Unit 9: Entropy, Gibbs Free Energy, and Electrochemistry

Entropy (S)

  • Entropy (S) is the total number of possible energy states in a system.
  • It describes how well dispersed a material is or the amount of disorder in a system.
  • Phases of matter, ordered by increasing entropy: solids < liquids < gases
    • Solids have the least entropy, while gases have the most.
  • Factors affecting entropy:
    • Higher temperature leads to greater entropy.
    • Greater volume leads to greater entropy.
    • More molecules of gas translate to higher entropy (more disorder).

Predicting Entropy Change (ΔS)

  • Predicting the sign of entropy change (ΔS) for reactions:
    • NaNO3(s) → Na^+(aq) + NO3^-(aq) (ΔS > 0, entropy increases)
    • 2Mg(s) + O_2(g) → 2MgO(s) (ΔS < 0, entropy decreases)
    • CO2(g) + 2H2(g) → CH_3OH(g) (ΔS < 0, entropy decreases)

Absolute Entropy & Entropy Change

  • Entropy change (ΔS°) for a reaction is calculated using the standard molar entropies (S°) of products and reactants:
    • ΔS° = ΣS°{products} - ΣS°{reactants}

Gibbs Free Energy & Thermodynamic Favorability

  • Thermodynamically favored processes are those that will occur spontaneously under a specific set of conditions.

  • Gibbs Free Energy (ΔG) is measured in energy units (e.g., kJ or kcal) and is used to determine thermodynamic favorability.

  • Conditions:

    • ΔG < 0: Thermodynamically favored process
    • ΔG > 0: Not thermodynamically favored process

  • Standard Conditions:

    • When you see the "°" symbol (e.g., ΔG°), it means standard conditions: 25°C (298 K), 1 atm pressure, and 1 M concentration.

  • Calculating Gibbs Free Energy:

    • ΔG = ΔH - T(ΔS)
    • Where:
      • ΔG = Change in Gibbs free energy
      • ΔH = Change in enthalpy
      • T = Temperature in Kelvin
      • ΔS = Change in entropy (in kJ)

  • The universe tends to favor exothermic reactions (ΔH < 0) or reactions where entropy increases (ΔS > 0).

  • Predicting Favorability Based on ΔH and ΔS:

    • ΔH (-), ΔS (+): Favored at all temperatures.
    • ΔH (+), ΔS (-): Never favored.
    • ΔH (-), ΔS (-): Favored at low temperatures only.
    • ΔH (+), ΔS (+): Favored at high temperatures only.

Thermodynamic vs. Kinetic Control

  • Thermodynamic Control: A reaction is thermodynamically favored (ΔG < 0).
  • Kinetic Control: A reaction may be thermodynamically favored but proceeds at an immeasurably slow rate due to a very high activation energy.

Free Energy and Equilibrium

  • Relationship between Gibbs Free Energy and the equilibrium constant (K):

    • ΔG = -RT \ln{K}
    • Where:
      • R = Universal gas constant (8.314 J/mol·K)
      • T = Temperature in Kelvin
      • K = Equilibrium constant

  • Importance of K value:

    • Small K value (K << 1): Not thermodynamically favored.
    • Larger K value (K >> 1): Thermodynamically favored.

Free Energy of Dissolution

  • For an ionic compound dissolving in water:
    • XY(s) → X^+(aq) + Y^-(aq)
  • If the compound dissolves freely, the ΔG for its dissolution will be a negative number.
  • If ΔG is a positive number, it will not dissolve freely.
  • If the ΔH of dissolution is exothermic, it will tend to be favored.
  • ΔG = ΔH - TΔS
    • ΔH is positive for endothermic processes.
    • T (in Kelvin) is always positive.
  • An endothermic dissolution can occur if its entropy increases enough to counteract its decreasing enthalpy.
  • If ΔS (increase in entropy) is positive enough, it can cause ΔG to be negative.

Coupled Reactions

  • Coupled reactions involve pairing a non-thermodynamically favored process with a thermodynamically favored one (adding external energy).
  • Example: Photosynthesis
  • Thermodynamic Coupling: Coupling reactions to achieve an overall favorable ΔG.
    • Cu2O(s) → 2Cu(s) + ½O2(g) ΔG = +140
    • Cu(s) + ½O_2(g) → CuO(s) ΔG = -144
    • Cu2O(s) + 2Cu(s) + O2(g) → 2CuO(s) ΔG = -4

Galvanic & Electrolytic Cells

  • Galvanic Cells:
    • Favored (spontaneous) redox reactions.
    • For a galvanic cell, E_{cell} must be positive.
    • Example:
      • Anode: Al → Al^{3+} + 3e^- E° = -1.66 V
      • Cathode: Ag^+ + e^- → Ag E° = +0.80 V
      • E{cell} = E{cathode} - E_{anode} = 0.80 - (-1.66) = 2.46 V
      • RED CAT (Reduction at Cathode), AN OX (Oxidation at Anode)

Cell Potential & Free Energy

  • Relationship between cell potential (E_{cell}) and Gibbs Free Energy (ΔG):
    • E_{cell} > 0: Thermodynamically favored.
    • E_{cell} < 0: Not thermodynamically favored.
    • ΔG = -nFE
      • n = number of moles of electrons transferred
      • F = Faraday's constant
      • E = Cell potential

Cell Potential at Standard Conditions

  • Nernst Equation: Describes cell potential under non-standard conditions.
    • E = E° - \frac{RT}{nF} \ln{Q}
      *R = gas constant
      *T = temperature
      *n = number of moles
      *F = Faraday's constant
      *Q = reaction quotient
  • As a galvanic cell runs:
    • The value of the whole term goes up, and potential decreases.
  • The concentration of products increases, and the concentration of reactants decreases.
    • Q Increases, so the potential decreases
  • E_{cell} at equilibrium = 0V (Dead Battery)

Electrolysis and Faraday's Law

  • Electrolysis: Driving a non-spontaneous reaction by adding an external current.
  • Faraday's Law: Relates the quantity of electric charge to the amount of substance produced or consumed in an electrolytic cell.
    • q = I * t
      • q = Quantity of electric charge (in Coulombs)
      • I = Current (in Amperes)
      • t = Time (in seconds)