Reaction Kinetics — Rate Laws, Orders & Arrhenius

Reaction kinetics is the study of reaction speed. It explains how fast reactants turn into products, how concentration changes the rate, and why higher temperature often makes a reaction go faster.

For many reactions, the experimentally determined rate law is written as

$$rate = k[A]^m[B]^n$$

Here, $k$ is the rate constant, $[A]$ and $[B]$ are concentrations, and $m$ and $n$ are the reaction orders. The overall order is $m+n$.

The quickest way to read this is: the exponents tell you how strongly rate responds to concentration, while the Arrhenius equation helps explain why $k$ usually increases when temperature increases.

What A Rate Law Means

A rate law connects reaction rate to concentration for a specific reaction under a specific set of conditions. If a reaction is first order in $A$, doubling $[A]$ doubles the rate. If it is second order in $A$, doubling $[A]$ makes the rate four times larger.

This is different from stoichiometry. Stoichiometry tells you how much reacts. Kinetics tells you how fast it reacts.

Do not assume the exponents in the rate law from the balanced equation unless you are explicitly dealing with an elementary step. For an overall reaction, the orders are usually determined from experiment.

Reaction Order In Plain Language

Reaction order tells you how sensitive the rate is to concentration.

• Zero order in $A$: changing $[A]$ does not change the rate in that range.
• First order in $A$: the rate is proportional to $[A]$.
• Second order in $A$: the rate is proportional to $[A]^2$.

Orders do not have to match coefficients in the overall equation, and they are not always whole numbers in more complicated mechanisms. For most beginner problems, though, zero, first, and second order are the main cases to recognize quickly.

Worked Example: Predicting The Rate Change

Suppose experiments show that

$$rate = k[A]^2[B]$$

Compare two experiments run at the same temperature.

In experiment 1, $[A] = 0.10$ and $[B] = 0.20$.

In experiment 2, $[A]$ is doubled to $0.20$ while $[B]$ stays the same.

Because the rate is proportional to $[A]^2$, doubling $[A]$ changes the rate by

$$2^2 = 4$$

So experiment 2 has a rate four times as large.

If instead you kept $[A]$ fixed and doubled $[B]$, the rate would only double because $[B]$ appears to the first power.

That is the core skill in rate-law questions: change one concentration at a time, read its exponent, and convert that exponent into a rate factor.

How The Arrhenius Equation Explains Temperature

Temperature affects rate mainly through the rate constant $k$. A standard model is

$$k = A e^{-E_a/(RT)}$$

Here:

• $A$ is the pre-exponential factor
• $E_a$ is the activation energy
• $R$ is the gas constant
• $T$ is the absolute temperature in kelvin

The main idea is more useful than memorizing the formula. When temperature rises, a larger fraction of collisions has enough energy to get over the activation barrier, so $k$ usually increases.

If $E_a$ is larger, the reaction is generally more sensitive to temperature. If a catalyst provides a different pathway with a lower activation energy, the reaction can become faster at the same temperature.

Rate Constant vs Reaction Order

Students often mix these up because both appear in the same equation.

The reaction order comes from the exponents in the rate law, so it tells you how rate changes with concentration. The rate constant $k$ is the proportionality constant for that law under a given set of conditions.

If temperature changes, $k$ often changes. The order usually does not change just because temperature changed slightly, although a different mechanism or concentration range can make the effective behavior more complicated.

Common Mistakes In Reaction Kinetics

Taking Orders From The Balanced Equation

That shortcut is not reliable for an overall reaction. Use experimental data unless the problem says the step is elementary.

Forgetting That Arrhenius Uses Kelvin

In the Arrhenius equation, temperature must be absolute temperature. Using Celsius directly gives the wrong relationship.

Confusing Fast Reaction With Large Equilibrium Yield

A fast reaction reaches its outcome quickly. That does not mean it makes more product at equilibrium. Rate and equilibrium answer different questions.

Treating Catalysts As If They Change Stoichiometry

A catalyst changes the pathway and often changes the rate, but it does not change the overall balanced reaction.

Where Reaction Kinetics Is Used

Reaction kinetics matters in industrial chemistry, combustion, atmospheric chemistry, enzyme studies, corrosion, battery science, and drug stability. In each case, the practical question is the same: how quickly does the system change under real conditions?

Outside the lab, the same idea helps explain shelf life, temperature effects, and why some reactions need a catalyst to happen on a useful timescale.

Try A Similar Problem

Take the rate law $rate = k[A][B]^2$. First predict what happens if $[A]$ doubles. Then predict what happens if $[B]$ doubles. If that feels clear, try one more case where $[B]$ is cut in half.