Law of Chemical Equilibrium and Equilibrium Constant

Quick Notes

• Law of Mass Action: At equilibrium, the rate of forward and reverse reactions is equal.
• For a reaction:

• Equilibrium constant (K_c) is:

• A large K_c (>10³) → reaction favours products.
• A small K_c (<10⁻³) → reaction favours reactants.
• K_c is unitless for balanced reactions involving equal numbers of moles of gases on both sides.
• The equilibrium constant is temperature dependent but independent of initial concentrations.

Full Notes

What Is the Equilibrium Law?

The equilibrium law relates the concentrations of reactants and products in a reversible reaction at equilibrium. It allows us to calculate the equilibrium constant (K).

The general form for a homogeneous reaction is:

The equilibrium expression is:

• Square brackets [ ] represent concentration in mol dm⁻³
• Each term is raised to the power of its stoichiometric coefficient from the balanced equation

Matt’s exam tip

Solids aren’t ever included in K_c expressions and if water is a solvent as well as a reactant or product, it also isn’t included.

Homogeneous Reactions

A reaction is homogeneous if all reactants and products are in the same phase (usually gaseous or aqueous).

Example: Gaseous reaction

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

K_c = [NH₃]² / ( [N₂] [H₂]³ )

Example: Aqueous reaction

Fe³⁺(aq) + SCN⁻(aq) ⇌ [FeSCN]²⁺(aq)

K_c = [[FeSCN]²⁺] / ( [Fe³⁺] [SCN⁻] )

Important Notes

• K is temperature dependent: changing temperature will change the value of K.
• K can have different units depending on the reaction.

Understanding the Equilibrium Constant (K_c)

• K_c is calculated only using concentrations at equilibrium.
• Its value is constant at a given temperature for a particular reaction.
• Important: K_c does not depend on initial concentrations of reactants/products – only on their values at equilibrium.

Interpreting the Value of K_c

• If K_c ≫ 1:
  Products dominate at equilibrium meaning forward direction is favoured and reaction goes (almost) to completion.
• If K_c ≪ 1:
  Reactants dominate meaning reverse direction is favoured with negligible product formation.
• If K_c ≈ 1:
  Comparable concentrations of reactants and products.

Effect of Changing Stoichiometric Coefficients on K_c

When a balanced chemical equation is multiplied by a factor, the equilibrium constant (K_c) must also be adjusted accordingly.

• If the equation is multiplied by ½, then the new equilibrium constant becomes √K_c.
• If it’s multiplied by n, the new K_c becomes K_cⁿ.

Key point: Since K_c values depend on how the equation is written, always specify the exact chemical equation when quoting or using an equilibrium constant.

A bit extra - deriving the Law

Consider a general reversible reaction: aA + bB ⇌ cC + dD

Forward reaction rate: R_f = k_f[A]^a[B]^b

Reverse reaction rate: R_r = k_r[C]^c[D]^d

At equilibrium: R_f = R_r ⇒ k_f[A]^a[B]^b = k_r[C]^c[D]^d

Rearranging gives: K_c = k_f / k_r = [C]^c[D]^d / ( [A]^a[B]^b )

Where: K_c is the equilibrium constant (in terms of concentration), indicates equilibrium concentration of species X.

Summary

• Write K_c using product concentrations over reactant concentrations raised to stoichiometric powers.
• K_c depends only on temperature and equilibrium concentrations.
• Magnitude of K_c indicates whether products or reactants are favoured.
• Changing the equation’s coefficients changes the reported K_c by the same factor.