What Is Chemical Kinetics?
Chemical kinetics is the branch of physical chemistry that studies the rates of chemical reactions — how fast reactants are consumed, products are formed, and how various factors (concentration, temperature, catalysts) influence speed. While thermodynamics tells us whether a reaction is possible, kinetics tells us how quickly it will actually occur.
Understanding reaction rates is critical in fields ranging from drug metabolism to industrial manufacturing.
Reaction Rate: Definition
The reaction rate is the change in concentration of a reactant or product per unit time. For a general reaction:
aA + bB → cC + dD
The rate can be expressed as:
Rate = −(1/a)(Δ[A]/Δt) = −(1/b)(Δ[B]/Δt) = (1/c)(Δ[C]/Δt) = (1/d)(Δ[D]/Δt)
The negative sign for reactants indicates their concentration decreases over time. Stoichiometric coefficients normalize the rate so that it is the same regardless of which species you measure.
Rate Laws
Experimental measurement reveals that reaction rates depend on reactant concentrations in a specific mathematical way called the rate law:
Rate = k[A]^m[B]^n
Where: - k is the rate constant (depends on temperature, not concentration) - [A] and [B] are molar concentrations of reactants - m and n are the reaction orders with respect to A and B (determined experimentally)
The overall reaction order is m + n.
Critical point: Reaction orders are NOT determined from stoichiometric coefficients. They must be determined experimentally.
Reaction Orders
Zero-order reactions (m = 0): - Rate = k (independent of concentration) - Concentration decreases linearly with time: [A] = [A]₀ − kt - Example: Some enzyme-catalyzed reactions when the enzyme is saturated
First-order reactions (m = 1): - Rate = k[A] - Concentration decreases exponentially: [A] = [A]₀ × e^(−kt) - Half-life: t₁/₂ = ln(2)/k = 0.693/k (constant, independent of initial concentration) - Example: Radioactive decay, many decomposition reactions
Second-order reactions (m = 2): - Rate = k[A]² or Rate = k[A][B] - Integrated rate law: 1/[A] = 1/[A]₀ + kt - Half-life: t₁/₂ = 1/(k[A]₀) (depends on initial concentration) - Example: NO₂(g) + CO(g) → NO(g) + CO₂(g) at low temperatures
Determining Reaction Order Experimentally
The method of initial rates is the most common experimental approach. By conducting multiple experiments with different initial concentrations and measuring initial rates, we can isolate the effect of each reactant.
Example procedure: 1. Double [A] while keeping [B] constant. If rate doubles → first order in A. 2. Triple [B] while keeping [A] constant. If rate increases ninefold → second order in B. 3. Rate law: Rate = k[A]¹[B]²
Once orders are known, k can be calculated by substituting any experimental data set into the rate law.
Integrated Rate Laws and Half-Life
The integrated rate law expresses concentration as a function of time, allowing predictions about how much reactant remains after a given time period. A useful diagnostic tool: plotting different functions of concentration versus time will yield a straight line only for the correct order.
| Order | Straight-line plot | Slope |
|---|---|---|
| Zero | [A] vs t | −k |
| First | ln[A] vs t | −k |
| Second | 1/[A] vs t | +k |
Half-life (t₁/₂) is the time required for the concentration to fall to half its initial value. First-order half-lives are widely used in medicine (drug half-life in the body) and nuclear chemistry.
The Rate Constant k
The rate constant k encodes all the temperature dependence of a reaction. It has units that depend on the overall reaction order: - Zero order: mol·L⁻¹·s⁻¹ - First order: s⁻¹ - Second order: L·mol⁻¹·s⁻¹
Real-World Applications
- Pharmacokinetics: Most drugs are eliminated from the body via first-order kinetics; the constant half-life allows predictable dosing schedules
- Food science: Spoilage reactions often follow first- or second-order kinetics; refrigeration slows k
- Industrial reactors: Chemical engineers design reactors based on rate laws to optimize yield and minimize waste
- Atmospheric chemistry: The rate laws for ozone depletion reactions (involving CFCs) determined international policy on refrigerants
- Nuclear medicine: Radioactive isotopes used in imaging (e.g., ⁹⁹ᵐTc, t₁/₂ = 6 hours) must decay at predictable rates for diagnostic accuracy
Summary
Rate laws are the mathematical language of chemical kinetics. By establishing the relationship between concentration and reaction rate, they allow chemists to predict how quickly reactions proceed, design efficient processes, and understand mechanisms at the molecular level. Combined with the Arrhenius equation, they provide a complete picture of reaction dynamics.