Chapter 18: Thermodynamics – Practice and Study Guide

Chapter 18: Thermodynamics

Introduction to Thermodynamics

Thermodynamics is the study of energy changes, particularly the exchange of heat and work, that accompany chemical and physical processes. It helps predict whether a reaction will occur spontaneously and the direction in which it will proceed.

• System: The part of the universe under study (e.g., a chemical reaction).

• Surroundings: Everything outside the system.

• State Functions: Properties that depend only on the state of the system (e.g., enthalpy, entropy, free energy).

Entropy (S)

Entropy is a measure of the disorder or randomness of a system. It is a key concept in predicting the spontaneity of processes.

• Increase in Entropy (ΔS > 0): Occurs when a system becomes more disordered (e.g., solid to liquid, liquid to gas, more moles of gas produced).

• Decrease in Entropy (ΔS < 0): Occurs when a system becomes more ordered (e.g., gas to liquid, liquid to solid, fewer moles of gas produced).

Example: The phase transition from a gas to a liquid results in a decrease in entropy.

Enthalpy (H)

Enthalpy is the heat content of a system at constant pressure. The change in enthalpy (ΔH) indicates whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).

• Exothermic Reaction (ΔH < 0): Releases heat to the surroundings.

• Endothermic Reaction (ΔH > 0): Absorbs heat from the surroundings.

Gibbs Free Energy (G)

Gibbs free energy combines enthalpy and entropy to predict the spontaneity of a process at constant temperature and pressure.

• The change in free energy is given by:

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

• Spontaneous Process: $\Delta G < 0$

• Nonspontaneous Process: $\Delta G > 0$

• Equilibrium: $\Delta G = 0$

Predicting Spontaneity

The signs of ΔH and ΔS determine the temperature dependence of spontaneity:

ΔH	ΔS	Spontaneity
−	+	Spontaneous at all temperatures
+	−	Nonspontaneous at all temperatures
−	−	Spontaneous at low temperatures
+	+	Spontaneous at high temperatures

Standard Entropy and Free Energy Changes

• Standard Molar Entropy (S°): The entropy of one mole of a substance in its standard state at 298 K.

• Standard Free Energy Change (ΔG°): The change in free energy when reactants in their standard states are converted to products in their standard states at 298 K.

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

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

Relationship Between ΔG° and Equilibrium Constant (K)

The standard free energy change is related to the equilibrium constant by:

$\Delta G^\circ = -RT \ln K$

• Where R = 8.314 J/(mol·K), T = temperature in Kelvin, and K = equilibrium constant.

• If $K > 1$, $\Delta G^\circ < 0$ (spontaneous as written).

• If $K < 1$, $\Delta G^\circ > 0$ (nonspontaneous as written).

Calculating ΔG Under Nonstandard Conditions

For reactions not at standard conditions, the free energy change is:

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

• Q is the reaction quotient, calculated using current concentrations or partial pressures.

Hess's Law for ΔG Calculations

Hess's Law states that the total enthalpy or free energy change for a reaction is the sum of the changes for individual steps.

• Apply the same principle to calculate $\Delta G^\circ_{\text{rxn}}$ using known values for related reactions.

Entropy Trends and Comparisons

• For elements in the same group, entropy increases with atomic number (e.g., He < Ne < Ar < Kr).

• For compounds, more atoms and greater molecular complexity generally mean higher entropy.

• For gases, more moles of gas mean higher entropy.

Sample Calculations

• Calculating ΔS° for a Reaction:

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

• Calculating ΔG° for a Reaction:

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

• Calculating K from ΔG°:

$K = e^{-\Delta G^\circ / RT}$

Key Concepts Table

Concept	Definition	Key Equation
Entropy (S)	Measure of disorder	—
Enthalpy (H)	Heat content at constant pressure	—
Gibbs Free Energy (G)	Predicts spontaneity	$\Delta G = \Delta H - T\Delta S$
Equilibrium Constant (K)	Extent of reaction at equilibrium	$\Delta G^\circ = -RT \ln K$

Example Problems

• Example 1: Calculate the entropy change for the reaction: $2Hg(l) + O_2(g) \rightarrow 2HgO(s)$ at 298 K, given $\Delta G^\circ = -180.8$ kJ, $P(Hg) = 0.025$ atm, $P(O_2) = 0.037$ atm.

• Example 2: Determine the temperature at which a reaction becomes nonspontaneous, given $\Delta H$ and $\Delta S$.

• Example 3: Place the noble gases in order of increasing entropy at 298 K: He, Ne, Ar, Kr.

Summary

• Spontaneity depends on both enthalpy and entropy changes.

• Entropy increases with disorder, number of particles, and phase changes from solid to liquid to gas.

• Gibbs free energy provides a criterion for spontaneity at constant temperature and pressure.

• Equilibrium constants and free energy changes are closely related.