Chemical Kinetics: Reaction Rates and Rate Law

• Chemical kinetics concerns itself with reaction rates

Reaction Rates

• Reaction rate is the speed at which reactants are converted into products

Factors Affecting Reaction Rate

• Higher concentrations of reactants usually increase the reaction rate
• Higher temperatures usually increase the reaction rate
• Increased surface area of solid reactants increases the reaction rate
• Catalysts speed up reactions without being consumed
• Increased pressure in gaseous reactions increases the reaction rate
• Light can initiate or accelerate certain reactions, known as photochemical reactions
• The solvent can affect the reaction rate

Rate Law

• Expresses the relationship between the rate of a reaction and the concentration of reactants, given by: $rate = k[A]^m[B]^n$
  • k is the rate constant
  • [A] and [B] are the concentrations of reactants.
  • m and n are the orders of the reaction with respect to reactants A and B

Reaction Order

• Determined experimentally and indicates how the rate is affected by the concentration of each reactant
  • Zero order: Rate is independent of reactant concentration
  • First Order: Rate is directly proportional to the reactant concentration
  • Second Order: Rate is proportional to the square of the reactant concentration

Rate constant

• The proportionality constant existing in the rate law

Factors Affecting Rate Constant

• The rate constant increases with increasing temperature, as described by the Arrhenius equation
• Lower activation energy leads to a larger rate constant
• Catalysts increase the rate constant by lowering the activation energy

Arrhenius Equation

• Describes the temperature dependence of the rate constant, given by: $k = Ae^{-\frac{E_a}{RT}}$
  • k is the rate constant
  • A is the pre-exponential factor
  • $E_a$ is the activation energy
  • R is the gas constant ($8.314 J mol^{-1} K^{-1}$)
  • T is the absolute temperature in Kelvin

Reaction Mechanisms

• The step-by-step sequence of elementary reactions by which the overall chemical change occurs

Elementary Steps

• Each step in a reaction mechanism
• Describes the actual molecular events that occur in a single step

Rate-Determining Step

• The slowest step in a reaction mechanism
• Determines the overall rate of the reaction

Intermediates

• Species that are produced in one step and consumed in a subsequent step
• Not present in the overall balanced equation

Activation Energy

• The minimum energy required for a reaction to occur

Transition State

• The highest energy state in a reaction
• Also known as the activated complex

Catalysts

• Substances that increase the reaction rate without being consumed in the reaction
• Provide an alternative reaction pathway with a lower activation energy

Types of Catalysis

• Homogeneous catalysis: Catalyst is in the same phase as the reactants
• Heterogeneous catalysis: Catalyst is in a different phase from the reactants
• Enzyme catalysis: Biological catalysts (enzymes) that are highly specific

Integrated Rate Laws

• Relate the concentration of reactants to time
• Used to determine the order of the reaction and calculate the rate constant

Zero-Order Reactions

• $[A]_t = -kt + [A]_0$
• $t_{1/2}=\frac{[A]_0}{2k}$

First-Order Reactions

• $ln[A]_t = -kt + ln[A]_0$
• $t_{1/2}=\frac{0.693}{k}$

Second-Order Reactions

• $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$
• $t_{1/2}=\frac{1}{k[A]_0}$

Equations definition

• $[A]_t$ is the concentration of reactant A at time t
• $[A]_0$ is the initial concentration of reactant A
• $t_{1/2}$ is the half-life

Collision Theory

• Explains the rate of reactions based on collisions between reactant molecules

Basic Principles

• Reactant particles must collide in order to react
• Collisions must occur with sufficient energy to overcome the activation energy barrier
• Collisions must occur with the proper orientation

Factors Affecting Collisions

• Concentration: Higher concentration leads to more frequent collisions
• Temperature: Higher temperature leads to more energetic and frequent collisions
• Surface Area: Larger surface area provides more sites for collisions to occur
• Catalysts: Catalysts increase the probability of successful collisions

Transition State Theory

• Reactions proceed through a high-energy intermediate state called the transition state
• The transition state is a short-lived species
• The rate of reaction depends on the concentration of the transition state and the frequency with which it decomposes to form products

Eyring Equation

• Relates the rate constant to the Gibbs free energy of activation, given by: $k = \frac{k_BT}{h}e^{\frac{-\Delta G^{\ddagger}}{RT}}$
  • $k_B$ is the Boltzmann constant ($1.38 \times 10^{-23} J/K$)
  • h is the Planck's constant ($6.626 \times 10^{-34} Js$)
  • $\Delta G^{\ddagger}$ is the Gibbs free energy of activation
  • R is the gas constant ($8.314 J mol^{-1} K^{-1}$)
  • T is the absolute temperature in Kelvin