Properties of the Equilibrium Constant

Learning Objective 7.6.A Represent a multistep process with an overall equilibrium expression, using the constituent K expressions for each individual reaction.

Quick Notes

Reversing a reaction means K is inverted:

If K₁ = [products]/[reactants], then K_reverse = 1/K₁.

Multiplying a reaction by n raises K to n:

Multiplying all coefficients by n gives Kⁿ.

Adding reactions together means K values must be multiplied:

For combined steps, K_overall = K₁ × K₂ × …

These rules also apply to Q (same form as K).

Full Notes

Recap — What is the Equilibrium Constant?

The equilibrium constant (K) shows the ratio of products to reactants at equilibrium as a single value.

General reaction: aA + bB reversible arrow to cC + dD

The K_c expression (based on concentration in mol L⁻¹) is:

Kc equals concentration of C to the power c times concentration of D to the power d divided by concentration of A to the power a times concentration of B to the power b

The K_p expression (based on partial pressures) is:

Kp expression written with partial pressures of gaseous species A, B, C, and D

How K Changes with Manipulations

1) Reversing the Reaction
If a reaction is written in the reverse direction, the equilibrium constant becomes the reciprocal.

Example:
Forward: A ⇌ B K = [B]/[A]
Reverse: B ⇌ A K = [A]/[B] = 1/K

2) Multiplying a Reaction
If all coefficients in a reaction are multiplied by a factor n, the new equilibrium constant is raised to the nth power.

Example:
A ⇌ B K = [B]/[A]
2A ⇌ 2B K = ([B]²)/([A]²) = K²

3) Adding Reactions
When two or more reactions are added, the overall equilibrium constant is the product of the individual K values.

Example:
Reaction 1: A ⇌ B    K₁
Reaction 2: B ⇌ C    K₂
Overall: A ⇌ C    K_overall = K₁ × K₂

4) Same Rules Apply to Q
The reaction quotient (Q) has the same form as K, and the same mathematical manipulations apply.

Matt’s Exam Tip

Don’t forget when working with Q and K that concentrations used in a Q expression don’t have to be from when the system is at equilibrium. All values used for K, however, must be equilibrium concentrations.

Summary

Reverse reaction → invert K.
Multiply coefficients → raise K to that power.
Add reactions → multiply the K values.

Use these rules to combine steps of a mechanism or analyze multistep equilibria.