Chemical Kinetics - Units of Reaction Rates

• Reaction rate

  • The change in concentration of reactants or products per unit time

• Units of reaction rate:

  • Molarity per second (M/s)
  • Moles per liter per second (mol/L·s)
  • Grams per liter per second (g/L·s)

• Example: Consider the reaction: 2A + B → C

  • The rate of this reaction can be defined as the rate of disappearance of A or B or the rate of appearance of C

• The rate of reaction can be determined experimentally by measuring the change in concentration of any reactant or product with time.

Chemical Kinetics - Units of Reaction Rates

Slide 11:

• Integrated Rate Laws
  • Describe how the concentration of a reactant or product changes with time
  • Different reactions have different rate laws based on their stoichiometry and mechanism

Slide 12:

• First-Order Reactions
  • Reaction rate is directly proportional to the concentration of a single reactant
  • Example: A → products
  • Rate = k[A]
  • The integrated rate law for a first-order reaction is given by: ln[A]t = -kt + ln[A]0

Slide 13:

• Second-Order Reactions
  • A reaction rate is directly proportional to the square of the concentration of a reactant or to the product of the concentrations of two reactants
  • Example: 2A → products
  • Rate = k[A]² or Rate = k[A][B]
  • The integrated rate law for a second-order reaction is given by: 1/[A]t = kt + 1/[A]0

Slide 14:

• Zero-Order Reactions
  • Reaction rate is independent of the concentration of a reactant
  • Example: A → products
  • Rate = k
  • The integrated rate law for a zero-order reaction is given by: [A]t = -kt + [A]0

Slide 15:

• Half-Life of a Reaction
  • The time required for the concentration of a reactant or product to decrease to half of its initial value
  • For first-order reactions, the half-life is constant and independent of initial concentration
  • For second-order reactions, the half-life depends on the initial concentration

Slide 16:

• Activation Energy
  • The minimum energy required for a reaction to occur
  • Denoted as Ea
  • Determines the rate of a reaction
  • Higher activation energy leads to slower reaction rates

Slide 17:

• Arrhenius Equation
  • Describes the temperature dependence of reaction rates
  • k = Ae^(-Ea/RT)
  • k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin

Slide 18:

• Factors Affecting Reaction Rates
  • Concentration: Increasing concentration of reactants leads to faster reaction rates
  • Temperature: Higher temperature increases the rate of reaction due to increased kinetic energy
  • Catalysts: Substances that increase the rate of a reaction by providing an alternate reaction pathway with lower activation energy

Slide 19:

• Reaction Mechanisms
  • Complex reactions often occur through a series of smaller steps called elementary reactions
  • Reaction mechanism explains the individual steps and intermediates involved in a reaction
  • Rate-determining step is the slowest step that determines the overall rate of the reaction

Slide 20:

• Collision Theory
  • Particles must collide with proper orientation and sufficient energy to react
  • Collision frequency and energy play crucial roles in determining reaction rates
  • Activation energy determines the fraction of particles with sufficient energy to react

Slide 21:

• Reaction Rate Law
  • Describes the relationship between the rate of a reaction and the concentrations of its reactants
  • The general form of a rate law is: Rate = k[A]^m[B]^n
  • The exponents m and n are determined experimentally and may not necessarily match the coefficients in the balanced chemical equation

Slide 22:

• Rate Determination by Initial Rates Method
  • In the initial rates method, the rate of the reaction is measured at different initial concentrations of reactants
  • By comparing the rates, the exponents (m and n) in the rate law can be determined
  • Example: 2A + B → C
    • Initial concentrations: [A] = 0.1 M, [B] = 0.2 M, [C] = 0 M
    • Rate 1 = k[A]^m[B]^n
    • Rate 2 = k’[A’]^m[B’]^n
    • Compare rates to determine m and n

Slide 23:

• Rate Determination by Integrated Rate Laws Method
  • In the integrated rate laws method, the concentrations of reactants/products are measured at different times
  • By using the appropriate integrated rate law, the rate constant (k) can be determined
  • Example: A → products
    • Initial concentration: [A] = [A]0
    • Concentration at time t: [A]t
    • Use the integrated rate law to determine k

Slide 24:

• Reaction Order
  • The sum of the exponents in the rate law equation is the reaction order
  • Reaction order can be zero, first, second, or even fractional/negative
  • For example, a reaction with the rate law Rate = k[A]²[B]³ has a reaction order of 2 + 3 = 5

Slide 25:

• Rate Constant
  • The rate constant (k) is a proportionality constant in the rate law equation
  • The value of k depends on the specific reaction and the temperature at which the reaction occurs
  • The units of k depend on the overall reaction order

Slide 26:

• Factors Affecting Rate Constant
  • Temperature: Increasing temperature usually increases the value of k due to increased collision frequency and energy
  • Presence of catalysts: Catalysts can increase the rate constant by providing an alternative reaction pathway with lower activation energy
  • Physical state: The rate constant may vary depending on whether the reactants are in the gas, liquid, or solid state

Slide 27:

• Reaction Mechanism and Elementary Steps
  • A reaction mechanism describes the sequence of individual steps by which a reaction occurs
  • Elementary steps are the individual chemical reactions that make up the overall reaction
  • The rate law for the overall reaction can be determined by the slowest step, known as the rate-determining step

Slide 28:

• Reaction Intermediate
  • An intermediate is a species that is formed during the course of a reaction but does not appear in the balanced chemical equation
  • Intermediates are consumed in subsequent steps and are not present in the final products

Slide 29:

• Reaction Intermediates and Catalysts
  • Catalysts are substances that increase the rate of a reaction without being consumed in the process
  • Catalysts provide an alternative reaction pathway with a lower activation energy, increasing the rate of the reaction
  • Catalysts can react with reactants to form intermediates, which are then regenerated in subsequent steps

Slide 30:

• Summary of Key Points
  • Reaction rate is the change in concentration of reactants or products per unit time
  • Reaction rates can be defined by the disappearance of reactants or the appearance of products
  • Rate laws describe the relationship between the rate of a reaction and the concentrations of its reactants
  • Rate constants (k) depend on temperature, presence of catalysts, and physical state of reactants
  • Reaction mechanisms describe the sequence of elementary steps and the rate-determining step.