5: Thermodynamics

Lecture 5 Announcements

• Lecture topics include spontaneous processes, the second law of thermodynamics, the molecular interpretation of entropy and the third law, entropy changes in chemical reactions, Gibbs free energy, and free energy and temperature.
• Problem Set 4 is due tomorrow before exercise 5 and uploaded on Moodle.
• Problem Set 5 is posted on Moodle; due before exercise 6 next week.
• Study center hours are Wednesdays, 6:00 PM - 8:00 PM in ETA F 5.
• Professor office hours are Thursdays, 5:00 PM - 6:00 PM in LEE P 210.

Lecture 6 Next Week

• Lecture topics will be the wave nature of light, quantized energy and photons, line spectra and the Bohr model, the wave behavior of matter, quantum mechanics and atomic orbitals, representation of orbitals, multi-electron atoms, electron configurations, electron configurations and the periodic table, effective nuclear charge, sizes of atoms and ions, ionization energy, and electron affinity.

Review

• Lecture 4 covered the first law of thermodynamics.
• The first law of thermodynamics includes the system and surroundings, internal energy (E), state functions (P, V, E), energy diagrams, endothermic and exothermic processes, enthalpy (H = E + PV), pressure-volume work, calorimetry, heat capacity, Hess’s law, heats of reaction, and heats of formation.

Heat and Work: Sign Convention

• Heat gained (q > 0), heat lost (q < 0).
• Work done on system (w > 0), work done by system (w < 0).
• Energy deposited into system (ΔE > 0)
• Energy withdrawn from system (ΔE < 0).

Enthalpy Diagram for Propane Combustion

• Diagram shows the enthalpy change for the combustion of propane.
• The reaction involves decomposition into elements, formation of 3 CO2, and formation of 4 H2O.

Thermodynamics II

• A spontaneous process occurs without any external assistance.
• Spontaneous processes seem to favor lowering their energy.
• At constant P, a process is spontaneous if ΔH < 0 (exothermic).
• Many spontaneous processes have ΔH > 0 (endothermic).
• Ice melting is an example of a spontaneous endothermic process.

Spontaneous versus Nonspontaneous Processes

• If a process is spontaneous, its reverse process is nonspontaneous.
• The experimental conditions, like temperature (T) and pressure (P), influence spontaneity.
• Spontaneity does not guarantee speed.

Reversible versus Irreversible Processes

• In a reversible process, no change occurs in surroundings when the process is reversed.
• In an irreversible process, the surroundings change when the process is reversed
• Hot objects transfer heat to cold objects is a spontaneous process
• Cold-to-hot heat transfer is nonspontaneous

Example: Heat Transfer

• Heat flows spontaneously from hot system to cold surroundings.
• For a reversible heat transfer, the system and surroundings' temperatures must differ infinitesimally.
• To reverse a heat flow, the difference in temperatures must change from positive to negative infinitesimally.

Another Example: Isothermal Expansion

• Expansion of ideal gas into a vacuum at constant temperature.
• To reverse the process, the surroundings must do work on the gas to compress it.

Real Processes

• All real processes are irreversible.
• All spontaneous processes are real processes.
• All spontaneous processes are irreversible.
• To return a system to its initial state after a spontaneous process, work is required which will lead to an increase of energy in system.
• During a spontaneous process, energy spreads out and becomes less useful for work.

Entropy, S

• Entropy (S) is a measure of the tendency for energy to spread which reduces a system's ability to do work
• Entropy is related to randomness or disorder in a system.
• Entropy is a state function
• For an isothermal process, ΔS = q_rev/T, where q_rev is the heat flow for a reversible process and T is absolute temperature.

ΔS for Phase Changes

• Melting and boiling are isothermal processes.
• For ice melting, the change in entropy of the system (ΔS_sys) is calculated.

Conservation of S

• When an ice cube melts, the total entropy of the universe increases.

2nd Law of Thermodynamics

• For a reversible process, ΔS_univ = 0.
• For an irreversible process, ΔS_univ > 0.
• The entropy of the universe increases during any spontaneous process.

Entropy: Molecular Theory of Gases

• Molecules move with a statistical distribution.
• Statistical thermodynamics connects macroscopic states to microscopic arrangements of molecules.
• A microstate is a particular arrangement of molecules.

Boltzmann's Equation

• S = k_B ln W.
• W = Number of microstates consistent with a specific macroscopic state
• k_B = Boltzmann constant.
• Entropy measures the number of microstates consistent with the macroscopic state of a system.
• The entropy of a system increases with the number of possible microstates.

Implications

• Entropy (S) and the number of possible molecular arrangements (W) increase with increases in volume(V), temperature(T), and the number of molecules present.
• Spontaneity occurs with changes like melting of solids and vaporization of liquids

Engineers: Entropy Warriors

• Engineers combat the 2nd Law of Thermodynamics by creating highly ordered materials.

3rd Law of Thermodynamics

• As a system cools, energy, degrees of freedom, and the number of microstates decrease.
• A pure, perfect crystalline solid substance at absolute zero (0 K) has zero entropy (S = 0).

Determining ΔS for Chemical Reactions

• ΔS for a chemical reaction is calculated using standard molar entropies (S°) for substances in their standard states.

Determining ΔS for Chemical Reactions?

• For the reaction N2(g) + 3H2(g) --> 2NH3(g), the value of ΔS is negative.

What Does This Mean for Spontaneity of a Reaction?

• To determine reaction spontaneity, analyses of both the system and surroundings are needed, because the entropy of the universe change is determined by two factors, the change in entropy of the reaction system and the change in entropy of the surroundings.

Gibbs Free Energy

• The Gibbs Free Energy (G) is related to enthalpy (H) and entropy (S) by the equation G = H − TS where T is temperature.
• The change in Gibbs free energy (ΔG) for a process is a criterion for spontaneity.
• A process is spontaneous if ΔG < 0; , process is non-spontaneous if ΔG > 0; and process is at equilibrium if ΔG = 0.

Standard Free Energy of Formation

• The standard free energy of formation (ΔG_f°) is the change in free energy during the formation of one mole of a substance from its elements under standard conditions (1 atm, 25 °C).

Summary of ΔH_rxn, ΔS°, and ΔG_rxn

• Formulas to calculate enthalpy(ΔH^o_rxn), entropy (ΔS^o), and Gibbs free energy (ΔG^o_rxn) for chemical reactions given standard molar enthalpy (ΔH^o_i) , standard molar entropy (S^o_i), and standard Gibbs free energy of formation (ΔG^o_i) from tabulated values

Importance of Temperature

• The spontaneity criteria ΔG < 0 depends on temperature.
• The spontaneity of a reaction can change depending on temperature based on factors like enthalpy and entropy changes.

What We Learned

• Summary of key topics from the lecture, Spontaneous/ Nonspontaneous processes, Reversible/Irreversible processes, Isothermal Processes, Entropy, 2nd Law of Thermodynamics, Boltzmann's equation, microstates, 3rd Law of Thermodynamics, Gibbs free energy, and standard free energies.

Test your knowledge on the concepts covered in Lecture 5 of Thermodynamics. This quiz includes questions about entropy, thermodynamic laws, and key definitions. Dive deeper into the principles that govern energy and its transformations.