PCH 202: Chemical Kinetics Study Notes

PCH 202: Chemical Kinetics

Introduction

  • Instructor: Professor Festus Basden Chiedu Okoye

Course Topics

  • General Introduction on Chemical Kinetics
  • Factors Affecting the Rate of Chemical Reactions
  • Different Mechanisms of Drug Degradation
  • Applications of Chemical Kinetics in Pharmacy

Topic 1: Introduction to Chemical Kinetics

Learning Outcomes
  • Definition of chemical kinetics: The study of the rates of chemical processes and the factors affecting them.
  • Concept of molecularity of reaction: The number of reactant molecules participating in an elementary step.
  • Concept of order of reactions: Determining how reactant concentration affects the rate of reaction.
  • Differentiation between molecularity and order of reactions.
  • Types of reaction orders.
  • Concept of half-life and shelf life of drugs.
  • Experimental determination of reaction order.

Overview of Drug Stability

  • Drug stability: The ability of a pharmaceutical product to maintain its physical, chemical, therapeutic, and microbiological properties during storage.
  • Importance of chemical kinetics: Understanding and predicting drug stability hinges on reaction rates and mechanisms.

Basic Concepts of Chemical Kinetics

  • Definition: Chemical kinetics is the study of the rates of chemical processes and the factors affecting them.
  • Reaction rate: The speed at which a chemical reaction proceeds.

Molecularity of a Chemical Reaction

  • Molecularity: Refers to the number of reactant molecules that participate in the reaction's rate-determining step.
  • Classification of reactions by molecularity:
    • Unimolecular: Involving one molecule.
    • Bimolecular: Involving two molecules.
    • Termolecular: Involving three molecules.
Unimolecular Reaction
  • Definition: A reaction where a single molecule undergoes transformation to form one or more products, typically in the rate-limiting step:
    • Example: Decomposition of tert-butyl bromide in nucleophilic substitution (e.g., ext{PCl}_5
      ightarrow ext{PCl}_3 + ext{Cl}_2).
Bimolecular Reaction
  • Definition: Involves the collision of two molecules or particles in the rate-limiting step.
  • Examples:
    • Same type: 2 ext{H}_2 ext{O}_2
      ightarrow 2 ext{H}_2 ext{O} + ext{O}_2
    • Different types: ext{CH}_3 ext{COOC}_2 ext{H}_5 + ext{NaOH}
      ightarrow ext{CH}_3 ext{COONa} + ext{C}_2 ext{H}_5 ext{OH}
Termolecular Reaction
  • Definition: Involves simultaneous collisions of three reactants, which is statistically rare.
  • Example: Reaction 2 ext{NO} + ext{O}_2
    ightarrow 2 ext{NO}_2.

Order of a Reaction

  • Order of reaction: The sum of the coefficients (or powers) of the reacting species in the rate equation. It is an experimentally determined value, not a theoretical one.
  • Determining order:
    • Order can be whole numbers, fractions, or even zero.
    • Represents the number of species whose concentration affects the reaction rate.
    • Not dependent on stoichiometric coefficients but on reactant concentrations.
Calculation of Order of Reactions
  • General Reaction Example: aA + bB + cC ightarrow ext{Products}
    • Rate expression: ext{Rate} = k[A]^eta[B]^
      u[C]^
      ho
    • Order of reaction: ext{Order} = eta +
      u +
      ho.
Examples of Reaction Orders
  • Example 1: ext{H}_2 + ext{Br}_2 ightarrow 2 ext{HBr}; ext{rate} = k[ ext{H}_2][ ext{Br}_2]^{1/2}
    • Order = (1+12)=32(1 + \frac{1}{2}) = \frac{3}{2}.
  • Example 2: ext{CO} + ext{Cl}_2 ightarrow ext{COCl}_2; ext{rate} = k[ ext{CO}]^2[ ext{Cl}_2]^{1/2}
    • Order = (2+12)=52(2 + \frac{1}{2}) = \frac{5}{2}.
  • Example 3: 2 ext{HI} ightarrow ext{H}_2 + ext{I}_2; ext{rate} = k[ ext{HI}]^2
    • Order = 22.

Difference Between Order and Molecularity

Order
  • Sum of coefficients from the rate equation.
  • Determined experimentally.
  • Can be fractional or zero.
  • Applicable to all chemical reactions.
Molecularity
  • Number of reacting species in simultaneous collisions in an elementary reaction.
  • Theoretical concept, derived from the reaction mechanism.
  • Always a whole number.
  • Not applicable if the reaction order is zero.

Common Orders of Reaction

  • Zero Order
  • First Order
  • Second Order
  • Pseudo First Order
Zeroth-Order Reactions
  • Definition: A reaction whose rate is constant, independent of reactant concentration; rate = k.
  • Graph: The concentration of reactants and products versus time produces a straight line.
  • Example: Decomposition of N2O on a platinum (Pt) surface, where concentration does not affect the reaction rate between certain temperatures.
Other Examples of Zeroth Order Reaction
  • Oxidation of ethanol in the human liver.
  • Dissolution of an API in suspension.
  • Half-life: t1/2=a2k0t_{1/2} = \frac{a}{2k_0}.
  • Shelf-life: t90=0.1ak0t_{90} = \frac{0.1a}{k_0}.
First-Order Reactions
  • Definition: Reaction rate is directly proportional to the concentration of one reactant.
  • General Form: A → products.
  • Differential Rate: Rate doubles when concentration of A doubles.
  • Units: Reciprocal seconds (s−1s^{-1}).
Integrated Rate Law for First Order Reaction
  • Exponential Form: [extA]=[extA]0e−kt[ ext{A}] = [ ext{A}]_0 e^{-kt}.
  • Logarithmic Form: extln[extA]=extln[extA]0−ktext{ln}[ ext{A}] = ext{ln}[ ext{A}]_0 - kt.
Examples of First Order Reaction
  • Hydrolysis of aspirin.
  • Hydrolysis of t-butyl bromide with water.
  • Hydrolysis of cisplatin (anticancer drug).
Half-Life and Shelf Life of First Order Reaction
  • Half-life: t1/2=0.693k1t_{1/2} = \frac{0.693}{k_1}.
  • Shelf-life: t90=0.105k1t_{90} = \frac{0.105}{k_1}.
Second-Order Reactions
  • Definition: The reaction rate is proportional to the concentration of two reactants or the square of one reactant's concentration.
  • Forms:
    • Dimerization: 2A
      ightarrow ext{products}.
    • Reaction: A + B
      ightarrow ext{products}.
Differential Rate Law for Second Order Reaction
  • For 2A
    ightarrow ext{products}, rate law is extrate=k[A]2ext{rate} = k[A]^2.
Integrated Rate Law for Second Order Reaction
  • 1[extA]=kt+1[extA]0\frac{1}{[ ext{A}]} = kt + \frac{1}{[ ext{A}]_0}.
Half-Life and Shelf Life of Second Order Reaction
  • Half-life: t1/2=1ak2t_{1/2} = \frac{1}{ak_2}.
Pseudo-First Order Reaction
  • Definition: Occurs when one reactant is in excess and constant; behaves like a first-order reaction.
  • Example: CH_3COOCH_3 + H_2O
    ightarrow CH_3COOH + CH_3OH (water present in excess).
Determination of Order of a Reaction
  • Graphical Method:
    • For First Order: Plot of ext{log}[ ext{A}] versus time gives a straight line.
    • For Second Order: Plot of rac{1}{[ ext{A}]} versus time gives a straight line.
  • Substitution Method: Use time course data and substitute into integral equations to determine k values.
  • Half-Life Method: Graph of log(t_{1/2}) versus log(a) provides a slope for determining order.
    • Half-life relations for different orders can reveal n.
Van't Hoff Differential Method
  • Equation: The rate varies as the n-th power of reactant concentration.
    • For two initial concentrations:
      log(dC1)=log(k)+nlogC1log(dC_1) = log(k) + n log C_1
      log(dC2)=log(k)+nlogC2log(dC_2) = log(k) + n log C_2
  • Conclusion: n is derived from the logarithmic relationships of the two states.