Premed · Premed · General Chemistry 2
Lecture 11: Thermodynamics: Entropy
General Chemistry II
Learning Objectives
By the end of this lecture, students will be able to:
- Distinguish between spontaneous and nonspontaneous processes
- Define entropy and relate it to the number of microstates
- State and apply the second and third laws of thermodynamics
- Predict the sign of entropy change for various physical and chemical processes
- Calculate standard entropy changes for reactions using standard molar entropies
- Explain the relationship between entropy and the direction of spontaneous change
Lecture Content
I. Spontaneous Processes
A spontaneous process is one that occurs without ongoing outside intervention, although it may require an initial input of energy to get started. A crucial point is that spontaneity says nothing about speed: a spontaneous process can be either fast or slow. The conversion of diamond to graphite is thermodynamically spontaneous but proceeds at an immeasurably slow rate under normal conditions. The combustion of gasoline, once ignited, is both spontaneous and fast. A nonspontaneous process, by contrast, requires a continuous input of energy to proceed. The reverse of any spontaneous process is necessarily nonspontaneous.
Neither enthalpy alone nor entropy alone determines whether a process is spontaneous. While many spontaneous processes are exothermic, some are endothermic, such as the melting of ice above 0 degrees C. A complete account of spontaneity requires considering both the energy change and the change in disorder.
II. Entropy: A Measure of Disorder
Entropy (S) is a thermodynamic quantity that describes the number of ways energy can be distributed among the particles and energy levels of a system. The statistical definition is given by Boltzmann's equation: S = k_B * ln(W), where k_B is the Boltzmann constant (1.38 x 10^-23 J/K) and W is the number of microstates, meaning the number of distinguishable arrangements of particles and energy. A system with more accessible microstates has higher entropy and greater disorder.
Entropy is a state function, so Delta S depends only on the initial and final states, not on the path taken between them. The standard unit of entropy is J/(mol*K), and it is worth noting that entropy is expressed in joules, not kilojoules, which becomes important when combining entropy and enthalpy values in calculations.
III. The Second Law of Thermodynamics
The second law of thermodynamics provides the fundamental criterion for spontaneity. It states that the total entropy of the universe increases for any spontaneous process: Delta S_universe = Delta S_system + Delta S_surroundings > 0 for a spontaneous process, Delta S_universe = 0 for a reversible process at equilibrium, and Delta S_universe < 0 for a nonspontaneous process (indicating that the reverse direction is spontaneous). The entropy of the universe is always increasing, and this principle explains why heat flows spontaneously from hot objects to cold ones: such flow increases the total entropy of the universe.
IV. The Third Law of Thermodynamics
The third law of thermodynamics states that the entropy of a perfect crystalline substance at absolute zero (0 K) is exactly zero: S(0 K) = 0. This provides an absolute reference point for entropy, unlike enthalpy, for which only relative values (changes) can be measured. As temperature increases from 0 K, entropy rises because more microstates become thermally accessible.
The standard molar entropy (S^0) is the absolute entropy of one mole of a substance at 1 atm and 25 degrees C. Because the third law establishes zero as the baseline, S^0 values are always positive (except for a perfect crystal at 0 K). This contrasts sharply with standard enthalpies of formation and standard free energies of formation, which can be negative, zero, or positive.
<image>A graph showing the standard molar entropy (S^0) of a substance (e.g., water) as a function of temperature from 0 K to 400 K. The curve starts at S = 0 at 0 K and increases. Discontinuous jumps (vertical rises) occur at phase transition temperatures: a jump at the melting point (labeled "Delta S_fusion") and a larger jump at the boiling point (labeled "Delta S_vaporization"). Between transitions, the curve rises smoothly. The solid, liquid, and gas regions are labeled. The vaporization jump is notably larger than the fusion jump, reflecting the much greater increase in disorder when going from liquid to gas.</image>
V. Predicting the Sign of Delta S
Several general guidelines help predict whether the entropy change for a process is positive or negative. Entropy increases (Delta S > 0) during phase transitions from solid to liquid to gas, because S_gas >> S_liquid > S_solid. Vaporization produces a larger entropy change than fusion. Dissolving a solid or liquid in a solvent usually increases entropy. Reactions that increase the number of moles of gas have positive Delta S. Increasing the temperature, expanding the volume of a gas, or mixing substances all increase entropy.
Conversely, entropy decreases (Delta S < 0) for the reverse processes: gas to liquid to solid transitions, decreases in the number of moles of gas, and precipitation from solution. Several molecular factors also influence the magnitude of S^0. Heavier molecules have more closely spaced energy levels and therefore more accessible microstates. More complex molecules with more atoms possess more vibrational modes and higher entropy. Among allotropes, rigid structures like diamond have lower S^0 than layered structures like graphite.
VI. Calculating Standard Entropy Change (Delta S^0_rxn)
The standard entropy change for a reaction is calculated as Delta S^0_rxn = Sum(n S^0_products) - Sum(n S^0_reactants), where n represents the stoichiometric coefficients. Unlike standard enthalpies of formation, you use absolute S^0 values here, not "entropy of formation" values. Importantly, elements in their standard states have nonzero S^0 values.
For example, for the reaction 2H2(g) + O2(g) -> 2H2O(l), Delta S^0 = 2(69.9) - [2(130.7) + 205.2] = 139.8 - 466.6 = -326.8 J/(mol*K). The large negative value makes physical sense: three moles of gas on the reactant side become zero moles of gas on the product side, representing a huge decrease in disorder.
<image>A conceptual diagram showing three molecular-level snapshots to illustrate entropy changes. Panel A: A solid crystal lattice with molecules in fixed, ordered positions (labeled "Low entropy, S_solid, few microstates"). Panel B: A liquid with molecules close together but in random orientations and positions (labeled "Medium entropy, S_liquid, more microstates"). Panel C: A gas with molecules widely spaced and moving in random directions with varying speeds (labeled "High entropy, S_gas, many microstates"). Below each panel, a representative W (number of microstates) value is shown, increasing dramatically from A to C.</image>
VII. Entropy of the Surroundings
For a process occurring at constant temperature and pressure, the entropy change of the surroundings is given by Delta S_surroundings = -Delta H_system / T. Exothermic reactions (Delta H < 0) release heat into the surroundings, increasing the thermal motion of surrounding molecules and producing a positive Delta S_surr. Endothermic reactions (Delta H > 0) absorb heat from the surroundings, decreasing Delta S_surr.
The magnitude of this effect depends on temperature. At low temperatures, a given amount of heat has a greater impact on entropy than at high temperatures, which explains why endothermic processes such as melting become spontaneous only above a certain temperature. Combining the system and surroundings contributions yields Delta S_universe = Delta S_system + (-Delta H_system / T) > 0 for spontaneity. Rearranging this expression as -T Delta S_universe = Delta H_system - T Delta S_system < 0 leads directly to the concept of Gibbs free energy, which will be developed in the next lecture.
