Reaction Order in Chemical Kinetics

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Understanding how the rate of a chemical reaction depends on the concentration of reactants is a cornerstone of chemical kinetics. This page explores reaction orders, with detailed coverage of zero, first, and second order reactions.



Fig. Determine reaction order in Chemical Kinetics by curve fitting - Screen shot from CHEMIX School

determine reaction order in chemical kinetics by curve-fitting

What is Reaction Order?

The reaction order indicates how the rate of a reaction depends on the concentration of reactants.

For a general reaction:

a+b→ProductsaA + bB \rightarrow \text{Products}

The rate law is typically expressed as:

Rate=k[A]m[B]n
\text{Rate} = k [A]^m [B]^n
mm and nn are the orders with respect to A and B.

The overall order is m+n
 
     kk is the rate constant.

These powers must be determined experimentally, unless the reaction is elementary (single-step), where the orders match the stoichiometric coefficients.

Zero Order Reactions

Rate Law:

Rate=k\text{Rate} = k

Integrated Rate Law:

[A]t=[A]0−kt[A]_t = [A]_0 - kt

Graphical Determination:

Plot: [A]t[A]_t vs. tt
Straight line with slope = −k-k

Half-Life:

t1/2=[A]02kt_{1/2} = \frac{[A]_0}{2

(Depends on initial concentration)

Characteristics:

Rate is constant regardless of [A].
Occurs often in surface-catalyzed reactions or saturated enzyme systems.

First Order Reactions

Rate Law:

Rate=k[A]\text{Rate} = k[A]

 Integrated Rate Law:

ln⁡[A]t=ln⁡[A]0−kt\ln[A]_t = \ln[A]_0 - kt

Graphical Determination:

Plot: ln⁡[A]t\ln[A]_t vs. tt
Straight line with slope = −k

Half-Life:

t1/2=0.693kt_{1/2} = \frac{0.693}{k}

(Constant for a first-order reaction)

Characteristics:

Common in radioactive decay, unimolecular decompositions.

Second Order Reactions

Rate Law:

Rate=k[A]2\text{Rate} = k[A]^2

Integrated Rate Law:

1[A]t=1[A]0+kt\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt

Graphical Determination:

Plot: 1[A]t\frac{1}{[A]_t} vs. tt
Straight line with slope = kk

Half-Life:

t1/2=1k[A]0t_{1/2} = \frac{1}{k[A]_0}

(Decreases with increasing [A])

Characteristics:

Often appears in bimolecular reactions.

How to Determine Reaction Order

Theoretically (for elementary reactions):

Use the stoichiometry of the elementary step

Example: For 2A→Products, rate law is Rate=k[A]2\text{Rate} = k[A]^2

For complex/multistep reactions, stoichiometry ≠ reaction order.

Summary Table

Order Rate Law Integrated Form Graph (Linear) Half-Life
0 Rate = k [A]t=[A]0−kt[A]_t = [A]_0 - kt [A][A] vs. tt t1/2=[A]02kt_{1/2} = \frac{[A]_0}{2k}
1 Rate = k[A] ln⁡[A]t=ln⁡[A]0−kt\ln[A]_t = \ln[A]_0 - kt ln⁡[A]\ln[A] vs. tt t1/2=0.693kt_{1/2} = \frac{0.693}{k}
2
Rate =k[A]2 		1[A]t=1[A]0+kt\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt 1/[A]1/[A] vs. tt t1/2=1k[A]0t_{1/2} = \frac{1}{k[A]_0}

Notes

Always determine reaction order experimentally for complex reactions.
Reaction order affects how fast reactions occur and how they can be controlled.
Mastery of reaction orders aids in fields ranging from pharmaceutical kinetics to environmental chemistry.
Related topics:

Determine Reaction Order From Experimental Data Using Curve Fitting

Order of Reaction Calculator


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