♨️Thermodynamics of Fluids Unit 12 – Chemical Reaction Equilibria

Key Concepts and Definitions

• Chemical equilibrium occurs when the rates of forward and reverse reactions are equal, resulting in no net change in concentrations of reactants and products over time
• Dynamic equilibrium maintains constant concentrations of reactants and products, but reactions continue to occur in both directions
• Equilibrium constant ($K$) quantifies the relationship between reactant and product concentrations at equilibrium, indicating the extent of a reaction
  • For a general reaction $aA + bB \rightleftharpoons cC + dD$, $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Homogeneous equilibria involve reactants and products in the same phase (gas or liquid)
• Heterogeneous equilibria involve reactants and products in different phases (solid, liquid, or gas)
• 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 a power equal to its stoichiometric coefficient
• Equilibrium position refers to the relative amounts of reactants and products at equilibrium, which can be shifted by changing conditions (temperature, pressure, or concentration)

Thermodynamic Foundations

• Gibbs free energy ($\Delta G$) determines the spontaneity of a reaction at constant temperature and pressure
  • $\Delta G < 0$: reaction is spontaneous and proceeds in the forward direction
  • $\Delta G > 0$: reaction is non-spontaneous and proceeds in the reverse direction
  • $\Delta G = 0$: system is at equilibrium
• Standard Gibbs free energy change ($\Delta G^\circ$) relates to the equilibrium constant ($K$) through the equation $\Delta G^\circ = -RT \ln K$
  • $R$ is the universal gas constant (8.314 J/mol·K)
  • $T$ is the absolute temperature in Kelvin
• Entropy ($S$) is a measure of the disorder or randomness of a system, influencing the spontaneity of a reaction
• Enthalpy ($H$) represents the heat content of a system and determines whether a reaction is exothermic (releases heat) or endothermic (absorbs heat)
• Van 't Hoff equation describes the temperature dependence of the equilibrium constant: $\ln \frac{K_2}{K_1} = \frac{-\Delta H^\circ}{R} (\frac{1}{T_2} - \frac{1}{T_1})$
  • $K_1$ and $K_2$ are equilibrium constants at temperatures $T_1$ and $T_2$, respectively
  • $\Delta H^\circ$ is the standard enthalpy change of the reaction

Types of Chemical Equilibria

• Acid-base equilibria involve the transfer of protons (H⁺) between species in solution
  • Acid dissociation constant ($K_a$) quantifies the strength of an acid
  • Base dissociation constant ($K_b$) quantifies the strength of a base
• Solubility equilibria occur when a solid substance dissolves in a solvent to form a saturated solution
  • Solubility product constant ($K_{sp}$) represents the equilibrium between a solid and its dissolved ions
• Complex ion equilibria involve the formation of complex ions from metal cations and ligands (Lewis bases)
  • Formation constant ($K_f$) measures the stability of a complex ion
• Redox equilibria involve the transfer of electrons between species, resulting in changes in oxidation states
  • Nernst equation relates the reduction potential of a half-reaction to its standard reduction potential and the concentrations of the oxidized and reduced species
• Gas-phase equilibria occur when gaseous reactants and products reach a state of dynamic equilibrium
  • Equilibrium partial pressures of gases are used instead of concentrations in the equilibrium constant expression

Equilibrium Constants and Their Significance

• Equilibrium constant ($K$) is a dimensionless quantity that represents the ratio of product concentrations to reactant concentrations at equilibrium, each raised to their stoichiometric coefficients
• $K$ is specific to a particular reaction at a given temperature
• Magnitude of $K$ indicates the extent of a reaction at equilibrium
  • $K > 1$: products are favored at equilibrium
  • $K < 1$: reactants are favored at equilibrium
  • $K \approx 1$: reactants and products are present in similar amounts at equilibrium
• Equilibrium constant expressions differ for homogeneous and heterogeneous equilibria
  • For homogeneous equilibria, all reactants and products are included in the expression
  • For heterogeneous equilibria, only gaseous and aqueous species are included; pure solids and liquids are omitted
• Reaction quotient ($Q$) has the same form as the equilibrium constant expression but uses instantaneous concentrations instead of equilibrium concentrations
  • Comparing $Q$ to $K$ predicts the direction of a reaction to reach equilibrium
• Equilibrium constants can be combined for multiple reactions using multiplication or division, depending on how the reactions are added or subtracted

Factors Affecting Chemical Equilibria

• Temperature changes affect the equilibrium position according to the Le Chatelier's principle
  • Increasing temperature shifts the equilibrium in the endothermic direction (absorbs heat)
  • Decreasing temperature shifts the equilibrium in the exothermic direction (releases heat)
• Pressure changes affect gaseous equilibria by altering the partial pressures of the gases involved
  • Increasing pressure shifts the equilibrium towards the side with fewer moles of gas
  • Decreasing pressure shifts the equilibrium towards the side with more moles of gas
• Concentration changes of reactants or products shift the equilibrium position to counteract the change
  • Adding reactants or removing products shifts the equilibrium towards the products
  • Removing reactants or adding products shifts the equilibrium towards the reactants
• Catalysts accelerate the rates of both forward and reverse reactions equally, reaching equilibrium faster without changing the equilibrium position
• Inert gases (non-reactive) added at constant volume do not affect the equilibrium position, as they do not change the partial pressures of the reactants or products

Le Chatelier's Principle and Its Applications

• Le Chatelier's principle states that when a system at equilibrium is subjected to a disturbance, the equilibrium shifts in the direction that minimizes the disturbance
• Applying Le Chatelier's principle helps predict the direction of equilibrium shift in response to changes in temperature, pressure, or concentration
• Temperature changes
  • Exothermic reactions (release heat): increasing temperature shifts equilibrium towards reactants; decreasing temperature shifts equilibrium towards products
  • Endothermic reactions (absorb heat): increasing temperature shifts equilibrium towards products; decreasing temperature shifts equilibrium towards reactants
• Pressure changes (gaseous equilibria)
  • Increasing pressure shifts equilibrium towards the side with fewer moles of gas
  • Decreasing pressure shifts equilibrium towards the side with more moles of gas
• Concentration changes
  • Adding reactants or removing products shifts equilibrium towards products
  • Removing reactants or adding products shifts equilibrium towards reactants
• Le Chatelier's principle has practical applications in industrial processes (Haber-Bosch process for ammonia synthesis) and biological systems (hemoglobin-oxygen binding in blood)

Calculating Equilibrium Compositions

• ICE tables (Initial, Change, Equilibrium) are used to organize information and solve for equilibrium concentrations or partial pressures
  • Initial: concentrations or partial pressures before the reaction starts
  • Change: changes in concentrations or partial pressures as the reaction proceeds to equilibrium
  • Equilibrium: final concentrations or partial pressures at equilibrium
• Equilibrium concentrations or partial pressures are calculated using the equilibrium constant expression and the ICE table
• For reactions with small equilibrium constants ($K << 1$), the assumption of x << [initial] can simplify calculations
• For reactions with large equilibrium constants ($K >> 1$), the assumption of [initial] ≈ x can simplify calculations
• Quadratic equations may be necessary to solve for equilibrium concentrations in more complex cases
• pH calculations for acid-base equilibria involve using the acid dissociation constant ($K_a$) or the base dissociation constant ($K_b$)
• Solubility calculations for slightly soluble salts involve using the solubility product constant ($K_{sp}$)

Real-World Applications and Case Studies

• Haber-Bosch process for ammonia synthesis
  • $\ce{N2(g) + 3H2(g) <=> 2NH3(g)}$, $\Delta H^\circ = -92.4$ kJ/mol
  • High pressure (200-300 atm) and moderate temperature (400-500°C) favor product formation
  • Iron catalyst accelerates the reaction
• Synthesis of methanol from syngas (CO and H₂)
  • $\ce{CO(g) + 2H2(g) <=> CH3OH(g)}$, $\Delta H^\circ = -90.6$ kJ/mol
  • High pressure (50-100 atm) and moderate temperature (250-300°C) favor product formation
  • Copper-zinc oxide catalyst accelerates the reaction
• Boudouard reaction in the production of carbon monoxide
  • $\ce{2CO(g) <=> CO2(g) + C(s)}$, $\Delta H^\circ = -172.4$ kJ/mol
  • High temperature (above 700°C) favors the reverse reaction, producing CO
• Hemoglobin-oxygen binding in blood
  • Hemoglobin (Hb) binds oxygen (O₂) in the lungs and releases it in the tissues
  • Oxygen binding exhibits cooperative behavior due to the quaternary structure of hemoglobin
  • Factors such as pH, CO₂ concentration, and 2,3-bisphosphoglycerate (BPG) levels affect the oxygen affinity of hemoglobin
• Calcium carbonate (CaCO₃) dissolution in ocean acidification
  • $\ce{CaCO3(s) <=> Ca^2+(aq) + CO3^2-(aq)}$, $K_{sp} = 3.36 \times 10^{-9}$ at 25°C
  • Increasing atmospheric CO₂ levels lead to ocean acidification, shifting the equilibrium towards the dissolution of calcium carbonate
  • Impacts marine organisms that rely on calcium carbonate for their shells or skeletons (corals, mollusks, and some plankton)