Chain Reactions

A chain reaction involves highly reactive transient species, such as free radicals, as intermediates that facilitate rapid reactions over extended periods. A reactive intermediate is consumed, reactants convert to products, and the intermediate regenerates, enabling continuous repetition. This cycle amplifies product formation with minimal intermediate amounts, exemplified by the H2 and Br2 reaction forming hydrogen bromide.

During initiation, a bromine molecule collides with a third body (M) that absorbs excess energy, splitting the molecule into two bromine radicals. This step generates the radicals required to begin the chain reaction. The rate constant k1 quantifies how quickly bromine molecules dissociate under given temperature and pressure conditions.

Propagation steps sustain the reaction by converting reactants to products while continuously regenerating radicals. A bromine radical reacts with hydrogen to form hydrogen bromide and a hydrogen radical, which then reacts with another bromine molecule, regenerating the bromine radical. This cycle allows the reaction to proceed in a chain-like fashion with rate constants k2 and k3 governing propagation efficiency.

Inhibition occurs when hydrogen bromide reacts with a hydrogen radical, consuming hydrogen radicals and slowing product formation. The rate constant k-2 measures this inhibitory pathway strength; larger values increase inhibition impact, reducing the net rate of hydrogen bromide formation. This step partially removes radicals from the reaction cycle.

Termination occurs when two bromine radicals recombine to form bromine in the presence of a third body (M), which absorbs the released energy. This radical-radical recombination irreversibly removes reactive intermediates, stopping the chain reaction. The rate constant k-1 describes how quickly radicals recombine and terminate the chain.

Although free radicals drive the reaction mechanism, the observed rate law depends only on stable species because radicals are transient intermediates present in low concentrations. The square-root dependence on bromine suggests radical formation, while hydrogen bromide in the denominator indicates product inhibition. This relationship emerges from applying rate laws and equilibrium constants for elementary reactions to the overall mechanism.

Rate constants quantify reaction speeds at each step: k1 governs bromine dissociation during initiation, k2 and k3 control propagation efficiency, and k-1 describes radical recombination during termination. Higher propagation rate constants indicate faster radical reactions and more efficient chain propagation, while higher termination constants accelerate chain termination and reduce overall product formation.