Units depend on overall order (e.g., M⁻¹s⁻¹ for 2nd order)
Rate Law Expression:
Rate = k × [A]
Rate = k × [A]^m × [B]^n
General rate law expression
k = rate constant
[A], [B] = reactant concentrations
m, n = reaction orders (experimentally determined)
Overall order = m + n
What is a Rate Law?
The rate law expresses how the reaction rate depends on the concentrations of reactants. It is experimentally determined and cannot be inferred from stoichiometry alone.
Reaction Order
The order with respect to each reactant indicates how the rate changes with concentration. A first-order reaction doubles in rate when concentration doubles.
Rate Constant (k)
The rate constant is specific to each reaction and changes with temperature. Its units depend on the overall reaction order.
Important Note
Rate law expressions are experimentally determined. Calculated rates are theoretical and assume ideal reaction conditions. The reaction order cannot be determined from balanced chemical equations and must be found experimentally.
A rate law (also called a rate equation) is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentrations of reactants. Unlike stoichiometric coefficients in balanced equations, the exponents in rate laws must be determined experimentally through kinetic studies.
The general form of a rate law is: Rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are reactant concentrations, and m and n are the orders with respect to each reactant. The overall reaction order is the sum of all individual orders (m + n). Rate laws are fundamental to understanding reaction mechanisms and predicting how changes in conditions affect reaction rates.
The reaction order with respect to a reactant indicates how the rate changes when that reactant's concentration changes. Understanding reaction orders is crucial for predicting reaction behavior and designing industrial processes.
Zero Order (n = 0)
Rate is independent of reactant concentration. Doubling the concentration has no effect on rate. Common in enzyme-catalyzed reactions at saturation or surface reactions where the surface is fully covered.
First Order (n = 1)
Rate is directly proportional to concentration. Doubling the concentration doubles the rate. Radioactive decay and many decomposition reactions follow first-order kinetics.
Second Order (n = 2)
Rate is proportional to the square of concentration (or product of two concentrations). Doubling concentration quadruples the rate. Many bimolecular reactions exhibit second-order kinetics.
Rate laws cannot be predicted from balanced equations - they must be determined through careful experimentation. Several methods are commonly used to establish rate laws.
Initial Rates Method
Compare initial rates at different starting concentrations. By varying one reactant while holding others constant, individual orders can be determined.
Integrated Rate Laws
Plot concentration vs. time data in different forms. The plot that gives a straight line indicates the reaction order (linear for first-order ln[A] vs. t).
Half-Life Method
For first-order reactions, half-life is constant regardless of initial concentration. For other orders, half-life depends on initial concentration.
Isolation Method
Use large excess of all reactants except one, making their concentrations effectively constant. This simplifies multi-reactant systems to pseudo-first-order.
Temperature Dependence
Rate constants increase exponentially with temperature according to the Arrhenius equation: k = A × e^(-Ea/RT). A 10°C increase typically doubles or triples the rate constant.
Activation Energy
The activation energy (Ea) represents the minimum energy required for reaction. Higher Ea means greater temperature sensitivity. Catalysts lower Ea without changing the rate law form.
Units of Rate Constants
Rate constant units depend on overall order: zero order (M/s), first order (s⁻¹), second order (M⁻¹s⁻¹), third order (M⁻²s⁻¹). The units ensure the rate always has units of M/s.
Why can't rate laws be determined from balanced equations?
Balanced equations show the overall stoichiometry but not the mechanism. Most reactions occur in multiple steps, and the rate law reflects the slowest (rate-determining) step, which may involve intermediates not in the overall equation.
Can reaction orders be negative or fractional?
Yes. Negative orders indicate inhibition - increasing that reactant's concentration decreases the rate. Fractional orders often arise from complex mechanisms involving pre-equilibria or chain reactions.
What is a rate-determining step?
In multi-step reactions, the slowest step controls the overall rate. The rate law typically reflects the molecularity and concentration dependence of this rate-determining step.
How do catalysts affect rate laws?
Catalysts lower activation energy, increasing k without changing the rate law form for most cases. However, they may appear in the rate law if they participate in the rate-determining step (homogeneous catalysis).