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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
Rate Expression:
Rate = k [NO]^x [H₂]^y
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.
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.
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)
Use of Rate Law:
Choose any experiment (e.g., Experiment 1)
Experiment 1 Data:
Rate = 1.25 x 10⁻⁵ M/s
[NO] = 0.005 M, [H₂] = 0.002 M
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
Given Concentrations:
[NO] = 0.012 M
[H₂] = 0.006 M
Use Rate Law:
Rate = k [NO]² [H₂]
k = 250 (found in Part C)
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.
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