Unit 7 · Topic 7.5 Beta

Magnitude of the Equilibrium Constant

Because K is products over reactants at equilibrium, its size describes the equilibrium mixture.

Practice 4: Model AnalysisPractice 6: Argumentation

Question set for this topic

Part 1 · Hook

Why this matters

The air around you is 78% nitrogen and 21% oxygen, and the two can react to form nitric oxide. They do not, at least not in any amount you could measure. The equilibrium constant for that reaction at room temperature is about 10−31. One glance at the size of K tells you the air is safe, without any calculation at all.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. In the expression for K, where do the products go?

  1. In the numerator (top)
  2. In the denominator (bottom)
  3. They are left out
  4. They are added to the reactants
Show the answer

K is products over reactants, each raised to its coefficient.

  • Correct: In the numerator (top):
  • In the denominator (bottom):
  • They are left out:
  • They are added to the reactants:

2. For A ⇌ B, an equilibrium mixture has [A] = 0.10 M and [B] = 0.50 M. What is K?

  1. 5.0
  2. 0.20
  3. 0.050
  4. 0.60
Show the answer

K = [B]/[A] = 0.50/0.10.

  • Correct: 5.0:
  • 0.20:
  • 0.050:
  • 0.60:

3. What does activation energy control?

  1. How fast a reaction proceeds
  2. How much product forms at equilibrium
  3. Whether a reaction is exothermic
  4. The coefficients in the equation
Show the answer

A higher activation energy means fewer effective collisions per second, so a slower reaction.

  • Correct: How fast a reaction proceeds:
  • How much product forms at equilibrium:
  • Whether a reaction is exothermic:
  • The coefficients in the equation:

Part 4 · See it

See it first

A logarithmic scale of K from 10 to the minus 12 on the left to 10 to the 12 on the right. Far left, K much less than 1: reactant-favored, mostly reactants at equilibrium with a little product. A shaded band around K = 1, roughly 10 to the minus 3 to 10 to the 3: appreciable amounts of both. Far right, K much greater than 1: product-favored, mostly products with a little reactant. A note says K tells where equilibrium lies, not how fast it is reached.
Large K: mostly products at equilibrium. Small K: mostly reactants. Near 1: both. The size of K says nothing about speed. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. K is products over reactants at equilibriumits size tells you which side dominates the equilibrium mixture
  2. K is much greater than 1the mixture is mostly products: product-favored
  3. K is much less than 1the mixture is mostly reactants, with a little product: reactant-favored
  4. K describes only the final mixtureit gives no information about how fast equilibrium is reached

Part 6 · Key ideas

Key ideas

  • K ≫ 1: product-favored; mostly products at equilibrium.
  • K ≪ 1: reactant-favored; mostly reactants, but some product forms.
  • K near 1: appreciable amounts of both reactants and products.
  • K tells you how far a reaction goes, never how fast.

Part 7 · Misconception

A common mistake

The wrong idea: A large K means the reaction is fast.

What actually happens: K describes the equilibrium mixture only. H₂ and O₂ have an enormous K for making water but do not react for years at room temperature, because the activation energy is high.

Part 8 · Check yourself

Check yourself

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

Data table

Equilibrium constants for four reactions

A student looks up Kc for four gas-phase reactions, each at 25 °C. Each reaction starts with only its reactants, at 1.0 M each.

Kc at 25 °C
ReactionEquationKc
1N2(g) + O2(g) ⇌ 2 NO(g)4.5 × 10−31
2H2(g) + Cl2(g) ⇌ 2 HCl(g)2.5 × 1033
3CO(g) + H2O(g) ⇌ CO2(g) + H2(g)1.0 × 105
4N2O4(g) ⇌ 2 NO2(g)4.6 × 10−3

1. In which reaction does the equilibrium mixture contain almost nothing but reactants?

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

The smaller K is, the less product the equilibrium mixture contains. K = 10⁻³¹ means the reaction barely proceeds.

  • Correct: Reaction 1: Right: K = 4.5 × 10⁻³¹ is extremely small, so at equilibrium the product, NO, is present in a tiny amount.
  • Reaction 2: K = 2.5 × 10³³ is huge: this reaction goes essentially to products.
  • Reaction 3: K = 1.0 × 10⁵ is large, so products are favored.
  • Reaction 4: K = 4.6 × 10⁻³ is small, so reactants are favored, but not nearly as strongly as in reaction 1.

2. The student concludes that reaction 2 must reach equilibrium within seconds because its K is so large. Is the conclusion justified?

  1. No: K shows where equilibrium lies, not how fast it is reached.
  2. Yes: a large K means a large rate constant for the forward reaction.
  3. Yes: products form quickly whenever K is greater than 1.
  4. No: a large K means the reaction is slow, because the reverse reaction is fast.
Show the answer

K describes the mixture once equilibrium is reached. How long that takes is kinetics (Unit 5). H₂ and Cl₂ can sit mixed in the dark for a long time, then react explosively in sunlight; K is the same either way.

  • Correct: No: K shows where equilibrium lies, not how fast it is reached.: Right: K is about the composition at equilibrium. Speed depends on the activation energy and the rate law, which K does not tell you.
  • Yes: a large K means a large rate constant for the forward reaction.: K compares forward and reverse at equilibrium; a large K is compatible with both reactions being very slow.
  • Yes: products form quickly whenever K is greater than 1.: Being product-favored says how much product there will be, not when. Some product-favored reactions take years.
  • No: a large K means the reaction is slow, because the reverse reaction is fast.: K does not set the speed in either direction, so it cannot tell you the reaction is slow either.

3. For reaction 4, a student starts with 1.0 M N2O4 and predicts that almost all of it will turn into NO2. Which response is best?

  1. The prediction is wrong: K < 1, so most N2O4 remains at equilibrium.
  2. The prediction is right: N2O4 is the one species present at the start.
  3. The prediction is right: K is positive, so products are favored.
  4. The prediction is wrong: no NO2 forms, because K is less than 1.
Show the answer

K much less than 1 means reactants are favored: some product forms, but most of the reactant is still there at equilibrium.

  • Correct: The prediction is wrong: K < 1, so most N2O4 remains at equilibrium.: Right: K = 4.6 × 10⁻³. With [N₂O₄] near 1.0 M, [NO₂]² ≈ 4.6 × 10⁻³, so [NO₂] ≈ 0.068 M: a few percent reacts.
  • The prediction is right: N2O4 is the one species present at the start.: Starting with reactant only tells you the net reaction is forward (Q = 0 < K). It does not tell you how far it goes.
  • The prediction is right: K is positive, so products are favored.: Every K is positive. What matters is whether K is much larger or much smaller than 1.
  • The prediction is wrong: no NO2 forms, because K is less than 1.: K < 1 does not mean zero product. Some NO₂ forms, just not much.

Particle view

Three reactions at equilibrium

Reaction IReaction IIReaction III

Key: X2Y2XY

Each container shows a different reaction of the form X2(g) + Y2(g) ⇌ 2 XY(g) at equilibrium. The containers have equal volumes and each started with 5 X2 and 5 Y2.

4. Which reaction has the largest equilibrium constant?

  1. Reaction I
  2. Reaction II
  3. Reaction III
  4. They are equal, because each started with the same amounts.
Show the answer

The equilibrium mixture with the most product relative to reactant has the largest K. Count: I has 8 XY to 1 + 1 reactant molecules.

  • Correct: Reaction I: Right: K = 8² / (1 × 1) = 64, by far the most product per reactant.
  • Reaction II: K = 2² / (4 × 4) = 0.25, the smallest of the three.
  • Reaction III: K = 4² / (3 × 3) ≈ 1.8, in between.
  • They are equal, because each started with the same amounts.: Same starting amounts but different reactions settle at different mixtures, so the K values differ.

5. Each particle in a container stands for 0.10 mol, and each container is 1.0 L. Calculate Kc for reaction II.

Type a number.

Show the answer

[XY] = 2 × 0.10 = 0.20 M; [X₂] = [Y₂] = 4 × 0.10 = 0.40 M. Kc = (0.20)² / (0.40 × 0.40) = 0.25.

  • Answer: 0.25

6. Which statement about reaction II is correct?

  1. Its K is less than 1, so reactants are favored.
  2. Its K is greater than 1, because product is present.
  3. It is not at equilibrium, because it has more reactant than product.
  4. It will react further toward products, because K is small.
Show the answer

A small K describes an equilibrium mixture that is mostly reactants. It is still an equilibrium: no further net change.

  • Correct: Its K is less than 1, so reactants are favored.: Right: K = 0.25, and the box holds 8 reactant molecules for every 2 product molecules.
  • Its K is greater than 1, because product is present.: Any equilibrium mixture contains some product. K > 1 needs products to outweigh reactants in the ratio, which they do not here.
  • It is not at equilibrium, because it has more reactant than product.: The question says each container is at equilibrium. Mostly-reactant mixtures are common equilibria.
  • It will react further toward products, because K is small.: At equilibrium, Q = K and there is no net reaction, whatever the size of K.

7. A cylinder of H2 and O2 gases can stand for years without forming water, though K for 2 H2(g) + O2(g) ⇌ 2 H2O(g) is enormous at room temperature. What explains this?

  1. The reaction has a high activation energy, so it is extremely slow at room temperature.
  2. The mixture is already at equilibrium.
  3. K is large, so the reverse reaction prevents water from forming.
  4. K applies once some water has already formed.
Show the answer

Thermodynamics (the size of K) and kinetics (the rate) are separate. A large K tells you where the reaction would end, not that it will get there quickly.

  • Correct: The reaction has a high activation energy, so it is extremely slow at room temperature.: Right: K says water is overwhelmingly favored at equilibrium, but without a spark or catalyst very few collisions get over the energy barrier.
  • The mixture is already at equilibrium.: At equilibrium with K this large, there would be almost no H₂ and O₂ left. The cylinder is far from equilibrium.
  • K is large, so the reverse reaction prevents water from forming.: A large K favors the forward reaction. The reverse reaction is negligible.
  • K applies once some water has already formed.: K applies to the reaction at any composition; Q = 0 here, so the net reaction should go forward. It just goes very slowly.

Part 9 · Summary

Summary

Because K is products over reactants at equilibrium, its size describes the equilibrium mixture. K much greater than 1 means product-favored (mostly products), K much less than 1 means reactant-favored (mostly reactants, a little product), and K near 1 means appreciable amounts of both. A small K lets you estimate product amounts by treating the reactant concentration as unchanged. K says how far a reaction goes, not how fast.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections