George Mason University General Chemistry 212 Chapter 20 Thermodynamics Acknowledgements

1. George Mason University General Chemistry 212 Chapter 20 Thermodynamics Acknowledgements Course Text: Chemistry: the Molecular Nature of Matter and Change, 6thed, 2011, Martin S. Silberberg, McGraw-Hill The Chemistry 211/212 General Chemistry courses taught at George Mason are intended for those students enrolled in a science /engineering oriented curricula, with particular emphasis on chemistry, biochemistry, and biology The material on these slides is taken primarily from the course text but the instructor has modified, condensed, or otherwise reorganized selected material.Additional material from other sources may also be included. Interpretation of course material to clarify concepts and solutions to problems is the sole responsibility of this instructor.

2. Thermodynamics • Thermodynamics: Enthalpy, Entropy, Free Energy The Direction of Chemical Reactions • The First Law of Thermodynamics Conservation of Energy • Limitations of the First Law • The Sign of H and Spontaneous Change • Freedom of Motion and Disposal of Energy • The Second Law of Thermodynamics • Predicting Spontaneous Change • Entropy and the Number of Microstates • Entropy and the Second Law • The Third Law of thermodynamics • Standard Molar Entropies

3. Thermodynamics • Calculating the Change in Entropy of a Reaction • The Standard Entropy of Reaction • Entropy Changes in the Surroundings • Entropy Change and the Equilibrium State • Spontaneous Exothermic and Endothermic Reactions • Entropy, Free Energy, and Work • Free Energy Change (∆G) and Reaction Spontaneity • Standard Free Energy Changes • G and Work • Temperature and Reaction Spontaneity • Coupling of Reactions • Free Energy, Equilibrium, and Reaction Direction

4. Thermodynamics Enthalpy (∆H) Sum of Internal Energy (E) plus Product of Pressure & Volume (Endothermic vs. Exothermic) ( Hrxn = Hf prod - Hf react) (Constant Pressure) Entropy (S) Measure of system order/disorder & the number of ways energy can can be dispersed throughthe motion of its particles All real processes occur spontaneously in the direction that increases the Entropy of the universe (universe = system + surroundings) (At Equilibrium) Gibbs Free Energy (∆G) Difference between Enthalpy and the product of absolute temperature and the Entropy

5. Thermodynamics • Thermodynamics - study of relationships between heat and other forms of energy in chemical reactions • The direction and extent of chemical reactions can be predicted through thermodynamics (i.e., feasibility) • Chemical reactions are driven by heat(Enthalpy) and/or randomness (Entropy) • A measure of randomness (disorder) is Entropy(S) • An increase in disorder is spontaneous • Spontaneous reactions are moving toward equilibrium • Spontaneous reactions move in the direction where energy is lowered, and move to Q/K = 1 (equilibrium)

6. Thermodynamics • Thermodynamics is used to determine spontaneity(a process which occurs by itself); what natural forces determine the extent of a chemical reaction (i.e., Kc)? • For a reaction to be useful it must be spontaneous (i.e., goes to near completion, i.e., far to the right) • Spontaneity of a reaction depends on: • Enthalpy - heat flow in chemical reactions • Entropy - measure of the order or randomness of a system (Entropy units - J/ oK) • Entropy is a state function; S = Sfinal - Sinitial • Higher disorder equates to an increase in Entropy • Entropy has positional and thermal disorder

7. Thermodynamics First Law of Thermodynamics • The first law of Thermodynamics is a version of the law of Conservation of Energy, specialized for Thermodynamical systems • It is usually formulated by stating that the change in the Internal Energy(E)of a closed system is equal to the amount of Heat(q) supplied to the system, minus the amount of Work(W = -PV) performed by the system on its surroundings • The law of conservation of energy can be stated The Energy of an Isolated System is Constant

8. Thermodynamics • First Law of Thermodynamics • Conservation of Energy, E (or U in some texts) Any change in the energy of the system mustcorrespond to the interchange of “heat” (work) with an “External” surrounding • Total Internal Energy(E) - The sum of the kinetic and potential energies of the particles making up a substance • Kinetic Energy(Ek) - The energy associated with an object by virtue of its motion, Ek = ½mv2 (kgm2/s2) (joules) • Potential Energy (Ep) - The energy an object has by virtue of its position in a field of force, Ep = mgh (kg  m/s2m = kgm2/s2)

9. Thermodynamics • Work – The energy transferred is moved by a force, such as the expansion of a gas in an open system under constant pressure Pressure = kg/(ms2) Volume = m3 Work (W) = kg/(ms2)  m3 = kgm2/s2 = joules (J) • Internal Energy • The Internal Energy of a system, E, is precisely defined as the heat at constant pressure (qp)plus the work(w) done by the system:

10. Thermodynamics • Enthalpy is defined as the internal energy plus the product of the pressure and volume – work • The change in Enthalpyis the change in internal energy plus the product of constant pressure and the change in Volume Recall  (At Constant Pressure) • The change in Enthalpy equals the heat gained or lost (heat of reaction) at constant pressure – the entire change in “internal energy” (E), minus any expansion “work” done by the system (PV) would have negative sign

11. Thermodynamics • E – total internal energy; the sum of kinetic and potential energies in the system • q – heat flow between system and surroundings (-q indicates that heat is lost to surroundings) • w – work (-w indicates work is lost to surroundings) • H – Enthalpy – extensive property dependent on quantity of substance and represents the heat energy tied up in the chemical bonds (heat of reaction) • Useful Units in Energy expressions • 1 J (joule) = 1 kgm2/s2 • 1 Pa (pascal) = 1 kg/ms2 • 1 atm = 1.01325 x 105 Pa • 1 atm = 760 torr = 760 mm Hg

12. Exchanges of Heat and Workwith the Surroundings Pressure xVolume Work = expansion of volume due to forming a gas q<0 q>0 w>0 on system w<0 by system

13. Practice Problem Consider the combustion of Methane (CH4) in Oxygen CH4(g) + 2 O2(g)  CO2(g) + 2 H2O(l) The heat of reaction (q) at 25 oC and 1.00 atm is -890.2 kJ. What is E for the change indicated by the chemical equation at 1 atm? n = 3 mol converted to 1 mol = -2 mol @ 25 oC and 1 atm, 1 mol of gas = 24.5 L, thus V = -2(24.5) = -49 L  (1m3/1000 L) = -0.049 m3 E = q - PV E = -890.2 kJ – 1 atm x (-0.049 m3) E = -890.2 kJ – (1.01 x 105 Pa)(-0.049 m3) E = -890.2 kJ – (1.01 x 105 kg/ms2)(-0.049m3) E = -890.2 kJ + (4949 J x 1 kJ/1000 J) E = -890.2 kJ + 4.949 kJ = -885 kJ

14. Thermodynamics The 2nd Law of Thermodynamics The total Entropy of a system and its surroundingsalways increases for a “Spontaneous” process • Entropy – A thermodynamic quantity related to the number of ways the energy of a system can be dispersed through the motions of its particles • Entropy is a state function; S = Sf - Si • Higher disorder equates to an increase in Entropy • Entropy has positional and thermal disorder • The Entropy, S, is conserved for a reversible process • The disorder of the system and thermal surroundings must increase for a spontaneous process • A process occurs spontaneously in the direction that increases the Entropy of the universe

15. Thermodynamics • A spontaneous change, whether a chemical or physical change, or just a change in location is one that: • Occurs by itself under specified conditions • Occurs without a continuous input of energy from outside the system • In a non-spontaneous change, the surroundings must supply the system with a continuous input of energy • Under a given set of conditions, a spontaneous change in one direction is not spontaneous in the “other” direction A limitation of the 1st Law of Thermodynamics • Spontaneous does not equate to “Instantaneous”

16. Thermodynamics • Limitations of the 1st law of Thermodynamics • The 1st Law accounts for the energy involved in a chemical process (reaction) • The internal energy (E) of a system, the sum of the kinetic and potential energy of all its particles, changes when heat(q) and/or work(w= -PV) are gained or lost by the system • Energy not part of the system is part of the surroundings

17. Thermodynamics • The surroundings (sur) and the system (sys) together constitute the “Universe (univ)” • Heat and/or work gained by system is lost by surroundings • The “total” energy of the Universe is constant

18. Thermodynamics • The first Law, however, does not account for the “direction” of the change in energy Ex. The burning of gas in your car • Potential energy difference between chemical bonds in fuel mixture and those in exhaust is converted to kinetic energy to move the car • Some of the converted energy is released to the environmental surroundings as heat (q) • Energy (E) is converted from one form to another, but there is a “net” conservation of energy • 1st law does not explain why the exhaust gas does not convert back into gasoline and oxygen • 1st law does not account for the “direction” of a spontaneous change

19. Thermodynamics • Spontaneous Change and Change in Enthalpy (H) • It was originally proposed (19th Century) that the “sign” of the Enthalpy change (H) – the heat lost or gained at constant pressure (qp) – was the criterion of spontaneity • Exothermic processes (H < 0) were “spontaneous” • Endothermic processes (H > 0) were “nonspontaneous” • Ex. Combustion (burning) of Methane in Oxygen is “Spontaneous” and “Exothermic” (H < 0) When Methane burns in your furnace, heat is released

20. Thermodynamics • The sign of the change in Enthalpy (H), however, does not indicate spontaneity in all cases • An Exothermic process can occur spontaneously under certain conditions and the opposite Endothermic process can also occur spontaneously under other conditions Ex. Water freezes below 0oC and melts above 0oC Both changes are spontaneous Freezing is Exothermic Melting (& Evaporation) is Endothermic Most Water-Soluble Salts have a positive Hsoln yet they dissolve spontaneously The decomposition of N2O5 is Endothermic and spontaneous

21. Thermodynamics • Freedom of motion & energy dispersion • Endothermic processes result in moreparticles (atoms, ions, molecules) with more freedom of motion – Entropy increases • During an Endothermic phase change, “fewer” moles of reactant produce “more” moles or product • The energy of the particles is dispersed over more quantized energy levels

22. Thermodynamics • Endothermic Spontaneous Process Less freedom of particle motion  more freedom of motion Localized energy of motion  dispersed energy of motion Phase Change: Solid  Liquid  Gas Dissolving of Salt: Crystalline Solid + Liquid  Ions in Solution Chemical Change: Crystalline Solids  Gases + Ions in Solution • In thermodynamic terms, a change in the freedom of motion of particles in a system, that is, in the dispersal of their energy of motion, is a key factor determining the direction of a spontaneous process

23. Thermodynamics • Quantized Energy Levels • Electronic • Kinetic - vibrational, rotational, translational • Microstate • A single quantized state at any instant • The total energy of the system is dispersed throughout the microstate • New microstates are created when system conditions change • At a given set of conditions, each microstate has the same total energy as any other • A given microstate is just as likely to occur as any other microstate

24. Thermodynamics • Microstates vs Entropy (Positional Disorder) • Boltzmann Equation where k – Boltzmann Constant where R = Universal Gas Constant NA = Avogadro’s Number where W = No. of Microstates

25. Thermodynamics • The number of microstates (W) possible for a given number of particles (n) as the volume changes is a function of the nth power of 2:

26. Thermodynamics • Compute Ssys • When n becomes NA , i.e. 1 mole • The Boltzman constant “k = R/NA” has become “R” • A system with fewer microstates (smaller Wfinal) has lower Entropy (Lower S) • A system with more microstates (larger Wfinal) has higher Entropy (higher S)

27. Thermodynamics • Entropy change – Volume, Pressure, Concentration

28. Thermodynamics • Changes in Entropy • The change in Entropy of the system (Ssys) depends only on the difference between its final and initial values • (Ssys) > 0 when its value increases during a change Ex. Sublimation of dry ice to gaseous CO2 • (Ssys) < 0 when its value decreases during a change Ex. Condensation of Water

29. Thermodynamics • Entropy Changes based on Heat Changes • The 2nd Law of Thermodynamics states that the change in Entropy for a gas expanding into a vacuum is related to the heat absorbed (qrev) and the temperature (T) at which the exchange occurs • Qrev refers to a “Reversible” process where the expansion of the gas can be reversed by the application of pressure (work, PV) • The heat absorbed by the expanding gas increases the dispersal of energy in the system, increasing the Entropy • If the change in Entropy, Ssys, is greater than the heat absorbed divided by the absolute temperature, the process occurs spontaneously

30. Thermodynamics • Determination of the Direction of a Spontaneous Process Second Law Restated All real processes occur spontaneously in the direction that increases the Entropy of the universe (system + surroundings) • When changes in both the system and the surroundings occur, the universe must be considered • Some spontaneous processes end up with higher Entropy • Other spontaneous processes end up with lower Entropy

31. Thermodynamics • The Entropy change in the system or surroundings can be positive or negative • For a spontaneous process, the “sum” of the Entropy changes must be positive • If the Entropy of the system decreases, the Entropy of the surroundings must increase, making the net increase to the universe positive

32. Thermodynamics The 3rd Law of Thermodynamics • Entropy & Enthalpy are both “state” functions • Absolute Enthalpies cannot be determined, only changes i.e., No reference point • Absolute Entropy of a substance provides a reference point and can be determined • The Entropy of a system approaches a constant value as the temperature approaches zero • The Entropy of a perfect crystal at “absolute zero” is zero • Perfect Crystal – all particles perfectly aligned with no defects of any kind Ssys = 0 at 0oK

33. Thermodynamics • Entropy values for substances are compared to “standard” states • Standard States • Gases – 1 atmosphere (atm) • Concentrations – Molarity (M) • Solids – Pure Substance • Standard Molar Entropy • So (Units – J/molK @ 298oK) • Values available in Reference Tables (Appendix “B”)

34. Thermodynamics • Predicting Relative So Values of a System • Temperature Changes • So increases as temperature increases • Temperature increases as “heat” is absorbed (q > 0) • As temperature increases, the Kinetic Energies of gases, liquids, and solids increase and are dispersed over larger areas increasing the number of microstates available, which increases Entropy

35. Thermodynamics • At any T > 0o K, each particle moves about its lattice position • As temperature increases through the addition of “heat”, movement is greater • Total energy is increased giving particles greater freedom of movement • Energy is more dispersed • Entropy is increased

36. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Physical States and Phase Changes • So increases for a substance as it changes from a solid to a liquid to a gas • Heat must be absorbed (q>0) for a change in phase to occur • Increase in Entropy from liquid to gas is much larger than from solid to liquid Svapo >> Sfuso

37. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Dissolving a solid or liquid • Entropy of a dissolved solid or liquid is greater than the Entropy of the “pure” solute • As the crystals breakdown, the ions have increased freedom of movement • Particle energy is more dispersed into more “microstates” Entropy is increased • Entropy increase is “greater” for ionic solutes than “molecular” solutes – more particles are produced • The slight increase in Entropy for “molecular” solutes in solution arises from the separation of molecules from one another when mixed with the solvent

38. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Dissolving a Gas • Gases have considerable freedom of motion and highly dispersed energy in the gaseous state • Dissolving a gas in a solvent results in diminished freedom of motion Entropy is “Decreased” • Mixing (dissolving) a gas in another gas • Molecules separate and mix increasing microstates and dispersion of energy Entropy “Increases”

39. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Atomic Size • Multiple substances in a given phase will have different Entropies based on Atomic Size and Molecular Complexity • Down a “Periodic” group energy levels become “closer” together as the atoms get “Heavier” • No. of microstates and molar Entropy increase

40. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Molecular Complexity • Allotropes – Elements that occur in different forms have higher Entropy in the form that allows more freedom of motion Ex. Diamond vs Graphite Diamond bonds extend the 3 dimensions, allowing limited movement – lower Entropy Graphite bonds extend only within two-dimensional sheets, which move relatively easy to each other – higher Entropy

41. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Molecular Complexity (Con’t) • Compounds • Entropy increases as the number of atoms (or ions) in a formula unit of a molecule increases • The trend is based on types of movement and the number of microstates possible • NO (Nitrous Oxide) in the chart below can vibrate only toward and away from each other • The 3 atoms of the NO2 molecule have more virbrational motions

42. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Molecular Complexity (Con’t) • Compounds of large molecules • A long organic hydrocarbon chain can rotate and vibrate in more ways than a short chain • Entropy increase with “Chain Length” • A ring compound with the same molecular formula as a corresponding chain compoundhas lower Entropy because a ring structure inhibits freedom of motion cyclopentane (C5H10) vs pentene (C5H10) Scyclopentane < Spentene

43. Thermodynamics • Predicting Relative So Values of a System (Con’t) • Physical State vs Molecular Complexity When gases are compared to liquids: The effect of physical state (g, l, s) usually dominates that of molecular complexity, i.e., the No. atoms in a formula unit or chain length

44. Practice Problem Choose the member with the higher Entropy in each of the following pairs, and justify the choice • 1 mol of SO2(g) or 1 mol SO3(g) SO3 has more types of atoms in the same state, i.e., more types of motion available More Entropy • 1 mol CO2(s) or 1 mol CO2(g) Entropy increases in the sequence: s < l < g

45. Practice Problem • 3 mol of O2(g) or 2 mol of O3(g) The two samples contain the same number of oxygen atoms (6), but different numbers of molecules O3 is more complex, but the greater number of molecules of O2 dominates – more moles of particles produces more microstates

46. Practice Problem (Con’t) • 1 mol of KBr(s) or 1 mol KBr(aq) Both molecules have the same number of ions (2) Motion in a crystal is more restricted and energy is less dispersed KBr(aq) has higher Entropy • Sea Water at 2oC or at 23oC Entropy increases with increasing temperature Seawater at 23oC has higher Entropy • 1 mol CF4(g) or 1 mol CCl4(g) For similar compounds Entropy increases with increasing molar moss S(CF4)(g)< S(CCl4)(g)

47. Practice Problem • Predict the sign of S for each process: • Alcohol Evaporates ΔSsys positive, the process described is liquid alcohol becoming gaseous alcohol The gas molecules have greater Entropy than the liquid molecules • A solid explosive converts to a gas ΔSsys positive, the process described is a change from solid to gas, an increase in possible energy states for the system • Perfume vapors diffuse through a room ΔSsys positive, the perfume molecules have more possible locations in the larger volume of the room than inside the bottle A system that has more possible arrangements has greater Entropy

48. Practice Problem Without using Appendix B predict the sign of S for: 2K(s) + F2(g) → 2KF(s) ΔSsys negative – reaction involves a gaseous reactant and no gaseous products, so Entropy decreases The number of particles also decreases, indicating a decrease in Entropy NH3(g) + HBr(g) → NH4Br(s) ΔSsys negative – gaseous reactants form solid product and number of particles decreases, so Entropy decreases NaClO3(s) → Na+(aq) + ClO3- ΔSsys positive – when a solid salt dissolves in water, Entropy generally increases

49. Thermodynamics • Calculating Change in Entropy • Gases • The sign of the Standard Entropy of Reaction (Sorxn) of a reaction involving gases can often be predicted when the reaction involves a change in the number of moles that occurs and all the reactants and products are in their “standard” states • Gases have great freedom of motion and high molar Entropies • If the number of moles of gas increases, Sorxn is usually positive • If the number of moles of gas decreases, Sorxn is usually negative

50. Practice Problem Calculate Sorxn for the combustion of 1 mol of Propane at 25oC Calculate Sorxn , using values from Appendix B