Chain Reactions and Explosion Limits

Core Idea

Chain reactions proceed via initiation (rare event creating radical), propagation (radical generates another radical), and termination (radicals are removed). When propagation exceeds termination, a chain branching explosion occurs—reaction rate increases explosively. Explosion limits define regions in the temperature-pressure diagram where explosions occur. Understanding chain reactions is crucial for combustion control, industrial safety, and atmospheric chemistry.

Explainer

From your study of elementary reaction steps, you know that complex reactions can be decomposed into sequences of simple steps. A chain reaction is a specific type of multi-step mechanism where a reactive intermediate — typically a free radical — is consumed in one step and regenerated in the next, creating a self-sustaining cycle. The classic example is the hydrogen-oxygen reaction: a single H· radical can trigger thousands of successive reactions before it is finally destroyed. The three phases — initiation, propagation, and termination — determine whether the reaction proceeds steadily, dies out, or explodes.

Initiation creates the first radicals, usually through bond homolysis caused by heat, light, or a spark. This step is slow and has a high activation energy, which is why a match is needed to ignite a gas mixture even though combustion is thermodynamically favorable. Once radicals exist, propagation takes over: each radical reacts with a stable molecule to form product and a new radical. In a simple (linear) chain, each propagation step produces exactly one new radical, so the radical population stays roughly constant. The reaction proceeds at a steady rate until reactants are consumed or radicals are removed by termination — when two radicals collide and combine, or a radical hits a wall and is deactivated.

The situation changes dramatically with chain branching, where a single propagation step produces two or more new radicals instead of one. In the H₂/O₂ system, the reaction H· + O₂ → OH· + O· is a branching step — one radical in, two radicals out. If branching outpaces termination, the radical population grows exponentially with each cycle, and the reaction rate accelerates without limit until it becomes an explosion. Whether this happens depends on the balance between branching rate (which increases with temperature and reactant concentration) and termination rate (which depends on pressure and vessel geometry).

This balance produces the famous explosion limits on a pressure–temperature diagram. At very low pressures (below the first limit), radicals diffuse to the vessel walls and are destroyed faster than branching can replace them — no explosion. As pressure increases past the first limit, gas-phase branching overwhelms wall termination and an explosion occurs. But at still higher pressures (the second limit), three-body collisions become frequent enough to deactivate radicals in the gas phase, quenching the explosion. Above the third limit, the sheer amount of heat generated by the exothermic reaction cannot be dissipated fast enough, causing a thermal explosion. These limits explain why the same H₂/O₂ mixture can be stable, explosive, stable again, and then explosive once more as pressure rises — a counterintuitive result that only makes sense when you think about the competing rates of branching and termination at each pressure regime.