---
title: "First-Order Kinetics — AP Chem Definition & Exam Guide"
description: "First-order kinetics means rate depends on one reactant's concentration to the first power. Learn the ln[A] vs. time test, constant half-life, and how AP Chem Unit 5 tests it."
canonical: "https://fiveable.me/ap-chem/key-terms/first-order-kinetics"
type: "key-term"
subject: "AP Chemistry"
unit: "Unit 5"
---

# First-Order Kinetics — AP Chem Definition & Exam Guide

## Definition

First-order kinetics describes a reaction whose rate is directly proportional to the concentration of a single reactant raised to the first power (rate = k[A]). Doubling [A] doubles the rate, a plot of ln[A] vs. time is a straight line, and the half-life stays constant, which is why radioactive decay is first order.

## What It Is

First-order kinetics is a [rate law](/ap-chem/unit-5/elementary-reactions/study-guide/SPsFzzECb4aCre0wFrGg "fv-autolink") where the reaction rate depends on the first power of one reactant's concentration. Written out, that's rate = k[A]¹, where k is the [rate constant](/ap-chem/key-terms/rate-constant "fv-autolink"). The CED (5.2.A.2 and 5.2.A.3) defines the order as the power each concentration is raised to in the rate law, so "first order" literally just means that exponent is 1. The practical consequence is simple proportionality. Double the concentration, the rate doubles. Triple it, the rate triples.

Two signatures make first-order reactions easy to spot. First, a plot of ln[A] versus time gives a straight line with slope equal to -k. Second, the [half-life](/ap-chem/key-terms/half-life "fv-autolink") is constant, meaning it takes the same amount of time to go from 100% to 50% as from 50% to 25%, no matter how much reactant you start with. That constant half-life is exactly why radioactive decay is the classic first-order example. A key point the CED stresses (5.2.A) is that order comes from experimental data, not from the balanced equation's coefficients. You can't look at 2N₂O₅ → 4NO₂ + O₂ and assume second order; you have to test the data.

## Why It Matters

First-order kinetics lives in Topic 5.2 (Introduction to Rate Law) in [Unit 5](/ap-chem/unit-5 "fv-autolink"): Kinetics, supporting learning objective 5.2.A, which asks you to represent experimental data with a consistent rate law expression. This is the workhorse skill of Unit 5. Almost every kinetics problem starts with "figure out the order," and first order is the most commonly tested case because it has the cleanest math (the exponential decay function and constant half-life) and the most famous real-world application, [radioactive decay](/ap-chem/key-terms/radioactive-decay "fv-autolink"). If you can recognize first-order behavior from a data table, a graph, or a half-life pattern, you've unlocked a huge fraction of Unit 5.

## Connections

### [First Order Reaction (Unit 5)](/ap-chem/key-terms/first-order-reaction)

These are two names for the same idea. "First-order kinetics" describes the behavior, and a "[first order reaction](/ap-chem/key-terms/first-order-reaction "fv-autolink")" is a reaction that shows that behavior. On the exam, both phrasings point to rate = k[A].

### [Second-Order Reaction (Unit 5)](/ap-chem/key-terms/second-order-reaction)

The most important contrast. In a [second-order reaction](/ap-chem/key-terms/second-order-reaction "fv-autolink"), doubling the concentration quadruples the rate (2² = 4), and the linear plot is 1/[A] vs. time instead of ln[A] vs. time. Practice questions love making you tell these two apart from data.

### [Zeroth Order Reaction (Unit 5)](/ap-chem/key-terms/zeroth-order-reaction)

The other end of the spectrum. In a [zeroth-order reaction](/ap-chem/key-terms/zeroth-order-reaction "fv-autolink"), concentration doesn't affect rate at all, and [A] vs. time itself is linear. Memorize the trio of straight-line plots ([A], ln[A], 1/[A] for orders 0, 1, 2) and graphical questions become free points.

### [Rate Constant (Unit 5)](/ap-chem/key-terms/rate-constant)

The k in rate = k[A]. For a first-order reaction, k has units of s⁻¹, and the slope of the ln[A] vs. time line equals -k. Units of k are actually a quick way to identify order, since each order has different units.

## On the AP Exam

First-order kinetics shows up in multiple-choice questions in a few predictable formats. One gives you a data table of concentration vs. time (like the decomposition of N₂O₅) and asks for the order n in rate = k[N₂O₅]ⁿ. Another describes a doubling experiment, where if doubling the concentration doubles the rate, it's first order (if the rate quadruples, that's second order, a favorite trap). Graphical stems are also common. If "a plot of ln[A] vs. time is a straight line with negative slope," the answer is first order, full stop. A straight line through the origin on a rate vs. concentration graph also means first order, since rate is directly proportional to [A]. On FRQs, kinetics questions typically hand you experimental data and ask you to determine the rate law, justify the order with evidence, and calculate k with correct units. The justification matters, so say explicitly that doubling [A] doubled the rate, therefore the order with respect to A is 1.

## first-order kinetics vs Second-order kinetics

Both depend on concentration, but the response is different. First order means doubling [A] doubles the rate; second order means doubling [A] quadruples it (2² = 4). The graphical tests differ too. First order gives a straight line on ln[A] vs. time, while second order gives a straight line on 1/[A] vs. time. And only first-order reactions have a constant half-life. A second-order half-life gets longer as the reactant runs out.

## Key Takeaways

- First-order kinetics means the rate law is rate = k[A], so the rate is directly proportional to one reactant's concentration.
- Doubling the concentration of the reactant doubles the rate; if the rate quadruples instead, the reaction is second order.
- A first-order reaction gives a straight line when you plot ln[A] versus time, and the slope of that line equals -k.
- First-order reactions have a constant half-life, which is why radioactive decay is the textbook first-order example.
- Reaction order must be determined from experimental data, never from the coefficients in the balanced equation.
- The rate constant k for a first-order reaction has units of s⁻¹, and checking k's units is a quick way to verify the order.

## FAQs

### What is first-order kinetics in AP Chem?

It's a rate law where the rate depends on one reactant's concentration to the first power, written rate = k[A]. Doubling the concentration doubles the rate, and a plot of ln[A] vs. time is linear. It's covered in Topic 5.2 of Unit 5 under learning objective 5.2.A.

### Can you tell a reaction is first order from the balanced equation?

No. The CED is explicit that rate laws come from experimental data, not coefficients. The decomposition of N₂O₅ has a coefficient of 2 in the balanced equation but is experimentally first order, which is exactly the kind of trap MCQs set.

### How is first-order different from second-order kinetics?

First order: doubling [A] doubles the rate, ln[A] vs. time is linear, and the half-life is constant. Second order: doubling [A] quadruples the rate, 1/[A] vs. time is linear, and the half-life grows as the reaction proceeds.

### Why does radioactive decay follow first-order kinetics?

Because each nucleus has a fixed probability of decaying per unit time, the decay rate is directly proportional to how many nuclei remain. That gives rate = k[A] and the famous constant half-life, like carbon-14's roughly 5,700 years.

### What graph is linear for a first-order reaction?

The plot of ln[A] versus time gives a straight line with slope -k. If the data table or graph in a question shows that natural-log plot is linear, the reaction is first order. As a bonus, a plot of rate vs. [A] for a first-order reaction is a straight line through the origin.

## Related Study Guides

- [5.2 Introduction to Rate Law](/ap-chem/unit-5/intro-rate-law/study-guide/oq5mJS35IadrTLHLjdqZ)

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