Dynamic Equilibrium

In a reversible reaction, the forward and reverse reactions can both occur. When a reversible reaction takes place in a closed system, it eventually reaches dynamic equilibrium -- a state where the rate of the forward reaction equals the rate of the reverse reaction. Macroscopic properties (concentrations, colour, pressure) remain constant, but reactions continue at the molecular level.

Reaching Equilibrium

Initially

Forward rate is high, reverse rate is zero

↓

Over time

Forward rate decreases, reverse rate increases

↓

At equilibrium

Forward rate = Reverse rate (both non-zero)

Key point: Equilibrium does NOT mean the concentrations of reactants and products are equal. It means the rates of the forward and reverse reactions are equal. The position of equilibrium may favour products or reactants depending on the reaction.

The Equilibrium Constant (K_eq)

For a general equilibrium: aA + bB ⇌ cC + dD, the equilibrium constant expression relates the concentrations of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients.

Equilibrium Expression

K_eq = [C]^c[D]^d / [A]^a[B]^b

K_eq >> 1

Products favoured

K_eq ≈ 1

Neither side favoured

K_eq << 1

Reactants favoured

Important Rules

Pure solids and liquids are NOT included in the equilibrium expression -- only aqueous (aq) and gaseous (g) species.

K_eq is constant at a given temperature. Changing concentration or pressure does NOT change K_eq.

Temperature changes are the only way to change the value of K_eq.

ICE Tables

An ICE table (Initial, Change, Equilibrium) is a systematic method for calculating equilibrium concentrations. You set up the table with initial concentrations, define the change using a variable x, and solve using the K_eq expression.

Example ICE Table: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

	N₂	3H₂	2NH₃
I (Initial)	1.00	3.00	0
C (Change)	-x	-3x	+2x
E (Equilibrium)	1.00 - x	3.00 - 3x	2x

Substitute the equilibrium row into the K_eq expression and solve for x.

ICE Table Strategy

1. Write the balanced equation and K_eq expression.
2. Fill in the I row with known initial concentrations.
3. Use stoichiometry for the C row (use +/- x multiplied by coefficients).
4. Write expressions for the E row (I + C).
5. Substitute the E row into K_eq and solve for x.

Key Vocabulary

Dynamic Equilibrium

A state in a closed system where the forward and reverse reaction rates are equal. Concentrations remain constant but both reactions continue at the molecular level.

Equilibrium Constant (K_eq)

A numerical value at a given temperature relating the ratio of product to reactant concentrations at equilibrium. A large K favours products; a small K favours reactants.

Closed System

A system in which matter cannot enter or leave, though energy can be exchanged. Essential for equilibrium to be established.

Reversible Reaction

A chemical reaction that can proceed in both the forward and reverse directions. Denoted by the double arrow symbol ⇌.

Worked Examples

1

Write the K_eq expression for: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

Step 1: Products over reactants, each raised to their coefficient.

Answer: K_eq = [SO₃]² / ([SO₂]²[O₂])

2

At equilibrium, [N₂] = 0.50 M, [H₂] = 0.30 M, [NH₃] = 0.20 M. Calculate K_eq for N₂(g) + 3H₂(g) ⇌ 2NH₃(g).

Step 1: K_eq = [NH₃]² / ([N₂][H₂]³)

Step 2: K_eq = (0.20)² / ((0.50)(0.30)³) = 0.040 / (0.50 × 0.027)

Answer: K_eq = 0.040 / 0.0135 ≈ 2.96

3

For A(g) ⇌ 2B(g), K_eq = 0.16. If 1.00 mol of A is placed in a 1.00 L container, find the equilibrium concentrations using an ICE table.

Step 1: ICE: I = [A]=1.00, [B]=0. C = [A]=-x, [B]=+2x. E = [A]=1.00-x, [B]=2x

Step 2: K_eq = [B]²/[A] = (2x)²/(1.00-x) = 4x²/(1-x) = 0.16

Step 3: 4x² = 0.16(1-x) → 4x² + 0.16x - 0.16 = 0 → x = 0.18 (using quadratic formula)

Answer: [A] = 1.00 - 0.18 = 0.82 M, [B] = 2(0.18) = 0.36 M

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

At dynamic equilibrium, the forward and reverse reaction rates are:

Equal and non-zero Both zero The forward rate is always greater Constantly changing

Question 2

For a reaction with K_eq = 4.5 × 10^-8, at equilibrium the mixture contains mostly:

Products Reactants Equal amounts of both Cannot be determined from K alone

Question 3

Which species is NOT included in the K_eq expression for: CaCO₃(s) ⇌ CaO(s) + CO₂(g)?

CO₂ All species are included CaCO₃ and CaO None of the species are included

Question 4

Adding more reactant to a system at equilibrium will:

Change the value of K_eq Stop the reaction Have no effect Shift equilibrium toward products without changing K_eq

Question 5

In an ICE table for X ⇌ 2Y, if x mol/L of X reacts, the change in [Y] is:

+2x +x -2x -x

Chemical Equilibrium

Dynamic Equilibrium

Reaching Equilibrium

The Equilibrium Constant (K_eq)

Equilibrium Expression

Important Rules

ICE Tables

Example ICE Table: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

ICE Table Strategy

Key Vocabulary

Dynamic Equilibrium

Equilibrium Constant (K_eq)

Closed System

Reversible Reaction

Worked Examples

Write the K_eq expression for: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

At equilibrium, [N₂] = 0.50 M, [H₂] = 0.30 M, [NH₃] = 0.20 M. Calculate K_eq for N₂(g) + 3H₂(g) ⇌ 2NH₃(g).

For A(g) ⇌ 2B(g), K_eq = 0.16. If 1.00 mol of A is placed in a 1.00 L container, find the equilibrium concentrations using an ICE table.

Knowledge Check

Key Concepts Summary

Chemical Equilibrium

Dynamic Equilibrium

Reaching Equilibrium

The Equilibrium Constant (Keq)

Equilibrium Expression

Important Rules

ICE Tables

Example ICE Table: N2(g) + 3H2(g) ⇌ 2NH3(g)

ICE Table Strategy

Key Vocabulary

Dynamic Equilibrium

Equilibrium Constant (Keq)

Closed System

Reversible Reaction

Worked Examples

Write the Keq expression for: 2SO2(g) + O2(g) ⇌ 2SO3(g)

At equilibrium, [N2] = 0.50 M, [H2] = 0.30 M, [NH3] = 0.20 M. Calculate Keq for N2(g) + 3H2(g) ⇌ 2NH3(g).

For A(g) ⇌ 2B(g), Keq = 0.16. If 1.00 mol of A is placed in a 1.00 L container, find the equilibrium concentrations using an ICE table.

Knowledge Check

Key Concepts Summary

The Equilibrium Constant (K_eq)

Example ICE Table: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Equilibrium Constant (K_eq)

Write the K_eq expression for: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

At equilibrium, [N₂] = 0.50 M, [H₂] = 0.30 M, [NH₃] = 0.20 M. Calculate K_eq for N₂(g) + 3H₂(g) ⇌ 2NH₃(g).

For A(g) ⇌ 2B(g), K_eq = 0.16. If 1.00 mol of A is placed in a 1.00 L container, find the equilibrium concentrations using an ICE table.