Chapter 13: Chemical Equilibrium and Equilibrium Constants

College Physics and Chemistry Overview

Chapter 13 Outline

• 13.1 Chemical Equilibrium

• 13.2 Equilibrium Constants

• 13.3 Shifting Equilibria: Le Châtelier’s Principle

• 13.4 Equilibrium Calculations

13.1 Chemical Equilibria

Learning Objectives

• Describe the nature of equilibrium systems.

• Explain the dynamic nature of a chemical equilibrium.

Establishment of Equilibrium

• Reversible Reactions: Reactions can proceed in both forward (left to right) and reverse (right to left) directions.

• Equilibrium Condition:

  • The system achieves equilibrium when the rates of the forward and reverse reactions are equal.

  • At this point, the concentrations of reactants and products remain constant over time.

• Concentration Variability: The concentrations of reactants and products can vary significantly across different equilibrium systems. Some may favor products, others may favor reactants, and some may have balanced amounts of both.

Example of Reversible Reaction:

• Reaction: $N<em>2O</em>4(g) ⇌ 2NO_2(g)$

  • $N<em>2O</em>4$ is colorless; $NO_2$ is brown.

  • The reaction is established in a closed container at 100 °C, resulting in a reddish-brown color due to $NO_2$ formation.

  • As $NO<em>2$ accumulates, it can revert to form $N</em>2O_4$, thus establishing equilibrium where the amounts of reactants and products remain unchanged.

Concentration Changes over Time

• At the start (t=0): $[N<em>2O</em>4]$ is finite, $[NO_2]$ is zero.

  • Forward reaction proceeds at a finite rate, reverse reaction rate is zero.

• As time progresses:

  • $[N<em>2O</em>4]$ decreases, $[NO_2]$ increases.

  • Forward reaction slows down and reverse speeds up due to concentration changes until equilibrium is reached.

Characteristics of Equilibrium

• Once equilibrium is achieved, concentrations of each reactant and product remain constant.

Common Misconceptions

• The amounts of reactants and products are typically not equal at equilibrium.

• Equilibrium is dynamic; reactions continue in both directions at the same rate.

Metaphor for Dynamic Equilibrium

• A juggling act: Each juggler (reaction) throws and catches clubs (molecules) at the same rate, maintaining a constant number of clubs in their hands (reactant/products).

13.2 Equilibrium Constants

Learning Objectives

• Derive reaction quotients from chemical equations representing homogeneous and heterogeneous reactions.

• Calculate values of reaction quotients and equilibrium constants, using concentrations and pressures.

• Relate the magnitude of an equilibrium constant to properties of the chemical system.

Definition of Reaction Quotient, Q

• For the general reaction:
  $mA + nB ⇌ xC + yD$
  where A, B, C, D are gases or aqueous species, and m, n, x, y are coefficients in the balanced equation.

• Concentration Reaction Quotient (Qc) is defined as follows:
  $Q_c = \frac{[C]^x[D]^y}{[A]^m[B]^n}$

Calculation of Reaction Quotient

• Concentration Units: All concentrations must be expressed in Molarity (M).

• Numerator: Concentrations of products multiplied together and raised to the power of their coefficients.

• Denominator: Concentrations of reactants multiplied together and raised to the power of their coefficients.

Example Calculations

• Sample for Reaction:
  (a) $4NH<em>3(g) + 7O</em>2(g) ⇌ 4NO<em>2(g) + 6H</em>2O(g)$
  (b) $C<em>4H</em>8(g) ⇌ 2C<em>2H</em>4(g)$
  Results:
  (a) $Q<em>c = \frac{[NO</em>2]^4[H<em>2O]^6}{[NH</em>3]^4[O<em>2]^7}$ (b) $Q</em>c = \frac{[C<em>2H</em>4]^2}{[C<em>4H</em>8]}$

Value of Qc

• The numeric value of Qc changes as the reaction progresses towards equilibrium.

• Initial concentrations can be used to calculate Qc.

Equilibrium Constant, K

• The equilibrium constant (K) is the value of Q when the reaction reaches equilibrium:

  • For the same reaction: $K = Q$ when the reactants/products are at equilibrium.

• Distinction from rate constant (k): K and k are different entities.

• K is dependent on temperature while initially set amounts do not affect K's value.

Magnitude of K

• If K >> 1: Reaction is product-favored (mostly products).

• If K << 1: Reaction is reactant-favored (mostly reactants).

Determining Direction of Reaction

• A system not at equilibrium shifts towards equilibrium based on the relationship between Q and K:

  • If Q < K: Reaction shifts forward (produces products).

  • If Q > K: Reaction shifts backward (produces reactants).

  • If $Q = K$: The system is at equilibrium.

13.3 Shifting Equilibria: Le Châtelier’s Principle

Learning Objectives

• Describe ways in which an equilibrium system can be stressed.

• Predict the response of a stressed equilibrium using Le Chatelier’s Principle.

Le Châtelier’s Principle

• Definition: When a chemical system at equilibrium is disturbed, it re-establishes equilibrium by counteracting the disturbance.

• The equilibrium constant remains unchanged unless the system's temperature changes.

Effects of Alterations on Equilibrium

• Adding a Component: If a reactant or product is added, the system shifts in the direction that consumes the added substance.

• Removing a Component: If a reactant or product is removed, the system shifts in the direction that restores the removed substance.

• Pure solids/liquids have no effect on equilibrium since they don’t appear in the equilibrium expression unless completely removed.

Changes in Temperature

• Increasing Temperature: Reactions absorb the additional heat, which shifts equilibrium based on the reaction's enthalpy (endothermic or exothermic characteristics).

• Endothermic Example: $N<em>2O</em>4(g) ⇌ 2NO_2(g), \, ΔH=+57.20\text{kJ}$; increasing temperature shifts right (product formation).

Catalysts and Equilibrium

• Catalysts affect the rate of reactions but not the equilibrium concentrations or K value; they speed up the attainment of equilibrium.

13.4 Equilibrium Calculations

Learning Objectives

• Identify changes in concentrations or pressures in equilibrium systems.

• Calculate equilibrium concentrations or partial pressures, and equilibrium constants using various algebraic methods.

Types of Equilibrium Calculations

1. Calculation of an equilibrium constant.

2. Calculation of missing equilibrium concentrations/partial pressures.

3. Calculation of equilibrium concentrations from initial concentrations.

Example: Iodine Reaction

• Reaction: $I<em>2(aq) + I^-(aq) ⇌ I</em>3^-(aq)$

• Initial conditions: $[I_2]=[I^-]= 1.000\times 10^{-3} M$

• Equilibrium conditions: $[I_2] = 6.61\times 10^{-4} M$

• Setup ICE table to calculate equilibrium concentrations.

Example: PCl5 Decomposition

• Reaction: $PCl<em>5(g) ⇌ PCl</em>3(g) + Cl_2(g)$

• Initial concentration of $PCl_5 = 1.00 M$, Kc = 0.0211.

• Determine direction and construct an ICE table to solve for equilibrium concentrations.

Example: Equilibrium Calculations for H2 + I2 Reaction

• Reaction: $H<em>2(g) + I</em>2(g) ⇌ 2HI(g)$

• ICE table approach for initial concentrations:

  • [H2]: 1.000 x 10^{-3}

  • [I2]: 2.000 x 10^{-3}

  • [HI]: 0

• Follow stoichiometric changes to arrive at final equilibrium concentrations.

Summary of Examples

• Use the ICE method to find missing concentrations and ensure the calculated equilibrium constant matches given values.

Final Notes

• Review and redo calculations to ensure accuracy.

• Engage with exercises presented to solidify understanding of equilibrium concepts.