10.7
Consider the reaction between hydrogen and bromine, forming hydrogen bromide. This reaction follows a multi-step mechanism involving bromine and hydrogen radicals. Since radicals are continuously formed and regenerated, this reaction is called a chain reaction.
The reaction begins with initiation. A bromine molecule collides with a third body, M, which provides energy to split it into two bromine radicals.
During propagation, a bromine radical reacts with hydrogen to form hydrogen bromide and a hydrogen radical. The hydrogen radical then reacts with another bromine molecule, continuing the chain.
Inhibition happens when hydrogen bromide reacts with a hydrogen radical. This reduces the concentration of hydrogen radicals and slows product formation.
Finally, termination happens when two bromine radicals recombine to form bromine in the presence of M, which absorbs the energy released during the reaction.
Although radicals drive the reaction, the observed rate law depends only on stable species. The square-root dependence on bromine suggests radical formation, while hydrogen bromide in the denominator indicates product inhibition.
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.
Consider the reaction between hydrogen and bromine, forming hydrogen bromide. This reaction follows a multi-step mechanism involving bromine and hydrogen radicals. Since radicals are continuously formed and regenerated, this reaction is called a chain reaction.
The reaction begins with initiation. A bromine molecule collides with a third body, M, which provides energy to split it into two bromine radicals.
During propagation, a bromine radical reacts with hydrogen to form hydrogen bromide and a hydrogen radical. The hydrogen radical then reacts with another bromine molecule, continuing the chain.
Inhibition happens when hydrogen bromide reacts with a hydrogen radical. This reduces the concentration of hydrogen radicals and slows product formation.
Finally, termination happens when two bromine radicals recombine to form bromine in the presence of M, which absorbs the energy released during the reaction.
Although radicals drive the reaction, the observed rate law depends only on stable species. The square-root dependence on bromine suggests radical formation, while hydrogen bromide in the denominator indicates product inhibition.
From Chapter 10:
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