Introduction
Rate laws quantify the relationship between reaction rate and reactant concentrations. They reveal kinetic behavior, mechanisms, and energy barriers. Essential to physical chemistry, rate laws enable prediction and control of reaction speed under varying conditions.
"Understanding rate laws is crucial to deciphering how reactions proceed and how to manipulate them for desired outcomes." -- IUPAC Gold Book
Definition of Rate Law
Basic Concept
Rate law expresses reaction rate (v) as a function of reactant concentrations raised to powers termed reaction orders.
General Form
v = k[A]^m[B]^n where k is rate constant; m, n are reaction orders with respect to A, B.
Dependence on Reaction Mechanism
Rate laws are empirical; derived from experimental data, not stoichiometry alone. Reflect underlying molecular steps.
Rate Constant (k)
Definition
Proportionality factor in rate law; temperature-dependent.
Units
Units vary with overall reaction order; ensure dimensional consistency.
Temperature Dependence
Arrhenius Equation: k = A exp(-Ea/RT), where A is frequency factor, Ea activation energy, R gas constant, T temperature.
k = A · e^(-Ea/RT)Order of Reaction
Definition
Exponent of concentration term in rate law; indicates sensitivity of rate to concentration changes.
Types
Zero order: rate independent of concentration. First order: rate proportional to single reactant concentration. Second order: rate proportional to square or product of two reactants.
Overall Order
Sum of individual orders; not necessarily equal to stoichiometric coefficients.
| Order | Rate Law Example | Rate Dependence |
|---|---|---|
| 0 | v = k | Independent of [A] |
| 1 | v = k[A] | Proportional to [A] |
| 2 | v = k[A]^2 or k[A][B] | Proportional to square or product |
Molecularity
Definition
Number of reactant molecules involved in a single elementary step.
Types
Unimolecular: one reactant molecule. Bimolecular: two molecules collide. Termolecular: three molecules simultaneously (rare).
Relation to Order
Molecularity applies only to elementary steps; order derives from experimental rate laws and may differ.
Differential Rate Law
Definition
Expresses rate as instantaneous function of reactant concentrations.
Form
v = -d[A]/dt = k[A]^m[B]^n
Experimental Determination
Initial rates method: measure initial rate at varying concentrations to deduce orders.
v = k[A]^m[B]^nwhere:v = rate,k = rate constant,[A], [B] = concentrations,m, n = ordersIntegrated Rate Law
Purpose
Relates reactant concentration to time elapsed; useful for kinetics monitoring.
Zero Order
[A] = [A]₀ - kt
First Order
ln[A] = ln[A]₀ - kt
Second Order
1/[A] = 1/[A]₀ + kt
| Order | Integrated Rate Law | Plot for Linearization |
|---|---|---|
| 0 | [A] = [A]₀ - kt | [A] vs. t |
| 1 | ln[A] = ln[A]₀ - kt | ln[A] vs. t |
| 2 | 1/[A] = 1/[A]₀ + kt | 1/[A] vs. t |
Methods of Determining Rate Laws
Initial Rates Method
Measure initial reaction rates at varying concentrations; plot log(rate) vs. log(concentration) to find orders.
Isolation Method
Keep all but one reactant concentration constant and vary the other to isolate order.
Integrated Rate Analysis
Fit concentration vs. time data to integrated rate laws; linear plots indicate correct order.
Complex Reaction Mechanisms
Elementary Steps
Individual molecular events; rate laws apply directly.
Rate-Determining Step
Slowest step controls overall rate; rate law depends on this step.
Steady-State Approximation
Assumes intermediate concentrations remain constant; used for complex rate laws.
Rate-determining step analysis:Step 1 (fast): A + B ⇌ I (intermediate)Step 2 (slow): I → ProductsRate law derived from step 2 and steady-state assumption on I.Effect of Temperature on Rate Laws
Arrhenius Equation
Describes temperature dependence of rate constant, k.
Activation Energy (Ea)
Minimum energy barrier for reaction progress; higher Ea means slower rate.
Temperature Coefficient
Rule of thumb: reaction rate doubles for every 10 °C increase in temperature.
Role of Catalysts in Rate Laws
Definition
Catalysts increase rate without being consumed; provide alternate pathway with lower Ea.
Effect on Rate Constant
Increase k by lowering activation energy; rate law form may change if catalyst participates.
Enzyme Kinetics
Michaelis-Menten kinetics exemplify catalyzed reactions with complex rate laws.
Applications of Rate Laws
Industrial Chemistry
Optimize reaction conditions for maximum yield and efficiency.
Pharmacokinetics
Model drug metabolism and clearance rates.
Environmental Chemistry
Predict pollutant degradation and atmospheric reactions.
References
- Atkins, P., de Paula, J. Physical Chemistry, 10th Ed., Oxford University Press, 2014, pp. 615-670.
- Laidler, K.J. Chemical Kinetics, 3rd Ed., Harper & Row, 1987, pp. 101-145.
- Espenson, J.H. Chemical Kinetics and Reaction Mechanisms, McGraw-Hill, 1995, pp. 50-95.
- Segel, I.H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems, Wiley, 1993, pp. 120-170.
- Glasstone, S., Lewis, D. Elements of Physical Chemistry, 2nd Ed., Macmillan, 1960, pp. 345-390.