Ch.18 – Free Energy and Thermodynamics: Study Notes

Free Energy and Thermodynamics

Spontaneous vs. Nonspontaneous Reactions

Spontaneity determines whether a reaction or process occurs naturally under a given set of conditions. It does not indicate the speed of the reaction, only whether it can occur without continuous external input.

• Spontaneous process: Occurs without ongoing outside intervention (e.g., combustion of gasoline, melting of ice at room temperature).

• Nonspontaneous process: Requires continuous energy input from the surroundings (e.g., electrolysis of water, photosynthesis).

Example: The combustion of glucose is spontaneous, while the synthesis of glucose from CO2 and H2O is nonspontaneous.

Entropy (S)

Entropy is a measure of molecular disorder or randomness in a system. It quantifies the number of possible arrangements (microstates) of a system's components.

• Second Law of Thermodynamics: The entropy of the universe increases for any spontaneous process.

• Factors affecting entropy:

  • Molecular degrees of freedom (ways in which a molecule can move)

  • Number of possible arrangements (microstates)

  • Number of moles of substances

Example: The entropy of a gas increases when it expands into a larger volume.

Table: Factors Affecting Entropy

Factor	Effect on Entropy
Increase in temperature	Increases entropy
Phase change (solid → liquid → gas)	Increases entropy
Increase in number of particles	Increases entropy
Mixing substances	Increases entropy

Standard Molar Entropy (So)

Standard molar entropy is the entropy content of one mole of a substance under standard conditions (1 atm, 25°C). Gases generally have higher standard molar entropy than liquids or solids due to greater molecular motion and disorder.

Change in Entropy: Physical and Chemical Changes

Entropy changes can result from physical changes (e.g., phase transitions) or chemical reactions. The change in entropy for a reaction is determined by the difference in the number of moles of gaseous products and reactants.

• Physical changes: Melting, vaporization, and sublimation increase entropy.

• Chemical changes: Reactions that produce more gas molecules generally increase entropy.

Entropy Calculations

Total Entropy Change

The total entropy change for a process is the sum of the entropy changes of the system and the surroundings:

$\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$

Entropy of the System

The entropy change of the system for a reaction is calculated as:

$\Delta S_{\text{rxn}} = \sum n S^\circ_{\text{products}} - \sum n S^\circ_{\text{reactants}}$

Entropy of the Surroundings

The entropy change of the surroundings is related to the enthalpy change of the system and the temperature:

$\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T}$

Entropy and Phase Changes

Entropy changes during phase transitions can be calculated using enthalpy changes and temperature:

$\Delta S_{\text{fus}} = \frac{\Delta H_{\text{fus}}}{T_{\text{fus}}}$ $\Delta S_{\text{vap}} = \frac{\Delta H_{\text{vap}}}{T_{\text{vap}}}$

Third Law of Thermodynamics

The Third Law states that the entropy of a perfect crystal at absolute zero (0 K) is zero. This provides a reference point for measuring absolute entropy values.

Boltzmann Equation

The Boltzmann equation relates entropy to the number of microstates (W):

$S = k \ln W$

where $k$ is the Boltzmann constant ($1.38 \times 10^{-23}$ J/K).

Gibbs Free Energy (G)

Gibbs Free Energy is a measure of the maximum reversible work that may be performed by a system at constant temperature and pressure. It determines the spontaneity of a process:

$\Delta G = \Delta H - T\Delta S$

• If $\Delta G < 0$, the process is spontaneous.

• If $\Delta G > 0$, the process is nonspontaneous.

• If $\Delta G = 0$, the system is at equilibrium.

Predicting Spontaneity

The signs of $\Delta H$ (enthalpy change) and $\Delta S$ (entropy change) can be used to predict the spontaneity of a reaction at a given temperature.

Table: Spontaneity Based on $\Delta H$ and $\Delta S$

$\Delta H$	$\Delta S$	Spontaneity
-	+	Always spontaneous
+	-	Never spontaneous
-	-	Spontaneous at low T
+	+	Spontaneous at high T

Gibbs Free Energy Calculations

To calculate the Gibbs free energy change for a reaction:

$\Delta G = \sum n \Delta G^\circ_{\text{f, products}} - \sum n \Delta G^\circ_{\text{f, reactants}}$

Alternatively, use $\Delta H$ and $\Delta S$ values:

$\Delta G = \Delta H - T\Delta S$

Gibbs Free Energy and Equilibrium

The relationship between Gibbs free energy and the equilibrium constant ($K$) is given by:

$\Delta G = -RT \ln K$

where $R$ is the gas constant (8.314 J/mol·K) and $T$ is the temperature in Kelvin.

For non-standard conditions, the reaction quotient ($Q$) is used:

$\Delta G = \Delta G^\circ + RT \ln Q$

Summary Table: Key Thermodynamic Equations

Equation	Description
$\Delta S_{\text{univ}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$	Total entropy change
$\Delta S_{\text{rxn}} = \sum n S^\circ_{\text{products}} - \sum n S^\circ_{\text{reactants}}$	Entropy change of reaction
$\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T}$	Entropy change of surroundings
$\Delta G = \Delta H - T\Delta S$	Gibbs free energy change
$\Delta G = -RT \ln K$	Gibbs free energy and equilibrium
$S = k \ln W$	Boltzmann equation for entropy

Additional info: These notes are based on the standard curriculum for General Chemistry, focusing on the thermodynamic principles of spontaneity, entropy, and free energy, as well as their calculations and applications to chemical reactions and equilibrium.