What Is a Zero Order Reaction? Definition, Formula & Real Examples
Most chemical reactions slow down as reactants are consumed. But some reactions proceed at a constant, unwavering rate regardless of how much reactant remains. These are zero order reactions, and understanding them explains everything from how your body processes alcohol to why certain drugs are delivered via skin patches rather than pills.
Zero Order Reaction Definition
A zero order reaction is a chemical reaction in which the rate of reaction is completely independent of the concentration of the reactant. Doubling the concentration of the reactant has no effect on how fast the reaction proceeds. Halving it has no effect either.
The rate law for a zero order reaction is:
k = rate constant (mol/L/s or M/s)
[A] = concentration of reactant A (mol/L)
[A]⁰ = 1 (any number to the power zero equals one)
The rate constant k has units of mol/(L·s) or M·s⁻¹ — the same units as rate itself, because concentration raised to the zero power disappears from the equation.
Why Does Zero Order Kinetics Occur?
Zero order behaviour seems paradoxical. If concentration does not matter, what controls the rate?
The answer is almost always a bottleneck in the reaction mechanism — something other than reactant concentration that limits how fast the reaction can proceed:
Catalyst saturation: When a reaction is catalysed by an enzyme or a solid surface and all available active sites are already occupied, adding more reactant cannot speed things up. The catalyst is the limiting factor, not the reactant. This is the most common cause of zero order kinetics in chemistry and biochemistry.
Light-driven (photochemical) reactions: In photochemical reactions, the rate depends on how much light is absorbed — not on reactant concentration. As long as reactant is present to absorb photons, the rate is constant.
Zeroth-order drug delivery: Certain drug delivery systems are designed to release medication at a constant rate independent of the drug concentration in the reservoir. This is the pharmaceutical engineering goal for many sustained-release formulations.
The Zero Order Rate Law and Integrated Equation
Starting from rate = k, we can derive the integrated rate law — the equation that tells us the concentration of reactant at any point in time.
Derivation
k = rate constant (M/s) | t = time elapsed (s)
This is a linear equation — concentration decreases at a constant rate over time. The graph of [A] versus time is a straight line with slope = −k and y-intercept = [A]₀.
The Zero Order Reaction Graph
The characteristic signature of a zero order reaction is a straight line when you plot concentration [A] against time t.
The graph shows:
- A straight line with negative slope = −k
- Y-intercept at [A]₀ (initial concentration)
- The line hits zero concentration at t = [A]₀/k (when all reactant is consumed)
- Unlike first or second order reactions, the line is perfectly straight — not a curve
This graphical test is how chemists determine reaction order from experimental data. If your concentration-vs-time plot gives a straight line, you have a zero order reaction. If it curves, you test ln[A] vs t (first order) and 1/[A] vs t (second order).
| Plot | Linear for Zero Order? | Linear for First Order? | Linear for Second Order? |
|---|---|---|---|
| [A] vs t | ✅ YES — straight line | ✗ Curved | ✗ Curved |
| ln[A] vs t | ✗ Curved | ✅ YES | ✗ Curved |
| 1/[A] vs t | ✗ Curved | ✗ Curved | ✅ YES |
Zero Order Half-Life Formula
The half-life (t½) is the time required for the concentration to fall to half its initial value.
Setting [A] = [A]₀/2 in the integrated rate law:
This reveals a critical and unusual property of zero order reactions: the half-life depends on the initial concentration.
The more reactant you start with, the longer it takes to reach the half-way point — because the reaction proceeds at the same absolute rate regardless of concentration. This contrasts sharply with first order reactions, where the half-life is constant regardless of starting concentration.
Each successive half-life for a zero order reaction is shorter than the previous one (because [A]₀ for each subsequent half-life is smaller):
Eventually the concentration reaches zero and the reaction stops completely — unlike first order reactions which theoretically never reach zero.
Use our Reaction Order Calculator to calculate the zero order half-life for any initial concentration and rate constant.
Worked Calculations — Zero Order Kinetics
Problem: A reaction follows zero order kinetics with k = 0.025 M/min and [A]₀ = 0.80 M. What is [A] after 12 minutes?
2. Substitute: [A] = 0.80 − (0.025 × 12)
3. [A] = 0.80 − 0.30
Problem: The concentration of a reactant drops from 1.00 M to 0.60 M in 20 seconds. Assuming zero order kinetics, find k.
2. k = (1.00 − 0.60) / 20
3. k = 0.40 / 20
Problem: Using k = 0.020 M/s and [A]₀ = 1.00 M (from Example 2), find the half-life. Show successive half-lives.
After 25 s: [A] = 0.50 M
2nd t½ = 0.50/(2 × 0.020) = 12.5 s (shorter!)
After 37.5 s: [A] = 0.25 M
Reaction reaches [A] = 0 at t = 1.00/0.020 = 50 s
Problem: How long does it take for [A] to drop from 2.0 M to 0.5 M if k = 0.10 M/min?
2. t = (2.0 − 0.5) / 0.10
3. t = 1.5 / 0.10
Zero Order vs First Order vs Second Order — Side-by-Side Comparison
| Property | Zero Order | First Order | Second Order |
|---|---|---|---|
| Rate law | rate = k | rate = k[A] | rate = k[A]² |
| Integrated law | [A] = [A]₀ − kt | ln[A] = ln[A]₀ − kt | 1/[A] = 1/[A]₀ + kt |
| Linear plot | [A] vs t ⭐ | ln[A] vs t | 1/[A] vs t |
| Linear plot slope | −k | −k | +k |
| Units of k | M·s⁻¹ | s⁻¹ | M⁻¹·s⁻¹ |
| Half-life formula | t½ = [A]₀/(2k) | t½ = 0.693/k | t½ = 1/(k[A]₀) |
| Half-life depends on [A]₀? | YES — decreases | NO — constant | YES — decreases |
| Successive half-lives | Getting shorter | All equal | Getting longer |
| Reaches zero concentration? | YES — at finite time | NO — asymptotic | NO — asymptotic |
Real-World Examples of Zero Order Reactions
Alcohol Metabolism in the Human Body
The most familiar example of zero order kinetics in everyday life is how your body processes alcohol (ethanol). The enzyme alcohol dehydrogenase (ADH) in your liver converts ethanol to acetaldehyde. Under typical drinking conditions, ADH is fully saturated — every active site on every enzyme molecule is occupied with an ethanol molecule.
Because the enzyme is the bottleneck, your body eliminates alcohol at a constant rate of approximately 0.015% BAC per hour — regardless of how much alcohol is in your blood. This is why you cannot speed up sobering. Drinking coffee, eating food, or exercising does not accelerate alcohol metabolism — ADH is already working at maximum capacity.
Photochemical Decomposition
The decomposition of ozone in the upper atmosphere driven by ultraviolet radiation follows approximately zero order kinetics. As long as ozone is present (well above zero concentration), the rate is determined by UV flux — the amount of sunlight — not by ozone concentration. This makes zero order modelling important in atmospheric chemistry.
Zero Order Drug Release Systems
Pharmaceutical engineers sometimes deliberately engineer zero order drug release — a constant release rate over time. This is highly desirable for drugs that need a steady blood level, such as hormone replacement patches, insulin pumps, and certain pain management systems. The Mirena IUD releases levonorgestrel at a near-zero-order rate for years. This is more effective than oral dosing, which creates peaks and troughs in blood concentration.
Surface-Catalysed Reactions
Many heterogeneous catalytic reactions (where the catalyst is a solid and the reactant is a gas or liquid) show zero order kinetics when the reactant concentration is high enough to saturate all catalyst surface sites. The decomposition of ammonia over a platinum catalyst and the Haber-Bosch process (ammonia synthesis) can show zero order behaviour under certain conditions.
Aspirin Hydrolysis at High Concentration
The hydrolysis of aspirin (acetylsalicylic acid) in highly acidic conditions follows zero order kinetics at high concentrations. Hydrogen ions catalyse the reaction, and when their concentration is very high (strongly acidic), they are essentially always available — making the reaction rate independent of aspirin concentration.
How to Identify Zero Order Kinetics Experimentally
Chemists determine reaction order from experimental concentration-vs-time data using three tests:
Test 1 — The Graph Test: Plot [A] vs t. If the result is a straight line, the reaction is zero order. The slope of that line = −k.
Test 2 — The Rate vs Concentration Test: Measure the initial rate at several different initial concentrations. If rate stays constant as [A] changes, you have zero order kinetics.
Test 3 — The Half-Life Test: Measure successive half-lives. If each half-life is shorter than the previous one (in proportion to the remaining concentration), you have zero order kinetics.
Common Mistakes with Zero Order Reactions
❌ Confusing Zero Order with “No Reaction”
Zero order means the rate is independent of concentration — not that there is no reaction. The reaction proceeds at a constant, non-zero rate.
❌ Wrong Units for k
For zero order reactions, k has units of M/s (or mol/(L·s)). Students often forget this and write k in s⁻¹ (which is the unit for first order k).
❌ Thinking Half-Life Is Constant
The constant half-life rule applies to first order reactions, not zero order. For zero order reactions, each successive half-life is half the previous one because the initial concentration for each new “half-life” is smaller.
❌ Plotting the Wrong Graph
The linear plot for zero order is [A] vs t — simple concentration against time. Students sometimes plot ln[A] vs t first (the first order test) and see a curve, then incorrectly conclude the reaction is not zero order.
Frequently Asked Questions
A reaction is zero order when something other than reactant concentration controls the rate — typically a saturated catalyst, limited light intensity, or a rate-limiting step that does not involve the reactant directly. The rate equals the rate constant k regardless of how much reactant is present.
A plot of concentration [A] versus time t gives a straight line with negative slope equal to −k and y-intercept equal to [A]₀. This straight line is the definitive signature of zero order kinetics.
The rate constant k for a zero order reaction has units of mol/(L·s) or M·s⁻¹ — the same units as rate itself. This is because [A]⁰ = 1 has no units, so k must carry all the units to give rate in M/s.
Yes — when enzyme active sites are fully saturated with substrate (at high substrate concentrations), the reaction rate is limited by the enzyme turnover rate, not the substrate concentration. This is the zero order plateau of Michaelis-Menten kinetics, called Vmax.
A truly zero order reaction has a rate that is fundamentally independent of concentration. A pseudo-zero order reaction is actually first or second order but appears zero order because one reactant is present in such large excess that its concentration barely changes — making the rate appear constant. Many reactions in water are “pseudo-zero order with respect to water” because water concentration is essentially constant.
⚗️ Calculate Zero Order Kinetics Instantly
Our Reaction Order Calculator handles all zero order calculations — find concentration at any time, calculate the rate constant from experimental data, determine half-life, and generate the characteristic [A] vs t graph. For the comparison with first order kinetics (including the constant half-life property), the same calculator covers all three reaction orders with full step-by-step working.