Review Sheet for Physical Chemistry I 330, Lycoming College, Fall 2004, Dr. Mahler
Chapter One (all sections) States of gases; p, V, T, n and how to measure these; Ideal Gas law and laws in it (Boyle's, Charles', Dalton's, Avogadro's); Zeroth Law of Thermodynamics; Real gases - repulsive and attractive forces, compression factor; other equations of state (van der Waals, virial); critical point and constants (p, V, T); principle of corresponding states.
Chapter 1: Exercises 1.4, 6 (Boyle’s Law), 8 (Ideal Gas Law), 11 (Density of gases, IGL), 13 (Dalton’s Law of Partial Pressures, mole fractions, IGL), 16 (van der Waals, IGL), 19 (part a) (Molar Volume, IGL), 22 (Dalton’s, IGL), 25 (Principle of Corresponding States).
Chapter Twenty Four (section 1) Molecular motion in
gases Kinetic Theory of Gases; Maxwell distribution and types of molecular
speed; collision- diameter, -frequency, -cross section, and mean-free path.
Chapter 24: Exercises 24.4 (mean speed), 5 (mean speed, mean free path, collision frequency), 7 (mean free path). Note 8 and 9 are also good practice.
Chapter Two (all sections) Definitions basic to Thermodynamics (system, surroundings, open, closed, isolated, energy, work, heat, diathermic, adiabatic, exothermic, endothermic, etc.); First Law of Thermodynamics and internal energy (U); State functions; Expansion work, types (free, (isothermal) reversible, against constant pressure); Reversible vs. irreversible processes and equilibrium; Calorimetry and thermochemistry; Enthalpy (heat at constant pressure), relation to U and temperature dependence; Heat capacities at constant pressure and volume; adiabatic changes, work, P,V, T; standard enthalpy changes and Hess' law, thermochemical equations; Standard enthalpies of formation; stoichiometric numbers; Kirchoff's law and enthalpy temperature dependence.
Chapter 2: Exercises 2.6 (pV work), 7 (work and q, ΔU, ΔH), 8 (isochoric heat), 12 (pV work of a reaction), 13 (heat of transition), 16 (adiabatic rev. work), 23, 27 (adiabatic w, q, ΔU, ΔH, ΔT), 32 , 37, 39 (Hess’ Law, ΔH of formation), 45 (Born-Haber cycle – more thermochemical equations).
Chapter Three (all sections) State functions and exact differentials; partial derivatives and their properties; partial derivative properties for all systems and for ideal gases, and their relations (heat capacities CP and CV, internal pressure πT, expansion coefficient α, isothermal compressibility κT, (isothermal) Joule-Thomson coefficient μ and μT, and inversion temperature); temperature dependence of enthalpy.
Chapter 3: Exercises 3.9 (partial derivative proof), 12a&b (partial derivatives), 13, 18 (Joule-Thomson coefficient). Problems 3.12, 13, 14, 24 (more partial derivative proofs).
Chapter Four (all sections) Second Law of Thermodynamics; spontaneous change, order-disorder, and entropy; definition and properties of entropy; applications of entropy - adiabatic processes, phase transitions (Trouton's rule), Clausius inequality, expansion of ideal gas, variation with temperature); Carnot cycle, engines, refrigerators and their efficiencies; Third Law of Thermodynamics and Nernst Heat theorem; Third law entropy and standard reaction entropies; Low temperatures and magnetic ways to reach them; Helmholtz, A, and Gibbs, G, (Free) Energies; A and maximum work; G and maximum non-expansion work; standard Gibbs energy of formation and reaction.
Chapter 4: Exercises 4.4 (ΔS rev. heat transfer), 6 (ΔS ideal gas heated, const. P), 8 (rev. adiabatic compression), 10 (ΔS, q reversible or not?), 11 (ΔH & ΔS cooling, const P), 12 (ΔS isothermal expansion ideal gas), 14 (ΔS two liquids at diff. Ti), 16 (non-rev. adiabatic exp.), 18, 20 (ΔS and ΔG of rxn), 22 (ΔG from ΔS and ΔH), 24 (ΔS for simultaneous heating and compression of ideal gas), 26 (heat engine efficiency).
Chapter Five (all sections) The fundamental equation (combining First and Second laws); Maxwell equations and other partial derivative relationships - VAT of UGly SHiPs; G variation with P and T; Thermodynamic equation of state; Gibbs-Helmholtz equation; chemical potential; fugacity and pressure, real and ideal gases
Chapter 5: Exercises 5.4 (Maxwell & partials), 5 (ΔG isothermal ideal gas expansion), 7, 12 (ΔG pressure change, incompressible substance); Problems 5.5, 6 (deriving Maxwell, side relations), 7, 8 (partial proofs galore).
Chapter Six (all sections but 9b and 10b) One-component system phase diagrams and definitions (triple point, critical point, normal, etc.); interpreting phase diagrams (real examples); simple phase rule; equilibrium and chemical potential - phase transition boundaries; Clapeyron and Clausius-Clapeyron equations; Ehrenfest classifications; Surfaces – surface tension, bubbles, cavities and droplets, capillary action. Chapter 6: Exercises 6.4 (Clausius-Clapeyron), 5, 8 (Clapeyron), 11 (Clausius-Clapeyron), 12 (Clapeyron), try 14 (droplet pressure); Problem 6.3 (Clapeyron and Clausius-Clapeyron comparison).
Chapter Seven (all sections but 8) Mixtures; Partial molar quantities - volume and chemical potential; Mixing and its thermodynamics; Liquid solutions - ideal, ideal-dilute, Raoult's and Henry's Laws; Colligative properties (b.p. elevation, f.p. depression, osmotic pressure); activity - solvent and solute in terms of mole fraction and molality. Chapter 7: Exercises 7.4 (Partial Molar Volume), 6, 7 (Henry’s Law), 8, 10, 11 (colligative properties), 12, 13 (mixing), 15 (Henry’s Law), 21 (chemical potential and activity).
Chapter Eight (all sections) Multiple component phase diagrams and the Phase Rule (component, constituent, phase, variance - degree of freedom); Two component systems; Liquid-Vapor systems: pressure-composition diagrams (interpretation, tie line, isopleth, lever rule); temperature-composition diagrams (fractional distillation and theoretical plates, azeotropes, immiscible liquids); Liquid-liquid systems (miscibility, upper and lower critical temperatures); Liquid-Solid systems (eutectics, compounds, congruent and incongruent melting, immiscible solids); Chapter 8: Exercises 8.4, 6 (composition of liquid and vapor), 9 (components and constituents), 12, 13, 14, try 15, 16 (solid-liquid phase diagrams), 17 (liquid-vapor phase diagrams), 18, 19 (solid-liquid phase diagrams).
Chapter Nine (all sections) Spontaneous Chemical Reactions and Equilibrium; Extent of reaction and Gibbs energy minimum; Equilibrium constant, reaction Quotient (Q), relations to G; LeChatelier's Principle - response of K and systems at equilibrium to changes in composition, pressure and temperature (van't Hoff equation); Applications of Equilibria (brief acid-base chemistry). Chapter 9: Exercises 9.5 (ΔG from K), 7, 8, 10, 15, (degree of dissociation, ΔG from K, van’t Hoff), 16 (K from ΔG), 17, 18 (van’t Hoff, Le Chatelier), 19 (ΔG, ΔH, ΔS from K and van’t Hoff).
Chapter Ten (sections 2, 3, 4, 5) Ions and Electrochemistry; Properties of Ions in solution (mean ionic activity coefficient); Debye-Hückel limiting law; Electrochemical cells & their conventions and definitions; Half cells and half reactions; Electrochemical relations (Nernst equation, standard potentials). Cell potential and Gibbs Free Energy, Equilibrium constant, electrochemical series, solubility product Ksp.
Chapter 10: Exercises 10.5 (Ksp), 8 (ionic strength), 12 (mean ionic activity coeff.), 15 (Ksp), 18 (electrode & cell rxns), 19 (devise cells to get rxns), 20, 21 (E° calcs), 24 (Nernst, ΔG), 29 (Nernst), 32 (Ksp).
Chapter Nineteen (sections 1, 2, 3, 4, 5, 6) Statistical Thermodynamics; Configurations and weights, dominating configuration; Boltzmann distribution, β; the molecular partition function and its interpretation; Internal energy, U, and q and β; Entropy,S, and q; Canonical ensemble, configurations, weight, canonical distribution function, Q.
No assigned homework, discussion exercises helpful.
Chapter Twenty (sections 1 and 2) Thermodynamic functions in terms of statistical thermodynamics: internal energy, entropy, Helmholtz, pressure, enthalpy and Gibbs; General contributions to the molecular partition function: translational, rotational, vibrational, and electronic modes. No assigned homework, discussion exercises helpful.