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Skill Check 0 / 10 complete

Properties of the equilibrium constant

If you can find K for a couple of reactions, you can build K for combinations of them — as long as you remember three rules: reverse inverts, scale exponentiates, add multiplies.

§1

Three manipulation rules.

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The equilibrium constant transforms in fixed ways when you manipulate a reaction. Reversing a reaction inverts K: K becomes 1/K.

Multiplying a reaction through by a factor n raises K to the n-th power: K becomes Kn. (Halving a reaction takes the square root.)

Adding two reactions multiplies their K values: K = K₁ × K₂. These three rules let you compute the K of a target reaction from known ones — the equilibrium analog of Hess's law.

UNIT 7 TOPIC 7.6 • PROPERTIES OF THE EQUILIBRIUM CONSTANT K MANIPULATOR 1. REVERSE REACTION 2. MULTIPLY REACTION 3. ADD REACTIONS A ⇌ B K = 8.0 B ⇌ A K = 1/8.0 = 0.125 Reversing a reaction inverts K. A ⇌ B K = 8.0 2A ⇌ 2B K = (8.0)² = 64 Multiplying coefficients raises K to that power. A ⇌ B K₁ B ⇌ C K₂ A ⇌ C Ktotal = K₁ × K₂ Adding reactions multiplies their equilibrium constants. CED ANCHOR K changes predictably when equations are reversed, multiplied, or added — these rules follow from how species cancel in the K expressions. AP Chemistry · Unit 7 · Equilibrium
Fig. 7.6.1 When you manipulate a reaction, K changes by fixed rules: reversing inverts K (K → 1/K), multiplying by n raises K to the nth power (K → Kⁿ), and adding reactions multiplies their K values.
§2

Applying the rules.

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Match the manipulation to its K rule.

  1. Reverse → invert. If you flip a reaction, replace K with 1/K.
  2. Scale → exponentiate. If you multiply a reaction by n, raise K to the n-th power.
  3. Add → multiply. If you add reactions, multiply their K values.
  4. Combine for a target. Chain the rules to build the K of a combined reaction.
§3

The pieces you'll meet.

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Reverse, scale, add — each has its rule.

reverse
Reverse
K → 1/K.
scale
Scale by n
K → Kⁿ.
add
Add reactions
K = K₁ × K₂.
invert
Inversion
Reversing inverts the constant.
power
Power
Scaling raises K to a power.
multiply
Multiplication
Adding reactions multiplies their K values.
§4

Worked example: build a target K.

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Reverse. A reaction has K = 4. Its reverse has K = 1/4 = 0.25.

Scale. Doubling a reaction with K = 3 gives K = 3² = 9. (Halving it would give √3.)

Add. Two reactions with K₁ = 2 and K₂ = 5, added together, give K = 2 × 5 = 10.

Combine. To build a target, reverse and scale the known reactions as needed (adjusting their K by the rules), then multiply the resulting K values for the sum.

§5

Mistakes that cost real points.

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Pitfall · 01

"Adding reactions means adding their K values."

Adding reactions multiplies their K values (K = K₁ × K₂), it does not add them. This mirrors how adding reactions adds ΔH but multiplies K. Adding the K's gives the wrong constant.

Fix. Multiply the K values when you add reactions; do not add them.

Pitfall · 02

"Scaling a reaction by n multiplies K by n."

Scaling raises K to the n-th power (K → Kⁿ), not multiplies by n. Doubling a reaction squares K; tripling cubes it. Multiplying K by n is incorrect.

Fix. Raise K to the power of the scaling factor; do not multiply K by it.

Pitfall · 03

"Reversing a reaction leaves K unchanged."

Reversing a reaction inverts K (K → 1/K). The forward and reverse reactions have reciprocal equilibrium constants, not equal ones. Leaving K unchanged when reversing is a common slip.

Fix. Take the reciprocal of K when you reverse the reaction.

§6

Skill Check.

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