Applications of Thermodynamics and Electrochemistry

Definition: Entropy describes the amount of disorder or randomness in a system.
Factors Increasing Entropy: * Temperature: Increasing temperature increases kinetic energy and disorder. * Phase Changes: Entropy increases significantly during state changes in the order: $\text{solid} \rightarrow \text{liquid} \rightarrow \text{gas}$ . * Complexity: Entropy increases as molecules become more complex with more modes of vibration. * Mixing: Pure substances generally have lower entropy than mixtures/solutions. * Volume/Moles: Entropy increases with an increased number of moles of gas or an increase in the volume occupied by a gas.

Third Law of Thermodynamics: Defines a perfect crystal at $0\,K$ as having an entropy value of zero.
Standard Molar Entropy ( $S^o$ ): Measured in $J\,mol^{-1}\,K^{-1}$ . It depends on temperature, structure, and number of particles.
Calculation: The change in entropy for a reaction is calculated as: $\Delta S^o = \sum S^o_{\text{products}} - \sum S^o_{\text{reactants}}$

The Gibbs Equation: A single value used to determine reaction spontaneity at a specific temperature: $\Delta G = \Delta H - T\Delta S$
Favorability Criteria: A reaction is thermodynamically favored (spontaneous) if \Delta G < 0.
Spontaneity Drivers: Reactions are more likely to be spontaneous if they are exothermic (\Delta H < 0) and involve an increase in entropy (\Delta S > 0).
Thermodynamic vs. Kinetic Control: Thermodynamics predicts if a reaction is feasible, but Reaction Kinetics determines the speed and mechanism. A favored reaction may be slow due to high activation energy.

Equilibrium Relationship: $\Delta G^o$ is related to the equilibrium constant ( $K$ ) by the equation: $\Delta G^o = -RT \ln(K)$
Non-Standard Conditions: Reaction quotient ( $Q$ ) is used to find $\Delta G$ under non-standard concentrations: $\Delta G_{\text{actual}} = \Delta G^o + RT \ln(Q)$
Dissolution: Solubility is predicted by \Delta G < 0. While dissolving often involves an endothermic enthalpy change (\Delta H > 0), the large increase in entropy (\Delta S > 0) often makes the process spontaneous.

Mechanism: A non-spontaneous reaction (\Delta G > 0) can be driven forward by coupling it with a highly spontaneous reaction such that the overall $\Delta G$ is negative.
Biological Example: The conversion of $ATP \rightarrow ADP$ ( $\Delta G^o = -31\,kJ\,mol^{-1}$ ) is often coupled with non-favored biological processes to ensure favorability.

Galvanic (Voltaic) Cells: Driven by spontaneous redox reactions (\Delta G < 0) to produce electricity (E^o_{\text{cell}} > 0).
Electrolytic Cells: Use external electrical energy to drive non-spontaneous redox reactions (\Delta G > 0).
Anode and Cathode: * Anode: Site of oxidation ( $A\text{N } O\text{X}$ ); electrons flow away from the anode. * Cathode: Site of reduction ( $R\text{ED } C\text{AT}$ ); electrons flow toward the cathode.
Salt Bridge: Essential for maintaining charge balance by allowing ions to move between compartments.

Standard Cell Potential: $E^o_{\text{cell}} = E^o_{\text{cathode}} - E^o_{\text{anode}}$ .
Calculating $\Delta G^o$ from ${E^o}$ : Specifically, $\Delta G^o = -nFE^o$ .
Constants: Faraday’s Constant ( $F$ ) is approximately $96,500\,C\,mol^{-1}$ of electrons.
Nernst Equation: Relates cell potential to concentration via $Q$ : $E_{\text{actual}} = E^o - \frac{RT}{nF} \ln(Q)$

Quantitative Electrolysis: The mass of product formed is proportional to the electricity transferred.
Charge/Current Equations: $q = I \times t$ (where $q = \text{charge in Coulombs}$ , $I = \text{current in Amperes}$ , and $t = \text{time in seconds}$ ).
Moles of Electrons: Calculated by dividing total charge by Faraday’s constant ( $n = \frac{q}{F}$ ). Stoichiometry from half-equations is then used to determine the mass or volume of the product.