Worked example 1
For 2 SO₂(g) + O₂(g) ⇌ 2 SO₃(g), K = 4.0 × 10²⁴. Find K for 2 SO₃(g) ⇌ 2 SO₂(g) + O₂(g).
Try it first: Identify which of the three operations has been applied.
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Chemical Equilibrium & SolubilityEquilibriumContent level: Core 18 min
Manipulating Equilibrium Constants: Reversing, Scaling and Adding
What you'll be able to do: Find K for a target reaction by reversing, scaling and adding reactions whose constants are known.
Introduction
Tables rarely list the exact reaction you need. Three simple rules let you build its K from reactions that are listed, in the same spirit as Hess's law.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Invert K when a reaction is reversed
- Raise K to a power when coefficients are scaled
- Multiply constants when reactions are added
- Assemble K for a target reaction from tabulated reactions
Lesson
Reversing a reaction
Swapping products and reactants swaps the numerator and denominator of the expression, so the new constant is the reciprocal of the old one. If K = 100 forward, the reverse reaction has K = 0.010.
K(reverse) = 1 / K(forward)
Scaling a reaction
Doubling every coefficient doubles every exponent, which squares the whole expression. Halving the coefficients takes the square root. In general, multiplying by n raises K to the n.
K(new) = K(old)ⁿ
Halving coefficients means n = 1/2, so take the square root, not half of K.
Adding reactions
When two reactions are added, the intermediate cancels and the two expressions multiply together, leaving the expression for the overall reaction.
K(overall) = K₁ x K₂
Working like Hess''s law
The procedure is the same as for enthalpy: manipulate each given reaction until adding them reproduces the target, then combine the constants. The only difference is the arithmetic. Enthalpies are added and their signs flipped; constants are multiplied and inverted.
Add ΔH values. Multiply K values.
Order of operations
Do the reversal and the scaling on each individual reaction first, then multiply the adjusted constants together. Scaling a reaction that has already been reversed is fine as long as both operations are applied to the same constant.
Key ideas
Rule
Reverse
K becomes 1/K.
Rule
Multiply coefficients by n
K becomes Kⁿ.
Rule
Add reactions
Constants multiply.
Key concept
Compare with Hess's law
Enthalpies add; equilibrium constants multiply.
Key concept
Sanity check
A reaction that is barely product-favored forward must be reactant-favored in reverse.
Equation
Reversed reaction
K' = 1/K
- K' = constant of the reversed reaction
Equation
Scaled reaction
K' = Kⁿ
- n = factor applied to every coefficient
Equation
Added reactions
K(total) = K₁ x K₂
- K₁, K₂ = constants of the reactions being added
Worked examples
Worked example 2
For N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g), K = 6.0 × 10⁵. Find K for (1/2) N₂(g) + (3/2) H₂(g) ⇌ NH₃(g).
Try it first: Compare coefficients to find the scaling factor.
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Worked example 3
Given A ⇌ B with K₁ = 2.0 and B ⇌ C with K₂ = 30, find K for A ⇌ C.
Try it first: Check that adding the two reactions cancels B.
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Common mistakes
Negating K when reversing a reaction.
Why it's wrong: Equilibrium constants are never negative; the reverse constant is the reciprocal.
Check instead: Take 1/K.
Halving K when the coefficients are halved.
Why it's wrong: Coefficients act as exponents, so halving means a square root.
Check instead: Raise K to the power n.
Adding constants when reactions are added.
Why it's wrong: Enthalpies add, but the expressions for K multiply.
Check instead: Multiply the constants.
Scaling before reversing and then applying only one of the two changes.
Why it's wrong: Both operations must act on the same reaction's constant.
Check instead: Adjust each reaction fully before combining.
Practice this skill
No practice questions are available for this topic yet. You can still practice the whole unit.
What you should now know
Reversing a reaction inverts its constant, multiplying a reaction by a factor n raises the constant to the power n, and adding two reactions multiplies their constants. These rules follow directly from the algebra of the equilibrium expression. They mirror Hess's law, but where enthalpies are added, equilibrium constants are multiplied, and where an enthalpy sign flips, a constant is inverted. Applying the rules in the right order lets you assemble K for almost any target reaction from tabulated data.
- Reversing a reaction inverts K
- Scaling coefficients by n raises K to the power n
- Adding reactions multiplies their constants
- Adjust each reaction first, then combine
- Same logic as Hess's law, but multiplicative
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.