Equilibrium Constant Keq: Kc, Kp, and Gibbs Relation
The equilibrium constant K quantifies the position of equilibrium. Kc uses concentrations; Kp uses partial pressures. They relate via Kp = Kc(RT)^Δn. Thermodynamic K° links to ΔG° = -RT ln K. Large K favors products; small K favors reactants.
Why This Chemistry Calculation Matters
Why: Equilibrium constants predict product yields, guide process design, and connect kinetics to thermodynamics. K changes only with temperature.
How: Kc = [C]^c[D]^d / ([A]^a[B]^b) at equilibrium. For gases, Kp = Kc(RT)^Δn. Use ICE tables to find equilibrium concentrations from initial conditions.
- ●Pure solids and liquids have activity 1 and are omitted from K.
- ●K depends only on temperature; concentration changes shift position, not K.
- ●ΔG° = -RT ln K links thermodynamics to equilibrium.
Equilibrium Examples
⚗️ Haber Process
N₂ + 3H₂ ⇌ 2NH₃ at 25°C
🧪 Acetic Acid Dissociation
CH₃COOH ⇌ CH₃COO⁻ + H⁺
🔄 Kc to Kp Conversion
Convert Kc = 3.5e8 to Kp
📊 ICE Table Example
Calculate Kc from ICE table
⚖️ Q vs K Comparison
Determine reaction direction
💨 Water Gas Shift
CO + H₂O ⇌ CO₂ + H₂
🌡️ N₂O₄ Decomposition
N₂O₄ ⇌ 2NO₂
📈 Kp from Pressures
Calculate Kp from partial pressures
Calculate Equilibrium Constant
Reactants
Products
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
Kc uses concentrations (M); Kp uses partial pressures (atm).
— IUPAC
Kp = Kc × (RT)^Δn where Δn = moles gas products − moles gas reactants.
— Physical chemistry
ΔG° = -RT ln K; K > 1 means ΔG° < 0 (spontaneous as written).
— IUPAC
ICE tables: Initial, Change, Equilibrium for solving equilibrium problems.
— NIST
What is an Equilibrium Constant?
The equilibrium constant (K) quantifies the position of equilibrium for a reversible chemical reaction. It relates the concentrations (Kc) or partial pressures (Kp) of products and reactants at equilibrium. A large K (>1) favors products, while a small K (<1) favors reactants.
For aA + bB ⇌ cC + dD: Kc = [C]^c[D]^d / [A]^a[B]^b
Kc vs Kp: Concentration vs Pressure
Kc (Concentration-Based)
Used for reactions in solution (aqueous or liquid phase). Units depend on stoichiometry.
Example: CH₃COOH(aq) ⇌ CH₃COO⁻(aq) + H⁺(aq)
Kp (Pressure-Based)
Used for gas-phase reactions. Expressed in terms of partial pressures.
Example: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
Conversion Formula
Where Δn = (moles of gas products) - (moles of gas reactants), R = 0.0821 L·atm/(mol·K), T = temperature in Kelvin
ICE Tables: Initial, Change, Equilibrium
ICE tables help organize information about initial concentrations, changes during reaction, and equilibrium concentrations. They're essential for solving equilibrium problems.
📊 ICE Table Structure
| Species | Initial (I) | Change (C) | Equilibrium (E) |
|---|---|---|---|
| CH₃COOH | 0.10 M | -x | 0.10 - x |
| CH₃COO⁻ | 0 | +x | x |
| H⁺ | 0 | +x | x |
For CH₃COOH ⇌ CH₃COO⁻ + H⁺, Kc = [CH₃COO⁻][H⁺] / [CH₃COOH] = x² / (0.10 - x) = 1.8 × 10⁻⁵
Reaction Quotient (Q) vs Equilibrium Constant (K)
The reaction quotient Q has the same form as K but uses current (non-equilibrium) concentrations. Comparing Q to K predicts the direction the reaction will shift.
Q < K
Reaction proceeds forward (toward products). System shifts right.
Q = K
System is at equilibrium. No net change occurs.
Q > K
Reaction proceeds in reverse (toward reactants). System shifts left.
How to Calculate Equilibrium Constants
Equilibrium constants are calculated from experimental data or derived from thermodynamic properties. The process depends on whether you're working with concentrations or pressures.
🔬 Step-by-Step Process
1. Write the Balanced Equation
Ensure the reaction is balanced: aA + bB ⇌ cC + dD
2. Set Up the Expression
Kc = [C]^c[D]^d / [A]^a[B]^b (products over reactants, raised to stoichiometric coefficients)
3. Use Equilibrium Concentrations
Only equilibrium concentrations are used. Pure solids and liquids are excluded (activity = 1).
4. Calculate K
Substitute values and calculate. K is dimensionless but has units implied by concentration units.
When to Use Equilibrium Constants
Equilibrium constants are fundamental in chemistry for predicting reaction behavior, designing processes, and understanding chemical systems.
Industrial Chemistry
Optimize reaction conditions for maximum yield in chemical manufacturing.
- Haber process (ammonia)
- Contact process (sulfuric acid)
- Ostwald process (nitric acid)
Analytical Chemistry
Determine concentrations, predict solubility, and analyze complex formation.
- Acid-base equilibria
- Complex ion formation
- Solubility products
Biochemistry
Understand enzyme kinetics, protein folding, and metabolic pathways.
- Enzyme-substrate binding
- Protein-ligand interactions
- Oxygen binding to hemoglobin
Common Equilibrium Reactions
| Reaction | Equation | Kc (25°C) | Type |
|---|---|---|---|
| Haber Process | N₂(g) + 3H₂(g) ⇌ 2NH₃(g) | 3.50e+8 | gas |
| Water Gas Shift | CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g) | 5.000 | gas |
| Dissociation of Acetic Acid | CH₃COOH(aq) ⇌ CH₃COO⁻(aq) + H⁺(aq) | 1.80e-5 | aqueous |
| Formation of HI | H₂(g) + I₂(g) ⇌ 2HI(g) | 54.30 | gas |
| Dissociation of Water | H₂O(l) ⇌ H⁺(aq) + OH⁻(aq) | 1.00e-14 | aqueous |
| Decomposition of N₂O₄ | N₂O₄(g) ⇌ 2NO₂(g) | 0.2110 | gas |
| Formation of NO | N₂(g) + O₂(g) ⇌ 2NO(g) | 4.10e-31 | gas |
| Dissociation of H₂S | H₂S(aq) ⇌ H⁺(aq) + HS⁻(aq) | 9.10e-8 | aqueous |
Le Chatelier's Principle
When a system at equilibrium is disturbed, it responds to minimize the disturbance. This principle helps predict how changes in concentration, pressure, or temperature affect equilibrium position.
📈 Effect of Changes
- • Increase reactant: Shifts right (toward products)
- • Increase product: Shifts left (toward reactants)
- • Increase pressure: Shifts toward fewer gas moles
- • Increase temperature: Shifts toward endothermic direction
- • Catalyst: No effect on equilibrium position
⚖️ Important Notes
- • K changes only with temperature (for a given reaction)
- • Changes in concentration/pressure shift position but not K
- • Pure solids/liquids don't affect equilibrium position
- • Dilution shifts toward side with more moles
- • Equilibrium is dynamic (forward = reverse rate)