First-Order Reaction in AP Chemistry

A first-order reaction is one whose rate depends on the concentration of a single reactant raised to the first power (rate = k[A]). On the AP Chem exam, you spot it by a linear plot of ln[A] versus time (slope = −k) and a half-life that stays constant: t½ = 0.693/k.

What is First-Order Reaction?

A first-order reaction has a rate law of rate = k[A]. Double the concentration of A and the rate doubles. That direct, one-to-one relationship is what "first order" means.

The AP exam cares less about the label and more about the fingerprints. Per EK 5.3.A.2, if a reaction is first order in the reactant you're monitoring, a plot of ln[A] versus time is a straight line, and the slope of that line is −k. The integrated rate law is ln[A]ₜ = ln[A]₀ − kt (it's on your equation sheet). First-order reactions also have a signature no other order shares. The half-life is constant: t½ = 0.693/k, no matter how much reactant you start with. Every half-life, the concentration cuts in half, which is why first-order kinetics is just exponential decay. Radioactive decay works exactly the same way.

Why First-Order Reaction matters in AP® Chemistry

First-order kinetics lives in Unit 5 (Kinetics) and threads through three topics. In Topic 5.3, learning objective AP Chem 5.3.A asks you to identify the rate law from concentration-versus-time data, and recognizing the linear ln[A] plot is the core move (EK 5.3.A.1-5.3.A.4). In Topic 5.4, AP Chem 5.4.A connects order to mechanism, since a unimolecular elementary step (one particle falling apart or rearranging) is automatically first order. And in Topic 5.6, the rate constant k for that elementary step depends on temperature and activation energy, which sets up the energy profile and Arrhenius ideas. If you can do one kinetics calculation cold for the exam, make it the first-order math, because it's the most heavily tested order.

How First-Order Reaction connects across the course

Integrated Rate Law (Unit 5)

The first-order integrated rate law, ln[A]ₜ = ln[A]₀ − kt, is the equation behind the straight-line ln plot. It's literally y = mx + b in disguise, where ln[A] is y, time is x, the slope is −k, and the intercept is ln[A]₀.

Half-Life (Unit 5)

Only first-order reactions have a half-life that doesn't change as the reaction runs (t½ = 0.693/k). That's a dead giveaway on data tables. If [A] drops 0.400 → 0.200 → 0.100 in equal time chunks, you're looking at first order.

Molecularity and Elementary Reactions (Unit 5)

For an elementary step, the rate law comes straight from stoichiometry (LO 5.4.A), so a unimolecular step is first order by definition. For an overall reaction, you can never read the order off the coefficients. It has to come from experimental data.

Arrhenius Equation (Unit 5)

Being first order tells you how rate depends on concentration, but k itself depends on temperature and activation energy. The Arrhenius equation explains why warming a first-order reaction shortens its half-life even though the order never changes.

Is First-Order Reaction on the AP® Chemistry exam?

Multiple-choice questions usually hand you data and make you work backward. You might get a concentration-versus-time table and have to recognize the constant half-life pattern (0.400 M → 0.283 → 0.200 → 0.141 halves every 20 minutes), or be told that a plot of ln[N₂O₅] versus time is linear with slope −3.6 × 10⁻⁴ s⁻¹ and asked how long until 25% remains (that's two half-lives, since 100% → 50% → 25%). Calculation questions give you k and [A]₀ and ask for [A] after some time, which means plugging into ln[A]ₜ = ln[A]₀ − kt. On FRQs, kinetics questions like the 2017 long FRQ ask you to justify the order from graphical data, so practice saying "the plot of ln[A] versus time is linear, therefore the reaction is first order in A, and k equals the negative of the slope." Also watch the units. A k in s⁻¹ or min⁻¹ (no concentration units) is itself a clue the reaction is first order.

First-Order Reaction vs Second-Order Reaction

Both show curved concentration-versus-time graphs, so the raw [A] vs. t plot can't tell them apart by eye. The test is which transformed plot is linear. First order gives a straight line for ln[A] vs. time (EK 5.3.A.2); second order gives a straight line for 1/[A] vs. time (EK 5.3.A.3). Half-life behavior also separates them. First-order half-life is constant, while second-order half-life gets longer as the reactant runs out.

Key things to remember about First-Order Reaction

• A first-order reaction has rate = k[A], so doubling the concentration of A doubles the rate.

• If a plot of ln[A] versus time is linear, the reaction is first order, and the rate constant k equals the negative of the slope.

• The first-order half-life is constant at t½ = 0.693/k, and it does not depend on the starting concentration. No other order works this way.

• Use the integrated rate law ln[A]ₜ = ln[A]₀ − kt to find a concentration after any amount of time, given k and [A]₀.

• A unimolecular elementary step is automatically first order, but for an overall reaction the order must come from experimental data, never from the balanced equation's coefficients.

• The units of k reveal the order: a first-order k has units of s⁻¹ or min⁻¹ with no concentration term.

Frequently asked questions about First-Order Reaction

What is a first-order reaction in AP Chem?

It's a reaction whose rate depends on one reactant's concentration to the first power, so rate = k[A]. You identify it on the exam by a linear ln[A] versus time plot or a half-life that stays constant, given by t½ = 0.693/k.

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

No, not for an overall reaction. Order must come from experimental data like a linear ln[A] plot. The only exception is an elementary step, where a unimolecular step is first order because its rate law comes directly from the particles colliding (LO 5.4.A).

How is a first-order reaction different from a second-order reaction?

First order gives a linear ln[A] vs. time plot and a constant half-life (0.693/k). Second order gives a linear 1/[A] vs. time plot, and its half-life grows as the reactant is used up. The units of k also differ: s⁻¹ for first order, M⁻¹s⁻¹ for second order.

Does the half-life of a first-order reaction change as the reaction proceeds?

No. That's the defining feature. Since t½ = 0.693/k depends only on k, every half-life takes the same amount of time. Going from 100% to 25% of the initial concentration always takes exactly two half-lives.

How do I find the rate constant k for a first-order reaction from a graph?

Plot ln[A] versus time. If it's linear, the reaction is first order and k is the negative of the slope. For example, a slope of −3.6 × 10⁻⁴ s⁻¹ means k = 3.6 × 10⁻⁴ s⁻¹, which gives a half-life of 0.693/k ≈ 1,925 seconds.