Chemistry of Energetics and Equilibria

Overview of Equilibrium in Chemical Reactions

Learning Objectives

• Write the correct expressions for the reaction quotient (Q) and equilibrium constant (K_c)
• Understand the difference between Q and K_c
• Interpret information conveyed by K_c expressions
• Solve problems related to chemical equilibrium

Chemical Reactions

• Reactions can sometimes go to completion, where reactants are fully converted to products.
• In other cases, they reach a state of equilibrium, where reactants and products co-exist over time.

Reaction Quotient (Q)

• For a general reaction:
  $aA + bB \rightleftharpoons cC + dD$
  The reaction quotient Q is defined as:
  $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Example: For the reaction of dinitrogen tetroxide:
  $N<em>2O</em>4(g) \rightleftharpoons 2NO_2(g)$
  We analyze Q at different time intervals to determine the system's progress toward equilibrium.

Calculation of Q

• At time = 0:

  • [N₂O₄] = 1 mol L^-1
  • [NO₂] = 0 mol L^-1
  • $Q = \frac{[NO<em>2]^2}{[N</em>2O_4]} = 0$

• At time = 5 min:

  • [N₂O₄] = 0.8 mol L^-1, [NO₂] = 0.4 mol L^-1
  • $Q = \frac{(0.4)^2}{0.8} = 0.2$

• At time = 10 min:

  • [N₂O₄] = 0.6 mol L^-1, [NO₂] = 0.8 mol L^-1
  • $Q = \frac{(0.8)^2}{0.6} = 1.07$

• At time = 20 min:

  • [N₂O₄] = 0.45 mol L^-1, [NO₂] = 1.1 mol L^-1
  • $Q = \frac{(1.1)^2}{0.45} = 2.7$

• At equilibrium, Q stabilizes; however, the reaction still proceeds in both directions (forward and reverse).

Dynamic Equilibrium

• At dynamic equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. Thus, the concentrations stabilize.
• The equilibrium constant (K_c) quantifies the system at equilibrium:
  $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Relationship Between Q and K_c

• If Q < K_c, the reaction proceeds towards products (right shift).
• If Q > K_c, the reaction proceeds towards reactants (left shift).
• K_c is constant at a given temperature, independent of initial concentrations.

Writing K_c Expressions

• Use products over reactants, each raised to the power of their coefficients.
  Example: For the reaction
  $CH<em>4(g) + H</em>2O(g) \rightleftharpoons CO(g) + 3H<em>2(g)$ The K_c expression is $K</em>c = \frac{[CO][H<em>2]^3}{[CH</em>4][H_2O]}$

Characteristics of K_c

• The value of K_c indicates the extent of the reaction at equilibrium:
  • High K_c suggests a product-favored reaction (equilibrium shifts to right).
  • Low K_c indicates a reactant-favored reaction (equilibrium shifts to left).

Solving K_c Problems

1. Set up an ICE (Initial, Change, Equilibrium) table for the reaction. Example for $2H<em>2(g) + O</em>2(g) \rightleftharpoons 2H_2O(g)$:
   • Calculate K_c from equilibrium concentrations.
2. Use stoichiometry to determine changes in concentrations.
3. Substitute into the K_c expression for the final calculation.

Response to Changes in Equilibrium

• Systems at equilibrium respond to disturbances (changes in concentration, pressure, temperature) following Le Châtelier's principle:
  "If a system at equilibrium is disturbed, it will adjust to counteract the disturbance."
• Compare Q and K to determine the direction of the shift in equilibrium.

Homework Assignments

• Practice Problems: 15.5, 15.16, 15.17, 15.18, 15.54 from Brown (15th Edition)
• Answers available on Blackboard.