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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
Number of methylene groups
0 10 20 30 40 50 60 70
Hfu
s (T fu
s)/ k
J m
ol-1
0e+0
5e+4
1e+5
2e+5
2e+5
Figure. Fusion enthalpies as a function of the number of methylene groups of the n-alkanes.
Number of methylene groups
0 10 20 30 40 50 60 70
tpce
Hm /
kJ m
ol-1
(tot
al p
hase
cha
nge
enth
alpy
, kJ m
ol-1
)
0e+0
5e+4
1e+5
2e+5
2e+5
Figure. Total phase change enthalpy of the n-alkanes as a function of the number of methylene groups.
Number of methylene groups
0 10 20 30 40 50 60 70
tpce
S m /
kJ m
ol-1
(tot
al p
hase
cha
nge
entro
py, J
mol
-1 K
-1)
0
100
200
300
400
500
600
Figure. Total phase change entropy of the n-alkanes as a function of the number of methylene groups.
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
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- 17.6secondary sp3 C >CH2 7.1 1.31a
tertiary sp3 C -CH< -16.4 0.60quaternary sp3 C >C< -34.8 0.66secondary sp2 C =CH2 17.3tertiary sp2 C =CH- 5.3 0.75quaternary sp2 C =C(R)- -10.7tertiary sp C H-C 14.9quaternary sp C -C -2.8aromatic tertiary sp2 C =CaH- 7.4quaternary aromatic sp2 C adjacent to an sp3 atom =Ca(R)- -9.6peripheral quaternary aromatic sp2 C adjacent to an sp2 atom =Ca(R)- -7.5internal 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
primary sp3 C
internal quaternary aromatic C
quaternary aromatic sp2 C
quaternary sp3 C
tertiary sp3 C
secondary sp2 C
tertiary sp2 C
quaternary sp2 C
tertiary sp C
quaternary sp C
CCH3
CH
CH3
CH
CH3CH3
CH2
secondary sp3 C
cyclic tertiary sp3 C
cyclic quaternary sp3 C
cyclic secondary sp3 C
cyclic tertiary sp2 C
tpce0SisoT(aac) =
iinCiGi + nCiGCH2
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
Table. Functional groups dependent on the substitution patternsFunctional 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;
Table. Contributions of the remaining functional groups Functional Groupsa Abbreviated Structure Group Value (Gk)a,
J/(mol-1 K-1) bromine R-Br 17.5fluorine on an sp2carbon R2-CHF 19.5fluorine on an aromatic carbon =CF- 16.63-fluorines on an sp3 carbon CF3-R 13.21-fluorine on an sp3 carbon R-CF-(R)2 12.7fluorine in perfluorinated compoundsb CnF2n+2 15.2one fluorine on a ring carbon -CHF-; 17.4two fluorines on a ring carbon -CF2- [17.5]iodine R-I 19.4phenol =C-(OH)- 20.3ether R-O-R 4.71aldehyde R-CH(=O) 21.5ketone R-C(=O)-R 4.6ester R-C(=O)O-R 7.7aromatic heterocyclic amine =N- [10.9]acyclic sp2 nitrogen =N- [-1.8]tertiary amine R-N(R2) -22.2secondary amine R-NH-R -5.3primary amine R-NH2 21.4nitro group R-NO2 17.7
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-CN 17.7isocyanide R-NC [17.5]tertiary amides R-C(=O)NR2 -11.2secondary amides R-C(=O)NH-R 1.5primary amide R-CONH2 27.9N,N-dialkylformamide HC(=O)NR2 [6.9]sulfides R-S-R 2.1disulfides R-SS-R 9.6thiols 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;
Estimations of acyclic and aromatic hydrocarbon derivatives
tpce0SisoT(aac) =
iinCiGi + nCiGCH2 +
kknCkGk
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
Estimations of cyclic hydrocarbonsTable. Contributions of the cyclic hydrocarbon portions of the molecule.
Contributions of Cyclic Carbons GroupValue(Gc)
J.mol-1.K-1
Group Coefficient Cc
Ring Equation for Non-aromatic Cyclic Compounds Sring = [33.4 ] + [3.7][n-3] ; n = number of ring atoms (1)Ring Equation for Non-aromatic Polycyclic Compounds
Sring = [33.4]N + [3.7][R-3N]; R = total number of ring atoms; N= number of rings (2)
cyclic tertiary sp3 carbon >CcH(R) -14.7
cyclic quaternary sp3 carbon >Cc(R)2 -34.6
cyclic tertiary sp2 carbon =CcH- -1.6 1.92
cyclic quaternary sp2 carbon =Cc(R)- -12.3cyclic quaternary sp carbon =Cc=; R-Cc -4.7all group values in this table are to be used with the ring equations 1 or 2; R: any alkyl oraryl group unless specified otherwise.
Estimations of cyclic hydrocarbons
tpce0SisoT(c) = Sring +
cinCcGc + iinCiGi + nCiGCH2
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 Kfluorene: Hfus(Tfus) = 19.58 kJ mol-1; Tfus = 387.9 K
Table. Contributions of the cyclic functional groups
Heteroatoms and functional GroupsComprising a Portion of a Ringa,b
Abbreviated structure Group Value (Gc)a
cyclic ketone R-C(=O)-R -1.4cyclic sp2 nitrogen R=N-R 0.5cyclic tertiary amine R2>N-R -19.3cyclic secondary amine RR-NH-R 2.2cyclic sulfide R-S-R 2.9
aR: any alkyl or aryl group unless specified otherwise; values in brackets are tentativeassignments; all group coefficients can be assumed to be 1; all group values in this tableare to be used with the ring equations 3 or 4; bthe R groups that are a part of the ringstructure are designated by italics.
tpce0SisoT(c) = Sring +
cinCcGc + iinCiGi + nCiGCH2 +
kknCkGk
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
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
O
HHOCH2
H
HO
H
HOH
OH
H
OH-D-glucose Tfus =432.2 K
fusHm = 34.3 kJ mol-1
l-menthol Tfus =316.2 K
fusHm = 11.88 kJ mol-1CH3
CH3
CH3
HHO
1-chlorodibenzodioxin
Tfus = 378.2 K
fusHm = 23.2 kJ mol-1
phenazine
Tfus = 450.2 K
fusHm = 20.92 kJ mol-1
O
OCl
N
N
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
0TisoStpce (exp), J mol-1K-1
0 200 400 600 800 1000 1200 1400
iso S
tpce
(cal
c), J
mol
-1K
-1
0
200
400
600
800
1000
1200
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 .
Standard deviation,
-10 -8 -6 -4 -2 0 2 4 6 8 10
Num
ber o
f com
poun
ds
0
200
400
600
800
1000
1200
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).
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.
Table. Calculated and Experimental Total Phase Change Entropies
Repeat Unit Expt Calc
CF2 poly(tetrafluoroethylene) 9.64 7.43CH2 poly(ethylene) 9.91 9.30CH2O poly(oxymethylene) 21.4 14.0C2ClF3 poly(chlorotrifluoroethylene) 10.2 10.9C2HF3 poly(trifluoroethylene) 11.0 7.9C2H2F2 poly(vinylidene fluoride) 13. 9 12.19C2H2O2 poly(glycolic acid) 19.4 14.8C2H3Cl poly(vinylchloride) 20.1 13.5C2H3F poly(vinylfluoride) 15.0 10.0C2H4O poly(oxyethylene) 25.3 23.3C2H4O polyvinyl alcohol 13.2 13.8C3H3N poly(acrylonitrile) 8. 5 15.0C3H4O2 poly(b-propiolactone) 29.8 26.3C3H6 poly(propylene) 18.9 8.3C3H6O poly(propyleneoxide) 24.1 19.6C3H6O poly(trimethyleneoxide) 30.6 32.6C3H6O2 poly(oxymethyleneoxyethylene) 50.9 35.1C4H3F3O2 poly(vinyl trifluoroacetate) 16.7 31.2C4H4O4 poly(ethylene oxalate 51.1 34.0C4H4O4 poly(g-butyrolactone) 41.5 35.6C4H5Cl trans-poly(chloroprene) 22.8 25.0C4H6 cis-poly(1,4-butadiene) 32.3 29.2C4H6 trans-poly(1,4-butadiene) 21.9 29.2C4H8 poly(1-butene) 17.0 19.8C4H8 poly(isobutylene) 37.9 7.5C4H8O poly(oxytetramethylene) 43.6 41.9C5H8 cis-poly(isoprene) 14.4 26.4C5H8 trans-poly(isoprene) 36.9 26.4C5H8Cl2O2 poly(2,2-bis(chloromethyl)trimethylene-3-oxide 69.1 30.7C6H18O2 poly(e-caprolactone) 52.3 54.2C5H8O2 poly(methyl methacrylate 21.1 27.0C5H8O2 poly(2,2-dimethylpropiolactone) 29.0 27.0C5H10 poly(1-pentene) 15.6 22.5C5H10O2 poly(oxymethyleneoxyoxytetramethylene) 48.3 53.7C6H4O poly(oxy-1,4-phenylene) 14.6 19.3C6H4S poly(thio-1,4-phenylene) 14. 6 15.4C6H10O2 poly(isopropyl acrylate) 14.0 30.3C6H11NO nylon 6 48.8 48.0C6H12 poly(4-methyl-1-pentene) 19.0 16.6C8H8 poly(styrene) 19.4 18.1
tpceS (Expt), J mol-1K-1
0 20 40 60 80 100 120 140 160 180
tpce
S (C
alcd
), J
mol
-1K
-1
0
20
40
60
80
100
120
140
160
180
200
r2: 0.9276m: 1.000b: -1.25
Estimated Total Phase Change Entropy for Some Polymers
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 0.6Stcpe Stcpe Htpce Htpce
expt calcd calcd expt calcdUNSUBSTITUTED DIBLOCK MOLECULES
C16H9F25 F3C(CF2)11(CH2)4H147.0 0.7 5314.0 1.4 4349.0 21.0 61 69.4 57.1 93.6 23.1 19.9
C16H13F21 F3C(CF2)9(CH2)6H306.0 4.2 14318.0 16.9 53 67 61.6 100.9 21.1 19.6
C16H17F17 F3C(CF2)7(CH2)8H301.2 9.5 31.6303.2 5.7 18.8 50.3 90.2 147.9 15.2 27.3
C17H21F15 (CF3)2CF(CF2)4(CH2)10H220.0 3 13.6261.0 18 69.0 82.6 84.6 138.6 21.0 18.9
T(K) Hpce Spce Stpce 0.6Stcpe Stcpe Htpce Htpce
expt calcd calcd expt calcd
C18H13F25 F3C(CF2)11(CH2)6H164.0 0.5 1316.0 3.5 11357.0 23.4 65.5 79.7 65.7 107.8 27.4 23.5
C18H21F17 F3C(CF2)7(CH2)10H288.0 3.5 12308.0 20.2 65 77.7 86.8 142.3 23.7 26.9
C19H21F19 (CF3)2CF(CF2)6(CH2)10H274.0 1 3.6298.0 25 83.9 87.5 84.6 138.6 26 22.1
C20H17F25 F3C(CF2)11(CH2)8H192.0 2.4 12.5329.0 6.4 19.5361.0 23.7 65.7 97.6 74.7 122 32.5 26.9
C20H21F21 F3C(CF2)9(CH2)10H317.0 4.0 12337.0 24.4 72 85 78.9 129.3 28.4 26.6
0
TfusStpce (experimental); J mol-1 K-1
20 40 60 80 100 120 140 160 180 200 220
0T fus
Stpc
e (ca
lcul
ated
); J
mol
-1 K
-1
40
60
80
100
120
140
160
180
Figure. A comparison of calculated and experimental total phase change entropies for the partially fluorinated amphiphilic compounds.