#Reaction Mechanisms & Rate Laws: Your AP Chem Survival Guide 🚀

Hey, future AP Chem rockstar! Let's break down reaction mechanisms and rate laws. This guide is designed to be your best friend the night before the exam—clear, concise, and super helpful. Let's do this!

#1. Reaction Mechanisms: The Step-by-Step Story

#What's a Mechanism? 🤔

• A mechanism is like a detailed recipe for a reaction, showing exactly how reactants turn into products.
• Most reactions happen in multiple steps, not just one big jump.
• Think of it as the behind-the-scenes action of a chemical reaction.

#Elementary Steps: The Building Blocks

• Each step in a mechanism is an elementary step.
• When you add up all the elementary steps, you get the overall balanced equation.
• It's like combining all the individual ingredients to get the final dish.

Example Mechanism:

• Overall Reaction: O₃ + 2I⁻ + H₂O → O₂ + I₂ + 2OH⁻
• Elementary Steps:
  1. O₃ + I⁻ → O₂ + IO⁻ (slow)
  2. IO⁻ + H₂O → HOI + OH⁻
  3. HOI + I⁻ → I₂ + OH⁻

#Catalysts and Intermediates: The Supporting Cast

• Catalysts: Speed up reactions but aren't consumed (they're like a chef's favorite pan).
• Intermediates: Formed and used up during the reaction (like a half-made dish).

• In the example above:
  • No catalysts are present.
  • Intermediates: IO⁻ (iodite) and HOI (hypoiodous acid).

#2. Rate-Determining Steps: The Bottleneck

#What's the Rate-Determining Step? 🐌

• The rate-determining step (RDS) is the slowest step in a mechanism.
• It's like the narrowest part of a funnel—it controls how fast the whole reaction can go.
• The RDS dictates the overall rate law of the reaction.

#Rate Laws from Mechanisms: How To

• Use the stoichiometric coefficients of the reactants in the RDS to write the rate law.
• Remember, rate laws must be verified experimentally.
• Mechanisms are proposed, and rate laws help us confirm if those mechanisms are valid.

#3. Example FRQ: Putting It All Together

Let's tackle a real AP Chem FRQ from the 2019 exam!

#The Setup

Reaction: 2 NO₂ (g) → 2 NO (g) + O₂ (g)

Experimental Data:

#Part (a): Determining Reaction Order

• Question: How do the graphs indicate the reaction is second order?
• Answer: The graph of 1/[NO₂] vs. time is linear, indicating a second-order reaction.

#Part (b): Writing the Rate Law

• Question: Write the rate law for the decomposition of NO₂ (g).
• Answer: Rate = k[NO₂]²

#Part (c.i): Verifying Mechanism I

Mechanism I:

• Question: Is Mechanism I consistent with the rate law from part (b)?
• Answer: Yes! The slow step (step 1) has the rate law Rate = k[NO₂][NO₂] = k[NO₂]², which matches the experimental rate law.

#Part (c.ii): Verifying Mechanism II

Mechanism II:

• Question: Is Mechanism II consistent with the rate law from part (b)?
• Answer: Yes, but it requires a bit more work! The slow step (step 2) has the rate law Rate = k[N₂O₄]. However, N₂O₄ is an intermediate, so it can't be in the final rate law.

#Using Equilibrium (Keq) to Find the Rate Law

• Step 1 is a fast equilibrium: NO₂ + NO₂ ⇌ N₂O₄
• $K_{eq} = \frac{[N₂O₄]}{[NO₂]^2}$
• Rearrange to solve for the intermediate: $[N₂O₄] = K_{eq}[NO₂]^2$
• Substitute into the rate law of the slow step: Rate = $kK_{eq}[NO₂]^2$
• This matches the experimental rate law! ✅

#4. Final Exam Focus

#High-Priority Topics 🎯

• Identifying Intermediates and Catalysts
• Determining the Rate-Determining Step
• Writing Rate Laws from Mechanisms
• Using Equilibrium to Substitute Intermediates
• Verifying Mechanisms with Experimental Rate Laws

Reaction mechanisms and rate laws are frequently tested. Master these concepts!

#Exam Tips 📝

• Time Management: Quickly identify the RDS and focus on that.
• Common Pitfalls: Don't include intermediates in the final rate law, and remember to use equilibrium if needed.
• Strategies: Practice, practice, practice! Work through multiple examples to build confidence.

#5. Practice Questions

Practice Question

#Multiple Choice Questions

1. The rate law for a reaction is determined to be rate = k[A][B]². Which of the following mechanisms is consistent with this rate law? (A) A + B → C (slow) ; C + B → D (fast) (B) A + B ⇌ C (fast) ; C + B → D (slow) (C) A + 2B → D (slow) (D) 2A + B → D (slow)

2. A reaction mechanism has two steps: Step 1: A + B → C (slow) , Step 2: C + D → E (fast). What is the overall rate law for the reaction? (A) rate = k[A][B]
   (B) rate = k[C][D] (C) rate = k[A][B][D] (D) rate = k[E]

3. In a multi-step reaction, which step determines the overall rate of the reaction? (A) The fastest step (B) The slowest step (C) The step with the highest activation energy (D) The step with the lowest activation energy

#Free Response Question

Consider the following reaction:

2NO(g) + O₂(g) → 2NO₂(g)

The following mechanism has been proposed:

Step 1: NO(g) + O₂(g) ⇌ NO₃(g) (fast equilibrium) Step 2: NO₃(g) + NO(g) → 2NO₂(g) (slow)

(a) Write the overall balanced equation for the reaction. (1 point)

(b) Identify any intermediates in the mechanism. (1 point)

(c) What is the rate law predicted by this mechanism? (3 points)

(d) If the experimentally determined rate law is rate = k[NO]²[O₂], does this mechanism agree with the experimental rate law? Explain. (2 points)

Answer Key & Scoring Rubric

Multiple Choice:

1. (B)
2. (A)
3. (B)

Free Response:

(a) 2NO(g) + O₂(g) → 2NO₂(g) (1 point)

(b) NO₃(g) (1 point)

(c) Rate = k[NO₃][NO] (1 point) $K_{eq} = \frac{[NO₃]}{[NO][O₂]}$ (1 point) [NO₃] = $K_{eq}[NO][O₂]$ Rate = $kK_{eq}[NO]²[O₂]$ (1 point)

(d) Yes. The rate law derived from the mechanism, rate = $kK_{eq}[NO]²[O₂]$, matches the experimental rate law, rate = k[NO]²[O₂]. (2 points)

You've got this! Go ace that AP Chem exam! 💪