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Understanding Rate Laws in Kinetics

Aug 14, 2024

Lecture Notes: Rate Laws and Reaction Kinetics

Introduction to Rate Laws

  • Rate Law: Mathematical expression that relates the rate of a reaction to the concentration of reactants.
  • General Formula: Rate = k [A]^x [B]^y
    • k: Rate constant
    • x, y: Orders of reaction concerning each reactant, determined experimentally.

Reaction Example: Nitric Oxide and Hydrogen

  • Reaction: NO + H₂ → N₂ + H₂O
  • Temperature: 1280°C

Part A: Determining the Rate Law

  1. Rate Expression: Rate = k [NO]^x [H₂]^y
  2. Finding x:
    • Use experiments where [H₂] is constant.
    • Experiment 1 & 2: [H₂] = 0.002 M
      • [NO] changes from 0.005 M to 0.010 M
      • Rate changes from 1.25 x 10⁻⁵ to 5 x 10⁻⁵ (4-fold increase)
      • Calculation: 2^x = 4, x = 2
      • Conclusion: Second order in NO.
  3. Finding y:
    • Use experiments where [NO] is constant.
    • Experiment 2 & 3: [NO] = 0.01 M
      • [H₂] changes from 0.002 M to 0.004 M
      • Rate changes from 5 x 10⁻⁵ to 1 x 10⁻⁴ (2-fold increase)
      • Calculation: 2^y = 2, y = 1
      • Conclusion: First order in H₂.
  4. Rate Law: Rate = k [NO]² [H₂]

Part B: Overall Order of the Reaction

  • Overall Order: Sum of exponents in rate law: 2 + 1 = 3
  • Note: Coefficients in balanced equations do not determine rate law exponents.

Part C: Calculating Rate Constant (k)

  1. Use of Rate Law: Choose any experiment (e.g., Experiment 1)
  2. Experiment 1 Data:
    • Rate = 1.25 x 10⁻⁵ M/s
    • [NO] = 0.005 M, [H₂] = 0.002 M
  3. Substitute & Solve for k:
    • Calculation: Rate = k [0.005]² [0.002]
    • Solve: k = 250
    • Units: 1/(M²·s) based on dimensional analysis

Part D: Calculating Reaction Rate with New Concentrations

  1. Given Concentrations:
    • [NO] = 0.012 M
    • [H₂] = 0.006 M
  2. Use Rate Law:
    • Rate = k [NO]² [H₂]
    • k = 250 (found in Part C)
  3. Calculate Rate:
    • Rate = 250 * (0.012)² * 0.006
    • Result: Rate = 2.2 x 10⁻⁴ M/s

Summary

  • Rate Laws are determined by experimental data, not stoichiometric coefficients.
  • Order of Reaction and Rate Constants are key to understanding the kinetics of a reaction.
  • Experimental Determination involves varying one reactant concentration while holding others constant.