Chain Reactions

Chain reactions involve highly reactive transient species, such as atoms or free radicals, as intermediates. These intermediates facilitate rapid reactions over an extended period. The process includes a series of steps: a reactive intermediate is consumed, reactants are converted to products, and the intermediate is regenerated. This cycle enables continuous repetition, amplifying the production of products with a small amount of intermediate. Chain reactions often utilize free radicals as intermediates. A well-studied example is the chain reaction between H₂ and Br₂, with an overall stoichiometry of H₂ + Br₂ → 2HBr. The observed rate law for this gas-phase reaction is established in the temperature range of 500 to 1500 K.

A simplified mechanism includes four classes of steps: initiation, propagation, inhibition, and termination.

In the initiation step, a bromine molecule dissociates into two bromine radicals:

\begin{equation*}\ce{Br2 + M ->[$k_1$] 2Br\!.\! + M}\end{equation*}

The third body (M) (which may be another molecule in the system) absorbs excess energy and stabilizes the process. This step is essential because it generates the radicals required to start the chain reaction. The rate constant k₁ represents how quickly bromine molecules split into radicals under given conditions, such as temperature and pressure.

The propagation steps sustain the reaction by converting reactants to products while regenerating radicals. First, a bromine radical reacts with hydrogen:

\begin{equation*}\ce{Br\!.{+} H2 ->[$k_2$] HBr + H\!.}\end{equation*}

Then, the hydrogen radical reacts with another bromine molecule:

\begin{equation*}\ce{H\!.{+} Br2 ->[$k_3$] HBr + Br\!.}\end{equation*}

These steps continuously regenerate radicals, allowing the reaction to proceed in a chain-like fashion. The rate constants k₂ and k₃ quantify the rates at which these propagation reactions occur. Higher values indicate faster radical reactions and more efficient chain propagation.

An important feature of this mechanism is the inhibition step, where radicals are partially removed:

\begin{equation*}\ce{H\!.{+} HBr ->[$k_{-2}$] H2 + Br\!.}\end{equation*}

This step slows the overall reaction by consuming hydrogen radicals. The rate constant k_-2 measures the strength of this inhibitory pathway. A larger k_-2 increases the impact of inhibition, reducing the net rate of HBr formation.

Finally, the termination step removes radicals irreversibly through radical–radical recombination:

\begin{equation*}\ce{M + 2Br\!. ->[$k_{-1}$] M + Br2}\end{equation*}

When radicals combine, the chain reaction stops because no reactive intermediates remain. The rate constant k_-1 describes how quickly radicals recombine and terminate the chain.