Reaction Kinetics

Definition: Reaction kinetics is the study of the rates at which chemical reactions proceed and the factors that influence how fast reactants convert into products.

How It Works

Reaction rate depends on concentration, temperature, surface area, and the presence of a catalyst, all of which affect how often and how energetically molecules collide
Collision theory holds that a reaction only occurs when reactant particles collide with both the correct orientation and enough kinetic energy to overcome the activation energy (Ea), the energy barrier separating reactants from products
Increasing temperature raises reaction rate mainly by increasing the fraction of molecules with energy at or above Ea, not just by increasing collision frequency, following the Boltzmann energy distribution
A rate law expresses how rate depends mathematically on reactant concentrations: rate = k[A]ᵐ[B]ⁿ, where m and n are the reaction orders with respect to each reactant and must be determined experimentally, not read off the balanced equation
Overall reaction order is the sum of the individual orders (m + n); common values are zero, first, and second order, each with distinct mathematical behavior
The rate constant k is specific to a given reaction at a given temperature and changes with temperature according to the Arrhenius equation
Catalysts speed up reactions by providing an alternative reaction pathway with a lower activation energy, without being consumed or appearing in the overall balanced equation
Most reactions proceed through a mechanism, a sequence of elementary steps that sum to the overall reaction; the slowest step, called the rate-determining step, controls the overall observed rate
Kinetics (how fast a reaction happens) and thermodynamics (whether a reaction is favorable) are independent; a reaction can be thermodynamically favorable yet kinetically very slow, like diamond’s very slow conversion to graphite at room temperature
Molecularity describes the number of species colliding in a single elementary step (unimolecular, bimolecular, termolecular), which is a different concept from the experimentally measured reaction order of the overall rate law

Under the Hood

Integrated rate laws describe concentration over time for each common order:

Zero order:   [A] = [A]₀ - kt            t½ = [A]₀ / 2k
First order:  ln[A] = ln[A]₀ - kt        t½ = ln(2) / k
Second order: 1/[A] = 1/[A]₀ + kt        t½ = 1 / (k[A]₀)

The Arrhenius equation links the rate constant to temperature and activation energy:

k = A·e^(-Ea/RT)      A = pre-exponential (frequency) factor, R = 8.314 J/(mol·K)

Worked example 1 — determining reaction order from data. For A → products, three trials give:

[A] = 0.10 M → rate = 0.005 M/s
[A] = 0.20 M → rate = 0.020 M/s   (doubling [A] quadrupled the rate)
[A] = 0.40 M → rate = 0.080 M/s   (doubling [A] again quadrupled the rate)

Rate quadruples (2²) each time concentration doubles, so the reaction is second order in A: rate = k[A]². Solving for k using the first data point: k = 0.005 / (0.10)² = 0.5 M⁻¹s⁻¹.

Worked example 2 — Arrhenius equation, finding Ea. A reaction’s rate constant is 1.0×10⁻³ s⁻¹ at 300 K and 3.0×10⁻³ s⁻¹ at 310 K. Find the activation energy.

ln(k₂/k₁) = -Ea/R × (1/T₂ - 1/T₁)
ln(3.0) = 1.099
1/300 - 1/310 = 1.075×10⁻⁴ K⁻¹
Ea = R × ln(k₂/k₁) / (1/T₁ - 1/T₂) = 8.314 × 1.099 / 1.075×10⁻⁴ ≈ 85,000 J/mol = 85.0 kJ/mol

An 85 kJ/mol activation energy is a realistic value for a moderate-speed reaction, roughly in line with many organic and inorganic reactions studied near room temperature.

Worked example 3 — first-order half-life. N₂O₅ decomposes by first-order kinetics with k = 3.4×10⁻⁵ s⁻¹ at 25°C. Find the half-life.

t½ = ln(2)/k = 0.693 / 3.4×10⁻⁵ ≈ 20,400 s ≈ 5.7 hours

Unlike zero- or second-order half-lives, a first-order half-life is constant, independent of starting concentration, exactly like radioactive decay.

Why It Matters

Industrial chemical process design depends on kinetics to size reactors, choose operating temperature and pressure, and predict throughput
Pharmacokinetics uses reaction-rate principles to predict how quickly a drug is absorbed, distributed, metabolized, and eliminated, which sets dosing schedules
Food preservation techniques like refrigeration and freezing work by slowing the kinetics of spoilage reactions, not by stopping them entirely
Catalytic converters in vehicles rely on catalysts that speed up the conversion of toxic exhaust gases into less harmful products within the brief time exhaust spends in the converter
Explosion and fire safety engineering depends on understanding how rate accelerates with temperature, since many hazardous reactions are highly temperature-sensitive
Enzyme kinetics in biochemistry explains how biological catalysts achieve reaction rates many orders of magnitude faster than the uncatalyzed reaction, essential for life at body temperature

Common Pitfalls

Assuming reaction order matches the stoichiometric coefficients in the balanced equation; order must be determined experimentally and often doesn’t match coefficients at all, except for genuine elementary steps
Confusing rate constant units across reaction orders; k has different units for zero order (M/s), first order (1/s), and second order (1/(M·s)), so a stated k value is meaningless without knowing the order
Forgetting that increasing temperature increases k for essentially all reactions, including reverse reactions, so it speeds approach to equilibrium without necessarily favoring products over reactants
Believing a catalyst changes the equilibrium position or the reaction’s thermodynamics; a catalyst only speeds up how fast equilibrium is reached, it doesn’t shift where that equilibrium lies
Mixing up average rate (measured over a time interval) with instantaneous rate (the slope of the tangent line at one specific moment), which matters when a reaction’s rate changes noticeably over the interval measured
Confusing molecularity (number of species in one elementary step) with reaction order (an empirical exponent in the overall rate law); they coincide only for single-step elementary reactions
Assuming a reaction with a large activation energy is always slow at every temperature; a large Ea simply means rate is highly temperature-sensitive, and a big enough temperature increase can still make the reaction fast

Comparison

Order	Rate law	Integrated law	Half-life	Linear plot
Zero	rate = k	[A] = [A]₀ - kt	[A]₀/2k (depends on [A]₀)	[A] vs. t
First	rate = k[A]	ln[A] = ln[A]₀ - kt	ln(2)/k (constant)	ln[A] vs. t
Second	rate = k[A]²	1/[A] = 1/[A]₀ + kt	1/(k[A]₀) (depends on [A]₀)	1/[A] vs. t

A reaction mechanism’s rate-determining step is always the slowest elementary step, and it alone dictates the overall rate law regardless of how many fast steps surround it:

Step 1 (slow): NO₂ + NO₂ → NO₃ + NO      rate-determining
Step 2 (fast): NO₃ + CO → NO₂ + CO₂

Overall:       NO₂ + CO → NO + CO₂
Observed rate law: rate = k[NO₂]²  (matches only the slow step, not the overall equation)

Notice the observed rate law depends on [NO₂]² even though CO appears in the overall balanced equation; CO only participates in the fast second step, so its concentration doesn’t show up in the rate law at all.

Example

The iodine clock reaction is a classic kinetics demonstration where two colorless solutions are mixed and stay clear for a predictable, adjustable delay before suddenly turning dark blue-black, letting students directly observe how changing concentration or temperature changes reaction rate by timing the color change.

Real-World Application

Pharmacokinetics often models drug elimination from the bloodstream as a first-order process, since elimination rate is typically proportional to the current drug concentration. A drug with an elimination half-life of 6 hours follows the same halving pattern as radioactive decay:

t = 0h:  100% of dose remains
t = 6h:   50% remains (1 half-life)
t = 12h:  25% remains (2 half-lives)
t = 24h:   6.25% remains (4 half-lives)

This is why drugs with short half-lives need frequent dosing to maintain a therapeutic concentration, while drugs with long half-lives can be dosed once daily or less, and why it takes roughly 4-5 half-lives for a drug to be considered essentially cleared from the body.

FAQ

Does a fast reaction always have a low activation energy? Not necessarily; rate depends on both Ea and temperature through the Arrhenius equation, so a high-Ea reaction can still be fast if the temperature is high enough to compensate.

Why do reaction rates usually roughly double for every 10°C rise in temperature? This is a common rule of thumb (not a strict law) that holds approximately for many reactions with moderate activation energies near room temperature, following directly from the exponential form of the Arrhenius equation.

Can a reaction have a negative order? Yes, in rare cases; a negative order with respect to a species means increasing that species’ concentration actually slows the reaction, often because it’s a product that inhibits a step in the mechanism.

Why does surface area affect the rate of reactions involving solids? Reaction happens at the interface between phases, so a solid ground into powder exposes far more surface area to the same volume of reactant than a single large chunk, letting far more collisions happen per second even though the total amount of solid hasn’t changed.

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