Reaction Rate Formula
Calculate the rate of a chemical reaction as the change in concentration over time.
Includes rate laws and worked examples.
The Formula
The reaction rate measures how fast a reactant is consumed or a product is formed. It is expressed as the change in concentration per unit time.
Variables
| Symbol | Meaning |
|---|---|
| Rate | Speed of the reaction (mol/(L·s) or M/s) |
| Δ[Reactant] | Change in reactant concentration (mol/L) |
| Δ[Product] | Change in product concentration (mol/L) |
| Δt | Change in time (seconds, s) |
Rate Law
The rate law relates reaction rate to the concentrations of reactants raised to their respective orders. The rate constant k and the orders m, n are determined experimentally.
| Symbol | Meaning |
|---|---|
| k | Rate constant (units depend on reaction order) |
| [A], [B] | Concentrations of reactants (mol/L) |
| m, n | Reaction orders with respect to each reactant |
Example 1
The concentration of a reactant decreases from 0.80 M to 0.60 M in 20 seconds. What is the rate?
Rate = -Δ[Reactant] / Δt
Rate = -(0.60 - 0.80) / 20
Rate = -(-0.20) / 20 = 0.20 / 20
Rate = 0.01 M/s
Example 2
For a first-order reaction with k = 0.05 s⁻¹ and [A] = 0.40 M, what is the rate?
Rate = k × [A]¹
Rate = 0.05 × 0.40
Rate = 0.02 M/s
When to Use It
Use the reaction rate formula in chemical kinetics:
- Measuring how quickly a reaction proceeds
- Comparing rates under different conditions (temperature, concentration)
- Determining the rate law and order of a reaction from experimental data
- Predicting how long a reaction will take to reach completion
Key Notes
- Rate definition: rate = −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt: The coefficients a and b normalize rates to the stoichiometry of the balanced equation, so the reaction rate is a single value regardless of which species is tracked. Rates of reactants are negative (decreasing); products are positive.
- Rate law: rate = k[A]ᵐ[B]ⁿ: The rate constant k and the reaction orders m, n must be determined experimentally — they cannot be read from the balanced equation (except for elementary steps). Overall reaction order = m + n.
- Arrhenius equation: k = Ae^(−Ea/RT): k increases with temperature. Ea is the activation energy (energy barrier). A rule of thumb: a 10°C temperature rise approximately doubles the rate for many reactions. Catalysts lower Ea, increasing k without changing temperature.
- Half-life: For first-order reactions, the half-life t₁/₂ = ln(2)/k is constant — independent of concentration. For second-order, t₁/₂ = 1/(k[A]₀) depends on initial concentration. Half-life is used in pharmacokinetics, radioactive decay, and chemical stability testing.
- Applications: Reaction rate analysis is used in industrial catalyst design, pharmaceutical shelf-life prediction, food preservation (Maillard reaction rates, spoilage kinetics), environmental fate modeling of pollutants, and chemical engineering reactor sizing.