Thermodynamics: Entropy, Gibbs & Phase

Learning Goal: Applying Chemical Thermodynamics: Entropy, Gibbs Free Energy, and Phase Equilibria in Multi-Component Systems. Students will build a solid progression from the foundational definitions of energy, enthalpy, and the First Law of Thermodynamics, up through statistical interpretations of entropy, the predictive power of Gibbs Free Energy, chemical equilibrium math, and multi-component phase thermodynamics.

• Prerequisites: College-level General Chemistry, basic multi-variable calculus (optional but helpful for partial derivatives), and algebra.
• Estimated Total Study Time: 16 Hours

Module 1: Foundations of Energy and the First Law

This module covers the core components of thermodynamic systems. You will learn to differentiate between open, closed, and isolated systems, comprehend the mechanical definitions of heat ($q$) and work ($w$), understand state functions vs. path functions, and analyze how energy is conserved through the mathematical statement of the First Law of Thermodynamics: $\Delta U = q + w$. Additionally, we introduce enthalpy ($H$) as a crucial state function for constant-pressure systems.

Recommended Videos

Enthalpy: Crash Course Chemistry #18

@crashcourse11:232899974

Enthalpy: Crash Course Chemistry #18

Enthalpy (ΔH) is a state function representing the heat transferred during a chemical reaction at constant pressure, calculated using Hess's Law which states that the total enthalpy change equals the sum of standard enthalpies of formation of products minus reactants; this allows chemists to predict heat production without direct measurement, as demonstrated by calculating the -1652 kJ released when 4 moles of iron react with oxygen to form iron(III) oxide in hand warmers.

@crashcourse · 11:23

• Why this video: This video introduces enthalpy in an intuitive and highly visual manner. It clarifies why enthalpy is considered a state function and demonstrates practical applications such as Hess's Law and calorimeter enthalpy calculations.
• Knowledge Checkpoint:
  • Differentiate between an endothermic process and an exothermic process in terms of system-surroundings heat exchange.
  • Explain why standard enthalpies of formation can be utilized to calculate the net enthalpy change of a reaction using Hess's Law.
  • State why enthalpy is classified as a state function while heat and work are path functions.

5.1 First Law of Thermodynamics and Enthalpy | General Chemistry

@ChadsPrep29:5971597

5.1 First Law of Thermodynamics and Enthalpy | General Chemistry

The First Law of Thermodynamics states that energy cannot be created or destroyed, expressed mathematically as ΔE = q + w, where ΔE is the change in internal energy, q is heat, and w is work; enthalpy (ΔH) equals heat (q) at constant pressure and is a state function, while heat (q) and work (w) are path functions; endothermic reactions absorb heat (ΔH > 0) causing surroundings to cool, while exothermic reactions release heat (ΔH < 0) causing surroundings to warm; phase changes include six proces

@ChadsPrep · 29:59

• Why this video: A deeper academic lecture on the mechanical derivation of the First Law ($\Delta E = q + w$ or $\Delta U = q + w$). It details the sign conventions of heat and work, expansion work ($w = -P\Delta V$), and the formal mathematical definition of enthalpy ($H = U + PV$).
• Knowledge Checkpoint:
  • Identify sign conventions: when is $q$ positive or negative? When is $w$ positive or negative from the system's perspective?
  • Derive why the enthalpy change $\Delta H$ is exactly equal to heat transferred at constant pressure ($q_p$).
  • Calculate work performed by an expanding gas against a constant external pressure.

Enthalpy | Thermodynamics

@NAJAMACADEMY10:55295804

Enthalpy | Thermodynamics

Enthalpy (H) is defined as the total heat content of a system, representing the sum of internal energy (U) and the product of pressure (P) and volume (V), expressed mathematically as ΔH = ΔU + PΔV. Unlike internal energy, which is the total energy of a system (kinetic plus potential energy), enthalpy specifically measures the heat absorbed or released during a process at constant pressure. Key properties include: enthalpy is a state function dependent only on initial and final states, not the pa

@NAJAMACADEMY · 10:55

• Why this video: This supplementary video offers a clear, highly simplified conceptual breakdown of enthalpy ($H = U + PV$) to solidify your grasp on the relationship between a system's internal energy and the energy required to "push back" the surroundings.
• Knowledge Checkpoint:
  • Explain the physical meaning of the $PV$ term in the enthalpy equation.
  • Define internal energy ($U$) as the sum of a system's microscopic kinetic and potential energies.

Module 2: Entropy and the Second Law

This module shifts focus from energy quantity (First Law) to energy dispersal and directionality (Second Law). You will explore the thermodynamic definition of entropy ($\Delta S = q_{\text{rev}}/T$), the Second Law's statement that the entropy of the universe always increases for spontaneous processes, and the microscopic statistical definition of entropy developed by Ludwig Boltzmann ($S = k_B \ln W$).

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Entropy: Embrace the Chaos! Crash Course Chemistry #20

@crashcourse13:401979427

Entropy: Embrace the Chaos! Crash Course Chemistry #20

Entropy (S) measures molecular randomness or disorder in a system, and the Second Law of Thermodynamics states that any spontaneous process increases the total entropy of the universe. Gibbs Free Energy (G) combines enthalpy change (ΔH) and entropy change (ΔS) through the equation ΔG = ΔH - TΔS, where T is temperature in Kelvin, to predict whether a reaction will occur spontaneously: if ΔG is negative, the reaction is spontaneous; if positive, the reverse reaction is spontaneous; and if zero, th

@crashcourse · 13:40

• Why this video: This video bridges Module 1 and Module 2 by introducing entropy ($S$) as a thermodynamic measure of randomness, outlining the Second Law of Thermodynamics, and showing how the universe's total entropy dictates spontaneity.
• Knowledge Checkpoint:
  • State the Second Law of Thermodynamics in terms of the system, surroundings, and universe.
  • Predict qualitative changes in entropy for phase changes (e.g., solid to liquid, liquid to gas) and chemical reactions that produce gas.

I wish I was taught Entropy this way!

@Mahesh_Shenoy31:58327122

I wish I was taught Entropy this way!

Entropy is fundamentally a measure of the number of microstates (specific microscopic arrangements) corresponding to a macrostate (observable state), not disorder; this statistical definition explains why irreversible processes like gas expansion and coffee-milk mixing occur naturally - because high-entropy macrostates have vastly more microstates and are therefore overwhelmingly probable, making entropy increase the statistical norm rather than a physical law.

@Mahesh_Shenoy · 31:58

• Why this video: An exceptionally thorough pedagogical deep-dive that deconstructs the common misconception of entropy as mere "disorder." Instead, it models entropy as the count of microscopic arrangements (microstates) that yield a specific macroscopic state.
• Knowledge Checkpoint:
  • Explain the difference between a macrostate and a microstate.
  • Describe how heat addition at lower temperatures creates a larger relative entropy increase compared to heat addition at higher temperatures.

The Statistical Definition of Entropy | OpenStax Chemistry 2e 16.2

@mevansthechemist17:4012689

The Statistical Definition of Entropy | OpenStax Chemistry 2e 16.2

Entropy (S) is statistically defined as S = k_B × ln(W), where k_B is Boltzmann's constant and W represents the number of distinct microstates corresponding to a particular macrostate; this equation shows that entropy increases when a system has more possible microstates, explaining why spontaneous processes like gas expansion occur naturally.

@mevansthechemist · 17:40

• Why this video: Focuses explicitly on Boltzmann's equation $S = k_B \ln W$. It features quantitative examples calculating microstates for particle distributions across containers, demonstrating why gas expansion is statistically inevitable.
• Knowledge Checkpoint:
  • State Boltzmann's statistical entropy equation and define the variables $S$, $k_B$, and $W$.
  • Calculate the change in entropy ($\Delta S$) when a system transitions from a macrostate with $W_1$ microstates to one with $W_2$ microstates ($\Delta S = k_B \ln(W_2 / W_1)$).

Module 3: Gibbs Free Energy and Spontaneity

In this module, you will learn to combine system enthalpy and system entropy into a single thermodynamic potential: Gibbs Free Energy ($G$). This enables us to predict chemical spontaneity at constant temperature and pressure without calculating the entropy change of the surroundings. We will study the master equation $\Delta G = \Delta H - T\Delta S$ and analyze how temperature dictates the feasibility of endothermic/exothermic and exentropic/endentropic processes.

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18.3 Gibbs Free Energy and the Relationship between Delta G, Delta H, & Delta S | General Chemistry

@ChadsPrep32:1073274

18.3 Gibbs Free Energy and the Relationship between Delta G, Delta H, & Delta S | General Chemistry

Gibbs free energy (ΔG) determines whether a chemical reaction is spontaneous under given conditions, calculated by the equation ΔG = ΔH - TΔS, where ΔH is the enthalpy change, T is the absolute temperature in Kelvin, and ΔS is the entropy change; when ΔG is negative, the reaction is spontaneous; when ΔG equals zero, the system is at equilibrium; and when ΔG is positive, the reaction is non-spontaneous. The spontaneity of a reaction depends on the signs of ΔH and ΔS: if both are negative, the rea

@ChadsPrep · 32:10

• Why this video: This video offers a clear, highly quantitative guide to calculating Gibbs Free Energy and analyzing its temperature dependence. It details the four main thermodynamic combinations of $\Delta H$ and $\Delta S$ and identifies the transition temperature where spontaneity changes.
• Knowledge Checkpoint:
  • State the sign of $\Delta G$ for spontaneous, non-spontaneous, and equilibrium processes.
  • Determine the conditions under which a reaction is: (a) spontaneous at all temperatures, (b) non-spontaneous at all temperatures, (c) spontaneous only at low temperatures, (d) spontaneous only at high temperatures.
  • Calculate the crossover temperature ($T_{\text{eq}}$) at which a reaction shifts spontaneity, given standard values of $\Delta H$ and $\Delta S$.

16. Thermodynamics: Gibbs Free Energy and Entropy

@mitocw32:01185426

16. Thermodynamics: Gibbs Free Energy and Entropy

Gibbs free energy (ΔG) determines whether a chemical reaction will proceed spontaneously under constant temperature and pressure conditions; ΔG = ΔH - TΔS, where ΔH is the enthalpy change, T is the absolute temperature, and ΔS is the entropy change. A negative ΔG indicates a spontaneous reaction, while a positive ΔG indicates a non-spontaneous reaction, and ΔG = 0 indicates equilibrium. Entropy (ΔS) measures the disorder or randomness of a system, with solids having lower entropy than liquids an

@mitocw · 32:01

• Why this video: An MIT OpenCourseWare lecture that provides a rigorous physical chemistry derivation of Gibbs Free Energy starting from the Clausius Inequality and the Second Law of Thermodynamics. It bridges foundational physics with chemical thermodynamic parameters.
• Knowledge Checkpoint:
  • Explain how the definition of $\Delta G \le 0$ directly originates from the condition that $\Delta S_{\text{univ}} \ge 0$.
  • Describe what standard state means for thermodynamic quantities ($\Delta G^\circ$, $\Delta H^\circ$, $\Delta S^\circ$).

Module 4: Chemical Equilibrium and Free Energy

This module connects thermodynamics to real, reversible chemical systems. You will transition from standard state properties ($\Delta G^\circ$) to non-standard state conditions ($\Delta G$), deriving the mathematical relationship between the reaction quotient ($Q$) and the equilibrium constant ($K$). We will focus heavily on calculations using the equations $\Delta G = \Delta G^\circ + RT \ln Q$ and the standard-state equilibrium relationship $\Delta G^\circ = -RT \ln K$.

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Equilibrium | Physical Chemistry | JEE Advanced 2025 | Questions | JEE Chemistry | Ashish Shekhar

@Aakash_JEE4:11147030

Equilibrium | Physical Chemistry | JEE Advanced 2025 | Questions | JEE Chemistry | Ashish Shekhar

The reaction quotient Q predicts reaction direction: if Q < K, the reaction proceeds forward; if Q > K, it proceeds backward. Thermodynamically, at equilibrium ΔG = 0, and ΔG° = -RT ln K connects free energy to equilibrium. The van't Hoff equation ln(K2/K1) = -(ΔH°/R)(1/T2 - 1/T1) shows how temperature affects K—exothermic reactions decrease K with increasing temperature. Le Chatelier's principle states that systems shift to counteract disturbances: adding reactants shifts forward, adding produc

@Aakash_JEE · 4:11

• Why this video: This segment focuses heavily on the thermodynamic aspects of chemical equilibrium. It shows how the reaction quotient ($Q$) and equilibrium constant ($K$) map to $\Delta G$ and $\Delta G^\circ$, highlighting that $\Delta G = 0$ is the criteria for dynamic equilibrium.
• Knowledge Checkpoint:
  • Differentiate between $\Delta G$ (the instantaneous free energy change) and $\Delta G^\circ$ (the standard free energy change).
  • Write the equation linking standard free energy to the equilibrium constant ($\Delta G^\circ = -RT \ln K$) and perform calculations to solve for $K$.
  • Explain why $\Delta G$ must equal zero at dynamic equilibrium.

10 MCQs Practice | Chemical Equilibrium | JEE(mains) NEET 2018 | Can U Score 10/10?

@vedantuneet3:29102491

10 MCQs Practice | Chemical Equilibrium | JEE(mains) NEET 2018 | Can U Score 10/10?

ΔG° = -RT ln(K) relates standard Gibbs free energy to equilibrium constant. If ΔG° < 0, reaction is spontaneous forward (K > 1). If ΔG° > 0, reaction is non-spontaneous forward (K < 1). The actual Gibbs energy is ΔG = ΔG° + RT ln(Q). At equilibrium, ΔG = 0 and Q = K.

@vedantuneet · 3:29

• Why this video: Solves specific multiple-choice quantitative problems linking standard Gibbs Free Energy change ($\Delta G^\circ$) to the equilibrium constant ($K$). It provides practice with signs and values: when $\Delta G^\circ < 0$, $K > 1$; when $\Delta G^\circ > 0$, $K < 1$.
• Knowledge Checkpoint:
  • Given $\Delta G^\circ$, calculate the numerical value of $K$ at a specified temperature (using the correct value of the gas constant $R = 8.314\text{ J/mol}\cdot\text{K}$).
  • Explain how a negative standard free energy change dictates a product-favored equilibrium.

Le Chatelier's Principle Explained: Predict Equilibrium Shifts

@ProfessorDaveExplains4:091410659

Le Chatelier's Principle Explained: Predict Equilibrium Shifts

Le Chatelier's principle states that if a system at equilibrium is subjected to a stress, it will shift in a direction that relieves that stress; this principle applies to three main types of stresses: (1) concentration changes where adding reactants shifts equilibrium right and adding products shifts it left, (2) temperature changes where exothermic reactions treat heat as a product and endothermic reactions treat heat as a reactant, and (3) pressure/volume changes where the system shifts towar

@ProfessorDaveExplains · 4:09

• Why this video: A clear exposition of how systems at chemical equilibrium respond to external stresses. This video provides the qualitative framework necessary to understand how changing pressure, concentration, or temperature shifts a system, matching the thermodynamic changes in $Q$ and $K$.
• Knowledge Checkpoint:
  • Predict the direction of shift when reactants or products are added or removed using the relationship between $Q$ and $K$.
  • Explain how changing the temperature of an exothermic or endothermic system changes the value of $K$ itself.

Module 5: Phase Equilibria and Multi-Component Systems

This module introduces advanced physical chemistry concepts, applying thermodynamics to mixtures, multi-component systems, and phase equilibria. We will cover the chemical potential ($\mu$), which is defined as the partial molar Gibbs free energy. We will also examine Raoult's Law, partial molar properties, and how to interpret ternary and multicomponent phase diagrams.

• Self-Directed Study Note on Gaps: While the provided video pool has excellent introductory phase and chemical potential videos, we highly recommend reading standard physical chemistry textbook chapters (such as Atkins or McQuarrie) to supplement calculations of partial molar volume, Gibbs-Duhem derivations, and plotting ternary tie lines.

Recommended Videos

Chemical Potential and Introduction to Phase Equilibria

@fredrickmwazighe213236:06344

Chemical Potential and Introduction to Phase Equilibria

Chemical potential (μi) is defined as the partial derivative of Gibbs free energy with respect to the number of moles of component i, while keeping temperature, pressure, and the number of moles of all other components constant. The fundamental equation of chemical thermodynamics states that dG = VdP - SdT + Σ(μi dNi). Chemical potential is an intensive property that acts as a force driving chemical systems toward equilibrium. At equilibrium, the chemical potential of any substance must be equal

@fredrickmwazighe2132 · 36:06

• Why this video: Provides a mathematical and conceptual definition of chemical potential ($\mu_i$). It explains how chemical potential acts as the driving force for phase transitions and material transport across phases.
• Knowledge Checkpoint:
  • Write the mathematical definition of chemical potential ($\mu_i = \left(\frac{\partial G}{\partial n_i}\right)_{T, P, n_{j \ne i}}$).
  • Explain the criteria for phase equilibrium between two phases $\alpha$ and $\beta$ in terms of chemical potential ($\mu_i^\alpha = \mu_i^\beta$).

Thermodynamics (Part-7): Partial Molar Quantities | Gibbs-Duhem Equation | Chemical Potential

@AllBoutChemistry1:4686465

Thermodynamics (Part-7): Partial Molar Quantities | Gibbs-Duhem Equation | Chemical Potential

Among all partial molar quantities, the partial molar Gibbs free energy holds the most importance and has a specific name: chemical potential (μᵢ). It is represented by μᵢ for component i. While other partial molar quantities exist (partial molar internal energy, partial molar enthalpy, partial molar work function), they are also referred to as chemical potentials when expressed under appropriate conditions. For example, (∂U/∂nᵢ)ₛ,ᵥ,ⱼ≠ᵢ = μᵢ (chemical potential related to internal energy), and (

@AllBoutChemistry · 1:46

• Why this video: Outlines the concept of partial molar properties in mixtures. It highlights why the partial molar Gibbs Free Energy is given the distinct title of chemical potential and introduces the Gibbs-Duhem equation.
• Knowledge Checkpoint:
  • Explain why a thermodynamic property (like volume or free energy) of a mixture is not simply the sum of the properties of its pure, isolated components.
  • State the physical consequence of the Gibbs-Duhem equation regarding the interdependent changes of chemical potentials in a mixture.

Partial Molar Properties

@LearnChemE3:2745771

Partial Molar Properties

Partial molar properties are thermodynamic quantities assigned to individual components in a mixture, representing how the total property (volume, enthalpy, entropy, etc.) changes per mole of that component added while keeping temperature, pressure, and the number of moles of all other components constant; the total molar property of a mixture equals the sum of each component's mole fraction multiplied by its partial molar property, and these values depend on the mixture composition and are gene

@LearnChemE · 3:27

• Why this video: A clear and intuitive visualization of partial molar volume. Using water and ethanol mixtures, it shows how adding a mole of substance to a mixture changes the total property by a different increment than the pure component molar property.
• Knowledge Checkpoint:
  • Describe the physical experiment (e.g., mixing water and ethanol) that demonstrates why partial molar volume varies with mixture composition.
  • Write the equation for calculating the total property of a binary system from its partial molar components: $M_{\text{total}} = n_1 \bar{M}_1 + n_2 \bar{M}_2$.

Vapor Pressure | Raoult's Law | Solution Class 12

@NAJAMACADEMY24:27196117

Vapor Pressure | Raoult's Law | Solution Class 12

Raoult's Law states that the partial vapor pressure of a volatile component in a solution is directly proportional to its mole fraction in the solution, expressed as P₁ = P₁° × X₁, where P₁ is the partial vapor pressure of the component in the solution, P₁° is the vapor pressure of the pure component, and X₁ is its mole fraction; this law explains how the presence of a solute lowers the vapor pressure of a solvent, with the total vapor pressure of a solution being the sum of the partial pressure

@NAJAMACADEMY · 24:27

• Why this video: This lecture outlines vapor pressure, ideal solutions, and Raoult's Law. It builds the foundation for multi-component liquid-gas equilibrium.
• Knowledge Checkpoint:
  • State Raoult's Law mathematically ($P_i = X_i P_i^\circ$) and identify ideal vs. non-ideal solution behaviors.
  • Calculate the total vapor pressure of a binary liquid mixture using Raoult's Law and Dalton's Law of partial pressures.

Phase Diagram 4: Ternary Example

@kennethbefus3:0940564

Phase Diagram 4: Ternary Example

Ternary phase diagrams extend binary systems to three components by combining three binary diagrams (diopside-anorthite, anorthite-forsterite, diopside-forsterite). They provide a bird's-eye view of a triangular surface where temperature contours (cotectics) indicate crystallization points. The ternary eutectic is where all three cotectics converge, allowing three phases to crystallize simultaneously. This approach is more powerful than binary diagrams for complex natural systems like basaltic m

@kennethbefus · 3:09

• Why this video: This video serves as an introductory guide to ternary phase diagrams. It walks through reading compositions in a three-component triangle plot, which is critical for multi-component geological and material systems.
• Knowledge Checkpoint:
  • Locate and identify a single point on a triangular ternary plot, reading off the precise weight or mole percentages of all three components (adding up to 100%).
  • Explain how binary eutectic curves boundary lines on a ternary diagram outline different mineral crystallization zones.

Course Map

Key People Index

• Ludwig Boltzmann (1844–1906)
  • Context: Austrian physicist who established the statistical interpretation of thermodynamics. He connected macroscopic entropy ($S$) with the number of microstates ($W$), carving his famous formula ($S = k \ln W$) on his tombstone.
• Rudolf Clausius (1822–1888)
  • Context: German physicist who formulated the Second Law of Thermodynamics, introduced the term "entropy" in 1865, and proposed the fundamental definition based on heat exchange ($\Delta S = q/T$).
• Josiah Willard Gibbs (1839–1903)
  • Context: American scientist who unified chemical, physical, and electromagnetic processes into a coherent thermodynamic framework. He created the concepts of chemical potential and free energy, paving the way for chemical engineering.
• François-Marie Raoult (1830–1901)
  • Context: French chemist who formulated the vapor-pressure relationship of solutions (Raoult's Law), showing how solute concentration affects solvent chemical potential and vapor pressure.

Final Self-Assessment

Complete this comprehensive self-assessment to verify your mastery over physical chemical thermodynamics:

• Explain the difference between enthalpy ($H$) and internal energy ($U$), and calculate change in internal energy ($\Delta U$) using heat and work parameters.
• Statistically calculate system entropy change when a partition is removed and a gas doubles its volume, using $S = k_B \ln W$.
• Differentiate between the thermodynamic entropy definition ($\Delta S = q_{\text{rev}}/T$) and statistical entropy definition ($S = - \sum p_i \ln p_i$).
• Determine the spontaneity of any chemical reaction by calculating its Gibbs Free Energy change ($\Delta G = \Delta H - T\Delta S$) at various temperatures.
• Mathematically derive the relation $\Delta G^\circ = -RT \ln K$ starting from the general non-standard equation $\Delta G = \Delta G^\circ + RT \ln Q$ at equilibrium conditions.
• Calculate the final equilibrium constant ($K$) for a given reaction at $298\text{ K}$ and $400\text{ K}$ given standard enthalpies of formation ($\Delta H_f^\circ$) and standard absolute entropies ($S^\circ$).
• Define chemical potential ($\mu$) as a partial molar derivative and explain why chemical potentials must equalize across boundaries at phase equilibrium.
• State the physical and mathematical significance of the Gibbs-Duhem equation for multi-component systems.
• Correctly read and extract binary and ternary composition values from a three-component phase diagram.
• Use Raoult's Law to calculate both liquid phase mole fractions ($X_i$) and vapor phase mole fractions ($Y_i$) for an ideal binary solution.