Reaction Quotient and Le Châtelier’s Principle
Use quotient algebra to justify a disturbance’s direction; temperature can also change K.
AP Chemistry Topic 7.10 · CED printed p. 138 / PDF p. 145. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Quotient algebra
- Equilibrium response
The quotient gives a precise reason for the response. At the old equilibrium Q = K. Apply the disturbance to the concentrations or pressures before any reaction takes place and calculate the new Q. If Q is now too small, net forward reaction raises it; if it is too large, net reverse reaction lowers it. The new equilibrium occurs when Q equals the applicable K again. You are comparing ratios, so “more products” needs to mean more of the appropriate powered ratio, not merely a larger total particle count.
At fixed temperature, adding or removing species, compressing gases, or diluting solutions changes Q but leaves K unchanged. For A ⇌ 2B, doubling every concentration multiplies the numerator by four and the denominator by two: Q doubles. For A + B ⇌ C, the same change halves Q. Temperature instead changes K; whether heating increases or decreases K follows whether the written forward reaction is endothermic or exothermic. Do not treat a newly heated mixture as automatically being at its new equilibrium. Describe the disturbance, then its response, and finally the equality it approaches.
Let's work through it
- A + B ⇌ C is at equilibrium. Dilute the solution to twice its volume at constant T; every concentration is halved immediately.
- Qnew = ([C]/2)/(([A]/2)([B]/2)) = 2Qold = 2K.
- Qnew > K, so the net reaction runs backward, consuming C and producing A and B. This favors the side with more dissolved particles.
- All concentrations are initially lower after dilution; a later increase in [A] relative to that immediate state does not imply [A] exceeds its original value.
Make the picture move
Interactive concept model
Q tells you which way; K tells you the destination ratio.
Predict first. Predict net direction from Q compared with K. Check whether the final concentrations must be equal, and whether the total concentration changes.
A(aq) ⇌ B(aq); Q = [B]/[A]; x = (K[A]₀ − [B]₀)/(1 + K)
On a small screen, scroll inside the graph or diagram to read its labels. The values and explanation also appear below.
Q = 0.25, K = 3.98: net forward: form B. Equilibrium [A] = 0.201 and [B] = 0.799 mol L⁻¹.
Read the data and comparisons
| ICE row | [A] (mol L⁻¹) | [B] (mol L⁻¹) |
|---|---|---|
| Initial | 0.8 | 0.2 |
| Change | −0.599 | +0.599 |
| Equilibrium | 0.201 | 0.799 |
Macroscopic / data. Concentration bars describe initial and final mixtures on one common scale.
Particle view. Net interconversion redistributes A and B while conserving their total; both directions continue at equilibrium.
Symbolic view. [A]eq = [A]₀ − x; [B]eq = [B]₀ + x; x = 0.599 mol L⁻¹.
Why it works. The signed x is the forward change in concentration. A decreases by x while B increases by x, preserving [A] + [B]. Substitute both final concentrations into K. Equilibrium requires equal forward and reverse rates; it does not generally require equal concentrations.
Conditions and limits. Abstract 1:1 dissolved interconversion at fixed temperature (298 K) and volume; ideal dilute activities are approximated by concentration divided by a 1 mol L⁻¹ standard state, which cancels in this ratio. Selecting K chooses a different hypothetical system at that fixed temperature, not a temperature change. This simple linear ICE solution does not cover other stoichiometries, solubility, or coupled equilibria.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
Why does compression not shift A ⇌ B in the ideal gas model?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
Why does compression not shift A ⇌ B in the ideal gas model?
Worked answer and reason
Both partial pressures multiply by the same factor, which cancels from Q.
Their exponents have equal sums.
Retrieval 2
Heating an endothermic forward reaction does what to K?
Worked answer and reason
It increases K, favoring the written product side.
The equilibrium composition changes with the energy balance.
Catch the tempting mistake
- Q keeps its old value while the mixture responds.
- Q changes with composition until it reaches the new equilibrium equality.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 7 problem 11 · ap application · symbolic
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For the teacher
- Ask for a multiplicative Q comparison; do not accept “less space” as the entire justification.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 7.10.A
- Explain the relationships between Q, K, and the direction in which a reversible reaction will proceed to reach equilibrium.
- 7.10.A.1
- A disturbance to a system at equilibrium causes Q to differ from K, thereby taking the system out of equilibrium. The system responds by bringing Q back into agreement with K, thereby establishing a new equilibrium state.
- 7.10.A.2
- Some stresses, such as changes in concentration, cause a change in Q only. A change in temperature causes a change in K. In either case, the concentrations or partial pressures of species redistribute to bring Q and K back into equality.
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 — Required topic-numbered learning objectives and essential knowledge, all continuations and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §13.2, Equilibrium Constants — Pressure/concentration quotients, pure-phase activities, and the distinction between composition and rate.
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Chemical equilibrium
Chemical equilibrium is a dynamic state in which forward and reverse reaction rates are equal. Macroscopic composition remains constant in a closed system under fixed conditions, but reactant and product concentrations need not be equal. For example, a reversible reaction can reach equilibrium with much more reactant than product.
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Dilution
Dilution lowers solute concentration by adding solvent while conserving the solute amount when no reaction or loss occurs. Concentration calculations use the final solution volume rather than simply the volume of solvent added. For example, increasing a solution's volume from 100 to 200 milliliters halves its concentration if its solute amount is unchanged.
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Endothermic process
An endothermic process absorbs heat into the chosen system. Under constant-pressure conditions with only pressure–volume work, its enthalpy change is positive. For example, melting ice absorbs heat while the phase change occurs.