Chemical Equilibrium

Chapter 17: Chemical Equilibrium

1. Chapter Goals

  • Basic Concepts

  • The Equilibrium Constant

  • Variation of Kc with the Form of the Balanced Equation

  • The Reaction Quotient

  • Uses of the Equilibrium Constant, Kc

  • Disturbing a System at Equilibrium: Predictions

  • The Haber Process: A Practical Application of Equilibrium

  • Disturbing a System at Equilibrium: Calculations

  • Partial Pressures and the Equilibrium Constant

  • Relationship between Kp and Kc

  • Heterogeneous Equilibria

  • Relationship between DG₀rxn and the Equilibrium Constant

  • Evaluation of Equilibrium Constants at Different Temperatures

2. Basic Concepts

  • Reversible Reactions:

    • Definition: Reversible reactions do not go to completion but can occur in either direction.

    • Symbolically represented.

  • Chemical Equilibrium:

    • Definition: Exists when two opposing reactions occur simultaneously at the same rate.

    • Characteristics:

    • Reversible: Forward reaction rate equals reverse reaction rate.

    • Dynamic Equilibrium: Molecules continually react, yet the overall composition remains unchanged.

  • Example of Dynamic Equilibrium:

    • Using radioactive 131I as a tracer in a saturated PbI₂ solution as a demonstration of equilibrium.

  • Graphical Representation:

    • Depicts the rates for both forward and reverse reactions in a general reaction.

  • Establishment of Equilibrium:

    • Can be initiated from either the forward or reverse direction of a reaction.

3. The Equilibrium Constant

  • Concept:

    • For a reversible reaction, at equilibrium, the forward and reverse rates are equal.

  • Rate Representation:

    • ext{Rate}f = ext{Rate}r

    • Forward reaction: k_1[A][B]

    • Reverse reaction: k_{-1}[C][D]

    • Rearranging gives:
      k_1 = rac{[C][D]}{[A][B]}

  • Equilibrium Constant Definition:

    • For the general reaction:
      aA(g) + bB(g) ⇌ cC(g) + dD(g)

    • The equilibrium constant, Kc, is defined as:
      K_c = rac{[C]^c [D]^d}{[A]^a [B]^b}

    • Kc is based on the concentrations (in M) of products and reactants raised to their stoichiometric coefficients in the balanced equation.

  • Example 17-1:

    • Write equilibrium constant expressions for reactions at 500°C.

4. Examples of Calculating Kc

  • Example 17-2:

    • Given: 0.172 mol of PCl₃, 0.086 mol of Cl₂, and 0.028 mol of PCl₅ in a 1 L container.

    • Calculate Kc:

    • Kc = rac{[PCl3][Cl2]}{[PCl5]}

    • Concentration values:

      • [PCl₃] = 0.172 M

      • [Cl₂] = 0.086 M

      • [PCl₅] = 0.028 M

    • Result: Compute Kc from these values.

  • Example 17-3:

    • Decomposition of PCl₅ where 0.60 moles of PCl₃ were present at equilibrium. Calculate Kc.

  • Example 17-4:

    • Initial moles of nitrogen and hydrogen are 0.80 and 0.90 respectively; 0.20 mole of NH₃ at equilibrium. Calculate Kc.

5. Variation of Kc with the Form of the Balanced Equation

  • Dependence on Equation Form:

    • Kc values vary with how the balanced equations are written.

    • For the following reaction:

    • PCl3 + Cl2 ⇌ PCl_5

    • Kc = 0.53 for this example.

  • Example 17-5:

    • Calculate equilibrium constant for the reverse reaction using two methods.

    • Confirm the results using $K = rac{[PCl5]}{[PCl3][Cl_2]}$.

6. The Reaction Quotient

  • Definition:

  • Mass action expression symbol Q, same form as Kc, but not at equilibrium values.

  • Purpose:

    • To predict how a system at equilibrium responds to applied stress (changes in concentrations, pressure, volume, etc.).

  • Comparison:

    • Compare Q with Kc to determine direction of shift:

    • If Q = K_c : system at equilibrium.

    • If Q > K_c : reaction shifts left (favoring reactants).

    • If Q < K_c : reaction shifts right (favoring products).

7. Uses of the Equilibrium Constant, Kc

  • Utilizing Kc for Calculations:

    • Example given of initial concentrations and change denoted as -XM and +XM for products and reactants respectively.

    • Final equilibrium concentrations can be represented in terms of Kc equation derived from the initial conditions.

8. Disturbing a System at Equilibrium: Predictions

  • Le Chatelier's Principle:

    • When stress is applied to a system in equilibrium, it shifts to reduce stress and establish a new equilibrium.

  • Stresses:

    • Changes in concentration, pressure, volume, and temperature.

  • Partial Pressures:

    • Use partial pressures instead of concentrations, utilizing the ideal gas law to express properties.

9. Disturbing a System at Equilibrium: Calculations

  • Determine directions by calculating Q and comparing measures with Kc to anticipate shifts in equilibrium.

  • Example of equilibrium mixture concentrations being disturbed and methods of recalculating the new equilibrium state.

10. Partial Pressures and the Equilibrium Constant

  • Expressing Kc in terms of partial pressures (Kp):

    • Illustrations and equations demonstrate equivalence between concentration/pressure measures.

11. Relationship between Kp and Kc

  • The relationship is expressed and calculated based on volumes and concentrations using gas law equations.

12. Heterogeneous Equilibria

  • Characteristics: presence of different phases (solid, liquid, gas) impacts Kc calculations.

    • Pure solids and liquids have activities of unity thereby not affecting the equilibrium expression significantly.

13. Relationship between ΔG₀rxn and the Equilibrium Constant

  • Definition of standard free energy change and its relevance in predicting reaction spontaneity.

  • Equivalence stating when ΔG = 0, system at equilibrium with Q = Kc.

  • Spontaneity based on ΔG compared with equilibrium states of K:

    • ΔG < 0 → Spontaneous Forward

    • ΔG = 0 → Equilibrium

    • ΔG > 0 → Spontaneous Reverse

  • Formula:
    K = e^{- rac{ ext{ΔG}^{ ext{°}}}{RT}}

  • Calculate K and verify conditions of spontaneity.

  • Common Errors:

    • Not converting ΔG from kJ to J when calculating K values.