Introduction to Chemical Equilibrium

What is Chemical Equilibrium?

Equilibrium: State where forward and reverse reaction rates are equal

Dynamic equilibrium:

• Reactions still occurring
• No net change in concentrations
• Forward rate = Reverse rate

Example:

$\ce{N2(g) + 3H2(g) <=> 2NH3(g)}$

At equilibrium: [N₂], [H₂], [NH₃] constant (but reactions ongoing)

Reversible Reactions

Notation:

• ⇌ or <=> indicates reversible
• Single arrow → indicates irreversible

Characteristics:

• Can proceed in both directions
• Eventually reach equilibrium
• Position depends on conditions

Equilibrium Constant (K_c)

For general reaction:

$\ce{aA + bB <=> cC + dD}$

Equilibrium expression:

$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Key points:

• Products in numerator
• Reactants in denominator
• Coefficients become exponents
• Concentrations at equilibrium (mol/L)
• Temperature dependent

Rules for K Expressions

What to Include:

Include: Gases and aqueous solutions

• Use [ ] for molarity (mol/L)

Exclude:

• Pure solids
• Pure liquids
• Solvents (usually water)

Examples:

1. CaCO₃(s) ⇌ CaO(s) + CO₂(g)

$K_c = [\ce{CO2}]$

(Solids omitted)

1. CH₃COOH(aq) + H₂O(l) ⇌ CH₃COO⁻(aq) + H₃O⁺(aq)

$K_c = \frac{[\ce{CH3COO-}][\ce{H3O+}]}{[\ce{CH3COOH}]}$

(Water omitted - solvent)

1. N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

$K_c = \frac{[\ce{NH3}]^2}{[\ce{N2}][\ce{H2}]^3}$

Equilibrium Constant (K_p)

For gas-phase reactions:

$K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$

Use partial pressures (atm) instead of concentrations

Relationship between K_c and K_p:

$K_p = K_c(RT)^{\Delta n}$

Where:

• R = 0.08206 L·atm/(mol·K)
• T = temperature (K)
• Δn = moles gas products - moles gas reactants

If Δn = 0: K_p = K_c

Magnitude of K

Interpretation:

| K value | Meaning | |---------|---------| | K >> 1 (>10³) | Products favored, equilibrium far right | | K ≈ 1 (10⁻³ to 10³) | Significant amounts of both | | K << 1 (<10⁻³) | Reactants favored, equilibrium far left |

Examples:

• K = 1.0 × 10⁵: Products dominate
• K = 1.0 × 10⁻⁵: Reactants dominate
• K = 5.0: Comparable amounts

Manipulating Equilibrium Expressions

Reverse Reaction:

If K_forward = x, then K_reverse = 1/x

Example: If K = 100 for A ⇌ B, then K = 0.01 for B ⇌ A

Multiply Equation:

If multiply by n, then K_new = (K_original)^n

Example: If K = 10 for A ⇌ B, then K = 100 for 2A ⇌ 2B

Add Equations:

If add reactions, multiply K values

K_overall = K₁ × K₂ × K₃...

Heterogeneous vs Homogeneous Equilibria

Homogeneous: All species in same phase

• Example: All gases or all aqueous

Heterogeneous: Multiple phases present

• Example: Solid + gas, solid + aqueous
• Remember: Omit pure solids and liquids from K expression

Writing K Expressions - Practice

General strategy:

1. Identify products and reactants
2. Omit pure solids, pure liquids, solvents
3. Products in numerator
4. Reactants in denominator
5. Use coefficients as exponents