Lecture Notes: Rate of Chemical Reactions

Definition of Rate of Reaction

• Rate of Chemical Reaction: Change in concentration of reactant/product over time.
  • Units: Molar per second (mol/L/s)
• Conceptual comparison to physics:
  • Similar to average velocity (change in x over time)

Example: Simple Reaction A -> B

• Initial Conditions:
  • At time = 0 seconds, concentration of A = 1 M, B = 0 M
• After 2 seconds:
  • Concentration of A = 0.98 M
  • Concentration of B = 0.02 M

Calculating Average Rate of Reaction

• For product B:
  • Change in concentration = 0.02 M - 0 M
  • Change in time = 2 s - 0 s
  • Rate = 0.02 M / 2 s = 0.01 M/s
• For reactant A:
  • Change in concentration = 0.98 M - 1 M
  • Change in time = 2 s - 0 s
  • Rate = (-0.02 M) / 2 s = -0.01 M/s
  • Add negative sign to make rate positive -> 0.01 M/s
• General expression:
  • Rate = -Δ[A]/Δt = Δ[B]/Δt

More Complex Reaction: Decomposition of Dinitrogen Pentoxide

• Balanced Equation: N2O5 -> NO2 + O2
• Given: Rate of formation of O2 = 9 x 10^-6 M/s

Calculating Rates for Other Products

• Rate of formation of NO2:
  • Mole ratio: 4 NO2 for every O2
  • Rate = 4 x 9 x 10^-6 M/s = 3.6 x 10^-5 M/s
• Rate of disappearance of N2O5:
  • Mole ratio: 2 N2O5 for every O2
  • Rate = 2 x (-9 x 10^-6 M/s) = -1.8 x 10^-5 M/s
• Expressing the rate:
  • Rate = Δ[O2]/Δt = 9 x 10^-6 M/s
  • Rate = (1/4) Δ[NO2]/Δt = 3.6 x 10^-5 M/s
  • Rate = - (1/2) Δ[N2O5]/Δt = 9 x 10^-6 M/s

General Pattern for Rate Expression

• Use coefficients from balanced equation:
  • N2O5 coefficient: 2
  • NO2 coefficient: 4
  • O2 coefficient: 1
• Express rate using coefficients to adjust for stoichiometry.