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:
  • $NaNO<em>3(s) → Na^+(aq) + NO</em>3^-(aq)$ (ΔS > 0, entropy increases)
  • $2Mg(s) + O_2(g) → 2MgO(s)$ (ΔS < 0, entropy decreases)
  • $CO<em>2(g) + 2H</em>2(g) → CH_3OH(g)$ (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:
  • $ΔS° = ΣS°<em>{products} - ΣS°</em>{reactants}$

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.
  • $Cu<em>2O(s) → 2Cu(s) + ½O</em>2(g) ΔG = +140$
  • $Cu(s) + ½O_2(g) → CuO(s) ΔG = -144$
  • $Cu<em>2O(s) + 2Cu(s) + O</em>2(g) → 2CuO(s) ΔG = -4$

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: $Ag^+ + e^- → Ag E° = +0.80 V$
    • $E<em>{cell} = E</em>{cathode} - E_{anode} = 0.80 - (-1.66) = 2.46 V$
    • 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)