Properties of the Equilibrium Constant
Reverse, scale and add equations while transforming their quotients and equilibrium constants consistently.
AP Chemistry Topic 7.6 · CED printed p. 134 / PDF p. 141. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Balanced equation addition
- Exponent rules
K belongs to the exact equation, including its direction and coefficients. Reverse the equation and you turn the quotient upside down, so K becomes 1/K. Multiply every coefficient by c and every exponent is multiplied by c, so the new constant is Kc. Halving an equation takes the square root; doubling it squares K. This follows from the quotient’s algebra, rather than an extra rule to memorize.
When you add equations, multiply their equilibrium constants after any needed reversals or coefficient changes. An intermediate appearing on opposite sides cancels from the overall equation; its concentration factors also cancel when the quotients are multiplied. Check the final balanced equation before calling your product of constants the answer. These operations apply to Q too, because Q has exactly the same algebraic form. The difference is that Q uses the current mixture and K uses equilibrium. All component K values used together must refer to the same temperature and compatible conventions.
Let's work through it
- Given A ⇌ B, K1 = 5.0, and C ⇌ B, K2 = 2.0, find K for A ⇌ C.
- Reverse the second equation: B ⇌ C has K = 1/2.0. Reversing the direction requires inverting, not negating, K.
- Add A ⇌ B and B ⇌ C. B cancels and Koverall = 5.0 × (1/2.0) = 2.5.
- For 2C ⇌ 2A, reverse and double: K = (1/2.5)2 = 0.16. Apply the same changes to its Q expression.
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
What happens to K when a reaction is reversed?
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
What happens to K when a reaction is reversed?
Worked answer and reason
It becomes its reciprocal.
Products and reactants exchange numerator and denominator.
Retrieval 2
Why multiply K values when equations add?
Worked answer and reason
Their quotient factors multiply, and intermediate species cancel.
The algebra mirrors the equation cancellation.
Retrieval 3
A ⇌ B has current Q = 3 and equilibrium K = 5. What are Q and K for 2A ⇌ 2B?
Worked answer and reason
The new quotient is [B]²/[A]², so Q = 9 and K = 25. Both are squared because every coefficient and thus every exponent doubles.
Q and K have identical algebraic forms, so coefficient scaling applies to each.
Catch the tempting mistake
- Equilibrium constants can be negative after reversing a reaction.
- Concentration/pressure activity ratios are positive; reversal takes a reciprocal.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 7 problem 6 · ap application · symbolic
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For the teacher
- Have students show the intermediate cancellation and write the new quotient rather than quoting a memorized operation.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 7.6.A
- Represent a multistep process with an overall equilibrium expression, using the constituent K expressions for each individual reaction.
- 7.6.A.1
- When a reaction is reversed, K is inverted.
- 7.6.A.2
- When the stoichiometric coefficients of a reaction are multiplied by a factor c, K is raised to the power c.
- 7.6.A.3
- When reactions are added together, the K of the resulting overall reaction is the product of the K’s for the reactions that were summed.
- 7.6.A.4
- Since the expressions for K and Q have identical mathematical forms, all valid algebraic manipulations of K also apply to Q.
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 · 2 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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Equilibrium constant
An equilibrium constant is the value of the reaction quotient at equilibrium for a specified reaction and temperature. Its magnitude indicates equilibrium composition preference rather than reaction speed. For example, a large constant often indicates a product-favored equilibrium, but the starting composition still determines the immediate net direction.
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Mixture
A mixture contains two or more substances whose proportions can vary. Its components retain their chemical identities until a chemical reaction changes them. For example, water and ethanol can form mixtures with many different compositions.