Kinetics

Kinetics: Rate of Reactions

Overview of Chemical Kinetics

• Definition: Chemical kinetics is the study of the rate of a reaction under various conditions.

• Important Point: A thermodynamically favorable reaction does NOT imply it will occur rapidly.

  • Example: The conversion of diamond to graphite demonstrates this principle.

Factors Affecting Reaction Rate

• Five major factors influence the rate of reactions:

  1. Temperature

  2. Concentration of Reactants

  3. States of Matter of Reactants

  4. Surface Area

  5. Catalysis

Details on Reaction Rate Factors

Physical State of Reactants

• Example:

  • Reaction between solid potassium sulfate (K2SO4) and solid barium nitrate (Ba(NO3)2): No reaction occurs because they are both in solid state.

  • The state matters significantly, e.g., gasoline in liquid vs. gas state has different rates of reaction.

Concentration of Reactants

• More molecules lead to more collisions, resulting in a faster reaction and a greater rate.

Temperature

• An increase in temperature increases kinetic energy, causing:

  • Molecules to move faster

  • More collisions and energetic collisions

  • General Rule: For many reactions, a 10°C increase will approximately double the reaction rate.

Surface Area

• Exposed surfaces exert a significant effect on the reaction rate.

  • For reactions at interfaces (two phases), greater exposed surface area increases collision frequency.

  • Example: Coal dust vs. charcoal demonstrates that a greater surface area can lead to faster reactions. Consider the grain dust explosion scenario.

Types of Chemical Reaction Rates

1. Instantaneous Reaction Rate: The rate at a specific moment.

2. Relative Reaction Rate: Expressed as a change in concentration over time.

3. Differential Rate Law or Rate Expression: Describes rate based on concentrations.

4. Integrated Rate Law or Rate Expression: Describes concentrations over time.

Measuring Reaction Rates

• Speed of Reaction Measurement: Expressed as a rate, which can be calculated as:
  $ext{Rate} = rac{- ext{change in concentration of reactant}}{ ext{time interval}}$ or $ext{Rate} = rac{+ ext{change in concentration of product}}{ ext{time interval}}$

• Rate can vary with time; graphing experimental data shows average reaction rates.

Instantaneous Reaction Rate

• To find the instantaneous rate at a given moment, calculate the slope of the tangent to the curve representing the data at that moment.

  • Tangent Line Guidelines:

  • Concave: Draw the tangent line above the curve.

  • Convex: Draw the tangent line below the curve.

Relative Reaction Rate

• Expressed as the change in concentration of a reactant or product per unit of time:
  $ext{Rate} = rac{ riangle [A]}{ riangle t}$

• The reaction stoichiometry dictates that changes in reactant concentration are negative, and changes in product concentration are positive.

• Example: For the equation: $2 ext{NO}<em>2(g) ightarrow ext{O}</em>2(g) + 2 ext{NO}(g)$

  • Relative rates are calculated from the coefficients in the balanced equation.

Practice Example

• Write the relative rates for: $ext{N}<em>2 + 3 ext{I}</em>2 ightarrow 2 ext{NI}_3$

  • Calculate the rate of appearance of NI3 if the rate of disappearance of I2 is $2.5 ext{M s}^{-1}$.

Collision Theory

• Particles must collide for a reaction to occur.

• Collision Types:

  • Successful Collisions: Molecules have sufficiently high energy to surpass the activation energy (Ea) and the right orientation.

  • Basic Definitions:

  • Activated Complex: A temporary state during a reaction.

  • Transition State: A configuration along the reaction coordinate where the potential energy is at a maximum.

Rate Law or Rate Expression

• For reactions that are reversible, when the rate of the forward reaction equals the rate of the reverse, the system reaches equilibrium.

• Initially, measure speeds using pure reactants, thoroughly mixed.

• Example of Rate Law:
  $ext{Rate} = k[ ext{NO}_2]^n$

• Derivation of rate constant (k) includes dimensional analysis to find units based on the order of reaction.

Order of Reaction

• Reaction order is the exponent in the rate expression based on concentration terms, summed for overall order.

  • Orders:

  • Zero Order: Rate = k (concentration has no effect)

  • First Order: Rate is proportional to reactant concentration: Rate = k[A]

  • Second Order: Quadruples rate if concentration is doubled: Rate = k[A]^2

Practice Problem

Example 1: Rate Law from Table Logic

• Given various experiments, determine orders based on relationship changes in concentrations versus initial rates. Record observations in tables.

Example 2: Determine Rate Constants

• Assess experiments involving differential rate laws, using collected initial concentration and rates to ascertain order and calculate k with units.

Catalysis

• Catalysis increases the reaction rate due to a catalyst that is not consumed during the process and can be rejuvenated.

• Biological Catalysts: Enzymes sensitive to shape and influenced by temperature and pH, can become denatured.

• Catalysts alter the energy pathway by lowering the activation energy (Ea).

Types of Catalysts

1. Homogeneous Catalysts: Exist in the same phase as reactants.

   • Example: CFCs like Freon, with chlorine acting as a catalyst.

2. Heterogeneous Catalysts: Have different phases from their reactants, often solid catalysts that interact with gaseous reactants, like those in catalytic converters.

Adsorption vs Absorption

• Adsorption: Particles adhere to the surface of another phase.

• Absorption: Particles are integrated into the bulk phase.

Reaction Mechanisms

• Includes the sequence of bond-breaking and bond-making steps in reactants to products.

• Must be determined through experimentation, adhering to stoichiometry and rate laws.

Molecularity of Reactions

• Unimolecular: Involves one reactant.

• Bimolecular: Involves two reactants colliding.

• Termolecular: Involves three reactants colliding, which is rare.

Rate Expressions for Elementary Steps

• The Rate Expression can only be derived from elementary steps.

• Identify the rate-determining step to write the rate law accurately.

Summary of Rate Expressions

• An elementary step's rate expressions relate directly to its molecularity, showing that the more reactants present, the higher the collision frequency.

Relationship of Reaction Mechanisms and Rate Laws

• Rate Laws must conform to experimentally established data; the slowest mechanism represents the rate-determining step, while intermediates do not appear in the rate law.

Practice Problems for Mechanisms

• Examine proposed mechanisms, checking their validity against experimentally determined rate laws, and calculate overall rates and molecularity.

Integrated Rate Laws

• Integrate reactions involving concentration and derive equations via graphical means.

• Types of Integrated Rate Laws:

  1. Zero Order: Concentration vs. Time

  2. First Order: Natural log concentration vs. Time

  3. Second Order: Reciprocal concentration vs. Time

Half-Life

• Focus on first-order reactions, expressed as:
  $t_{1/2} = rac{0.693}{k}$

• Half-life Characteristics:

  • Zero Order: Varies inversely with concentration.

  • First Order: Constant half-life.

  • Second Order: Increases with decreased concentration.

Arrhenius Equation

• Establishes temperature dependence of the rate constant (k) with activation energy (Ea).

• Ensure temperatures are in Kelvin: $k = Ae^{(- rac{Ea}{RT})}$

  • Where R (gas constant) = 8.314 J·K⁻¹·mol⁻¹.

Beer’s Law

• Describes the relationship between absorbance and concentration: $A = ext{εbc}$

  • Variables:

  • Absorbance (A)

  • Molar absorptivity (ε)

  • Path length (b)

  • Concentration (c)