Reaction Rate Order Calculator

Determine reaction order and rate constant from experimental concentration-time data.

Initial concentration [A]0 (mol/L) (M)

Concentration [A] at time t (M)

Time t (s or min) (s)

Rate constant k (if known)

0 = calculate from data

Please check your inputs and try again.

What Reaction Order Means

Order describes how the rate responds to concentration — and it must be determined experimentally, not read off the balanced equation. A reaction written with a coefficient of 2 is not necessarily second order, because the balanced equation describes overall stoichiometry while order reflects the rate-determining step.

Order	Rate law	Integrated form	Linear plot	Half-life
Zero	rate = k	[A] = [A]₀ − kt	[A] vs t	[A]₀/2k — shortens
First	rate = k[A]	ln[A] = ln[A]₀ − kt	ln[A] vs t	0.693/k — constant
Second	rate = k[A]²	1/[A] = 1/[A]₀ + kt	1/[A] vs t	1/(k[A]₀) — lengthens

The half-life behaviour is the quickest diagnostic. Only first-order reactions have a constant half-life independent of starting concentration. For zero order each successive half-life is shorter; for second order each is longer. Measuring two consecutive half-lives usually identifies the order without any plotting.

Determining Order Experimentally

Method	How it works	Best for
Graphical	Plot all three integrated forms; the linear one gives the order	Single-reactant reactions
Half-life comparison	Check whether successive half-lives are equal	Quick identification
Initial rates	Double one concentration, see how rate responds	Multiple reactants
Isolation	Flood with excess of all but one reactant	Complex rate laws

The initial-rates method is the most direct for multiple reactants. Doubling [A] while holding [B] fixed reveals the order in A: unchanged rate means zero order, doubled means first, quadrupled means second.

Rate constant units are themselves a useful check, since they depend on overall order: zero order gives M/s, first order s⁻¹, and second order M⁻¹s⁻¹. If your fitted k has units that do not match the order you assumed, something is wrong.

Worked Examples

Example 1: A0=1.0M, A=0.5M at t=10s

k0=0.05, k1=0.0693, k2=0.1

Result: Compare half-lives to determine order

If t1/2 is constant: first order

Example 2: Drug elimination: A0=100, A=50 at t=6hr

k1=ln(2)/6=0.1155 /hr

Result: First-order elimination (constant t1/2)

Most drugs follow first-order kinetics

Example 3: Identifying order from half-lives

Successive half-lives measured as 30 s, 60 s, 120 s

Result: Second order

Each half-life doubles as concentration halves, which matches t½ = 1/(k[A]₀). A first-order reaction would show 30, 30, 30.

Example 4: Initial rates with two reactants

Doubling [A] doubles rate; doubling [B] quadruples it

Result: rate = k[A][B]², third order overall

First order in A, second in B. The overall order is the sum, and k would carry units of M⁻²s⁻¹.

Example 5: Pharmacokinetics

Drug at 100 mg/L falls to 50 in 6 h, then to 25 in a further 6 h

Result: First order, k = 0.1155 h⁻¹

Constant half-life confirms first order. Most drug elimination follows this, which is why dosing intervals are set in multiples of half-life.

Common Mistakes

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Reading order from the balanced equation

Order comes from the rate-determining step, not stoichiometry. Many reactions with a coefficient of 2 are first order overall, and some are fractional order.

⚠️

Assuming half-life is always constant

Only first-order reactions have concentration-independent half-life. Applying t½ = 0.693/k to a second-order reaction gives a wrong answer that grows worse as concentration falls.

⚠️

Fitting one plot and stopping

A single dataset can look linear on more than one plot over a narrow range. Test all three integrated forms and compare fit quality across a wide extent of reaction.

⚠️

Ignoring the units of k

Rate constant units are diagnostic of overall order. If a fitted k comes out in s⁻¹ but you assumed second order, the assumption is wrong.

Frequently Asked Questions

How to determine reaction order experimentally?

Method 1: Integrated law plots - which linearizes? Method 2: Initial rates - double [A], if rate doubles: 1st order; quadruples: 2nd order. Method 3: Half-life constancy - constant t1/2 = first order.

Rate constant units?

Zero order: mol/L/s. First order: /s (or /min). Second order: L/mol/s. Units always consistent with rate = k[A]^n having units of mol/L/s.

How do I determine reaction order experimentally?

Plot the three integrated rate laws and see which gives a straight line, or compare successive half-lives. For multiple reactants, vary one concentration at a time and observe the rate response.

Why is half-life constant only for first order?

Because the first-order half-life expression contains no concentration term. Zero-order half-life is proportional to concentration and second-order is inversely proportional.

Can order be determined from the balanced equation?

No. Order reflects the rate-determining step of the mechanism, which the overall stoichiometry does not reveal. It must be measured.

What are the units of the rate constant?

They depend on overall order: M/s for zero, s⁻¹ for first, and M⁻¹s⁻¹ for second. The units are a useful check on your assumed order.

Can reaction order be fractional or negative?

Yes. Fractional orders arise in chain and radical mechanisms, and negative orders occur when a species inhibits the reaction, typically by binding a catalyst.

Formula Explorer connections

Interpretation: This formula connects concentration, time, temperature or transport to the speed of a chemical process. Assumption: The reaction order and mechanism must match the model. Temperature, catalyst, mixing and mass-transfer limitations can alter the observed rate.

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