Unit 5 · Topic 5.4 Beta

Elementary Reactions

An elementary reaction happens in a single event, so its rate law follows from its coefficients and its molecularity is the number of particles in that event.

Practice 1: Models and RepresentationsPractice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

A dance floor gets more crowded and couples bump into each other more often. Put twice as many dancers of one kind in the room and there are twice as many chances for a bump. Molecules work the same way, and for a reaction that happens in one single bump, you can write its rate law just by counting who has to meet.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. A reaction has rate = k[A][B]. If [A] doubles and [B] is unchanged, the rate:

  1. doubles
  2. is unchanged
  3. quadruples
  4. halves
Show the answer

The rate is first order in A, so it changes by the same factor as [A].

  • Correct: doubles:
  • is unchanged:
  • quadruples:
  • halves:

2. Why do orders in a rate law have to be measured for an overall reaction?

  1. They need not match the coefficients of the balanced equation
  2. Concentrations cannot be calculated
  3. The rate constant changes with concentration
  4. Rates can only be measured for gases
Show the answer

The overall equation shows totals, not how the rate depends on each concentration.

  • Correct: They need not match the coefficients of the balanced equation:
  • Concentrations cannot be calculated:
  • The rate constant changes with concentration:
  • Rates can only be measured for gases:

Part 4 · See it

See it first

Three particle pictures. Unimolecular: a single molecule of two atoms falls apart into two atoms; its rate law is rate equals k times the concentration of A. Bimolecular: two particles collide and rearrange; rate equals k times the concentration of A times the concentration of B. Termolecular: three particles must meet at the same moment, which is rare; rate equals k times the concentration of A squared times the concentration of B.
One, two or three particles come together in a single elementary step. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. An elementary step happens in a single collision or eventits rate depends on how often those exact particles meet
  2. Doubling the number of one kind of particle doubles its collisionseach particle in the step contributes one power of its concentration
  3. So the coefficients of an elementary step are its ordersyou can write its rate law without an experiment
  4. An overall equation is usually several stepsits rate law must still come from data

Part 6 · Key ideas

Key ideas

  • An elementary reaction is one event: a single collision or one particle breaking apart.
  • The rate law of an elementary step uses its coefficients as orders: 2 A + B → products has rate = k[A]²[B].
  • Molecularity: unimolecular (1), bimolecular (2, most common), termolecular (3, rare).
  • Only elementary steps follow this rule. Overall rate laws are measured.

Part 7 · Misconception

A common mistake

The wrong idea: Any balanced equation's coefficients give its rate law.

What actually happens: Only an elementary step's coefficients give its rate law. Most overall equations happen in several steps, so their rate laws must be measured.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Particle view

Three boxes of the same gas mixture

The elementary reaction A + B → AB happens in one collision between an A molecule and a B molecule. Three identical containers at the same temperature hold the mixtures shown.

Box 1Box 2Box 3

Key: dark filled circle, a molecule of A; light ringed circle, a molecule of B.

1. What is the rate law for this elementary step?

  1. rate = k[A][B]
  2. rate = k[AB]
  3. rate = k[A]²
  4. rate = k[A] + k[B]
Show the answer

For an elementary step the rate law comes straight from the step: one A and one B collide, so rate = k[A][B].

  • Correct: rate = k[A][B]: Right: first order in each of the two colliding reactants.
  • rate = k[AB]: AB is the product; a rate law uses the reactants.
  • rate = k[A]²: That would describe two A molecules colliding.
  • rate = k[A] + k[B]: Rate laws multiply concentrations; they are not sums.

2. How does the initial rate in Box 2 compare with Box 1?

  1. Half as fast
  2. The same
  3. Twice as fast
  4. Four times as fast
Show the answer

Box 2 has twice as many A molecules and the same number of B. With rate = k[A][B], doubling [A] doubles the rate: there are twice as many possible A–B pairs to collide.

  • Half as fast: Box 2 has more molecules, not fewer.
  • The same: More A molecules means more A–B collisions per second.
  • Correct: Twice as fast: Right: [A] doubles, [B] stays the same.
  • Four times as fast: Four times would need both [A] and [B] doubled, as in Box 3.

3. How does the initial rate in Box 3 compare with Box 1?

  1. The same
  2. Twice as fast
  3. Four times as fast
  4. Eight times as fast
Show the answer

Both [A] and [B] double: rate × 2 × 2 = 4. Box 1 has 2 × 2 = 4 possible A–B pairs; Box 3 has 4 × 4 = 16.

  • The same: More molecules of both kinds means more collisions.
  • Twice as fast: That counts only the doubling of one reactant.
  • Correct: Four times as fast: Right: 2 × 2 = 4.
  • Eight times as fast: That would be a third-order step.

Model

Four elementary steps

Each equation below is an elementary step, one single event at the particle level:

  1. O₃ → O₂ + O
  2. NO + O₃ → NO₂ + O₂
  3. 2 NO₂ → NO₃ + NO
  4. 2 NO + O₂ → 2 NO₂

4. What is the rate law for step 3, 2 NO₂ → NO₃ + NO?

  1. rate = k[NO₂]²
  2. rate = k[NO₂]
  3. rate = k[NO₃][NO]
  4. rate = 2k[NO₂]
Show the answer

Two NO₂ molecules collide in this step, so the rate is proportional to [NO₂] × [NO₂] = [NO₂]².

  • Correct: rate = k[NO₂]²: Right: the coefficient 2 becomes the exponent for an elementary step.
  • rate = k[NO₂]: That would be a single NO₂ falling apart.
  • rate = k[NO₃][NO]: Those are the products; a forward rate law uses reactants.
  • rate = 2k[NO₂]: The coefficient goes in the exponent, not in front of k.

5. Which step is termolecular?

  1. Step 1
  2. Step 2
  3. Step 3
  4. Step 4
Show the answer

Step 4 needs two NO molecules and one O₂ to meet at once: three particles.

  • Step 1: Step 1 is one O₃ breaking apart: unimolecular.
  • Step 2: Step 2 is NO meeting O₃: bimolecular.
  • Step 3: Step 3 is two NO₂ meeting: bimolecular.
  • Correct: Step 4: Right: 2 NO + O₂ is three particles.

6. The overall reaction 2 H₂ + 2 NO → N₂ + 2 H₂O has the measured rate law rate = k[H₂][NO]². What can you conclude?

  1. It is not one step: the orders differ from the coefficients
  2. The reaction is a single step in which four molecules collide at once
  3. The measured rate law is wrong, since the order in H₂ should be 2
  4. Rate laws for overall reactions follow their coefficients
Show the answer

If the overall equation were one elementary step, the rate law would be k[H₂]²[NO]². The measured order in H₂ is 1, so the reaction happens in more than one step (a mechanism, topic 5.7).

  • Correct: It is not one step: the orders differ from the coefficients: Right: an elementary rate law follows its coefficients, and this one does not.
  • The reaction is a single step in which four molecules collide at once: Four particles meeting at once is essentially impossible; the data also rule it out.
  • The measured rate law is wrong, since the order in H₂ should be 2: Measured orders are the facts; it is the "single step" idea that fails.
  • Rate laws for overall reactions follow their coefficients: This is the misconception: only elementary steps follow their coefficients.

Part 9 · Summary

Summary

An elementary reaction happens in a single event, so its rate law follows from its coefficients and its molecularity is the number of particles in that event. Bimolecular steps are the most common and termolecular steps are rare. Overall reactions usually happen in several steps, so their rate laws must be measured.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections