solid ==> liquid )S fusion > 0 liquid ==> gas )S vap > 0 - entropy increases with increasing number of atoms (increasing complexity)

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1 CHEM*880 - Physical Chemistry FALL 005 Assignment #3: Problems hermodynamics: entropy and free energy. a) From the following data, calculate and vap for methyl alcohol; ethyl alcohol, C H 5 OH; and n-propyl alcohol, C 3 H 7 OH. Compound t m ( o C) (kj - ) t b ( o C) vap (kj - ) CH 3 OH C H 5 OH C 3 H 7 OH From the lectures you should know: - entropy increases with melting and vaporization solid > liuid )S ion > 0 liuid > gas )S vap > 0 - entropy increases with increasing number of atoms (increasing complexity) For instance, for this series of gases methane (CH 4 ), ethane (C H 6 ), propane (C 3 H 8 ) : S o (methane)86j <S o (ethane)30 J <S o (propane)70j Similarly for this series of alcohols: CH 3 OH m C H 5 OH m C 3 H 7 OH m 377J. ( ) 8.J.. 50J. ( ) J ( ) 3.6J J.. )S (C 3 H 7 OH) > )S (C H 5 OH)> )S (CH 3 OH)

2 liuid > gas )S vap > 0 CH 3 OH vap b vap 37570J. ( ).J.. C H 5 OH vap b vap 40480J. ( ) 5.0J.. C 3 H 7 OH vap b vap 43600J. ( ) 7.7J.. )S vap (C 3 H 7 OH) > )S vap (C H 5 OH)> )S vap (CH 3 OH) b) Arrange the compounds NH 3, CH 4 and H O in order of increasing vap values. Give reasons for your ordering. In liuid phase: water and ammonia > hydrogen bonds, but the O H... O hydrogen bond in water is stronger than N H... N hydrogen bond in ammonia. In gas phase: the three compounds are more and less similar, therefore )S vap (H O) > )S vap (NH 3 ) > )S vap (CH 4 ) You do not need to know the values to solve the problem. Entropies of vaporization at atm and the normal boiling point: )S vap (H O)06. J >)S vap (NH 3 ) 97.4 J. -. -

3 . Arrange the following substances in order of increasing ar entropy: C Br 6 (g), Na(s), NaCl (s), Br (l), Br (g) See notes: Na(s) < NaCl(s) < Br (l) < Br (g) < C Br 6 (g) Strategy: i) Classify the substances according to their aggregation state. S(solids) < S(liuids) < S(gases) Na(s), NaCl(s) < Br (l) < Br (g), C Br 6 (g) ii) Entropy increases with increasing number of atoms (increasing complexity) : Br (g) < C Br 6 (g) Na(s) < NaCl (s) 3. Predict whether the entropy of the substance increases, decreases, or remains the same in the following processes: From LECURES: (a) H O (g, 75 torr, 300) H O (g, 50 torr, 300) Pressure increases (ENROPY DECREASES) S o gas decreases with increasing pressures at constant temperature. (more ordered, more constrained). S V ds nr dv V P S nr ln nr ln ( ideal gas) V V V P Assumption: water can be described as an ideal gas PVnR (b) Br (l, atm, 5 o C) Br (g, atm, 5 o C)

4 Phase transition: liuid > gas (ENROPY INCREASES) (c) I (g, atm, 5 o C) I (g, atm, 00 o C) emperature increases (ENROPY INCREASES) (d) Fe (s, atm, 50 o C) Fe(s, atm, 5 o C) emperature decreases (ENROPY DECREASES) Less thermal disorder 4. For each of the following reactions, will be positive or negative? Justify your answers. (a) H O (g) H O (l) (standard conditions) NEGAIVE (phase transition gas > liuid) (b) CO (g) + O (g) CO (g) (standard conditions) NEGAIVE (number of es of gas decreases) (c) NaCl (s) Na + (a) + Cl - (a) (standard conditions) POSIIVE (solid dissolves) (d) N (g, atm) N (g, 0 atm) NEGAIVE ( pressure increases) (e) dm 3 Ar, SP + dm 3 He, SP dm 3 of He-Ar mixture, SP POSIIVE (ENROPY OF MIXING): mixing - R [ na ln xa + nb ln xb] (f) H O (l, 98) H O (l, 353) POSIIVE (temperature increases) 5. Calculate the entropy change when argon at 5 o C and.00 atm pressure in a container of volume 500 cm 3 is allowed to expand to 000 cm 3 and is simultaneously heated to 00 o C. ake C v (argon).48 J - - ( Ans J - ).

5 We need to choose the most convenient path from the initial state (n es of argon, 5 o C,.00 atm, 500 cm 3 ) to the final state (n es of argon, 00 o C, 000 cm 3 ) he best path, a two step process: a) isothermal expansion from 500 to 000 cm 3 b) constant volume heating from 98 to 373 at the final volume 000 cm 3 n of es of argon (assuming ideal gas behaviour) > n PV/R (initial or final conditions) > n For step a) r ev V nrln V isothermal ( ideal gas) U (0.004)(8.34J. 0 w 000 )ln 0.76J. 500 ln V nr V For step b) r ev ncvd cons tant volume U nc v ln ncvd (0.004)(.48J. 373 )ln 0.057J. 98 )S )S (step a) + )S (step b) J Let 56 g of nitrogen at 7 o C and 0.00 atm pressure, expand isothermally and ersibly until the pressure is atm. Assume ideal behaviour. Calculate )U, )H, )S, and )G. 56 g of N Ideal gas behaviour (see text) > )U0 and )H0 )G )H - )S )G - )S

6 r ev P nr ln 6.76J. P isothermal exp ansion ( ideal gas) U 0 P G G nr ln P w 0 V nr ln V ( ) (8.34J. )(300)ln 808 J. 7. Discuss the following statements: (see Notes and inoco et al.) (a) Euilibrium corresponds to the condition of minimum free energy. (b) In all spontanous processes, the entropy of the system increases. (c) Reactions for which and are both positive become spontaneous at sufficiently high temperatures. (d) he free energy change in a process is directly proportional to the amount of substance taking part in the reaction. 8. he standard free energy of formation of ethylene, C H 4 (g), at 98 is 69. kj -. In view of its positive G o f, why does not ethylene convert spontaneously to graphite and H in storage? Needs a catalyst (see notes) 9. Chapter 3 - inoco et al. (4 th edition). Problems 0,,, 3, 7, 8, 9, 6.

Entropy Changes & Processes

Entropy Changes & Processes Chapter 4 of Atkins: he Second Law: he Concepts Section 4.3 Entropy of Phase ransition at the ransition emperature Expansion of the Perfect Gas Variation of Entropy with emperature