Unit 9: Applications of Thermodynamics

Entropy (S)

A thermodynamic state function that measures energy dispersal; microscopically, higher S corresponds to more possible microstates.

State function

A property that depends only on the current state of the system, not the path taken to reach it (e.g., S, H, G).

Microstate

A specific microscopic arrangement of particles/energy consistent with a macroscopic state; more microstates means higher entropy.

Energy dispersal (entropy interpretation)

A way to understand entropy: S increases when energy is spread out among more particles, motions, or locations.

Second Law of Thermodynamics

A process is spontaneous if it increases the entropy of the universe: ΔS_univ > 0.

Entropy change of the universe (ΔS_univ)

The total entropy change: ΔSuniv = ΔSsys + ΔS_surr.

Spontaneous process (thermodynamic)

A process that is thermodynamically favored as written; occurs when ΔS_univ > 0 (or under constant T,P when ΔG < 0).

Thermodynamic equilibrium

Condition where there is no net driving force: ΔS_univ = 0 and (at constant T,P) ΔG = 0.

System

The part of the universe being studied (the reacting mixture/process of interest).

Surroundings

Everything outside the system that can exchange energy (and sometimes matter) with it.

Entropy of the surroundings formula

At constant pressure: ΔSsurr = −ΔHsys/T (T in kelvin).

Exothermic vs. endothermic effect on ΔS_surr

Exothermic (ΔHsys < 0) makes ΔSsurr > 0; endothermic (ΔHsys > 0) makes ΔSsurr < 0.

Phase change entropy trend

Entropy increases for solid→liquid and liquid→gas; decreases for gas→liquid and liquid→solid (gases have highest S).

Entropy of mixing

Mixing (especially gases) typically increases entropy because particles become more dispersed and microstates increase.

Moles of gas criterion for ΔS_sys

If moles of gaseous products > moles of gaseous reactants, ΔSsys tends to be positive; fewer moles of gas tends to give negative ΔSsys.

Standard molar entropy (S°)

Tabulated absolute entropy of a substance in its standard state (commonly at 298 K); usually positive and larger for gases than liquids/solids.

Third Law of Thermodynamics

The entropy of a perfect crystal at 0 K is zero; provides the reference for absolute entropies.

Standard-state conditions (thermodynamics)

Common reference conditions for tables: 1 M solutes, 1 atm gases, pure solids/liquids, typically at 298 K (25 °C).

Standard entropy change of reaction (ΔS°_rxn)

Calculated as products minus reactants: ΔS°_rxn = ΣνS°(products) − ΣνS°(reactants).

Stoichiometric coefficient (ν)

The multiplier in a balanced equation used when summing S°, ΔG_f°, etc.; coefficients must be included in calculations.

Entropy change of a reversible phase transition (ΔS_trans)

At the transition temperature for a reversible phase change: ΔStrans = ΔHtrans/T.

Hydration shell

An ordered arrangement of water molecules around ions; can decrease solvent entropy and make dissolution ΔS_sys less positive (or negative).

Gibbs free energy (G)

A state function that combines enthalpy and entropy effects; used to predict spontaneity at constant temperature and pressure.

Gibbs free energy equation

ΔG = ΔH − TΔS (T in kelvin; unit consistency required, often converting J↔kJ).

ΔG criterion for spontaneity (constant T,P)

ΔG < 0 spontaneous; ΔG = 0 equilibrium; ΔG > 0 nonspontaneous as written.

Temperature dependence (ΔH/ΔS sign analysis)

Spontaneity can depend on T because the entropy term is TΔS; changing T can change the sign of ΔG.

Thermodynamic favorability vs. reaction rate

A negative ΔG indicates products are favored, but it does not imply the reaction is fast (rate depends on kinetics).

Activation energy (E_a)

The energy barrier that must be overcome for a reaction to proceed; controls reaction rate.

Catalyst

Provides an alternative pathway with lower activation energy; does not change ΔG, ΔH, ΔS, or the equilibrium constant K.

Thermodynamic product

The most stable (lowest G) product; dominates at equilibrium if products can interconvert and equilibrium is reached.

Kinetic product

The product formed fastest (lowest activation energy pathway), even if it is not the most stable product.

Metastable

Thermodynamically unstable but persists because conversion requires overcoming a large activation energy barrier (kinetically trapped).

Reaction quotient (Q)

A ratio of product to reactant activities (like K but for current, not necessarily equilibrium, conditions).

Nonstandard Gibbs free energy relation

ΔG = ΔG° + RT ln Q; reaction direction depends on Q relative to K.

Equilibrium constant (K)

The value of Q at equilibrium; indicates extent of reaction under given conditions.

Free energy–equilibrium relationship

ΔG° = −RT ln K (uses natural log); links thermodynamic driving force to equilibrium position.

Standard Gibbs free energy of formation (ΔG_f°)

Free energy change to form 1 mol of a compound from elements in standard states; equals 0 for elements in their standard states.

Electrochemical cell

A device that couples a redox reaction to electron flow through a circuit, converting chemical driving force into electrical work (or vice versa).

Galvanic (voltaic) cell

An electrochemical cell in which a spontaneous redox reaction produces electrical energy (E_cell > 0 under the conditions).

Electrolytic cell

An electrochemical cell in which an external power source drives a nonspontaneous redox reaction (requires electrical work input).

Oxidation

Loss of electrons (electrons appear as products in the half-reaction).

Reduction

Gain of electrons (electrons appear as reactants in the half-reaction).

Anode

The electrode where oxidation occurs (negative in galvanic cells, positive in electrolytic cells).

Cathode

The electrode where reduction occurs (positive in galvanic cells, negative in electrolytic cells).

Salt bridge

Completes the circuit and maintains electrical neutrality by allowing ions to migrate between half-cells during cell operation.

Standard reduction potential (E°_red)

Tabulated potential for a half-reaction written as a reduction under standard conditions; reversing a half-reaction flips the sign.

Standard cell potential (E°_cell)

Cell voltage under standard conditions, computed as E°cell = E°cathode − E°_anode (using reduction potentials).

Intensive property (electrode potential)

A property independent of amount; electrode potentials (volts) are not multiplied by stoichiometric coefficients when balancing electrons.

Faraday constant (F)

Charge per mole of electrons: F = 96485 C·mol⁻¹ e⁻.

Faraday’s law (charge–current–time)

Charge transferred is q = It; moles of electrons = q/F, then use half-reaction stoichiometry to find mass plated or gas produced.

Nernst equation

Relates nonstandard cell potential to composition: E = E° − (RT/nF) ln Q (at 298 K: E = E° − (0.0592/n) log Q).