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:

  • $rate = v<em>{R→P} = – (C</em>R(t<em>2) – C</em>R(t<em>1))/(t</em>2 – t<em>1) = – ΔC</em>R/ Δt$
  • $= + (C<em>P(t</em>2) – C<em>P(t</em>1))/(t<em>2 – t</em>1) = + ΔC_P/ Δt$

• Stoichiometry affects the rate:

  • $2R → P: rate = v<em>{2R→P} = – ½ ΔC</em>R / Δt = ΔC_P/ Δt$
  • $2A + B → 3C + D: rate = v<em>{2A+B→3C+D} = – ½ ΔC</em>A/ Δt = – ΔC<em>B/ Δt = ⅓ ΔC</em>C/ Δt = ΔC_D/ Δt$

• 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: $2I → I<em>2$, $2NOBr → 2NO + Br</em>2$

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:
  • $t<em>{1/2} = 1/(k [A</em>o])$
• 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: $H<em>2 + C</em>2H<em>4 = C</em>2H_6$
• Hydrolysis/saponification of an ester: $CH<em>3COOC</em>2H<em>5 + OH^- = CH</em>3COO^- + C<em>2H</em>5OH$

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: $t<em>{1/2} = [A]</em>0 / 2k$
• 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: $t</em>{1/2} = ln(2)/k$
• 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: $t<em>{1/2} = 1/[A]</em>0k$

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., $N<em>2O</em>5 → N<em>2O</em>4 + ½O_2$).
• Bimolecular: two reactant molecules involved (e.g., $NO<em>2 + CO → NO + CO</em>2$).
• 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.