---
title: "Chain Reactions, Branching and Explosion Limits"
description: "Some mechanisms regenerate their own reactive intermediate, so one initiation event drives many product-forming cycles. When a step makes more radicals than it consumes, the rate can run away."
canonical: https://lightmysky.com/learn/science/chain-reactions-branching-and-explosion-limits-mt_8SDv_5iRMu
source: https://lightmysky.com/learn/science/chain-reactions-branching-and-explosion-limits-mt_8SDv_5iRMu.md
retrieved: 2026-09-12
---

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# Chain Reactions, Branching and Explosion Limits

Some mechanisms regenerate their own reactive intermediate, so one initiation event drives many product-forming cycles. When a step makes more radicals than it consumes, the rate can run away.

Subject: Science · Area: Chemistry · Ages 20 to 21
Page: https://lightmysky.com/learn/science/chain-reactions-branching-and-explosion-limits-mt_8SDv_5iRMu

## Ready when they can

- Labels initiation, propagation, branching and termination steps in a written mechanism
- Derives a chain-reaction rate law using the steady-state approximation on the carrier
- Defines chain length and calculates it from the rates of propagation and initiation
- Explains the pressure limits of the hydrogen and oxygen reaction in terms of branching against wall termination

## Lesson: Chains that copy their own carriers

Some mechanisms regenerate their own reactive intermediate, so one starting event drives many product cycles. Initiation breeds the first carriers. Propagation spends one carrier and grows a replacement. Branching grows more than one. Termination buries carriers for good.

**Example.** In the hydrogen bromine chain, splitting Br2 starts the chain. Each propagation step spends one radical and makes another, so the carrier count stays level. Steady state sets each carrier net rate to zero, solves for it, and plugs it back, so the final law lists only stable species.

To get the rate law you apply the steady-state approximation to the carrier. Chain length tells you how many cycles each start buys: divide the propagation rate by the initiation rate. If propagation runs at 300 units and initiation at 3, the chain length is 100.

**Tip.** The hydrogen oxygen reaction explodes only between two pressures. At low pressure, carriers hit the wall and die, so termination wins. At higher pressure, gas collisions let branching multiply carriers faster than the wall can bury them. At very high pressure the balance tips back toward termination.

**Recap.** Label each step, steady state the carrier, and read explosions as branching racing termination.

## Practice

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

## Needs first

- [Steady-State and Pre-Equilibrium Approximations](https://lightmysky.com/learn/science/steady-state-and-pre-equilibrium-approximations-mt_9ESWVl28-3)
- [Free-Radical Substitution in Alkanes](https://lightmysky.com/learn/science/free-radical-substitution-in-alkanes-mt_QkreYC9e2d)

## Opens up

- [Transition State Theory and the Eyring Equation](https://lightmysky.com/learn/science/transition-state-theory-and-the-eyring-equation-mt_JVjDMcXds1)