💏Intro to Chemistry Unit 13 – Fundamental Equilibrium Concepts

Key Concepts and Definitions

• Equilibrium occurs when the forward and reverse reactions proceed at the same rate resulting in no net change in the concentrations of reactants and products over time
• Dynamic equilibrium is a state where the forward and reverse reactions continue to occur but there is no net change in the concentrations of reactants and products
• The equilibrium constant (K) is the ratio of the concentrations of products to reactants at equilibrium each raised to the power of their stoichiometric coefficients
• The law of mass action states that the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants each raised to the power of their stoichiometric coefficients
• The reaction quotient (Q) is the ratio of the concentrations of products to reactants at any given time during a reaction each raised to the power of their stoichiometric coefficients
  • If Q < K, the reaction will proceed in the forward direction until equilibrium is reached
  • If Q > K, the reaction will proceed in the reverse direction until equilibrium is reached
  • If Q = K, the reaction is at equilibrium
• Homogeneous equilibrium involves reactants and products in the same phase (gas or aqueous solution) while heterogeneous equilibrium involves reactants and products in different phases (solid, liquid, or gas)

Types of Equilibrium

• Physical equilibrium involves changes in physical states or phases without any chemical reactions occurring (evaporation and condensation of water)
• Chemical equilibrium involves a reversible chemical reaction where the forward and reverse reactions proceed at the same rate resulting in no net change in the concentrations of reactants and products over time
• Acid-base equilibrium involves the transfer of protons (H+) between an acid and a base resulting in the formation of a conjugate acid-base pair (acetic acid and acetate ion in a buffer solution)
• Solubility equilibrium involves the dissolution and precipitation of a solid in a saturated solution where the rate of dissolution equals the rate of precipitation (calcium carbonate in hard water)
• Redox equilibrium involves the transfer of electrons between species resulting in changes in oxidation states (iron(II) and iron(III) in a solution)
• Phase equilibrium involves the distribution of a substance between different phases (liquid-vapor equilibrium of a pure substance)
• Ionic equilibrium involves the dissociation and association of ions in a solution (dissociation of a weak electrolyte like acetic acid in water)

Equilibrium Constants

• The equilibrium constant (K) is a mathematical expression that relates the concentrations of reactants and products at equilibrium for a specific chemical reaction at a given temperature
• For a general chemical reaction: aA + bB ⇌ cC + dD, the equilibrium constant expression is: K = [C]^c [D]^d / [A]^a [B]^b, where the brackets denote the molar concentrations at equilibrium
• The value of K indicates the extent or position of the equilibrium
  • If K > 1, the equilibrium favors the products (product-favored)
  • If K < 1, the equilibrium favors the reactants (reactant-favored)
  • If K ≈ 1, the equilibrium is neither product-favored nor reactant-favored
• The magnitude of K also indicates the completeness of the reaction
  • If K is very large (K >> 1), the reaction is essentially complete and proceeds mostly to products
  • If K is very small (K << 1), the reaction is incomplete and only a small amount of products are formed
• For heterogeneous equilibria involving pure solids or liquids, their concentrations are constant and not included in the equilibrium constant expression (solubility product constant, Ksp, for the dissolution of a sparingly soluble salt)
• For gas-phase reactions, the equilibrium constant can be expressed in terms of partial pressures (Kp) instead of concentrations (Kc) using the ideal gas law: Kp = Kc (RT)^Δn, where Δn is the change in the number of moles of gas

Le Chatelier's Principle

• Le Chatelier's principle states that when a system at equilibrium is subjected to a stress or change in conditions, the equilibrium will shift in the direction that minimizes the stress or opposes the change to re-establish equilibrium
• Stresses that can disturb equilibrium include changes in concentration, pressure, volume, and temperature
• Adding a reactant or product will shift the equilibrium in the direction that consumes the added species to minimize the stress (adding a reactant shifts equilibrium to the right, forming more products)
• Removing a reactant or product will shift the equilibrium in the direction that replenishes the removed species (removing a product shifts equilibrium to the right, forming more products)
• Increasing the pressure or decreasing the volume (for gas-phase reactions) will shift the equilibrium in the direction that reduces the number of moles of gas to minimize the stress (formation of fewer gas molecules)
• Decreasing the pressure or increasing the volume will shift the equilibrium in the direction that increases the number of moles of gas (formation of more gas molecules)
• Increasing the temperature will shift the equilibrium in the endothermic direction to absorb the added heat and minimize the stress (favoring the reaction that absorbs heat)
• Decreasing the temperature will shift the equilibrium in the exothermic direction to release heat and minimize the stress (favoring the reaction that releases heat)
• Catalysts do not affect the position of equilibrium as they accelerate both the forward and reverse reactions equally, only reducing the time required to reach equilibrium

Factors Affecting Equilibrium

• Concentration affects equilibrium by shifting it in the direction that minimizes the stress of the concentration change (increasing the concentration of a reactant shifts equilibrium to the right, forming more products)
• Pressure affects gas-phase equilibria by shifting it in the direction that reduces the number of moles of gas and minimizes the stress of the pressure change (increasing pressure shifts equilibrium to the side with fewer gas molecules)
• Volume is inversely related to pressure for gas-phase reactions, so decreasing the volume (increasing pressure) shifts equilibrium to the side with fewer gas molecules, while increasing the volume (decreasing pressure) shifts it to the side with more gas molecules
• Temperature affects equilibrium by shifting it in the direction that minimizes the stress of the temperature change (increasing temperature shifts equilibrium in the endothermic direction, while decreasing temperature shifts it in the exothermic direction)
  • The effect of temperature on equilibrium is determined by the sign of the enthalpy change (ΔH) for the reaction
  • For endothermic reactions (ΔH > 0), increasing temperature shifts equilibrium to the right, forming more products
  • For exothermic reactions (ΔH < 0), increasing temperature shifts equilibrium to the left, forming more reactants
• Catalysts do not affect the position of equilibrium but accelerate the rate at which equilibrium is reached by lowering the activation energy for both the forward and reverse reactions equally
• Inert gases (noble gases) added to a gas-phase reaction at constant volume do not affect the equilibrium as they do not change the partial pressures of the reactants and products
• Ionic strength can affect equilibrium in aqueous solutions by altering the activities of the ions involved in the reaction, with higher ionic strength generally favoring the side with fewer ions (common ion effect, salt effect)

Equilibrium Calculations

• Equilibrium calculations involve determining the concentrations of reactants and products at equilibrium given the initial concentrations and the equilibrium constant (K) or solving for the equilibrium constant given the equilibrium concentrations
• The ICE table method is a systematic approach to solving equilibrium problems, where ICE stands for Initial, Change, and Equilibrium concentrations
  • Initial concentrations are the starting amounts of reactants and products before the reaction begins
  • Change in concentrations is determined by the stoichiometry of the reaction and the variable x, which represents the amount of reactant consumed or product formed
  • Equilibrium concentrations are the sum of the initial concentrations and the change in concentrations
• The equilibrium constant expression is set up using the equilibrium concentrations from the ICE table, and the resulting equation is solved for x (often using the quadratic formula for more complex problems)
• The calculated value of x is then substituted back into the equilibrium concentration expressions to determine the concentrations of all species at equilibrium
• For problems involving the calculation of equilibrium constant (K), the given equilibrium concentrations are substituted directly into the equilibrium constant expression, and the resulting value of K is calculated
• In some cases, simplifying assumptions can be made to solve equilibrium problems more easily
  • For example, if the equilibrium constant is very large (K >> 1), the reaction can be assumed to go to completion, and the equilibrium concentrations can be approximated using the stoichiometry of the reaction
  • If the equilibrium constant is very small (K << 1), the reaction can be assumed to proceed to a negligible extent, and the equilibrium concentrations can be approximated as the initial concentrations
• When dealing with weak acids or bases, the equilibrium calculations involve the acid dissociation constant (Ka) or the base dissociation constant (Kb), which are special cases of the equilibrium constant (K)
  • The Ka and Kb expressions are set up using the equilibrium concentrations of the weak acid or base, and the resulting equations are solved for the equilibrium concentrations and pH

Real-World Applications

• Hemoglobin-oxygen binding in the blood is an example of equilibrium, where hemoglobin (Hb) reversibly binds to oxygen (O2) to form oxyhemoglobin (HbO2): Hb + O2 ⇌ HbO2
  • The oxygen-binding affinity of hemoglobin is affected by factors such as pH, CO2 concentration, and temperature, which can shift the equilibrium and alter the oxygen delivery to tissues
• The Haber-Bosch process for ammonia synthesis is an industrial application of equilibrium: N2(g) + 3H2(g) ⇌ 2NH3(g)
  • The process is carried out at high pressure and moderate temperature with an iron catalyst to shift the equilibrium towards the production of ammonia, which is used in fertilizers and other nitrogen-containing compounds
• Buffer solutions resist changes in pH when small amounts of acid or base are added, maintaining a relatively constant pH through equilibrium reactions between a weak acid and its conjugate base (or a weak base and its conjugate acid)
  • Buffer solutions are crucial in biological systems (blood pH regulation) and in various industrial and laboratory applications (pH control in chemical reactions, food processing, and water treatment)
• The solubility of gases in liquids (Henry's law) is an equilibrium process, where the amount of dissolved gas is proportional to its partial pressure above the liquid: C = kP
  • This principle is important in understanding the solubility of oxygen in water (aquatic life), the formation of carbonated beverages, and the removal of dissolved gases from liquids (degassing)
• The distribution of a solute between two immiscible solvents (liquid-liquid extraction) is an equilibrium process governed by the distribution coefficient (Kd), which is the ratio of the solute concentrations in the two solvents at equilibrium
  • This principle is used in the purification and separation of compounds in chemical and pharmaceutical industries (extraction of antibiotics, removal of impurities)
• The formation of stalactites and stalagmites in caves is an example of a dynamic equilibrium involving the dissolution and precipitation of calcium carbonate (CaCO3): CaCO3(s) + H2O(l) + CO2(aq) ⇌ Ca^2+(aq) + 2HCO3^-(aq)
  • Changes in factors such as water acidity, temperature, and CO2 concentration can shift the equilibrium and affect the growth or dissolution of these geological formations over time

Common Misconceptions and FAQs

• Misconception: Equilibrium is a static state where no reactions occur.

  • Fact: Equilibrium is a dynamic state where forward and reverse reactions continue to occur at equal rates, resulting in no net change in the concentrations of reactants and products.

• Misconception: Once equilibrium is reached, the concentrations of reactants and products are equal.

  • Fact: The concentrations of reactants and products at equilibrium are not necessarily equal; their ratios are determined by the equilibrium constant (K) and the stoichiometry of the reaction.

• Misconception: Adding a catalyst will shift the equilibrium towards the products.

  • Fact: Catalysts do not affect the position of equilibrium; they only accelerate the rate at which equilibrium is reached by lowering the activation energy for both the forward and reverse reactions equally.

• FAQ: What is the difference between the equilibrium constant (K) and the reaction quotient (Q)?

  • Answer: The equilibrium constant (K) is the ratio of the concentrations of products to reactants at equilibrium, while the reaction quotient (Q) is the ratio of the concentrations of products to reactants at any given time during the reaction. Q is used to determine the direction in which the reaction will proceed to reach equilibrium.

• FAQ: How does temperature affect the equilibrium constant (K)?

  • Answer: The equilibrium constant (K) is temperature-dependent. For endothermic reactions (ΔH > 0), increasing the temperature will increase the value of K, shifting the equilibrium towards the products. For exothermic reactions (ΔH < 0), increasing the temperature will decrease the value of K, shifting the equilibrium towards the reactants.

• FAQ: Can a reaction have multiple equilibrium constants?

  • Answer: A reaction can have multiple equilibrium constants depending on the units used to express the concentrations or partial pressures of the reactants and products. For example, a gas-phase reaction can have an equilibrium constant expressed in terms of molar concentrations (Kc) or partial pressures (Kp), which are related by the ideal gas law.

• FAQ: How do you determine the direction of equilibrium shift when multiple factors are changed simultaneously?

  • Answer: When multiple factors affecting equilibrium are changed simultaneously, you need to consider the effect of each factor independently and then combine their effects to determine the overall direction of the equilibrium shift. In some cases, the effects may oppose each other, and the dominant factor will determine the direction of the shift.

• FAQ: Can equilibrium be achieved in an open system?

  • Answer: Equilibrium can be achieved in an open system, but it is more challenging to maintain because matter and energy can be exchanged with the surroundings. In open systems, steady-state equilibrium can be reached when the rates of input and output of matter and energy are equal, resulting in constant concentrations of reactants and products over time.