Thermodynamics: Entropy, Spontaneity, and Gibbs Free Energy

Comprehensive vocabulary flashcards covering chemical thermodynamics, entropy, the First and Second Laws of Thermodynamics, standard molar entropies, and the temperature-dependent spontaneity criteria of Gibbs free energy.

Spontaneous Process

A physical or chemical change that occurs naturally on its own without requiring continuous input of energy or external intervention.

Spontaneity vs. Reaction Rate

The thermodynamic property determining whether a reaction can proceed on its own; spontaneous is not synonymous with fast, as a spontaneous reaction may occur very slowly if it has a high activation energy ($E_a$), such as the rusting of iron.

Catalyst Effect on Spontaneity

A catalyst increases reaction rate by lowering the activation energy barrier, but it does not change the free energy change ($\Delta G$), enthalpy ($\Delta H$), or entropy ($\Delta S$), and thus has no effect on reaction spontaneity.

Entropy ($S$)

A thermodynamic state function that serves as a measure of the molecular disorder, randomness, or distribution of energy within a system.

Translational Motion

The movement of an entire molecule through space from one coordinate to another.

Vibrational Motion

The periodic movement of bonded atoms within a molecule toward and away from each other along bond axes, or changes in bond angles.

Rotational Motion

The spinning of a molecule around an internal axis in space.

Modes of Molecular Motion

The three microscopic forms of motion—translational motion, vibrational motion, and rotational motion—by which molecules store kinetic energy and contribute to system entropy.

Temperature Dependence of Entropy

An increase in temperature increases a substance's entropy because higher thermal energy produces higher molecular speeds, a broader distribution of individual kinetic energies, and greater randomness.

Standard Molar Entropy ($S^\circ$)

The absolute entropy of $1\,\text{mol}$ of a pure substance at a standard state of $1\,\text{atm}$ and $25\,^\circ\text{C}$, expressed in units of $J\,mol^{-1}\,K^{-1}$.

Entropy and Phase Changes

The abrupt, discontinuous increases in entropy that occur at constant temperature during melting and boiling as a solid transitions into a liquid and subsequently into a gas, resulting from sharp jumps in molecular randomness and freedom of motion.

Allotropic Entropy of Diamond vs. Graphite

Graphite possesses a higher standard molar entropy ($S^\circ = 5.69\,J\,mol^{-1}\,K^{-1}$) than diamond ($S^\circ = 2.4\,J\,mol^{-1}\,K^{-1}$) because diamond's rigid, three-dimensional tetrahedral covalent lattice severely restricts atomic vibrations compared to graphite's loosely stacked sheets.

Standard Entropy of Reaction ($\Delta S^\circ_{\text{rxn}}$) Formula

The standard entropy change of a chemical transformation, calculated from standard molar entropies as $\Delta S^\circ_{\text{rxn}} = \sum c\,S^\circ(\text{products}) - \sum a\,S^\circ(\text{reactants})$.

First Law of Thermodynamics

The principle of conservation of energy, which dictates that energy cannot be created or destroyed, only transferred or transformed from one form to another.

Second Law of Thermodynamics

The law stating that for any spontaneous process, the total entropy of the system and its surroundings always increases: $\Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0$.

Entropy Change of the Surroundings ($\Delta S_{\text{surroundings}}$) Formula

The entropy change in the surroundings resulting from heat exchange with the system at temperature $T$, defined as $\Delta S_{\text{surroundings}} = -\frac{\Delta H_{\text{system}}}{T}$.

Gibbs Free Energy ($G$)

A thermodynamic state function defined by the equation $\Delta G = \Delta H - T\Delta S$ that determines the spontaneity of a process under constant temperature and pressure by considering only the system.

Spontaneity Criteria for $\Delta G$

A process at constant temperature and pressure is spontaneous when $\Delta G < 0$, at dynamic equilibrium when $\Delta G = 0$, and nonspontaneous when $\Delta G > 0$.

"Free" Energy

The maximum portion of a system's total energy change ($\Delta G$) that is available to do useful work, with any remaining energy released as heat to warm the surroundings.

Crossover Temperature

The specific temperature at which a process reaches dynamic equilibrium ($\Delta G = 0$) and transitions between spontaneous and nonspontaneous behavior, calculated as $T = \frac{\Delta H}{\Delta S}$.

Spontaneity of Exothermic Reactions with Entropy Increase ($-\Delta H$, $+\Delta S$)

A condition where enthalpy is negative and entropy is positive, ensuring $\Delta G < 0$ and making the reaction spontaneous at all temperatures.

Spontaneity of Endothermic Reactions with Entropy Decrease ($+\Delta H$, $-\Delta S$)

A condition where enthalpy is positive and entropy is negative, ensuring $\Delta G > 0$ and making the reaction nonspontaneous at all temperatures.

Spontaneity of Endothermic Reactions with Entropy Increase ($+\Delta H$, $+\Delta S$)

A condition (such as the sublimation of dry ice) where the process is nonspontaneous at low temperatures and becomes spontaneous only at high temperatures when $T > \frac{\Delta H}{\Delta S}$.

Spontaneity of Exothermic Reactions with Entropy Decrease ($-\Delta H$, $-\Delta S$)

A condition (such as the freezing of water) where the process is nonspontaneous at high temperatures and becomes spontaneous only at low temperatures when $T < \frac{\Delta H}{\Delta S}$.

Standard Free Energy of Formation ($\Delta G^\circ_f$)

The free energy change that occurs when $1\,\text{mol}$ of a compound is formed from its constituent elements in their standard states at $1\,\text{atm}$ and $25\,^\circ\text{C}$.

Standard State Conditions

Thermodynamic reference conditions specified as pure solids, pure liquids, gases at a partial pressure of $1\,\text{atm}$, solutes at a concentration of $1\,\text{M}$, and typically a temperature of $25\,^\circ\text{C}$ ($298.15\,\text{K}$).

Non-Standard Free Energy Equation

The relationship used to calculate free energy changes under non-standard conditions: $\Delta G_{\text{rxn}} = \Delta G^\circ_{\text{rxn}} + RT\ln(Q)$, where $R = 8.314\,J\,mol^{-1}\,K^{-1}$ and $Q$ is the reaction quotient.

Equilibrium Free Energy Relationship ($\Delta G^\circ_{\text{rxn}} = -RT\ln(K)$)

The equation derived at equilibrium where $\Delta G_{\text{rxn}} = 0$ and $Q = K$, directly relating a reaction's standard free energy change to its equilibrium constant.

Free Energy Minimum at Equilibrium

The thermodynamic principle that any chemical system out of equilibrium will proceed spontaneously in whichever direction minimizes its total free energy until it reaches the energy minimum where $\Delta G = 0$ and dynamic equilibrium is established.

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Polar Covalent Bonds

are formed when two atoms with different electronegativities share electrons unequally, resulting in a partial positive charge on one atom and a partial negative charge on the other. (exhibit electronegativity difference of 0.5 or greater)

Covalent bonds

are formed when two atoms share electron pairs, which can be either single, double, or triple bonds, depending on the number of shared electron pairs. (exhibit an electronegativity difference of less than 0.5)

Ionic Bonds

A bond between metal and nonmetals, donating of electrons.