---
title: "Rate Constant (k) — AP Chem Definition & Exam Guide"
description: "The rate constant k links reaction rate to reactant concentrations in a rate law. Learn its units, Arrhenius temperature dependence, and how lowercase k differs from equilibrium K."
canonical: "https://fiveable.me/ap-chem/key-terms/rate-constant-k"
type: "key-term"
subject: "AP Chemistry"
---

# Rate Constant (k) — AP Chem Definition & Exam Guide

## Definition

The rate constant (k) is the proportionality constant in a rate law (rate = k[A]^m[B]^n) that connects a reaction's rate to its reactant concentrations; its value depends on temperature and activation energy, and its units change with overall reaction order.

## What It Is

The [rate constant](/ap-chem/key-terms/rate-constant "fv-autolink") k is the number that turns [concentrations](/ap-chem/unit-3/beer-lambert-law/study-guide/smCHzraorVz6qlWW1oeB "fv-autolink") into an actual rate. In a rate law like rate = k[A]^m[B]^n, the exponents tell you *how* the rate responds to concentration, but k tells you *how fast* the reaction intrinsically is at a given temperature. A big k means a fast reaction; a tiny k means you'll be waiting a while even with plenty of reactant.

Two things about k trip people up. First, k is only constant at a fixed temperature. [Heat](/ap-chem/unit-6/heat-capacity-calorimetry/study-guide/jShImkrhZMnPWxlEjdwN "fv-autolink") the system up and k gets bigger, because more collisions have enough energy to clear the activation energy barrier (that's the Arrhenius relationship). Second, the units of k aren't fixed. They depend on the overall order of the reaction, so a zero-order k has units of M/s, a first-order k is 1/s, and a second-order k is 1/(M·s). You can actually use the units of k to work backward and figure out the reaction order.

## Why It Matters

The rate constant is the centerpiece of [AP Chem](/ap-chem "fv-autolink") kinetics ([Unit 5](/ap-chem/unit-5 "fv-autolink")), where you determine rate laws from experimental data, calculate k from concentration and rate values, and use integrated rate laws and half-life expressions that all contain k. But it also matters in Unit 9, Topic 9.5, for a sneakier reason. Learning objective 9.5.A asks you to explain thermodynamic favorability using K, ΔG°, and T, where K = e^(-ΔG°/RT) is the *equilibrium* constant. The exam loves the distinction hiding here. The rate constant k answers "how fast?" while the equilibrium constant K answers "how far?" A reaction can be thermodynamically favored (ΔG° < 0, K > 1) and still be painfully slow because its rate constant k is tiny. Keeping kinetics and thermodynamics in separate mental boxes is one of the highest-value skills in the course.

## Connections

### Free Energy and the Equilibrium Constant K (Unit 9)

Topic 9.5 uses K = e^(-ΔG°/RT) to link free energy to where equilibrium sits. That K is the equilibrium constant, not the rate constant. The classic exam insight is that ΔG° and K say nothing about speed, so a favored reaction (like diamond turning to [graphite](/ap-chem/key-terms/graphite "fv-autolink")) can have a rate constant so small that nothing visibly happens.

### [Activation Energy (Unit 5)](/ap-chem/key-terms/activation-energy)

The Arrhenius equation, k = Ae^(-Ea/RT), is where k gets its personality. A higher [activation energy](/ap-chem/key-terms/activation-energy "fv-autolink") means a smaller k at the same temperature. A catalyst speeds up a reaction by lowering Ea, which raises k, without touching the equilibrium constant at all.

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

The order determines the exponents in the [rate law](/ap-chem/unit-5/elementary-reactions/study-guide/SPsFzzECb4aCre0wFrGg "fv-autolink"), and together with k it fully describes the kinetics. Order also sets the units of k, so 1/s screams first order and 1/(M·s) screams second order. That unit trick shows up in multiple-choice questions.

### [Temperature Dependence (Unit 5)](/ap-chem/key-terms/temperature-dependence)

Concentration changes the rate, but only temperature (or a catalyst) changes k itself. Raising T increases the fraction of collisions that beat the activation energy, so k climbs exponentially. Notice that T also appears in K = e^(-ΔG°/RT), so temperature is the one variable that moves both the kinetic and thermodynamic constants.

## On the AP Exam

Rate constant questions show up most in multiple choice and in the kinetics-heavy parts of FRQs. You're typically asked to determine a rate law from a table of initial rates and then solve for k (with correct units), use an integrated rate law or half-life equation that contains k, or explain why k changes with temperature or a catalyst using collision theory and activation energy. In Unit 9 contexts tied to 9.5.A, the trap is conceptual rather than computational. A stem might describe a reaction with ΔG° < 0 that doesn't proceed and ask why; the answer is kinetics, meaning a small k from a large activation energy, not thermodynamics. Always check the case of the letter in any equation you're handed. Lowercase k means rate; uppercase K means equilibrium.

## Rate constant (k) vs Equilibrium constant (K)

Lowercase k is the rate constant from kinetics, and it tells you how fast a reaction goes at a given temperature. Uppercase K is the equilibrium constant from thermodynamics, and it tells you the ratio of products to reactants once the reaction settles. They are not related by any simple formula on the AP exam. K connects to ΔG° through K = e^(-ΔG°/RT) (Topic 9.5), while k connects to activation energy through Arrhenius. A reaction can have K = 10^30 and still crawl because k is microscopic.

## Key Takeaways

- The rate constant k is the proportionality constant in the rate law (rate = k[A]^m[B]^n) and measures how intrinsically fast a reaction is at a given temperature.
- The units of k depend on the overall reaction order, so you can identify the order just from k's units (1/s means first order, 1/(M·s) means second order).
- Only temperature and catalysts change k; changing concentrations changes the rate but never the rate constant itself.
- Raising temperature increases k because more collisions have enough energy to overcome the activation energy, which is the Arrhenius relationship.
- Lowercase k (rate constant, kinetics) is completely different from uppercase K (equilibrium constant, Topic 9.5), and a thermodynamically favored reaction with K > 1 can still be extremely slow if k is small.

## FAQs

### What is the rate constant k in AP Chem?

It's the proportionality constant in a rate law, rate = k[A]^m[B]^n, that connects reactant concentrations to reaction rate. A larger k means a faster reaction at that temperature.

### Is the rate constant k the same as the equilibrium constant K?

No. Lowercase k describes speed (kinetics) and depends on activation energy and temperature, while uppercase K describes the position of equilibrium and connects to free energy through ΔG° = -RT ln K in Topic 9.5. A reaction can have a huge K and a tiny k at the same time.

### Does the rate constant change when you change concentration?

No. Changing concentration changes the rate, but k stays the same. Only changing the temperature or adding a catalyst (which lowers activation energy) actually changes the value of k.

### What are the units of the rate constant?

They depend on the overall reaction order. For zero order k is in M/s, for first order it's 1/s (or s⁻¹), and for second order it's 1/(M·s). This works in reverse too, so the units of k tell you the overall order.

### Why can a reaction with ΔG° < 0 still be slow?

Because thermodynamic favorability (ΔG° < 0, K > 1) says nothing about rate. If the activation energy is high, the rate constant k is tiny and the reaction barely proceeds, even though products are favored at equilibrium. This kinetics-versus-thermodynamics distinction is a favorite exam concept.

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