Applications of Thermodynamics - In Depth Notes

Unit 9: Applications of Thermodynamics

• Importance: 7-9% AP Exam Weight

9.1 Introduction to Entropy

• Enduring Understanding: Some chemical or physical processes cannot occur without intervention.
• Entropy:
  • Measures molecular randomness and disorder.
  • Always increases naturally in the universe.
  • Driving force for spontaneous reactions.
  • Entropy increases with matter dispersal and phase changes:
  • Solid to liquid or liquid to gas increases disorder and volume.
  • Gas Phase: Entropy increases when:
  • Volume increases at constant temperature.
  • The total number of moles of gas-phase products exceeds reactants.

9.2 Absolute Entropy and Entropy Change

• Entropy Change Calculation:
  • Formula: \Delta S^ullet{rxn} = \Sigma S^ullet{prod} - \Sigma S^ullet_{rxt}
  • Example 1:
  • Reaction: $Pb(NO<em>3)</em>2(aq) + 2KI(aq) → Pbl<em>2(s) + 2KNO</em>3(aq)$
  • Absolute Entropies:
    • $Pb(NO<em>3)</em>2(aq) = 250 J/(K imes mol)$
    • $KI(aq) = 125$
    • $Pbl_2(s) = 175$
    • $KNO_3(aq) = 150$
  • Calculate:
    • $\Delta S_{reaction} = [175 + 2(150)] - [250 + 2(125)] = -25 J/(K imes mol)$

9.3 Gibbs Free Energy & Thermodynamic Favorability

• Gibbs Free Energy Change:
  • Measures thermodynamic favorability.
  • Standard conditions:
  • Pure substances, 1.0 M solutions, gases at 1.0 atm.
  • Thermodynamically favored: \Delta G^\circ < 0
  • Distinction:
  • "Spontaneous" replaced with "thermodynamically favored" to avoid misunderstanding.
• Formula for Gibbs Free Energy:
  • $\Delta G^\circ<em>{reaction} = \Sigma \Delta G^\circ</em>f(products) - \Sigma \Delta G^\circ_f(reactants)$
  • Determine $\Delta G^\circ$ based on temperature and reaction conditions.

9.4 Thermodynamic and Kinetic Control

• Kinetic Control:
  • Processes may be thermodynamically favored but occur slowly due to high activation energy.
• Thermodynamic Control:
  • Indicates processes that are ultimately feasible under certain conditions.
• The rates of reaction can reflect the common barriers as well as favorability.

9.5 Free Energy and Equilibrium

• Relation: $\Delta G^\circ$ and equilibrium constant (K):
  • $K = e^{-\Delta G^\circ/RT}$
  • $\Delta G^\circ = -RT \ln K$
• Connections can be qualitatively assessed with respect to reaction favorability and equilibrium states.

9.6 Free Energy of Dissolution

• Factors affecting free energy change for dissolution:
  • Breaking intermolecular interactions, solvent reorganization, and interactions with the solvent.
• Prediction of the total change in free energy can be complex due to interdependencies.

9.7 Coupled Reactions

• External energy sources can drive thermodynamically unfavorable processes, such as:
  • Electrolytic processes, photosynthesis using light energy.
• Coupled processes yield an overall reaction that is thermodynamically favored.

9.8 Galvanic (Voltaic) & Electrolytic Cells

• Galvanic Cells:
  • Involve thermodynamically favored reactions.
• Electrolytic Cells:
  • Require external energy to drive non-favorable reactions.
• Electron flow direction is critical in understanding reaction outcomes and energy generation.

9.9 Cell Potential and Free Energy

• Cell potential (E) indicates the feasibility of electrochemical processes.
  • $\Delta G^\circ = -nFE$ where E is cell potential under standard conditions.
  • Positive E indicates thermodynamically favored reactions; negative E indicates non-favored.

9.10 Cell Potential Under Nonstandard Conditions

• Cell potential varies with the concentrations of reactants and products.
• Nernst Equation:
  • $E = E^\circ - (RT/nF) \ln Q$
  • Indicates how conditions change potential based on deviations from standard practices.

9.11 Electrolysis and Faraday’s Law

• Applications in determining stoichiometry concerning the reaction occurring within an electrochemical cell.
  • Key Equations:
  • $I = q/t$ where I is current, q is total charge, and t is time.
• Practical applications demonstrate how current and charge inform about material deposition and reaction kinetics.