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 H s (298 K) =  H v (298 K) +  H fus (298 K)

 H s (298 K) =  H v (298 K) +  H fus (298 K). We have discussed methods to estimate  H v (298 K); are there any ways to estimate  H fus (298 K) or  H fus ( T fus ) ? Walden’s Rule:  H fus ( T fus ) / T fus = 54.4 J mol -1 K -1.

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 H s (298 K) =  H v (298 K) +  H fus (298 K)

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  1. Hs(298 K) = Hv(298 K) + Hfus(298 K) We have discussed methods to estimate Hv(298 K); are there any ways to estimate Hfus(298 K) or Hfus(Tfus) ? Walden’s Rule: Hfus(Tfus) / Tfus=54.4 J mol-1 K-1

  2. Figure. Fusion enthalpies as a function of the number of methylene groups of the n-alkanes.

  3. Figure. Total phase change enthalpy of the n-alkanes as a function of the number of methylene groups.

  4. Figure. Total phase change entropy of the n-alkanes as a function of the number of methylene groups.

  5. Fusion enthalpies as a function of the number of methylene groups (N) of the n-alkanes. Hfus(Tfus) = (2929±178)N - (3281±13006); r2 = 0.8823 Total phase change enthalpies as a function of the number of methylene groups (N) of the n-alkanes. Hfus(Tfus) = (3552±80)N + (972±5868); r2 = 0.9818 Total phase change entropy as a function of the number of methylene groups (N) of the n-alkanes. Sfus(Tfus) = (9.027±0.25)N + (45.1±18.44); r2 = 0.9725

  6. Table. Contributions by the hydrocarbon portion of acyclic and aromatic molecules Acyclic and Aromatic Carbon Groups Group Value Gi, Group Coefficient Ci J.mol-1.K-1 primary sp3 C CH3- 17.6 secondary sp3 C >CH2 7.1 1.31a tertiary sp3 C -CH< -16.4 0.60 quaternary sp3 C >C< -34.8 0.66 secondary sp2 C =CH2 17.3 tertiary sp2 C =CH- 5.3 0.75 quaternary sp2 C =C(R)- -10.7 tertiary sp C H-C 14.9 quaternary sp C -C -2.8 aromatic tertiary sp2 C =CaH- 7.4 quaternary aromatic sp2 C adjacent to an sp3 atom =Ca(R)- -9.6 peripheral quaternary aromatic sp2 C adjacent to an sp2 atom =Ca(R)- -7.5 internal quaternary aromatic sp2 C adjacent to an sp2 atom =Ca(R)- -0.7 aThe group coefficient of 1.31 for is applied only when the number of consecutive methylene groups equals or exceeds the sum of the remaining groups; R: any alkyl or aryl group unless specified otherwise

  7. Estimations of acyclic and aromatic hydrocarbons Examples: ethylbenzene: Hfus(Tfus) = 9.16 kJ mol-1; Tfus =178.2 K octylbenzene: Hfus(Tfus) = 29.96 kJ mol-1; Tfus =234.2 K 4-methyl-1-pentene: Hfus(Tfus) = 4.93 kJ mol-1; Tfus =118.9 K

  8. Table.Functional groups dependent on the substitution patterns Functional Groups Group Value (Gk) Group Coefficient (Ck) J/(mol-1 K-1) Total number of functional groups in the molecule: k; Gk k = 2 3 4 5 6 chlorine R-Cl 10.8 1.5 1.5 1.5 1.5 1.5 2-fluorines on an sp3 C R-CF2-R 13.2 1.06 1.06 1.06 1.06 1.06 hydroxyl group R-OH 1.7 10.4 9.7 13.1 12.1 13.1 carboxylic acid R-C(=O)OH 13.4 1.21 2.25 2.25 2.25 2.25 R: any alkyl or aryl group unless specified otherwise;

  9. Table. Contributions of the remaining functional groups Functional Groupsa Abbreviated Structure Group Value (Gk)a, J/(mol-1 K-1) bromine R-Br 17.5 fluorine on an sp2carbon R2-CHF 19.5 fluorine on an aromatic carbon =CF- 16.6 3-fluorines on an sp3 carbon CF3-R 13.2 1-fluorine on an sp3 carbon R-CF-(R)2 12.7 fluorine in perfluorinated compoundsb CnF2n+2 15.2 one fluorine on a ring carbon -CHF-; 17.4 two fluorines on a ring carbon -CF2- [17.5] iodine R-I 19.4 phenol =C-(OH)- 20.3 ether R-O-R 4.71 aldehyde R-CH(=O) 21.5 ketone R-C(=O)-R 4.6 ester R-C(=O)O-R 7.7 aromatic heterocyclic amine =N- [10.9] acyclic sp2 nitrogen =N- [-1.8] tertiary amine R-N(R2) -22.2 secondary amine R-NH-R -5.3 primary amine R-NH2 21.4 nitro group R-NO2 17.7

  10. Table. Contributions of the remaining functional groups Functional Groupsa Abbreviated Structure Group Value (Gk)a, J/(mol-1 K-1) azoxy nitrogen N=N(O)- [6.8] nitrile R-CN 17.7 isocyanide R-NC [17.5] tertiary amides R-C(=O)NR2 -11.2 secondary amides R-C(=O)NH-R 1.5 primary amide R-CONH2 27.9 N,N-dialkylformamide HC(=O)NR2 [6.9] sulfides R-S-R 2.1 disulfides R-SS-R 9.6 thiols R-SH 23.0 aR: any alkyl or aryl group unless specified otherwise; values in brackets are tentative assignments; all group coefficients can be assumed to be 1; the functional groups are in bold;

  11. Estimations of acyclic and aromatic hydrocarbon derivatives Examples: 3-heptanone: Hfus(Tfus) = 17.53 kJ mol-1; Tfus =236 K p--cumylphenol: Hfus(Tfus) = 21. 68 kJ mol-1; Tfus =346.4 K 2,3,4,5-tetrachlorobiphenyl: Hfus(Tfus) = 25.2 kJ mol-1; Tfus =363.9 K

  12. Estimations of cyclic hydrocarbons

  13. Estimations of cyclic hydrocarbons Examples: cyclohexylbenzene: Hfus(Tfus) = 15.3 kJ mol-1; Tfus =280.5 K adamantane: Hfus(Tfus) = 10.9 kJ mol-1; Tfus =541.2 K; Htran(Ttrans) = 3.38; Ttrans = 208.6 K fluorene: Hfus(Tfus) = 19.58 kJ mol-1; Tfus =387.9 K

  14. Estimations of cyclic hydrocarbon derivatives C27H46O cholesterol Hfus(Tfus) = 27.41 kJ mol-1; Tfus =420.2 K; Htran(Ttrans) = 2.5; Ttrans = 304.8 K

  15. Estimate Stpce(Tfus) of dibenzothiophene Tfus 373.2 Hfus(Tfus) 21.6 kJ mol-1 Estimate Stpce(Tfus) of C11H16N4O2 8-butyltheophylline Tfus 509.2 Hfus(Tfus) 32.3 kJ mol-1 theophylline

  16. -D-glucose Tfus =432.2 K fusHm = 34.3 kJ mol-1 l-menthol Tfus =316.2 K fusHm = 11.88 kJ mol-1

  17. 1-chlorodibenzodioxin Tfus = 378.2 K fusHm = 23.2 kJ mol-1 phenazine Tfus = 450.2 K fusHm = 20.92 kJ mol-1

  18. Octyl methacrylate Tfus = 230.3 K fusHm = 24.9 kJ mol-1 2-n-propy1-5-(4-bromophenyl)thiophene Tfus = 360.4 K fusHm = 15.7 kJ mol-1

  19. How good are these parameters at estimating Stpce(Tfus)? Fig. A comparison of the experimental and calculated total phase change entropies of 2637 compounds. The area between the two lines represents 2 .

  20. Fig. A histogram of the distribution of errors in (exp) - (calc) for the database compounds of Fig. 1. Each interval represents one standard deviation (15.3 J.mol-1.K-1).

  21. Applications of Group Values Used to Calculate Stpce(Tfus) Although polymers are not completely crystalline, they can be made highly crystalline and they have a melting temperature associated with their melting. The degree of crystallinity can be determine by X-Ray crystallography.

  22. Estimated Total Phase Change Entropy for Some Polymers

  23. Table. Molar Transition Enthalpies (kJ mol-1) and Entropies (J mol-1 K-1) of Select Amphiphilic Semiperfluorinated-Semiper-hydrogenated Diblock and Triblock Organic Compoundsa T(K) HpceSpceStpce 0.6StcpeStcpe HtpceHtpce expt calcd calcd expt calcd UNSUBSTITUTED DIBLOCK MOLECULES C16H9F25 F3C(CF2)11(CH2)4H 147.0 0.7 5 314.0 1.4 4 349.0 21.0 61 69.4 57.1 93.6 23.1 19.9 C16H13F21 F3C(CF2)9(CH2)6H 306.0 4.2 14 318.0 16.9 53 67 61.6 100.9 21.1 19.6 C16H17F17F3C(CF2)7(CH2)8H 301.2 9.5 31.6 303.2 5.7 18.8 50.3 90.2 147.9 15.2 27.3 C17H21F15 (CF3)2CF(CF2)4(CH2)10H 220.0 3 13.6 261.0 18 69.0 82.6 84.6 138.6 21.0 18.9

  24. T(K) HpceSpceStpce 0.6StcpeStcpe HtpceHtpce expt calcd calcd expt calcd C18H13F25 F3C(CF2)11(CH2)6H 164.0 0.5 1 316.0 3.5 11 357.0 23.4 65.5 79.7 65.7 107.8 27.4 23.5 C18H21F17 F3C(CF2)7(CH2)10H 288.0 3.5 12 308.0 20.2 65 77.7 86.8 142.3 23.7 26.9 C19H21F19 (CF3)2CF(CF2)6(CH2)10H 274.0 1 3.6 298.0 25 83.9 87.5 84.6 138.6 26 22.1 C20H17F25 F3C(CF2)11(CH2)8H 192.0 2.4 12.5 329.0 6.4 19.5 361.0 23.7 65.7 97.6 74.7 122 32.5 26.9 C20H21F21 F3C(CF2)9(CH2)10H 317.0 4.0 12 337.0 24.4 72 85 78.9 129.3 28.4 26.6

  25. Figure. A comparison of calculated and experimental total phase change entropies for the partially fluorinated amphiphilic compounds.

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