🧪AP Chemistry Unit 7 – Equilibrium

Key Concepts and Definitions

• Equilibrium occurs when the rate of the forward reaction equals the rate of the reverse reaction in a closed system
• At equilibrium, the concentrations of reactants and products remain constant over time, but the reactions continue to occur
• The equilibrium state is dynamic, meaning that both forward and reverse reactions are still taking place, but there is no net change in concentrations
• The equilibrium constant (K) quantifies the relationship between the concentrations of reactants and products at equilibrium
  • Represented as a ratio of the product of the concentrations of the products raised to their stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their stoichiometric coefficients
• Equilibrium can be approached from either direction (reactants to products or products to reactants) and the same equilibrium state will be reached
• The position of equilibrium refers to the relative amounts of reactants and products present at equilibrium
• Equilibrium is temperature-dependent, and changing the temperature will shift the position of equilibrium

Types of Equilibrium

• Chemical equilibrium involves the balance between the forward and reverse reactions in a closed system (N2 + 3H2 ⇌ 2NH3)
• Physical equilibrium occurs when a substance can exist in more than one physical state (solid, liquid, or gas) and the rates of interconversion between these states are equal
  • Vapor-liquid equilibrium (H2O(l) ⇌ H2O(g))
  • Solid-liquid equilibrium (H2O(s) ⇌ H2O(l))
• Acid-base equilibrium involves the transfer of protons (H+) between species in a solution (HF + H2O ⇌ H3O+ + F-)
• Solubility equilibrium occurs when a solid substance dissolves in a solvent to form a saturated solution, and the rates of dissolution and crystallization are equal (NaCl(s) ⇌ Na+(aq) + Cl-(aq))
• Complexation equilibrium involves the formation and dissociation of complex ions in solution (Fe3+ + 6CN- ⇌ [Fe(CN)6]3-)

Le Chatelier's Principle

• States that when a system at equilibrium is subjected to a stress or change in conditions, the equilibrium will shift to counteract the stress and establish a new equilibrium
• Changing the concentration of a reactant or product will cause the equilibrium to shift in the direction that reduces the change
  • Adding a reactant will shift the equilibrium towards the products
  • Removing a product will shift the equilibrium towards the products
• Changing the pressure of a gaseous system will cause the equilibrium to shift in the direction that reduces the pressure change
  • Increasing pressure favors the side with fewer moles of gas
  • Decreasing pressure favors the side with more moles of gas
• Changing the temperature will shift the equilibrium in the direction that opposes the temperature change
  • Increasing temperature favors the endothermic reaction
  • Decreasing temperature favors the exothermic reaction
• Adding a catalyst does not shift the equilibrium position but increases the rate at which equilibrium is reached

Equilibrium Constants

• The equilibrium constant (K) is a mathematical expression that relates the concentrations of reactants and products at equilibrium
• For a general reaction aA + bB ⇌ cC + dD, the equilibrium constant is expressed as:
  • $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• The value of K indicates the position of equilibrium
  • K > 1 means the equilibrium favors the products
  • K < 1 means the equilibrium favors the reactants
  • K = 1 means the reactants and products are equally favored
• The magnitude of K also indicates the completeness of the reaction
  • Large K values (K >> 1) indicate the reaction is essentially complete, with mostly products at equilibrium
  • Small K values (K << 1) indicate the reaction is minimally complete, with mostly reactants at equilibrium
• Equilibrium constants are temperature-dependent, and their values change with temperature changes
• Different types of equilibrium constants include:
  • Kc (concentration equilibrium constant)
  • Kp (pressure equilibrium constant)
  • Ka (acid dissociation constant)
  • Kb (base dissociation constant)
  • Ksp (solubility product constant)

Calculating Equilibrium Concentrations

• The equilibrium constant expression and initial concentrations of reactants and products can be used to calculate the equilibrium concentrations
• The ICE table method (Initial, Change, Equilibrium) is a systematic approach to solve equilibrium problems
  • Initial concentrations are listed under "I"
  • Changes in concentrations are listed under "C" using the stoichiometric coefficients and a variable (usually x)
  • Equilibrium concentrations are listed under "E" by adding the initial concentrations and the changes
• Substitute the equilibrium concentrations into the equilibrium constant expression and solve for the variable
• Quadratic equations may be required for more complex problems involving polynomials with degrees greater than one
• The calculated equilibrium concentrations can be used to determine the direction in which the reaction proceeds to reach equilibrium and the concentrations of all species at equilibrium

Factors Affecting Equilibrium

• Temperature changes affect the equilibrium constant and the position of equilibrium
  • Increasing temperature shifts the equilibrium in the endothermic direction
  • Decreasing temperature shifts the equilibrium in the exothermic direction
• Pressure changes affect gaseous equilibria by altering the partial pressures of the reactants and products
  • Increasing pressure favors the side with fewer moles of gas
  • Decreasing pressure favors the side with more moles of gas
• Concentration changes of reactants or products shift the equilibrium position to counteract the change
  • Adding a reactant or removing a product shifts the equilibrium towards the products
  • Removing a reactant or adding a product shifts the equilibrium towards the reactants
• Volume changes affect gaseous equilibria by altering the concentrations of the reactants and products
  • Decreasing volume (increasing concentration) shifts the equilibrium towards the side with fewer moles of gas
  • Increasing volume (decreasing concentration) shifts the equilibrium towards the side with more moles of gas
• Catalysts do not affect the position of equilibrium but increase the rate at which equilibrium is reached by lowering the activation energy

Real-World Applications

• Haber-Bosch process for ammonia synthesis (N2 + 3H2 ⇌ 2NH3)
  • High pressure and moderate temperature are used to maximize yield
  • Iron catalyst is used to increase the rate of reaction
• Hemoglobin-oxygen binding in blood (Hb + 4O2 ⇌ Hb(O2)4)
  • Oxygen binding to hemoglobin is affected by pH, CO2 concentration, and 2,3-bisphosphoglycerate (BPG) levels
• Ocean acidification due to increased atmospheric CO2 (CO2 + H2O ⇌ H2CO3 ⇌ H+ + HCO3-)
  • Increased CO2 levels shift the equilibrium towards the products, lowering ocean pH
• Buffer solutions in biological systems (HA ⇌ H+ + A-)
  • Maintain relatively constant pH by resisting changes in H+ concentration
• Solubility of minerals and salts in water (CaCO3(s) ⇌ Ca2+(aq) + CO32-(aq))
  • Affected by factors such as temperature, pH, and the presence of common ions

Common Mistakes and Tips

• Not setting up the ICE table correctly
  • Ensure that the initial concentrations, changes, and equilibrium concentrations are properly represented
• Forgetting to use the stoichiometric coefficients when setting up the equilibrium constant expression
  • Remember to raise the concentrations to their respective powers based on the balanced chemical equation
• Incorrectly applying Le Chatelier's principle
  • Carefully analyze the effect of the stress on the reactants and products to determine the direction of the shift
• Not considering the effect of temperature on the equilibrium constant
  • Remember that the equilibrium constant is temperature-dependent, and its value changes with temperature changes
• Confusing the direction of the shift when dealing with gaseous equilibria
  • Increasing pressure favors the side with fewer moles of gas, while decreasing pressure favors the side with more moles of gas
• Double-check your calculations and ensure that the units cancel out correctly
• Practice a variety of equilibrium problems to familiarize yourself with different scenarios and problem-solving strategies
• Understand the underlying concepts and principles rather than just memorizing formulas and equations