Chemical Kinetics and Rate Laws

Chemical Kinetics

• Chemical kinetics studies reaction rates.
• Reaction rate refers to the speed at which reactants disappear or products appear.
• For the reaction A → B, the rate is expressed as Rate = -Δ[A]/Δt = Δ[B]/Δt, where Δ[A] represents the change in concentration of A over time Δt.
• Because [A] decreases during the reaction, Δ[A] is negative and multiplied by -1 to yield a positive rate value.

Rate Laws

• Rate laws depict the relationship between reactant concentrations and reaction rate.
• For the reaction A + B → C + D, the rate law is generally expressed as Rate = k[A]^m[B]^n.
  • k denotes the rate constant
  • m indicates the order with respect to A
  • n indicates the order with respect to B
  • m + n represents the overall reaction order
• The values of m and n are experimentally determined and are unrelated to the coefficients in the balanced equation.

Integrated Rate Laws

• Integrated rate laws illustrate the relationship between reactant concentrations and time.
• The specific integrated rate law depends on the reaction order.

First Order

• For A → B, Rate = -Δ[A]/Δt = k[A]
• Integrated rate law forms:
  • ln[A]t - ln[A]0 = -kt
  • ln[A]t = ln[A]0 - kt
  • ln([A]t/[A]0) = -kt
  • [A]t = [A]0e^(-kt)
• Half-life: t1/2 = 0.693/k

Second Order

• For A → B, Rate = -Δ[A]/Δt = k[A]^2
• Integrated rate law forms:
  • 1/[A]t - 1/[A]0 = kt
  • 1/[A]t = 1/[A]0 + kt
• Half-life: t1/2 = 1/(k[A]0)

Zero Order

• For A → B, Rate = -Δ[A]/Δt = k
• Integrated rate law forms:
  • [A]t - [A]0 = -kt
  • [A]t = [A]0 - kt
• Half-life: t1/2 = [A]0/(2k)

Reaction Mechanisms

• Most reactions occur through a series of elementary steps that make up the reaction mechanism.
• Elementary steps must sum up to the overall balanced equation.
• The rate-determining step dictates the reaction rate since it's the slowest step.
• Intermediates are present in the mechanism but not the overall balanced equation.
• A catalyst accelerates a reaction by offering an alternative mechanism.

Arrhenius Equation

• The Arrhenius equation quantitatively describes how temperature affects the rate constant: k = Ae^(-Ea/RT)
  • Ea is the activation energy
  • R is the gas constant (8.314 J/mol·K)
  • A is the frequency factor
• Linear forms:
  • ln k = -Ea/R(1/T) + ln A
  • ln(k2/k1) = Ea/R(1/T1 - 1/T2)