AP Chemistry: Reaction Mechanisms and Rate‑Determining Step

AP Chemistry – Reaction Mechanisms and Rate‑Determining Step

AP Chemistry: Reaction Mechanisms & Rate-Determining Step

What This Is

A reaction mechanism is a step-by-step sequence of elementary reactions that shows how a chemical reaction actually happens at the molecular level. The rate-determining step (RDS) is the slowest step in this sequence—it acts like a bottleneck, controlling the overall reaction rate. This topic is critical on the AP exam because it connects kinetics (how fast reactions occur) to molecular behavior. For example, imagine a factory assembly line: if one station (like painting) is slower than the others, it limits how fast the entire product can be made—this is the RDS in action. A real-world example is the ozone depletion reaction (O₃ + O → 2O₂), where the slow step determines how quickly ozone breaks down in the atmosphere.

Key Terms & Concepts

• Reaction Mechanism: A series of elementary steps that describe the actual pathway a reaction takes, including intermediates and transition states.
• Elementary Step: A single, simple reaction step that occurs exactly as written (unlike overall reactions, which are summaries). The molecularity (unimolecular, bimolecular, termolecular) describes how many molecules collide in the step.
• Intermediate: A species produced in one step and consumed in a later step—it doesn’t appear in the overall reaction. Example: In the mechanism for NO₂ + CO → NO + CO₂, NO₃ is an intermediate.
• Rate-Determining Step (RDS): The slowest elementary step in a mechanism; it determines the rate law for the overall reaction.
• Rate Law from Mechanism: For the RDS, the rate law is written directly from its stoichiometry (e.g., a bimolecular RDS: rate = k[A][B]).
• Catalyst in Mechanisms: A species that appears in an early step and is regenerated in a later step—it speeds up the reaction but isn’t consumed.
• Steady-State Approximation: A method to derive rate laws for mechanisms with fast equilibrium steps (used when intermediates are hard to isolate).
• Pre-Equilibrium: When the first step of a mechanism is fast and reversible, and the second step is slow (RDS). The rate law often includes the equilibrium constant (K) of the first step.
• Molecularity vs. Order:
• Molecularity = number of molecules colliding in an elementary step (unimolecular, bimolecular, termolecular).
• Order = exponent in the rate law (e.g., rate = k[A]² is second-order in A).
• Transition State: The high-energy, unstable arrangement of atoms at the peak of an energy diagram for an elementary step (not an intermediate!).
• Energy Profile Diagram: A graph of potential energy vs. reaction progress, showing intermediates (valleys) and transition states (peaks). The RDS has the highest activation energy (Eₐ).

Step-by-Step: Determining the Rate Law from a Mechanism

Problem: Given the mechanism below, derive the rate law for the overall reaction: Overall: 2NO + O₂ → 2NO₂ Mechanism:
1. NO + NO ⇌ N₂O₂ (fast equilibrium) 2. N₂O₂ + O₂ → 2NO₂ (slow, RDS)

Steps:
1. Identify the RDS: The slow step (Step 2) is the RDS. Write its rate law directly from its stoichiometry:
- Rate = k₂[N₂O₂][O₂] 2. Express intermediates in terms of reactants: N₂O₂ is an intermediate (produced in Step 1, consumed in Step 2). Since Step 1 is a fast equilibrium, use its equilibrium constant (K):
- K = [N₂O₂] / [NO]² → [N₂O₂] = K[NO]² 3. Substitute into the RDS rate law:
- Rate = k₂(K[NO]²)[O₂] = k[NO]²[O₂] (where k = k₂K) 4. Check the overall order: The rate law is second-order in NO and first-order in O₂, matching experimental data for this reaction.

Key Takeaway: If the RDS involves an intermediate, always replace it using equilibrium expressions from earlier steps.

Common Mistakes

• Mistake: Assuming the rate law comes from the overall reaction stoichiometry.
  Correction: Rate laws are determined experimentally or from the RDS. The overall reaction is just a summary—it doesn’t show the mechanism!

• Mistake: Forgetting that intermediates cannot appear in the final rate law.
  Correction: Intermediates must be replaced using equilibrium expressions (e.g., [N₂O₂] = K[NO]²) or the steady-state approximation.

• Mistake: Confusing molecularity (for elementary steps) with order (for the overall rate law).
  Correction: Molecularity applies to individual steps (e.g., a bimolecular step has 2 molecules colliding). Order is the exponent in the final rate law (e.g., rate = k[A]² is second-order in A).

• Mistake: Ignoring the fast equilibrium assumption when deriving rate laws.
  Correction: If the first step is fast and reversible, use its equilibrium constant (K) to substitute for intermediates.

• Mistake: Drawing energy profiles with intermediates as peaks (instead of valleys).
  Correction: Intermediates are stable (valleys), while transition states are unstable (peaks). The RDS has the highest peak (largest Eₐ).

AP Exam Insights

1. FRQ Favorite: The exam loves asking you to derive a rate law from a mechanism (like the NO + O₂ example above). Expect to:
2. Identify the RDS.
3. Replace intermediates using equilibrium expressions.

4. Justify why a step is the RDS (e.g., "Step 2 is slow because it has a high activation energy").

5. Multiple-Choice Traps:

6. Trick: A question gives a mechanism and asks for the rate law, but the RDS isn’t the first step. Always find the slow step first!

7. Trick: A catalyst is included in the mechanism. Remember: catalysts appear in the rate law (e.g., rate = k[A][catalyst]) but aren’t consumed.

8. Energy Diagrams: You might be asked to:

9. Label intermediates, transition states, and the RDS.
10. Compare activation energies (Eₐ) of steps.

11. Explain why a catalyst lowers the Eₐ of the RDS.

12. Terminology Pitfalls:

13. Intermediate vs. Transition State: Intermediates are stable (valleys), while transition states are unstable (peaks).
14. Rate-Determining Step vs. Rate-Limiting Step: These are the same thing—don’t overthink it!

Quick Check Questions

1. Multiple Choice: The following mechanism is proposed for the reaction 2A + B → C:
2. Step 1: A + B → D (slow)
3. Step 2: D + A → C (fast)
   What is the rate law for the overall reaction?
   (A) rate = k[A][B]
   (B) rate = k[A]²[B]
   (C) rate = k[D][A]
   (D) rate = k[A]²

Answer: (A) rate = k[A][B]
Explanation: The slow step (Step 1) is the RDS, and its rate law is written directly from its stoichiometry.

1. Short FRQ: The reaction 2NO + Cl₂ → 2NOCl has the following mechanism:
2. Step 1: NO + Cl₂ ⇌ NOCl₂ (fast equilibrium)
3. Step 2: NOCl₂ + NO → 2NOCl (slow)
   (a) Identify the intermediate.
   (b) Derive the rate law for the overall reaction.

Answer:
(a) Intermediate: NOCl₂ (produced in Step 1, consumed in Step 2).
(b) Rate Law:
- RDS is Step 2: rate = k₂[NOCl₂][NO]
- From Step 1 (fast equilibrium): K = [NOCl₂] / [NO][Cl₂] → [NOCl₂] = K[NO][Cl₂]
- Substitute: rate = k₂(K[NO][Cl₂])[NO] = k[NO]²[Cl₂] (where k = k₂K)

1. Multiple Choice: Which of the following is not true about the rate-determining step?
   (A) It has the highest activation energy in the mechanism.
   (B) Its rate law determines the overall rate law.
   (C) It is always the first step in the mechanism.
   (D) It can involve an intermediate.

Answer: (C) It is always the first step in the mechanism.
Explanation: The RDS can be any step in the mechanism—it’s just the slowest one!

Last-Minute Cram Sheet

1. Rate law = rate of RDS (slowest step).
2. Intermediates are produced then consumed; never in the final rate law.
3. Fast equilibrium steps → use K to replace intermediates (e.g., [X] = K[A][B]).
4. Molecularity = number of molecules in an elementary step (uni-, bi-, termolecular).
5. Order = exponent in the rate law (e.g., rate = k[A]² is second-order in A).
6. Catalysts appear in the rate law but are not consumed.
7. Energy diagrams: Peaks = transition states; valleys = intermediates.
8. RDS has the highest Eₐ (biggest peak on the energy diagram).
9. ⚠️ Don’t assume the first step is the RDS! Always check for the slow step.
10. ⚠️ Termolecular steps are rare (three molecules colliding is unlikely—look for errors in mechanisms!).