Spontaneity, Entropy, and Free Energy

Flashcards based on lecture notes covering the principles of spontaneity, entropy, the laws of thermodynamics, and Gibbs free energy.

First Law of Thermodynamics

A statement of the law of conservation of energy: Energy can be neither created nor destroyed; the energy of the universe is constant.

Spontaneous Process

A process that occurs without outside intervention; thermodynamics can determine the direction of the process but says nothing about its rate.

Chemical Kinetics

The study of reaction rates which focuses on the pathway between reactants and products.

Thermodynamics

The study of energy and its transformations that considers only the initial and final states of a system, not the pathway between them.

Entropy ($S$)

A thermodynamic property reflecting the number of arrangements (microstates) available to a system; nature spontaneously proceeds toward states that have the highest probabilities of existing.

Microstate

Each specific configuration that gives a particular arrangement or state for a system.

Positional Probability

A type of probability that depends on the number of configurations in space (positional microstates) that yield a particular state; it increases from solid to liquid to gas.

Isothermal Process

A process in which the temperatures of the system and the surroundings remain constant at all times.

Free Expansion

An expansion where the external pressure ($P_{external}$) is zero, resulting in no heat flow and no work ($w=0$) being performed.

Reversible Process

A hypothetical process carried out so that the system is always at equilibrium; in a cyclic reversible process, both the system and surroundings are returned exactly to their original conditions.

Irreversible Process

Any real process in which, even when the system is recycled to its original state, the surroundings are changed in a permanent way.

Boltzmann's Constant ($k_B$)

The universal gas constant per molecule, defined as $R / N_A$, used in the formula $S = k_B \ln(\Omega)$.

Second Law of Thermodynamics

States that in any spontaneous process, there is always an increase in the entropy of the universe ($\Delta S_{univ} > 0$).

Third Law of Thermodynamics

States that the entropy of a perfect crystal at $0\,K$ is zero.

Free Energy ($G$)

A thermodynamic function defined as $G = H - TS$; at constant temperature and pressure, a process is spontaneous only if $\Delta G$ is negative.

Standard Free Energy Change ($\Delta G^\circ$)

The change in free energy that occurs if the reactants in their standard states are converted to the products in their standard states.

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

The change in free energy that accompanies the formation of $1\,mol$ of a substance from its constituent elements with all reactants and products in their standard states.

Reaction Quotient ($Q$)

A ratio that relates relative amounts of products and reactants in a reaction, used in the equation $\Delta G = \Delta G^\circ + RT \ln(Q)$.

Equilibrium Position

The point in a reaction where the system achieves the lowest possible free energy; at this point $\Delta G = 0$ and $Q = K$.

van’t Hoff equation

An equation relating the equilibrium constant and temperature: $\ln\left(\frac{K_2}{K_1}\right) = \frac{-\Delta H^\circ}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right)$.

Maximum Useful Work ($w_{max}$)

The total energy available to do useful work from a process at constant temperature and pressure, equal to the change in free energy ($\Delta G$).

Adiabatic Process

A process in which no energy as heat flows into or out of the system ($q = 0$).