5.2 Reaction mechanisms and their representation

Reaction Mechanisms

Reaction mechanisms break down complex chemical processes into a sequence of simple steps. Each step describes a specific molecular event, and together they show the full pathway from reactants to products. Understanding mechanisms is central to predicting rate laws, because the rate law for a reaction depends on how the reaction actually proceeds at the molecular level, not just on the balanced equation.

Components of Reaction Mechanisms

A reaction mechanism is a step-by-step description of the pathway a reaction follows from reactants to products. It consists of a series of elementary reactions that, when added together, give the overall balanced equation.

Here are the key components you need to know:

• Reactants are the starting materials that undergo the reaction (e.g., ethanol and oxygen in combustion).
• Products are the final compounds formed (e.g., carbon dioxide and water).
• Intermediates are species that form during the reaction but don't appear in the overall balanced equation. They're produced in one step and consumed in a later step. For example, the hydroxyl radical ($OH \cdot$) can appear as an intermediate in combustion mechanisms.
• Elementary reactions are the individual steps in a mechanism. Each one describes a single molecular event, such as a bond breaking or forming. Every elementary reaction passes through exactly one transition state (also called an activated complex), which is the highest-energy point along that step's reaction coordinate.

Molecularity describes how many reactant particles collide or rearrange in a single elementary step:

• Unimolecular: one molecule rearranges or decomposes (e.g., $H_2O_2 \rightarrow H_2O + \frac{1}{2}O_2$)
• Bimolecular: two particles collide and react (e.g., $H_2 + I_2 \rightarrow 2HI$). This is the most common type.
• Termolecular: three particles collide simultaneously. These are extremely rare because the probability of three molecules colliding at the same instant with the right orientation and energy is very low.

The rate-determining step (RDS) is the slowest elementary reaction in the mechanism. Because every step must occur for the reaction to proceed, the slowest step acts as a bottleneck and controls the overall reaction rate. Think of it like a slow cashier in a grocery store: no matter how fast the other lines move, the overall throughput is limited by the slowest one.

Building Blocks of Elementary Reactions

To propose a mechanism, you work backward and forward between the overall reaction and plausible molecular-level steps. Here's the general process, illustrated with the chlorination of methane ($CH_4 + Cl_2 \rightarrow CH_3Cl + HCl$):

1. Identify the reactants and products of the overall reaction. Here: methane and chlorine gas in, chloromethane and hydrogen chloride out.

2. Determine which bonds break and form. C–H and Cl–Cl bonds break; C–Cl and H–Cl bonds form. This tells you what kinds of elementary steps are needed.

3. Propose elementary steps that connect reactants to products, accounting for any intermediates. For methane chlorination, this is a free-radical chain mechanism:

   • Initiation: $Cl_2 \rightarrow 2Cl \cdot$
   • Propagation: $Cl \cdot + CH_4 \rightarrow CH_3 \cdot + HCl$
   • Propagation: $CH_3 \cdot + Cl_2 \rightarrow CH_3Cl + Cl \cdot$
   • Termination: $2Cl \cdot \rightarrow Cl_2$, or $CH_3 \cdot + Cl \cdot \rightarrow CH_3Cl$, or $2CH_3 \cdot \rightarrow C_2H_6$ Notice how the intermediates $Cl \cdot$ and $CH_3 \cdot$ are generated in one step and consumed in another. The propagation steps cycle, which is what makes it a chain reaction.

4. Verify the mechanism by adding the elementary steps together. The intermediates should cancel out, and the sum should match the overall balanced equation.

Symbols in Reaction Mechanisms

Mechanisms use specific notation to convey information clearly:

• A single arrow ($\rightarrow$) indicates an irreversible or forward-only step.
• Equilibrium arrows ($\rightleftharpoons$) indicate a reversible step where both forward and reverse reactions occur.
• The rate-determining step is typically labeled "slow" next to the arrow, or marked as "RDS." Fast steps are labeled "fast."
• Plus signs (+) separate multiple reactants or products within a single step.
• Stoichiometric coefficients balance each elementary step individually (e.g., $N_2 + 3H_2 \rightleftharpoons 2NH_3$).

One note on intermediates: while some textbooks place square brackets around intermediates (e.g., $[CH_3 \cdot]$), this isn't universal. The more reliable way to identify an intermediate is to check whether a species appears in the mechanism's steps but not in the overall balanced equation.

Mechanisms vs. Overall Equations

The overall balanced equation tells you what reacts and what forms, but it says nothing about how the reaction happens. That's what the mechanism provides. Here are the key relationships:

• The elementary steps must sum to the overall equation. When you add all the steps and cancel intermediates that appear on both sides, you should recover the balanced equation exactly. If you don't, the proposed mechanism is inconsistent with the known reaction.
• The rate-determining step controls the rate law. You can write the rate law directly from the RDS because it's the bottleneck. For example, if the RDS is $H_2 + I_2 \rightarrow 2HI$ (bimolecular), the rate law is $rate = k[H_2][I_2]$, which is second-order overall.
• If an intermediate appears in the RDS, you can't leave it in the rate law (since intermediates aren't measurable reactant concentrations). Instead, you use a prior fast equilibrium step to express the intermediate's concentration in terms of actual reactants. This substitution is one of the trickier parts of mechanism problems, so watch for it.
• The molecularity of the RDS often determines the overall reaction order. A unimolecular RDS gives a first-order rate law; a bimolecular RDS gives a second-order rate law. But remember: molecularity only applies to elementary steps, never to the overall reaction.