Advanced Chemistry - Chemical Kinetics Summary

Module Structure: Advanced Chemistry

  • Reaction kinetics: rate laws, rate constants, steady state approximation, Arrhenius equation.
  • Catalysis: homogeneous, heterogeneous, and enzymatic.
  • Surface and interface chemistry: adsorption isotherms (e.g., Langmuir).
  • Thermodynamics: heat and matter transfer in combustion reactions, fires, and explosions.
  • Synthetic pathways of drugs
  • Intermediates and by-products of drug syntheses
  • Purification of drugs from natural sources
  • Polymeric materials: polymerization reactions and characterization.

Coursework/Continuous Assessment Breakdown

  • Coursework & Continuous Assessment: 30%
    • Written Short Answer Questions: 15% (Week 5, Outcomes 1,2,3)
    • Written Short Answer Questions: 15% (Week 10, Outcomes 4,5)
  • End of Semester / Year Formal Exam: 70%
    • Final Exam: Closed Book Exam, 70% (End of Term, Outcomes 1,2,3,4,5)

Chemical Kinetics

  • Study of the rates of chemical reactions, their measurement, and interpretation.
  • Considered part of Physical Chemistry.
  • Addresses reaction mechanisms and the dependence of rates on external conditions like temperature.

Reaction Rate

  • Measure of change of reagent mixture in time:

    • rate = v{R→P} = – (CR(t2) – CR(t1))/(t2 – t1) = – ΔCR/ Δt
    • = + (CP(t2) – CP(t1))/(t2 – t1) = + ΔC_P/ Δt

  • Stoichiometry affects the rate:

    • 2R → P: rate = v{2R→P} = – ½ ΔCR / Δt = ΔC_P/ Δt
    • 2A + B → 3C + D: rate = v{2A+B→3C+D} = – ½ ΔCA/ Δt = – ΔCB/ Δt = ⅓ ΔCC/ Δt = ΔC_D/ Δt

  • Reaction rates vary with time, slowing as the reaction progresses due to diminishing driving force.

Rate Law

  • The rate of a reaction is often proportional to the concentrations of the reactants raised to some power:
    • aA + bB → cC + dD
    • rate = k [A]^x [B]^y
    • Important: k is the rate constant, dependent on reaction nature and temperature, but independent of concentration.

Reaction Order

  • Zero order: rate = k [A]^0 = k
  • First order: rate = k [A]^1 = k [A]
  • Second order: rate = k [A]^2 or = k [A] [B]
  • Third order: rate = k [A]^3 or = k [A] [B] [C] etc.
  • The order of a reaction is defined by the exponents in the rate law.
  • Overall order is the sum of the exponents (x+y).
  • No direct relation between reaction order and stoichiometric coefficients.
  • Complex multi-stage reactions may have non-integer orders.
  • Third and higher-order reactions are rare.

Zero Order Reactions

  • Rate is independent of reactant concentration.
  • Units of rate constant: mole L-1 s-1.

Zero Order Reactions - Integration

  • Integration between t=0 and t=t at concentrations [A]o and [A] gives

Example of Zero Order Reaction

  • Oxidation of ethanol in the human body. The rate of elimination is constant.
  • Average rate: 18 mg/100 ml blood per hour.

Half Life time for Zero order reaction

  • The half life t_{1/2} is defined as the time taken for the concentration of a reactant to fall to half of its initial value

First Order Reactions

  • Rate depends only on the concentration of one reactant raised to the first power.
  • rate = k [A], where k has units of s-1.
  • Integration between t=0 and t=t at concentrations [A]o and [A] gives

First Order Reactions - Exponential Decay

  • Exponential decrease in reactant concentration with time.
  • Plotting ln([A]/[Ao]) against t gives a straight line with a slope of –k.

Example of First Order Reaction

  • Cocaine elimination in human blood over time.
  • Rate of elimination is greatest at the beginning and decreases as the reaction progresses.
  • Most common drugs follow first-order reaction rates.

Pseudo First Order

  • Occurs when one reactant is in large excess (e.g., solvent).
  • Its concentration is included in the rate constant, giving a 'pseudo' rate constant k'.
  • Example: Hydrolysis of an ester in aqueous solution.
    • Rate = k [A]^x [B]^y ≈ k’ [B]^y

Half Life time for First order reaction

  • The half life t_{1/2} is defined as the time taken for the concentration of a reactant to fall to half its concentration value.
  • Constant half-life, independent of initial concentration.
  • Used widely in biochemistry and medicine (radioactive isotopes).

Second Order Reactions

  • Rate depends on two concentration terms.
  • May refer to the same or two different reactants.
  • Plot of 1/[A] versus t gives a straight line with slope = k.
  • Examples: 2I → I2, 2NOBr → 2NO + Br2

Second Order Reactions - Integration

  • Integration between t =0 and t=t at concentrations [A]o and [A] gives:

Half Life for Second order reaction

  • Varies inversely with the initial concentration:
    • t{1/2} = 1/(k [Ao])
  • Higher initial concentration, shorter half-life.
  • Compounds may persist in low concentrations for long periods.

Examples of Second Order Reactions

  • Hydrogenation of ethylene to yield ethane: H2 + C2H4 = C2H_6
  • Hydrolysis/saponification of an ester: CH3COOC2H5 + OH^- = CH3COO^- + C2H5OH

Rate Law & Reaction Order Summary

  • Zero-Order: d[A]/dt = k, [A] = [A]_0 - kt
    • units of k: M/s, linear plot: [A] vs. t, half-life: t{1/2} = [A]0 / 2k
  • First-Order: d[A]/dt = k[A], ln([A]/[A]_0) = -kt
    • units of k: 1/s, linear plot: ln([A]/[A]0) vs t, half-life: t{1/2} = ln(2)/k
  • Second-Order: d[A]/dt = k[A]^2, 1/[A] = 1/[A]_0 + kt
    • units of k: 1/M.s, linear plot: 1/[A] vs. t, half-life: t{1/2} = 1/[A]0k

Reaction Order Testing – Example

  • Gaseous decomposition of acetaldehyde @ 518 K.
  • If t_{1/2} is not constant, the reaction is not first order.
  • If the reaction is second order, then the product of the initial concentration (or pressure) and t_{1/2} should be a constant.

Molecularity of a Reaction

  • Classifies reactions by the number of molecules coming together in a single step.
  • Reactions occur in a series of steps called the mechanism.

Molecularity of a Reaction – Examples

  • Unimolecular: one molecule involved (e.g., N2O5 → N2O4 + ½O_2).
  • Bimolecular: two reactant molecules involved (e.g., NO2 + CO → NO + CO2).
  • Termolecular: three molecules involved (e.g., 2NO + X_2 → 2NOX).

Relating Reaction Order and Molecularity

  • Reaction order reflects the overall change.
  • Molecularity refers to a single kinetic process.

Chemical Kinetics and Temperature

  • Specific rate may increase by a factor of 2 to 3 for every 10°C (or K) rise (van't Hoff's rule).

Rate Constants and Temperature

  • Increase in reaction rates with increasing temperature.
  • Arrhenius equation: k = A e^{-E_a/RT}
    • k – rate constant
    • A – pre-exponential factor
    • Ea – Activation energy
    • R – gas constant
    • T – absolute temperature

Importance of Arrhenius Equation

  • Plot of lnk versus 1/T yields a straight line with slope = – E_a / R
  • The pre-exponential factor represents the number of collisions between reactant molecules also depending on molecules’ geometry.

Significance of Arrhenius Equation

  • Higher activation energy means stronger temperature dependence of rate constant.
  • Zero activation energy means rate is independent of temperature.

Usage of Arrhenius Equation

  • Allows calculation of rate constant at a different temperature if E_a is known.

Reversible Reactions and the Equilibrium Constant

  • Most reactions are reversible.
  • K = k/k': equilibrium constant, the ratio of specific rates for the forward and reverse reactions.

Consecutive Reactions

  • Most reactions proceed in stages.
  • Kinetics of the overall reaction are those of the rate-determining step.

Steady State Approximation

  • Assumes rate of formation of B – rate of loss of B.
  • Applies when B is a reactive, high-energy species.

Collision Theory of Reaction Rates

  1. Molecules must collide for a reaction to take place.
  2. Collisions must have high energy.
  3. Colliding particles must be properly oriented.