Equilibrium Constant (K)
Relates products and reactants at equilibrium
Understanding Equilibrium Constants
The equilibrium constant (K) quantifies the balance between products and reactants when a reversible reaction reaches equilibrium. At equilibrium, the forward and reverse reaction rates are equal, resulting in constant concentrations. The magnitude of K indicates whether products or reactants are favored: K > 1 favors products, while K < 1 favors reactants.
Equilibrium constants are temperature-dependent but independent of initial concentrations or the presence of catalysts. Catalysts accelerate the approach to equilibrium but do not change the equilibrium position itself. Each reaction has its own unique K value at a given temperature, making it a characteristic property.
There are different types of equilibrium constants: Kc (concentration basis), Kp (pressure basis for gases), Ka (acid dissociation), Kb (base dissociation), and Ksp (solubility product). All follow the same fundamental principle of products divided by reactants, each raised to their stoichiometric coefficients.
General Expression
For aA + bB ⇌ cC + dD:
Kc = ([C]^c [D]^d) / ([A]^a [B]^b)
Use activities/activities approximated by molar concentrations for dilute solutions. For gases, use partial pressures for Kp.
Important Rules:
- Pure solids and liquids are omitted (activity = 1)
- Aqueous solutions use molar concentrations [M]
- Gas-phase reactions can use Kp with partial pressures
- Exponents must match stoichiometric coefficients
Relationship Between Kp and Kc
Kp = Kc (RT)^Δn
Where:
- R = gas constant (0.08206 L·atm/mol·K)
- T = absolute temperature (K)
- Δn = (moles gas products) − (moles gas reactants)
Note: If Δn = 0, then Kp = Kc
Worked Example
Reaction: N2 + 3 H2 ⇌ 2 NH3
At equilibrium: [N2]=0.10 M, [H2]=0.30 M, [NH3]=0.20 M.
Kc = [NH3]² / ([N2][H2]³)
Kc = (0.20)² / ((0.10)(0.30)³)
Kc = 0.04 / (0.10 × 0.027)
Kc = 0.04 / 0.0027 ≈ 14.8
Answer: Kc ≈ 14.8
Since K > 1, products are favored at equilibrium for this ammonia synthesis reaction.
Temperature Effects and van't Hoff Equation
Temperature is the only factor that changes the equilibrium constant value. The van't Hoff equation relates K to temperature:
ln(K2/K1) = -(ΔH°/R)(1/T2 - 1/T1)
Endothermic Reactions (ΔH° > 0)
Increasing temperature increases K, favoring products.
Exothermic Reactions (ΔH° < 0)
Increasing temperature decreases K, favoring reactants.
Common Mistakes
Including solids/liquids
Pure solids and liquids are omitted (activity = 1). Only include aqueous and gaseous species.
Wrong exponents
Exponents come from balanced equation stoichiometric coefficients, not molecular subscripts.
Mixing concentration and pressure
Don't mix [M] and atm in the same K expression. Use either Kc or Kp consistently.
Forgetting equilibrium values
K expressions require equilibrium concentrations, not initial concentrations.
FAQ
How does temperature affect K?
Use van't Hoff equation; endothermic reactions increase K with temperature.
Can K be less than 1?
Yes; small K indicates reactants favored at equilibrium.