Spontaneous Processes and Entropy

• Spontaneous processes occur without external intervention, with varying speeds, like iron rusting, gas expansion into a vacuum, and radioactive decay.
• Entropy (S) measures a system's randomness or disorder and is related to the probability of energy and matter dispersion; it is a state function measured in J/K or J/(mol·K).

Entropy on the Molecular Scale:

• Entropy (S) can be quantified using the equation S = k ln(W), where k is the Boltzmann constant (1.38 x 10^-23 J/K) and W is the number of microstates.
• A microstate is a specific configuration of molecular positions and energies within a system.

Predicting Entropy Changes:

• Entropy generally increases from solid to liquid to gas ($S_{solid} < S_{liquid} < S_{gas}$).
• Entropy increases when the number of gas molecules increases in a chemical reaction.
• Entropy usually increases with increasing temperature, because more energy is correlated to less organisation.
• For a spontaneous process, the change in the entropy of the universe ($\Delta S_{universe}$) is positive ($\Delta S_{universe} > 0$).
• A nonspontaneous process is indicated by $\Delta S_{universe} < 0$, and a system at equilibrium registers $\Delta S_{universe} = 0$

Entropy Changes in Chemical Reactions

• $\Delta S^\circ$ is the entropy change for a reaction under standard conditions (298 K and 1 atm).
• $S^\circ$ represents the standard molar entropy, which is always positive at 298 K and 1 atm.
• Calculating Standard Entropy Changes:*
• Calculate the standard entropy change using $\Delta S_{rxn}^\circ = \sum nS^\circ(\text{products}) - \sum mS^\circ(\text{reactants})$, where n and m are stoichiometric coefficients.

Free Energy

• Gibbs Free Energy (G) is a thermodynamic state function combining enthalpy and entropy to determine spontaneity.
• It is defined by the equation G = H - TS, where H is enthalpy, T is temperature in Kelvin, and S is entropy.

Free Energy Change

• ($\Delta G$) is calculated as (\Delta G = \Delta H - T\Delta S)
• Spontaneity at constant temp and pressure is indicated as follows:
  • (\Delta G < 0): spontaneous
  • (\Delta G > 0): nonspontaneous
  • (\Delta G = 0): at equilibrium
• Standard Free Energy Change ($\Delta G^\circ$):*
• The free energy change under standard conditions is denoted as $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$
• An alternative calculation is $\Delta G_{rxn}^\circ = \sum n\Delta G_f^\circ(\text{products}) - \sum m\Delta G_f^\circ(\text{reactants})$, using standard free energies of formation.

Free Energy and Equilibrium

• The relationship between free energy and equilibrium is given by $\Delta G = -RT\ln{K}$, where R is the ideal gas constant (8.314 J/(mol·K)), T is temperature in Kelvin, and K is the equilibrium constant.
• Under nonstandard conditions, $\Delta G = \Delta G^\circ + RT\ln{Q}$, where Q is the reaction quotient.

Spontaneity

Diagrams

• Diagram showing the change in entropy ((\Delta S)) from solid to liquid to gas. As state changes from solid to liquid to gas, the entropy increases.
• The Standard Free-Energy Change diagram illustrates reactants at higher energy than products ($G_{products} < G_{reactants}$), indicating a spontaneous reaction ($\Delta G$ is negative).