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Kp: Gas-Phase Equilibrium Constant

Kp = Π(P_product^ν) / Π(P_reactant^ν) for gas-phase reactions. Partial pressures at equilibrium. Kp = Kc(RT)^Δn. From ΔG°: Kp = exp(-ΔG°/RT). Governs reaction direction and extent.

Concept Fundamentals
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Kp
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Kc
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Δn
Kp = exp(-ΔG°/RT)
ΔG°
Calculate KpGas-phase equilibrium | Partial pressures

Why This Chemistry Calculation Matters

Why: Kp describes gas-phase equilibrium position. Kp > 1 favors products; Kp < 1 favors reactants. Links to ΔG° and temperature.

How: Enter partial pressures at equilibrium, or ΔG° and T. Kp = Π(P_prod^ν)/Π(P_react^ν). Kp = Kc(RT)^Δn.

  • ●Kp uses partial pressures; Kc uses concentrations.
  • ●Kp = Kc(RT)^Δn for ideal gases.
  • ●ΔG° = -RT ln Kp.
Sources:IUPAC Gold BookNIST Chemistry WebBook

Reaction Examples

🏭 Ammonia Synthesis (Haber-Bosch)

N₂ + 3H₂ ⇌ 2NH₃ at 298 K

⚗️ Water Gas Shift Reaction

CO + H₂O ⇌ CO₂ + H₂

🔥 Methane Combustion

CH₄ + 2O₂ ⇌ CO₂ + 2H₂O

🌡️ NO₂ Dimerization

2NO₂ ⇌ N₂O₄ equilibrium

🧪 HI Decomposition

2HI ⇌ H₂ + I₂

🏭 SO₃ Formation

2SO₂ + O₂ ⇌ 2SO₃

📊 Degree of Dissociation

PCl₅ ⇌ PCl₃ + Cl₂

Calculate Kp

Use ⇌ for equilibrium

Reactants

Products

For educational and informational purposes only. Verify with a qualified professional.

🔬 Chemistry Facts

⚗️

Kp = Π(P_prod^ν)/Π(P_react^ν). Partial pressures.

— IUPAC

⚡

Kp = Kc(RT)^Δn. Δn = Σν_products − Σν_reactants.

— Equilibrium

🔬

ΔG° = -RT ln Kp. Thermodynamic relation.

— Thermo

📐

Kp > 1: products favored. Kp < 1: reactants favored.

— Chemistry

What is Kp?

Kp is the equilibrium constant expressed in terms of partial pressures for gas-phase reactions. It relates the partial pressures of products and reactants at equilibrium, providing insight into the position of equilibrium and reaction favorability.

Kp = (P_products)^n / (P_reactants)^m

Where P represents partial pressures and n, m are stoichiometric coefficients

Relationship to Gibbs Free Energy

The equilibrium constant Kp is directly related to the standard Gibbs free energy change (ΔG°) through the relationship:

ΔG° = -RT ln(Kp)

Rearranging: Kp = e^(-ΔG°/RT)

ΔG° < 0

Kp > 1, reaction favors products

ΔG° > 0

Kp < 1, reaction favors reactants

How to Calculate Kp

Method 1: From Partial Pressures

For reaction: aA + bB ⇌ cC + dD

Kp = [P(C)^c × P(D)^d] / [P(A)^a × P(B)^b]

Example: N₂ + 3H₂ ⇌ 2NH₃

Kp = P(NH₃)² / [P(N₂) × P(H₂)³]

Method 2: From Gibbs Free Energy

Given: ΔG° = -16.4 kJ/mol at 298 K

Kp = exp(-ΔG° / RT)

Kp = exp(-(-16.4) / (0.008314 × 298))

Kp = 6.8 × 10⁵

Method 3: From Degree of Dissociation

For: PCl₅ ⇌ PCl₃ + Cl₂

If α = degree of dissociation, P₀ = initial pressure

P(PCl₅) = P₀(1 - α)

P(PCl₃) = P(Cl₂) = P₀ × α

Kp = [P(PCl₃) × P(Cl₂)] / P(PCl₅) = (P₀ × α)² / [P₀(1 - α)]

Relationship Between Kp and Kc

For gas-phase reactions, Kp and Kc are related through the ideal gas law:

Kp = Kc(RT)^(Δn)

Where Δn = Σ(products coefficients) - Σ(reactants coefficients)

Δn > 0

More moles products, Kp > Kc

Δn = 0

Equal moles, Kp = Kc

Δn < 0

More moles reactants, Kp < Kc

When to Use Kp

Kp is essential for understanding gas-phase equilibria in various chemical and industrial processes.

🏭

Industrial Processes

Optimize reaction conditions for maximum yield in chemical manufacturing.

  • Ammonia synthesis (Haber-Bosch)
  • Sulfuric acid production
  • Methanol synthesis
🔥

Combustion Analysis

Understand equilibrium in combustion reactions and exhaust systems.

  • Engine efficiency
  • Pollution control
  • Fuel optimization
🌍

Atmospheric Chemistry

Model gas-phase reactions in the atmosphere and environmental systems.

  • Ozone formation
  • NOx chemistry
  • Air quality modeling

Common Gas-Phase Reactions

ReactionΔG° (kJ/mol)Kp (298 K)Application
N₂ + 3H₂ ⇌ 2NH₃-16.46.80e+5Fertilizer production
CO + H₂O ⇌ CO₂ + H₂-28.51.00e+5Syngas processing
CH₄ + 2O₂ ⇌ CO₂ + 2H₂O-800.81.00e+140Energy production
2NO₂ ⇌ N₂O₄-5.46.700Atmospheric chemistry
2HI ⇌ H₂ + I₂2.60.01600Chemical education
2SO₂ + O₂ ⇌ 2SO₃-141.82.50e+12Industrial chemistry
2CO + O₂ ⇌ 2CO₂-514.41.20e+89Combustion processes

Temperature Dependence

The equilibrium constant Kp changes with temperature according to the van't Hoff equation. For exothermic reactions (ΔH < 0), increasing temperature decreases Kp. For endothermic reactions (ΔH > 0), increasing temperature increases Kp.

Le Chatelier's Principle

Exothermic Reaction

↑ Temperature → ↓ Kp → Shift left

Example: N₂ + 3H₂ ⇌ 2NH₃ (ΔH = -92 kJ/mol)

Endothermic Reaction

↑ Temperature → ↑ Kp → Shift right

Example: N₂O₄ ⇌ 2NO₂ (ΔH = +58 kJ/mol)

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