---
title: "Reading Orders and Half-Lives from Rate Graphs"
description: "A concentration-time curve and a rate-concentration graph each give the order away. A half-life that stays the same is the signature of first order."
canonical: https://lightmysky.com/learn/science/reading-orders-and-half-lives-from-rate-graphs-mt_gCToNUUYll
source: https://lightmysky.com/learn/science/reading-orders-and-half-lives-from-rate-graphs-mt_gCToNUUYll.md
retrieved: 2026-11-12
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Reading Orders and Half-Lives from Rate Graphs

A concentration-time curve and a rate-concentration graph each give the order away. A half-life that stays the same is the signature of first order.

Subject: Science · Area: Chemistry · Ages 17 to 18
Page: https://lightmysky.com/learn/science/reading-orders-and-half-lives-from-rate-graphs-mt_gCToNUUYll

## Ready when they can

- Takes tangents from a concentration-time curve to get rates and plots rate against concentration
- Identifies zero, first and second order from the shape of a rate-concentration graph
- Measures successive half-lives and uses their constancy to argue for first order
- Finds the rate constant from a gradient or from a half-life

## Lesson: Reading order from rate graphs

Pick a few times on a concentration-time curve and draw a tangent at each one. The steepness of each tangent is the rate at that moment, and you then plot those rates against the concentration left at each time.

**Example.** Picture the rate against concentration plot for hydrogen peroxide breaking down. A flat line means zero order, a straight line through the start means first order, and a curve bending upward means second order among the three shapes compared here.

Now watch the half-life, the time for the concentration to halve, again and again. If every halving takes the same time, your reaction is first order, and if the times drift, it is not.

For the rate constant, take a gradient magnitude: the gradient of the rate against concentration line for a first order reaction, or minus the gradient of the straight concentration-time line for a zero order one. You can also use k = 0.693 divided by the half-life, which gives k in matching inverse time units, per second when the half-life is in seconds.

**Recap.** Tangents give rates, shapes give orders, steady half-lives mean first order, and gradients or half-lives give k.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Rate Equations and Orders of Reaction](https://lightmysky.com/learn/science/rate-equations-and-orders-of-reaction-mt_1x3ogDKGxC)

## Optional connections

- [Compound Growth and Decay](https://lightmysky.com/learn/mathematics/compound-growth-and-decay-mt_xf5FQ2sugf)

## Opens up

- [The Rate-Determining Step and Reaction Mechanisms](https://lightmysky.com/learn/science/the-rate-determining-step-and-reaction-mechanisms-mt_PM1Vo2CkVD)