Lecture on Equilibrium Constants (Keq, Kc, Kp)

Introduction

• Equilibrium constants can be expressed in terms of concentrations (Kc) or pressures (Kp).
• Kc is used when dealing with concentrations.
• Kp is used when dealing with gases and can utilize partial pressures.

Example of Equilibrium Expression

• Consider the reaction: 2 SO3(g) ⇌ 2 SO2(g) + O2(g)
  • Kc expression:
    • [ Kc = \frac{[SO2]^2[O2]}{[SO3]^2} ]
  • Kp expression:
    • [ Kp = \frac{(P_{SO2})^2(P_{O2})}{(P_{SO3})^2} ]
  • Note: Use parentheses to indicate what's being squared or cubed.

Relationship Between Kc and Kp

• Kp and Kc are not numerically equal due to different units.
• Conversion between Kc and Kp:
  • [ Kp = Kc \times (RT)^{\Delta n} ]
  • ( \Delta n ) is the change in moles of gas (products minus reactants).
  • Example: For 2 SO3(g) ⇌ 2 SO2(g) + O2(g):
    • Products: 2 moles SO2 + 1 mole O2 = 3 moles
    • Reactants: 2 moles SO3 = 2 moles
    • ( \Delta n = 3 - 2 = 1 )

Unitless Nature of Equilibrium Constants

• Equilibrium constants (Kc, Kp) have no units.
• Values are referenced against a standard (1 M for concentrations, 1 atm for pressures) which cancels units.
• Example: NO2 concentration of 1.5 M is considered as 1.5/1 M, leading to a unitless expression.

Treatment of Solids and Liquids in Equilibrium

• Concentrations of pure solids and liquids are constant and don’t appear in equilibrium expressions.
• Their activity is considered as 1.

Example of Equilibrium with Solids and Gases

1. CaCO3(s) ⇌ CaO(s) + O2(g)

   • Equilibrium expression: ( K = P_{O2} )
   • Only O2(g) is included because CaCO3 and CaO are solids.

2. Fe2O3(s) + 3CO(g) ⇌ 2Fe(s) + 3CO2(g)

   • Products/Reactants: Include gases only
   • Equilibrium expression:
     • [ K = \frac{[CO2]^3}{[CO]^3} ]
   • Solid components are excluded from the equation.

Conclusion

• Understanding when to use Kc vs. Kp is key in equilibrium chemistry.
• Consideration of phases (solid, liquid, gas) affects the formulation of equilibrium expressions.