The equilibrium constant

IB Chemistry HL· 45 min read

1. Writing Equilibrium Constant Expressions★★☆☆☆⏱ 15 min

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For the general equilibrium reaction $a A + b B ⇌ c C + d D$ , $K$ is defined as the ratio of product activities over reactant activities, each raised to the power of their stoichiometric coefficients. For dilute solutions, activity ≈ concentration ( $[X]$ ) for $K_{c}$ ; for gases, activity ≈ partial pressure ( $P_{X}$ ) for $K_{p}$ .

📘 Definition

Equilibrium Constant

$K_{c}$ (mol dm⁻³ⁿ), $K_{p}$ (kPaⁿ / atmⁿ)

A temperature-dependent constant that describes the ratio of products to reactants at equilibrium, independent of initial reaction concentrations.

📐 Worked Example

Write the $K_{c}$ expression for the heterogeneous equilibrium: $C a C O_{3} (s) ⇌ C a O (s) + C O_{2} (g)$

1
1. Identify species that are not pure solids: only gaseous $C O_{2}$ is included
2
1. Omit $C a C O_{3}$ and $C a O$ (pure solids, activity = 1)
3
$K_c = [CO_2]$

Exam tip:

Always check the state symbols of all species when writing a K expression, don't forget to omit solids and liquids.

2. Manipulating Equilibrium Constants★★★☆☆⏱ 20 min

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When the stoichiometry of a reaction is modified (reversed, scaled, or combined with another reaction), the equilibrium constant must be adjusted based on the original $K$ value for the original reaction.

Reversed reaction: $K_{r e v er se} = \frac{1}{K _{f or w a r d}}$
Reaction scaled by factor $n$ : $K_{n e w} = (K_{or i g ina l})^{n}$
Two reactions added together: $K_{t o t a l} = K_{1} \times K_{2}$

📐 Worked Example

Given $N_{2} (g) + O_{2} (g) ⇌ 2 N O (g)$ has $K_{c} = 4.8 \times 1 0^{- 31}$ at 25°C. Calculate $K_{c}$ for $N O (g) ⇌ \frac{1}{2} N_{2} (g) + \frac{1}{2} O_{2} (g)$

1
1. The target reaction is the original reaction reversed, then multiplied by $\frac{1}{2}$
2
1. First reverse the original K, then raise to the power of $\frac{1}{2}$ (square root)
3
$K_c = \left(\frac{1}{4.8 \times 10^{-31}}\right)^{1/2} = \sqrt{2.1 \times 10^{30}} = 1.4 \times 10^{15}$

Exam tip:

This is a common multiple choice question: remember scaling raises K to the power n, do not multiply K by n.

3. Calculating K from Initial and Equilibrium Data★★★☆☆⏱ 25 min

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To calculate K, you need the equilibrium concentrations of all included species. If only initial quantities and one equilibrium quantity are given, use an ICE (Initial, Change, Equilibrium) table to find all unknown equilibrium values.

📘 Definition

ICE Table

I = Initial, C = Change, E = Equilibrium

A table to organise concentration data, using stoichiometry to find unknown equilibrium concentrations

📐 Worked Example

0.100 mol $P C l_{5}$ is placed in a 1.00 dm³ container. At equilibrium, 0.060 mol $P C l_{5}$ remains. For $P C l_{5} (g) ⇌ P C l_{3} (g) + C l_{2} (g)$ , calculate $K_{c}$ .

1
1. Moles = concentration for 1 dm³ volume: Initial $[P C l_{5}] = 0.100$ , others = 0
2
1. Change in $[P C l_{5}] = - (0.100 - 0.060) = - 0.040$ . Stoichiometry gives $Δ [P C l_{3}] = Δ [C l_{2}] = + 0.040$
3
1. Equilibrium concentrations: $[P C l_{5}] = 0.060$ , $[P C l_{3}] = [C l_{2}] = 0.040$
4
$K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]} = \frac{(0.040)(0.040)}{0.060} = 0.027 \text{ mol dm}^{-3}$

4. Interpreting the Magnitude of K★★☆☆☆⏱ 10 min

The value of K tells us how far the reaction proceeds at equilibrium at a given temperature. It gives no information about how fast the reaction reaches equilibrium.

$K > 1 0^{3}$ : Equilibrium lies far right, mostly products, reaction almost complete
$1 0^{- 3} < K < 1 0^{3}$ : Significant amounts of both reactants and products
$K < 1 0^{- 3}$ : Equilibrium lies far left, mostly reactants, reaction barely proceeds

✓ Quick check

Test your understanding

What does $K = 2.1 \times 1 0^{- 4}$ tell you about the equilibrium?
- The reaction is very slow
- Mostly reactants at equilibrium
- Mostly products at equilibrium
- Equal amounts of reactants and products
Reveal answer
1 —
Correct! K does not describe reaction rate, and K < 10⁻³ means mostly reactants at equilibrium.

5. Common Pitfalls

Wrong move:

Including pure solids/liquids in the K expression

Why:

Students forget that pure solids/liquids have constant activity that does not change

Correct move:

Always omit pure solids and pure liquids from K expressions

Wrong move:

Multiplying K by n when a reaction is scaled by n

Why:

Confusing stoichiometric scaling of the reaction with how K is defined

Correct move:

Raise the original K to the power of the scaling factor n

Wrong move:

Using initial concentrations instead of equilibrium concentrations to calculate K

Why:

Rushing the calculation and forgetting K only applies to equilibrium

Correct move:

Use an ICE table to find all equilibrium concentrations before calculating K

Wrong move:

Claiming K always increases when temperature increases

Why:

Forgetting K change depends on the enthalpy of the forward reaction

Correct move:

K increases with T for endothermic forward reactions, decreases for exothermic forward reactions

Wrong move:

Claiming K depends on initial concentrations of reactants

Why:

Misunderstanding the definition of an equilibrium constant

Correct move:

K depends only on temperature and reaction stoichiometry, not initial concentrations

6. Quick Reference Cheatsheet

Rule Type	Outcome
Reverse reaction	K_new = 1/K_original
Scale by n	K_new = (K_original)ⁿ
Add two reactions	K_total = K₁ × K₂
Heterogeneous equilibrium	Omit pure solids / pure liquids
K >> 1 (K > 10³)	Mostly products at equilibrium
K << 1 (K < 10⁻³)	Mostly reactants at equilibrium
What changes K?	Only temperature and stoichiometry

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · 2
Calculate Kc from equilibrium concentrations
2024 · 1
Manipulate K for reversed reaction
2023 · 2
Write Kp for heterogeneous equilibrium

What's Next

The equilibrium constant is the foundation for all subsequent equilibrium topics in IB Chemistry HL. The skills you learned writing K expressions, manipulating K values, and calculating K from experimental data are used repeatedly in acid-base equilibria, solubility equilibria, and when applying Le Chatelier's principle to predict equilibrium shifts. Mastery of this sub-topic is essential for earning high marks on extended response questions in Paper 2, which often combine multiple equilibrium concepts.