (Ea) and increasing temperature (T)
    d) Increasing activation energy (Ea) and increasing temperature (T)

  5. For the reaction 2A + B → C, the rate law is given by Rate = k[A][B]. If the concentration of A is doubled and B is halved, the rate of reaction will:
    a) Double
    b) Halve
    c) Remain the same
    d) Become four times

  6. Molecularity of a reaction:
    a) Is always equal to the overall order of reaction.
    b) Can be zero or fractional.
    c) Is the number of molecules involved in the rate-determining step of a complex reaction.
    d) Is the sum of stoichiometric coefficients of reactants in a balanced equation.

  7. The slope of the plot of ln k versus 1/T for the Arrhenius equation gives:
    a) -Ea / R
    b) -Ea / 2.303 R
    c) Ea / R
    d) k / A

  8. A reaction is found to be zero order. What will happen to the rate if the concentration of the reactant is doubled?
    a) It doubles
    b) It becomes four times
    c) It is halved
    d) It remains unchanged

  9. Hydrolysis of ethyl acetate in acidic medium (CH₃COOC₂H₅ + H₂O --(H⁺)--> CH₃COOH + C₂H₅OH) is an example of:
    a) Zero-order reaction
    b) First-order reaction
    c) Second-order reaction
    d) Pseudo-first order reaction

  10. In collision theory, the factor 'P' represents:
    a) Pressure factor
    b) Pre-exponential factor
    c) Probability or Steric factor
    d) Partition coefficient

Answer Key for MCQs:

  1. (c)
  2. (c)
  3. (c)
  4. (c)
  5. (c) [New Rate = k(2[A])([B]/2) = k[A][B] = Original Rate]
  6. (c) [Applies to elementary steps; for complex reactions, it's related to the slowest step]
  7. (a)
  8. (d)
  9. (d) [Water is in excess]
  10. (c)

Make sure you understand the concepts behind each point and MCQ. Revise these notes regularly, focusing on definitions, units, formulas, graphical representations, and the differences between key terms like order and molecularity. Good luck with your preparation!

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