Thermodynamics Entropy, Energy and equilibrium

1. ThermodynamicsEntropy, Energy and equilibrium Chapter 19

2. 19.1 Thermodynamics • Thermo: heat Dynamics: power • Study of energy flow and its transformations (heat and energy flow) • Determines direction of reactions (spontaneous or nonspontaneous under given conditions) • State Functions: considers only initial and final states • Does not consider pathways or rate • Organized into three laws: • 1st Law (ΔU = qp + w = qp – PΔV ) • 2nd Law • 3rd Law

3. 19.1 Basic Definitions • System • Surrounding • Open system • Closed system • Isolated system • State of system: defined by values of composition, pressure, T, V. • State Function: defined only by initial and final condition of the system (Enthalpy, Entropy, Gibbs Free Energy). • Energy change signaled by: accomplishment of work and/or appearance or disappearance of heat.

4. 19.1 1st Law of Thermodynamics 1. A gas does 135 J of work while expanding, and at the same time it absorbs 156 J of heat. What is the change in internal energy? (21 J) 2. The internal energy of a fixed quantity of ideal gas depends only on its temperature. If a sample of an ideal gas is allowed to expand against a constant pressure at a constant temperature, a) What is ΔU for the gas? b) Does the gas do work? c) If any heat exchanged with the surroundings? a) 0 b) w = -P ΔV c)no, only work done by gas is energy leaving the system. Internal energy should decrease, so the temp; but temp is const.; therefore the int energy does not change; gas has to absorb enough heat from surroundings to compensate for the work. Q = -w; ΔU = -w+w

5. 19.1 First Law of Thermodynamics • 1st Law: Energy can be neither created nor destroyed, but it can be converted from one form to anotheror transferred from a system to the surroundings or vice versa. Energy of the universe is constant • Important concepts from thermochemistry • Enthalpy • Hess’s law • Purpose of 1st Law • Energy bookkeeping • How much energy? • Exothermic or endothermic? • What type of energy? • Δu = q + w • q = heat; w = work system does on the surroundings (-PΔV)

6. 19.2 Spontaneous Processes: Expansion • Spontaneous processes are those that can proceed without any outside intervention. Product favored at equilibrium. • Product-favored at equilibrium • May be fast or slow • May be influenced by temperature • The gas in vessel B will spontaneously effuse into vessel A, but once the gas is in both vessels, it will not spontaneously separate

7. 19.1 Spontaneous Processes Processes that are spontaneous in one direction are nonspontaneous in the reverse direction. Examples: rusting, neutralization reaction, dissolution of sugar in water, heat flow, expansion of gas, spontaneous combustion (CH4 + O2), reaction of sodium with water

8. 19.1 Spontaneous Processes • Processes that are spontaneous at one temperature may be nonspontaneous at other temperatures. • Above 0C it is spontaneous for ice to melt. • Below 0C the reverse process is spontaneous.

9. 19.2 Spontaneous vs. Nonspontaneous 3. Determine if the following processes are spontaneous or not and if they are exothermic or endothermic. (a) Gases expand into larger volumes at constant temperature ________________ (b) H2O(s) melts above 0C ____________ (c) H2O(l) freezes below 0C ____________ (d) NH4NO3 dissolves spontaneously in H2O ___________ (e) Steel (iron) rusts in presence of O2 and H2O ________ (f) Wood burns to form CO2 and H2O __________ (g) CH4 gas burns to form CO2 and H2O __________ Evolution of Heat (Exothermicity) : not enough to predict spontaneity

10. 19.2 Spontaneous vs Nonspontaneous • Nonspontaneous process • Does not occur unless there is outside assistance (energy?) • Reactants-favored at equilibrium • All processes which are spontaneous in one direction cannot be spontaneous in the reverse direction • Spontaneous processes have a definite direction • Spontaneous processes are irreversible. Can be reversed with considerable input of energy.

11. 19.2 Factors That Favor Spontaneity • Spontaneous Processes driven by • Enthalpy, H (Joules) • Many, but not all, spontaneous processes tend to be exothermic. • Entropy, S (Joules/K) • Measure of the disorder of a system • Many, but not all, spontaneous processes tend to increase disorder of the system • Exothermicity favors spontaneity, but does not guarantee it.

12. 19.2 Factors That Favor Spontaneity: Enthalpy • Example of spontaneous reaction that is not exothermic: NH4NO3(s) → NH4+ (aq) + NO3-(aq) ΔH = 25 kJ/mol • Expansion of gas: energy neutral • Phase changes: endothermic processes that occurs spontaneously (ice to water). • Chemical system: H2(g) + I2(g) ↔ 2HI(g)Equilibrium can be approached from both sides (spontaneous both ways) even though the forward reaction is endothermic and the reverse is exothermic.

13. 19.2 Spontaneity: Examples 4. Based on your experience, predict whether the following processes are spontaneous, are spontaneous in reverse direction, or are in equilibrium: • When a piece of metal heated to 150 ºC is added to water at 40 ºC, the water gets hotter. • Water at room temperature decomposes into hydrogen and oxygen gases • Benzene vapor, C6H6(g), at a pressure of 1 atm condenses to liquid benzene at the normal boiling point of benzene, 80.1 ºC.

14. 19.2 Reversible Processes In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process. Example: melting ice at its melting point

15. 19.2 Irreversible Processes • Irreversible processes cannot be undone by exactly reversing the change to the system. Different path has to be used. • Spontaneous processes are irreversible. • Example: expansion a gas into vacuum.

16. 19.2 Entropy q T • Entropy (S) is a term coined by Rudolph Clausius in the 19th century. • Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered,

17. 19.2 Entropy • Direct measure of the randomness or disorder of the system. • Related to probability • describes # of ways the particles in a system can be arranged in a given state (position and/or energy levels) • The most likely state – the most random • More possible arrangements, the higher disorder, higher entropy • Ordered state – low probability of occurring • Disordered state: high probability of occurring

18. 19.2 Entropy on the Molecular Scale • Ludwig Boltzmann described the concept of entropy on the molecular level. • Temperature is a measure of the average kinetic energy of the molecules in a sample.

19. 19.2 Entropy on the Molecular Scale • Molecules exhibit several types of motion: • Translational: Movement of the entire molecule from one place to another. • Vibrational: Periodic motion of atoms within a molecule. • Rotational: Rotation of the molecule on about an axis or rotation about  bonds.

20. 19.2 Entropy on the Molecular Scale • Boltzmann envisioned the motions of a sample of molecules at a particular instant in time. • This would be akin to taking a snapshot of all the molecules. • He referred to this sampling as a microstate of the thermodynamic system.

21. 19.2 Entropy on the Molecular Scale • Each thermodynamic state has a specific number of microstates, W, associated with it. • Entropy is S = k lnW where k is the Boltzmann constant, 1.38  1023 J/K; W: number of microstates

22. 19.2 Entropy on the Molecular Scale S= k ln lnWfinal lnWinitial • The change in entropy for a process, then, is S = k lnWfinalk lnWinitial • Entropy increases with the number of microstates in the system.

23. 19.2 Spontaneous Processes: Dispersal of Matter • Isothermal (constant temperature) expansion of gas Two molecules present: 25% probability After opening stopcock the molecules could be in any arrangement shown (4 arrangements) Probability for each arrangement = (1/2)2 S = k (ln(4)

24. 19.2 Spontaneous Process: Isothermal Gas Expansion Consider why gases tend to isothermally (constant temp.) expand into larger volumes. Gas Container = two bulbed flask Ordered State Gas Molecules

25. 19.2 Spontaneous Process: Isothermal Gas Expansion Gas Container Ordered State S = k ln (W) = k (ln 1) = (1.38 x 10-23 J/K)(0) = 0 J/K For 3 particles, probability = (1/2)3 For N particles, probability = (1/2)N

26. Disordered States More probable that the gas molecules will disperse between two halves than remain on one side

27. Disordered States Driving force for expansion is entropy (probability); gas molecules have a tendency to spread out

28. Disordered States S = k(ln 7) = (1.38 x 10-23 J/K)(1.95) = 2.7 x 10-23 J/K

29. Total Arrangements Stotal = k(ln 23) = k(ln 8) = (1.38 x 10-23 J/K)(1.79) = 2.9 x 10-23 J/K

30. 19.2 Entropy on the Molecular Scale • The number of microstates and, therefore, the entropy tends to increase with increases in • Temperature. • Volume. • The number of independently moving molecules.

31. 19.2 Entropy and Temperature (a) A substance at a higher temperature has greater molecular motion, more disorder, and greater entropy than (b) the same substance at a lower temperature.

32. 19.2 Entropy and Physical States • Entropy increases with the freedom of motion of molecules. • Therefore, S(g) > S(l) > S(s)

33. 19.2 Entropy Changes • In general, entropy increases when • Gases are formed from liquids and solids. • Liquids or solutions are formed from solids. • The number of gas molecules increases. • The number of moles increases.

34. 19.2 Entropy in Temperature

35. What kind of changes are represented here? 50 40 30 Standard entropy,S°(J/K) 20 10 0 50 100 150 200 250 300 Temperature (K)

36. 19.2 Solutions Generally, when a solid is dissolved in a solvent, entropy increases.

37. 19.2 Patterns of Entropy Change 6. Describe in words the entropy of the system

38. 19.2 Entropy • Like total energy, E, and enthalpy, H, entropy is a state function. • Therefore, S = SfinalSinitial •  S > 0 represents increased randomness or disorder • Note: The magnitude of change in entropy depends on temperature.

39. 19.2 Entropy qrev T S = • For a process occurring at constant temperature (an isothermal process), the change in entropy is equal to the heat that would be transferred if the process were reversible divided by the temperature: Units: Joule/K

40. 19.2 Entropy: Example 5. ΔS = q/T The element mercury, Hg, is a silvery liquid at room temperature. The normal freezing point of mercury is -38.9 ºC, and its molar enthalpy of fusion is ΔHfusion = 2.331 kJ/mol. What is the entropy change when 50.0 g of Hg(l) freezes at the normal freezing point? (-2.48 J/K)

41. 19.2 Entropy: Examples 7. Predict if ΔS increases, decreases or does not change • Freezing liquid mercury • Condensing H2O(vapor) • Precipitating AgCl • Heating H2(g) from 60.0 ºC to 80 ºC • Subliming iodine crystals • Rusting iron nail

42. 19.2 Entropy - Examples 8. Predict which substance has the higher entropy: a) NO2(g) or N2O4(g) b) I2(g) or l2(s) 9. Predict whether each of the following leads to increase or decrease in entropy of a system If in doubt, explain why. a) The synthesis of ammonia: N2(g) + 3H2(g) ↔ 2NH3(g) b) C12H22O11(s) →C12H22O11(aq) c) Evaporation to dryness of a solution of urea, CO(NH2)2 in vapor. CO(NH2)2(aq) → CO(NH2)2(s)

43. 19.3 Second Law of Thermodynamics

44. 19.3 Second Law of Thermodynamics: System 10. Predict the sign of ΔS0 for each of the following reactions: a) Ca+2(aq) + 2OH-(aq) → Ca(OH)2(s) b) MgCO3(s) → MgO(s) + CO2(g) d) H2(g) + Br2(g) → 2HBr(g)

45. Second Law of Thermodynamics The second law of thermodynamics states that the entropy of the universe increases for spontaneous processes, and the entropy of the universe does not change for reversible processes. In other words: For reversible processes: Suniv = Ssystem + Ssurroundings = 0 For irreversible processes: Suniv = Ssystem + Ssurroundings > 0 For nonspontaneous Process: ΔS univ= ΔS syst. + ΔS surr. <0

46. Second Law of Thermodynamics These last truths mean that as a result of all spontaneous processes the entropy of the universe increases.

47. 19.3 Second Law: Entropy Changes EQUILIBRIUM PROCESSES (reversible) • ΔS universe= ΔS syst. + ΔS surr. =0 • ΔS syst = ΔS surr • ΔS syst = ΔSº final - ΔS0initial

48. 19.3 Entropy Changes in a System (Reactions) • Entropy changes in a system aA + bB → cC + dD • Standard entropy change ΔSº (25 ºC, 1atm). • Only changes in entropy can be measured. • Each element has an entropy value (compare to enthalpy). • Absolute value for each substance can be determined. • For a chemical system: S° = nS°(products) - mS°(reactants) where n and m are the coefficients in the balanced chemical equation. Standard Molar entropy, S0, is the entropy of one mole of a substance in its standard state (298 K)

49. 19.2 Standard Entropies • These are molar entropy values of substances in their standard states. • Standard entropies tend to increase with increasing molar mass.

50. 19.2 Standard Entropies Larger and more complex molecules have greater entropies.