Problem 125 - Chemistry The Molecular Nature of Matter

Question

The following question is based on Chemistry Outside the Classroom 13.1. The reaction of hydrogen and bromine appears to follow the mechanism shown, $$\begin{aligned}\mathrm{Br}_{2} & \longrightarrow 2 \mathrm{Br}^{*} \\\\\mathrm{Br} \cdot+\mathrm{H}_{2} & \longrightarrow \mathrm{HBr}+\mathrm{H} \\\\\mathrm{H} \cdot+\mathrm{Br}_{2} & \longrightarrow \mathrm{HBr}+\mathrm{Br} \\\2 \mathrm{Br} \cdot &\longrightarrow\mathrm{Br}_{2}\end{aligned}$$ (a) Identify the initiation step in the mechanism. (b) Identify any propagation steps. (c) Identify the termination step. (d) The mechanism also contains the reaction $$\mathrm{H} \cdot+\mathrm{HBr} \longrightarrow \mathrm{H}_{2}+\mathrm{Br}$$ How does this reaction affect the rate of formation of \(\mathrm{HBr}\) ?

Step-by-Step Solution

Answer

The initiation step is \(\mathrm{Br}_{2} \longrightarrow 2 \mathrm{Br}^\cdot\), the propagation steps are \(\mathrm{Br} ^\cdot + \mathrm{H}_{2} \longrightarrow \mathrm{HBr} + \mathrm{H} ^\cdot\) and \(\mathrm{H} ^\cdot + \mathrm{Br}_{2} \longrightarrow \mathrm{HBr} + \mathrm{Br}^\cdot\), and the termination step is \(2 \mathrm{Br}^\cdot \longrightarrow \mathrm{Br}_{2}\). The side reaction \(\mathrm{H} \cdot + \mathrm{HBr} \longrightarrow \mathrm{H}_{2}+\mathrm{Br}^\cdot\) decreases the rate of formation of HBr by reducing the concentration of H radicals.

Step 1 - Identify the Initiation Step

The initiation step in a reaction mechanism is the step where reactive species, such as free radicals, are first created. Look in the provided mechanism for the step that involves the breaking of a stable molecule into free radicals without the requirement of any existing free radicals.

Step 2 - Identify the Propagation Steps

Propagation steps in a chain reaction mechanism include steps that involve free radicals and produce other free radicals. These steps perpetuate the reaction. Identify the steps in the mechanism where a radical reacts with a stable molecule to create a product and another free radical.

Step 3 - Identify the Termination Step

The termination steps are the ones where free radicals are removed from the reaction mixture by forming a stable product. This can involve two free radicals joining together. Find the step in the mechanism that results in the decrease of free radicals without creating new ones.

Step 4 - Determine the Effect of a Side Reaction on the Rate of HBr Formation

The side reaction provided can affect the rate of formation of HBr by removing one of the reactive species, the H radical, thus decreasing the overall rate at which HBr is formed. Determine how the removal of H radicals through this side reaction influences the overall rate of the reaction.

Key Concepts

Initiation Step in Reaction Mechanism

In chemistry, the initiation step is akin to the starting pistol in a race; it's the pivotal moment when stable molecules break apart to form highly reactive species, usually free radicals. The stability of molecules like \(\mathrm{Br}_2\) means they don't usually split apart on their own. Yet, when provided the right conditions—like energy from light or heat—these bonds can be severed, as indicated in the first equation of the mechanism: \(\mathrm{Br}_{2} \longrightarrow 2 \mathrm{Br}^*\).

This equation marks the initiation step because it's where stable bromine molecules (\(\mathrm{Br}_{2}\)) decompose into two bromine radicals (\(\mathrm{Br}^*\)), without the help of other radicals. Having these radicals available sets the stage for the subsequent chain of reactions, driving the process forward.

Propagation Steps

Imagine a relay race where the baton is continuously passed forward; the propagation steps carry the momentum of the chemical race. These steps typically involve a free radical reacting with a stable molecule, which not only generates a product but also another free radical. This freshly minted radical then proceeds to induce further reactions, propagating the chain reaction sequence.

In our reaction, the two middle equations represent propagation steps. The bromine radical (\(\mathrm{Br}^*\)) reacts with hydrogen gas (\(\mathrm{H}_2\)), yielding hydrobromic acid (\(\mathrm{HBr}\)) and a hydrogen radical (\(\mathrm{H}^*\)). This generated hydrogen radical doesn't rest; it attacks a bromine molecule (\(\mathrm{Br}_2\)) to produce another molecule of hydrobromic acid and a new bromine radical, keeping the reaction's momentum going.

Termination Step

The termination step is the finish line of our chemical relay, halting the ongoing race of reactions. In this crucial phase, free radicals are neutralized as they combine to form stable, non-radical products. These can be thought of like the cool-down after an intense bout of physical activity; the radicals are 'retired' and stop propelling the reaction forward.

The final equation of our mechanism illustrates this phase: two bromine radicals (\(\mathrm{Br}^*\)) unite to reform a bromine molecule (\(\mathrm{Br}_2\)). Without any free radicals left to sustain the reaction sequence, the chemical race comes to a close. The ability to pinpoint this step within the mechanism is vital for understanding when and how the reaction ceases.

Rate of Chemical Reactions

The speed at which a product is formed in a chemical reaction is the crux of understanding reaction rates. Factors such as concentration, temperature, and the presence of a catalyst can dramatically influence this pace. In our reaction mechanism, the side reaction \(\mathrm{H}^* + \mathrm{HBr} \longrightarrow \mathrm{H}_2 + \mathrm{Br}^*\) acts like a roadblock slowing down the production of hydrobromic acid (\(\mathrm{HBr}\)).

By removing the hydrogen radical (\(\mathrm{H}^*\)), a key player in the propagation steps, this side reaction decreases the amount of \(\mathrm{H}^*\) available to continue the chain. Think of it as reducing the number of runners in our relay race; with fewer participants, fewer batons (or in our case, \(\mathrm{HBr}\) molecules) cross the finish line per unit of time. This diversion lowers the overall rate of \(\mathrm{HBr}\) formation, showcasing the intricate dance between reaction pathways and how they dictate the time frame of a reaction reaching completion.