14.3 Reaction Mechanisms, Catalysts, and Reaction Coordinate Diagrams
PRE-HEALTH PREP
Reaction Mechanisms & Reaction Coordinate Diagrams
General Chemistry 14.3
Lesson Overview
Reaction mechanisms describe the stepwise molecular-level pathway by which reactants become products, with each elementary step classified by its molecularity as unimolecular, bimolecular, or termolecular. The rate-determining step — the slowest step in a mechanism — governs the overall rate law, and intermediates produced during the mechanism must be algebraically eliminated from the final rate expression using equilibrium assumptions. Reaction coordinate diagrams provide a visual framework for identifying transition states, intermediates, and activation energies, while catalysts lower the activation energy by providing an alternate pathway without shifting the equilibrium position.
Table of Contents
- Elementary Steps & Molecularity
- Catalysts & Intermediates
- Rate Laws from Mechanisms
- The Rate-Determining Step
- Case 1: Slow First Step
- Case 2: Slow Second Step
- Catalysts: Properties & Behavior
- Reaction Coordinate Diagrams
- Transition States vs. Intermediates
- Multi-Step Diagrams
- Calculating ΔH from Activation Energies
- Key Takeaways
Elementary Steps & Molecularity
What Is a Reaction Mechanism?
A reaction mechanism is a sequence of individual steps that describes, at the molecular level, exactly how reactants are converted into products. Each step in a mechanism must be an elementary reaction — a step so simple that it cannot be broken down further. Think of it as the atomic unit of chemical change.
Most overall reactions are composed of more than one elementary step. This is precisely why you generally cannot read the stoichiometric coefficients of a balanced overall equation and use them directly as the orders in a rate law. The rate law reflects the sequence of elementary steps — and in particular, it reflects the slowest step among them, which we call the rate-determining step.
The 3 Types of Molecularity: Unimolecular, Bimolecular, and Termolecular
Elementary steps are classified by their molecularity — the number of reactant molecules involved in that step:
- Unimolecular: one reactant molecule (e.g., a molecule spontaneously falling apart)
- Bimolecular: two reactant molecules colliding
- Termolecular: three reactant molecules simultaneously colliding — extremely rare
Why nothing higher than termolecular? For a bimolecular step, two molecules simply need to collide — a commonplace event. For a termolecular step, three molecules must all converge on the same point in space at precisely the same instant. That is already vanishingly rare. Requiring four molecules to do the same thing simultaneously is, for all practical purposes, impossible. Imagine hearing that eight cars coming from eight different directions all collided at a single intersection at the exact same moment — that does not happen spontaneously. Neither do quadrimolecular reactions.
Catalysts & Intermediates: How to Tell Them Apart
Finding the Overall Reaction from a Mechanism
To find the overall balanced reaction from a multi-step mechanism, simply add all the steps together. Place all reactants on one side and all products on the other, then cancel any species that appear on both sides. What remains is the overall reaction.
Identifying Intermediates
Any species that cancels out — appearing on both sides — is either an intermediate or a catalyst. The key is figuring out which role it plays.
An intermediate is, literally, something present only "in the middle." It is produced in an early step and then consumed in a later step before the reaction is complete. You do not begin with an intermediate, and you do not end up with it. It is neither a starting reactant nor a final product.
The identifying signature: an intermediate is a product first, reactant second.
Identifying Catalysts
A catalyst has the opposite signature: it is a reactant first, product second. A catalyst participates as a reactant early in the mechanism but is regenerated — reproduced — before the reaction ends. Because it is restored at the end, it does not appear in the overall balanced equation.
Example: Hydrogenation of Ethylene over Platinum
Consider a two-step mechanism for the hydrogenation of ethylene:
- Step 1: H₂ + Pt → H₂Pt
- Step 2: H₂Pt + C₂H₄ → C₂H₆ + Pt
Adding the two steps and canceling species that appear on both sides (Pt and H₂Pt), the overall reaction is:
H₂ + C₂H₄ → C₂H₆
H₂Pt is the intermediate — produced in step 1, consumed in step 2.
Pt is the catalyst — consumed in step 1, regenerated in step 2.
Practice Problem: Identify the Intermediate and Catalyst
Given the following two-step mechanism for the decomposition of hydrogen peroxide catalyzed by iodide ion:
Step 1: H2O2 + I− → H2O + IO−
Step 2: H2O2 + IO− → H2O + O2 + I−
Identify the overall reaction, the intermediate, and the catalyst.
How to Write Rate Laws from Reaction Mechanisms
Writing Rate Laws for Elementary Steps
Because every step in a mechanism is an elementary reaction, you can determine its rate law directly from the coefficients of its reactants. This is the key distinction: for an overall balanced equation, you cannot assume the coefficients equal the reaction orders. But for a confirmed elementary step, you can — the stoichiometric coefficients of the reactants are the orders in the rate law for that step.
When can you read rate orders directly from coefficients? Only when you know a reaction is elementary. You know this in 2 situations: (1) the problem explicitly states "this is an elementary reaction," or (2) the step appears within a mechanism, since mechanisms are always composed of elementary steps exclusively.
Example: Ozone Decomposition Mechanism
Consider the following two-step mechanism for the decomposition of ozone:
- Step 1 (unimolecular): O₃ → O₂ + O
- Step 2 (bimolecular): O + O₃ → 2 O₂
The atomic oxygen O is produced in step 1 and consumed in step 2, making it an intermediate. Adding both steps and canceling the intermediate gives the overall reaction:
2 O₃ → 3 O₂
The individual rate laws are:
Step 2: rate = k₂[O][O₃]
Practice Problem: Ozone Decomposition with Rapid Equilibrium
Given the following two-step mechanism:
O3 ⇌ O2 + O (rapid equilibrium)
O + O3 → 2O2 (slow)
1. What is the intermediate?
2. What is the rate law?
The Rate-Determining Step
In a multi-step mechanism, the rate-determining step is the slowest step — and it controls the overall rate of the reaction. All the other steps, no matter how fast, cannot compensate for a single slow step. The slowest step is the bottleneck.
Analogy: Imagine a four-person Olympic relay team where three runners each finish their lap in under 60 seconds. The fourth runner — a four-year-old — takes three hours. The team's final time is effectively three hours. Whether the three fast runners shave a few seconds off their laps is irrelevant. The four-year-old's leg is the rate-determining step. In chemistry, the slow step sets the pace for the entire reaction.
Case 1: The Slow Step Is the First Step
When the first step of a mechanism is the rate-determining step, the problem is at its simplest. Everything after the slow step has no effect on the overall rate. The rate law of the slow step is the rate law of the entire reaction — no further work required.
Example: First Step Is Slow (Ozone Decomposition)
If step 1 (O₃ → O₂ + O) is the slow step for the reaction 2 O₃ → 3 O₂, then:
This is the complete rate law for the overall reaction. The second step is fast and does not influence the rate.
Case 2: The Slow Step Is the Second Step
When the first step is fast (often described as reaching a rapid equilibrium) and the second step is slow, the problem is considerably more involved. You cannot simply use the first step's rate law, and you also cannot use the second step's rate law as written — because it contains an intermediate, which must be eliminated.
Why Intermediates Cannot Appear in the Final Rate Law
A properly written overall rate law may contain rate constants, reactants, and products — but not intermediates. Intermediates are transient species whose concentrations cannot be independently controlled or measured in a straightforward way. An intermediate concentration in a rate law must be replaced with an equivalent expression written in terms of reactants and products.
Using the Rapid Equilibrium Assumption to Eliminate the Intermediate
When the first step reaches rapid equilibrium, its forward and reverse rates are equal. This equality gives you an algebraic relationship that lets you solve for the intermediate's concentration.
Example: Second Step Is Slow (Ozone Decomposition)
The mechanism:
- Step 1 (fast, rapid equilibrium): O₃ ⇌ O₂ + O
- Step 2 (slow): O + O₃ → 2 O₂
Start with the slow step's rate law:
Set forward rate equal to reverse rate for step 1:
Solve for the intermediate [O]:
Substitute into the slow step rate law:
rate = (k₁k₂ / k‐₁) × [O₃]² / [O₂]
rate = k′ [O₃]² / [O₂]
Interpreting the Resulting Rate Law
This rate law has some striking features worth pausing on. The reaction is second order with respect to O₃ and negative first order with respect to O₂. Dividing by [O₂] is equivalent to raising it to the power of −1, so the exponent is literally −1.
A negative reaction order is uncommon, but it does arise in mechanisms where the second step is slow and the first step's equilibrium is pushed backward by a product. Notice also that O₂ is a product of the overall reaction appearing in the rate law — also unusual, but permissible in complex mechanisms.
The overall reaction order is 2 + (−1) = 1. The reaction is overall first order, reached through a remarkably indirect path.
Summary of the 2 cases: If the first step is slow, its rate law is the entire reaction's rate law. If the second step is slow, start with the slow step's rate law, recognize that any intermediate in it must be replaced, set the fast step's forward and reverse rates equal to express the intermediate concentration in terms of reactants and products, then substitute and simplify.
Catalysts: 4 Key Properties You Need to Know
What Does a Catalyst Do?
A catalyst is a substance that speeds up a chemical reaction. The most abundant catalysts in your life are inside your own body: enzymes are biological catalysts, almost all of them proteins, that facilitate the thousands of chemical reactions required for life. Beyond biology, inorganic catalysts are central to industrial chemistry and everyday laboratory reactions.
A catalyst speeds up a reaction by lowering the activation energy. It does not somehow push more energy into the system — it provides an entirely different pathway, an alternate mechanism, through which the same reactants are converted to the same products via a lower-energy route. The uncatalyzed and catalyzed pathways need not even have the same number of steps; what matters is that the new pathway has a lower activation energy barrier.
The 4 Properties of Catalysts
Four properties of catalysts that you should know:
- Speeds up the reaction by lowering the activation energy.
- Provides an alternate mechanism — a different pathway from reactants to products.
- Is not consumed in the overall reaction. It is used up early in the mechanism but regenerated before the reaction ends, which is why it cancels out of the overall equation.
- Does not shift the equilibrium. A catalyst gets you to the equilibrium position faster, but it does not change where that equilibrium lies. You obtain the same amount of product — just more quickly.
Important distinction: A catalyst changes the rate of a reaction but not the equilibrium. Adding a catalyst will not increase your yield; it only shortens the time needed to reach the same equilibrium composition.
How to Read a Reaction Coordinate Diagram
What Is a Reaction Coordinate Diagram?
A reaction coordinate diagram (also called an energy diagram or potential energy diagram) displays the energy of the system on the y-axis and the reaction coordinate — a measure of progress through the reaction — on the x-axis. As you move left to right across the diagram, you follow the reaction from reactants through any intermediates to products.
The path is not a flat line. There is always an energy hill to climb. The height of that hill, measured from the energy level of the reactants to the peak, is the activation energy (Eₐ). At any given temperature, molecules in a sample possess a distribution of kinetic energies; only those with energy equal to or greater than Eₐ can successfully react. This is why a higher activation energy means a slower reaction: fewer molecules have enough energy to surmount the barrier.
Endothermic vs. Exothermic Reactions on an Energy Diagram
The overall energy difference between reactants and products is ΔH, the enthalpy change for the reaction.
- If products are higher in energy than reactants, the system must absorb heat: ΔH > 0 and the reaction is endothermic.
- If products are lower in energy than reactants, the system releases heat: ΔH < 0 and the reaction is exothermic.
Reading ΔH from the diagram: ΔH corresponds to the vertical distance between the reactant energy level and the product energy level — regardless of what the curve does in between. The activation energy and any intermediate peaks are irrelevant to the value of ΔH.
Transition States vs. Intermediates: What Is the Difference?
The peak of each hill in a reaction coordinate diagram is called a transition state (abbreviated with a double-dagger symbol, ‡). The transition state is sometimes called the activated complex. It represents the highest-energy, most unstable arrangement of atoms along the reaction pathway — the point of no return, where the system commits either to forming product or reverting to reactant.
Critical distinction — transition state vs. intermediate: A transition state cannot be isolated. It is not a real stable species; it exists only at the fleeting top of the energy barrier. An intermediate, by contrast, occupies a local energy minimum (a valley between peaks). Because it has a finite lifetime, an intermediate can potentially be isolated if the reaction is interrupted at the right moment.
Multi-Step Reaction Coordinate Diagrams
The number of hills in a reaction coordinate diagram equals the number of elementary steps in the mechanism. A one-step (elementary) reaction has a single hill and a single transition state. A two-step reaction has two hills, two transition states, and a valley between them.
That valley — the local energy minimum between two hills — represents an intermediate. In step 1, the reactant climbs to the first transition state and descends into the valley, forming the intermediate. In step 2, the intermediate climbs the second hill and descends to the products. As a general rule:
- A 2-step mechanism has 1 intermediate and 2 transition states.
- A 3-step mechanism has 2 intermediates and 3 transition states.
- An n-step mechanism has (n − 1) intermediates and n transition states.
Identifying the Rate-Determining Step from the Diagram
In a multi-step diagram, the rate-determining step corresponds to the hill with the higher activation energy. The larger the hill, the slower that step, and the slower step controls the overall rate. If the first hill is taller than the second, step 1 is rate-determining; if the second hill is taller, step 2 is rate-determining.
Example: Reading a Two-Step Reaction Coordinate Diagram
Suppose a two-step reaction coordinate diagram shows:
- Step 1: activation energy of 80 kJ/mol (taller hill)
- Step 2: activation energy of 30 kJ/mol (shorter hill)
Step 1 has the higher activation energy, so step 1 is the rate-determining step. The rate law for step 1 is also the rate law for the overall reaction.
Calculating ΔH from Forward and Reverse Activation Energies
A reaction coordinate diagram can be read in both directions. The forward activation energy (Eₐ,fwd) is the height from the reactant level to the peak. The reverse activation energy (Eₐ,rev) is the height from the product level to the same peak.
These 3 quantities are related by a simple equation:
Example: Calculating ΔH from Activation Energies
Suppose the forward activation energy is 50 kJ/mol and the reverse activation energy is 30 kJ/mol:
The positive value confirms that the forward reaction is endothermic. Had the result been negative, the reaction would be exothermic — and you could verify this by noting that a negative ΔH means the products are lower in energy than the reactants, consistent with an exothermic diagram.
Quick check: For an endothermic reaction, the forward Eₐ is always larger than the reverse Eₐ (because you must climb more going forward than going backward). For an exothermic reaction, the reverse Eₐ is always larger than the forward Eₐ. This relationship provides a built-in consistency check on your diagram.
Key Takeaways
- A reaction mechanism is a sequence of elementary steps. Elementary steps are classified by molecularity: unimolecular, bimolecular, or termolecular (termolecular is rare; nothing higher exists).
- To find the overall reaction from a mechanism, add all steps and cancel species that appear on both sides. Species that cancel are either intermediates (product first, reactant second) or catalysts (reactant first, product second).
- For elementary steps only, you can read reaction orders directly from stoichiometric coefficients. This is not valid for overall balanced equations.
- The rate-determining step is the slowest step and governs the overall rate law. When the first step is slow, its rate law is the entire reaction's rate law.
- When the second step is slow, start with the slow step's rate law, then use the fast step's rapid equilibrium to express any intermediate concentration in terms of reactants and products. Intermediates must not appear in the final rate law.
- A catalyst speeds up a reaction by lowering the activation energy via an alternate mechanism. It is not consumed overall and does not shift the equilibrium position.
- On a reaction coordinate diagram, the activation energy (Eₐ) is the height from the reactant energy level to the peak. ΔH is the energy difference between reactants and products. A positive ΔH indicates an endothermic reaction; negative indicates exothermic.
- Transition states (at peaks) cannot be isolated. Intermediates (at valleys between peaks) can potentially be isolated, as they are real, if transient, chemical species.
- In a multi-step energy diagram, the step with the higher activation energy hill is the rate-determining step. An n-step mechanism has exactly (n − 1) intermediates.
- The relationship ΔH = Eₐ(fwd) − Eₐ(rev) allows you to calculate the enthalpy change from forward and reverse activation energies, and to verify whether a reaction is endothermic or exothermic.