Reaction order: zeroth, first, and second
Understand what reaction order means, how zeroth, first, and second order behave, and how to tell them apart from data.
Quick answer
Reaction order is the exponent on a reactant's concentration in the rate law. It tells you how sensitive the rate is to that reactant: doubling the concentration multiplies the rate by 2^order.
Example: In rate = k[A]², doubling [A] multiplies the rate by 2² = 4, so the reaction is second order in A.
What you will learn
- Explain what reaction order means for a single reactant and for the overall reaction.
- Predict how the rate changes when a concentration doubles for orders 0, 1, and 2.
- Use concentration-time graphs and straight-line plots to identify order.
- Distinguish order from molecularity.
What order means
The order with respect to a reactant is simply the exponent on its concentration in the rate law. In
the reaction is second order in A, first order in B, and third order overall (2 + 1). Order is always defined relative to something: a reactant order, or the overall order which is the sum.
Orders are experimental facts, not bookkeeping from the balanced equation. They describe how the measured rate responds when you change one concentration while holding everything else fixed.
Zeroth, first, and second order
The three common orders behave very differently when you double a concentration:
- Zeroth order (m = 0): rate = k. Doubling the concentration does nothing — the rate stays flat. This happens when a catalyst surface is saturated or the reactant enters only after the slow step.
- First order (m = 1): doubling the concentration doubles the rate. Rate is directly proportional to concentration.
- Second order (m = 2): doubling the concentration quadruples the rate (). The rate is proportional to concentration squared.
Fractional orders (like 1/2) show up in chain reactions, and negative orders mean more reactant slows things down — for example when a reactant blocks the catalyst.
Spotting order from graphs
Each order gives a different straight line when you plot the right quantity against time:
- Zeroth order: [A] versus t is a straight line (slope −k)
- First order: ln[A] versus t is a straight line (slope −k)
- Second order: 1/[A] versus t is a straight line (slope +k)
Whichever plot comes out linear reveals the order. This graphical test is one of the most reliable ways to assign orders, because real data that only approximately fits can still show a clear best line.
Order versus molecularity
Molecularity counts how many particles collide in a single elementary step: unimolecular (one), bimolecular (two), termolecular (three). It is a property of a proposed step, and it is always a whole number.
Order is the measured exponent in the rate law of the overall reaction. The two coincide only when the reaction happens in one step. In a multi-step mechanism, the measured orders reflect the slow step's molecularity — which is why measuring orders is a window into the mechanism.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Order in a reactant | unitless | Exponent on a reactant concentration in the rate law | |
| Overall order | unitless | Sum of all reactant orders |
Common mistakes
Order is measured; molecularity is drawn. The number of molecules in the balanced equation tells you nothing reliable about the rate law. A reaction A → products can be zeroth, first, or second order depending on its mechanism.
Order describes sensitivity to concentration, not absolute speed. A second-order reaction with a tiny rate constant can be far slower than a first-order reaction with a large one.
Zeroth-order behavior means the rate is independent of that reactant's concentration — often because a catalyst surface is already saturated or the reactant only enters after the slow step. The reactant is still there and still reacting.
Real-world applications
Drug dosing: many drug eliminations are approximately first order, so half-life reasoning sets dosing intervals.
Nuclear medicine: radioactive decay is strictly first order, which is why half-lives are meaningful.
Industrial reactors: order determines whether adding more reactant is worth the cost.
Catalysis research: a zeroth-order region reveals when a catalyst surface is saturated.
Frequently asked questions
What does it mean to say a reaction is second order?
It means the step involves two particles colliding — but be careful: molecularity describes one elementary step, while order describes the measured rate law of the overall reaction. They match only for a single-step reaction.
Why is third order rare?
It is rare as an overall order because three particles must collide simultaneously. Termolecular elementary steps exist but are uncommon, so most real rate laws top out at second order.
Is a reaction with one reactant always first order?
Only when the slow step involves a single molecule and no other concentration matters. Many decompositions and radioactive decays are first order, but never assume it — check the data.
Can the balanced equation itself have a fractional order?
A reaction cannot be 'order 1.5 in the balanced equation' — the equation has coefficients, not orders. Fractional orders appear in measured rate laws of chain reactions and surface-catalyzed reactions.