Are there any other ways of estimating fusion enthalpies and melting temperatures?

Mobile Order and Disorder Theory

ln x = -[(fusH/R)(1/T-1/Tfus)+(transH/R)(1/T-1/Ttrans)] – ln ,

where x is the observed solubility in mole fraction, fusH is the enthalpy of fusion, Tfus is the melting point of the compound of interest, and R and T refer to the gas constant and temperature of measurement, respectively and represents the activity coefficient.

Mobile Order and Disorder Theory (MOD)

ln B = A + B + D + F + O + OH (1)where the solubility B on a volume fraction scale (B = xBVB/(xBVB-(1-xB)VS) of a solute B in a solvent S is evaluated by a series of terms.

ln B = A + B + D + F + O + OH (2)

A = - (fusH/R)(1/T-1/Tfus) - (transH/R)(1/T-1/Ttrans) (3)

B = 0.5 S(VB/VS – 1) + 0.5 ln(B + SVB/VS) (4)

D = - S2 VB(B - S)

2/[RT(1.0 + max(KOH, KO)S/VS)] (5)

F = - rSSVB/VS + OHi S(rS +bi) (6)

O = Oiln[(1 + KOi(S/VS - OiB/VB)] (7)

OH = OHi[ln(1 + KOHiS/VS + KBBiB/VB) – ln(1 +KBBiVB)] (8)

The terms represent different factors that can influence the solubility of each respective compound, including such factors as hydrogen bonding, nonspecific cohesion forces, entropic factors, and others.

S is the volume fraction of the solvent, S; calculated from 1- B

B is the volume fraction of the solute; calculated from solubility

VB is the molar volumes of the solute

VS is the molar volumes of the solute

VB & VS can be estimated by group additivity

B & S are modified cohesion parameters; S values are tabulated

for most common solvents; B is an unknown.

KO, KOH, & KBB refer to stability constants that describe the

strength of association between solute-solvent and solute-solute molecules respectively resulting from hydrogen bonding

rS & b are structuration factors associated with amphiphilic

solvents

Table. Standard group interaction stability constants and related parameters at 298 Ka

Term Value CommentrS 0 for non-associated solvents (all hydrocarbons, esters, ketones

nitriles)rS 1 for strongly associated solvents forming single hydrogen

bonds (alcohols)rS 2 for water and diols (molecules involved in double hydrogen

bonded chainsb 0 for non-aqueous solventsKOH 40 solute donor : –OH; solvent acceptor: -CN; -NO2

KOH 200 solute donor :–OH; solvent acceptor: aromatic ring;CH2Cl2

KOH 230 solute donor : secondary amine; solvent acceptor: -OH

KOH 300 solute donor : –OH; solvent acceptor: CHCl3

KOH 1000 solute donor : secondary amide; solvent acceptor: -OH

KOH 1500 solute donor: aromatic or conjugated amine; solvent

acceptor: -OHKOH 2000 solute donor: –OH; solvent acceptor: ketone

KOH 2500 solute donor: –OH; solvent acceptor: ester; ether

KOH 5000 solute donor: –OH; solvent acceptor: -OH

KO 110 solute acceptor: ester. ether; HN-N= ; solvent

donor: -OH KO 170 solute acceptor: ketone; solvent donor: -OH

KO 300 solute acceptor: tertiary amine; solvent donor: -OH

KO 600 solute acceptor: tertiary amide; solvent donor: -OH

KBB 0 solute acceptor: secondary amine; solvent donor:

secondary amineKBB 1000 solute acceptor: secondary amide; solvent donor :

secondary amideKBB 1500 solute acceptor: aromatic or conjugated amine;

solvent donor: aromatic or conjugated amine KBB 5000 solute acceptor: -OH; all steroids; solvent donor: -

OH ; all steroids

Oi refers to the number of KO, KOH interations in polyfunctional

molecules

ln B = A + B + D + F + O + OH (2)

Assuming no additional phase transitions between Tfus and 298 K

A = - (fusH/R)(1/T-1/Tfus) (3)

B = 0.5 S(VB/VS – 1) + 0.5 ln(B + SVB/VS)

S = 1 - B

represents a correction factor for the entropy of mixingaccounting for the different sizes of the solute and solvent molecules

D = - S2 VB(B - S)

2/[RT(1.0 + max(KOH, KO)S/VS)]

represents the change in the non-hydrogen bonding cohesion forces when fluid solute is mixed with solvent

Solvent S VS

chloroform 18.77 80.7

CCl4 17.04 97.1

benzene 18.95 89.4

toluene 18.1 106.9

CH2ClCH2Cl 20.99 78.8

cyclohexane 14.82 108.8

butyl acetate 19.66 132.5

acetone 21.91 74.0

ethyl acetate 20.79 98.5

hexane 14.56 131.6

octane 14.85 163.5

1-butanol 17.16 92.0

1-propanol 17.29 75.1

methanol 19.25 40.7

F = - rSSVB/VS + OHi S(rS +bi)

represents the structuration of the solvent when thesolvent is an alcohol or water b = 0 for alcoholic solvents,

O = Oiln[(1 + KOi(S/VS - OiB/VB)]

represents the proton acceptor solute-solvent interaction on the solute. It reflects the effect of hydrogen bonding on solubility between a hydroxylic solvent and proton acceptor sites on the solute.

OH represents the proton donor solute solvent interaction describing the the effect on solubility of a proton donor site on the solute which both self associates (KBB) and interacts with the solvent (KOH).

For non-aqueous solventsOH = 0

Calculation of solubility of methyl hexadecanoate

The following is needed:

1. The melting point and the molar enthalpy of fusion in order to calculate A

2. The formula in order to calculate the molar volume

3. The values of KO, KOH

4. The cohesion parameter B. This is obtained by

measuring the solubility of the compound in a solvent that does not form hydrogen bonds such as hexane. .

Calculation of B for methyl hexadecanoate

For non-hydrogen bonded solvents KOH, KO are not found,

therefore K = 0, rS = 0

ln B = A + B + D

D = ln B - A - B

S2 VB(B - S)

2/RT = ln B - A - B

(B - S)2 = -RT(ln B - A – B)/ S

2 VB

mol fraction XB = 0.394 ; VB = 309cm3/mol

A = -0.797

VS(hexane) = 131.6cm3/mol

S = 14.56(J/cm3).5

Calculation of solubility of methyl hexadecanoate

For non-hydrogen bonded solvents KOH, KO are not found,

therefore K = 0, rS = 0

For alcohols

KO = 110; solute acceptor: ester; solvent donor: -OH

rS = 1

fusH (303.8) = 55.65 kJ mol-1

VB = 309 cm3/mol

B = 17.63 J0.5/cm-1.5

Suppose we use experimental solubilities and MOD theory

For a known compound with an unknown mp and fusion enthalpy and a known solubility in a known solvent

ln B = A + B + D + F + O + OH

We know ln B; all the terms in B, all the terms in D except

B; all the terms in F, O and OH

By measuring the solubility in two or more solvents, we have two (or more equations) and two unknowns and we can solve for A and B

Solvent SO VSO Bexpt B D F O lnBcalcd Bexpt

chloroform 18.77 80.7 0.83 0.436 -0.016 0 0 -0.33 -0.186

CCl4 17.04 97.1 0.792 0.415 -0.001 0 0 -0.336 -0.234

benzene 18.95 89.4 0.775 0.497 -0.033 0 0 -0.286 -0.255

toluene 18.1 106.9 0.743 0.441 -0.016 0 0 -0.325 -0.297

CH2ClCH2Cl 20.99 78.8 0.797 0.53 -0.096 0 0 -0.317 -0.227

cyclohexane 14.82 108.8 0.689 0.513 -0.043 0 0 -0.281 -0.373

butyl acetate 19.66 132.5 0.596 0.485 -0.182 0 0 -0.447 -0.518

acetone 21.91 74.0 0.691 0.832 -0.328 0 0 -0.246 -0.369

ethyl acetate 20.79 98.5 0.687 0.59 -0.207 0 0 -0.367 -0.375

hexane 14.56 131.6 0.604 0.481 -0.091 0 0 -0.36 -0.504

octane 14.85 163.5 0.553 0.366 -0.087 0 0 -0.471 -0.592

1-butanol 17.16 92 0.308 1.3 -0.007 -2.324 0.541 -1.24 -1.178

1-propanol 17.29 75.1 0.304 1.66 -0.011 -2.862 0.647 -1.316 -1.19

methanol 19.25 40.7 0.206 3.533 -0.165 -6.03 1.123 -2.289 -1.581

A = - (fusH/R)(1/T-1/Tfus)

RA = - fusH/T + fusS

SinceT = 293.2 KfusS = tpceS = 2*17.6 + 14*7.1*1.31 + 7.7 = 173

RA = (8.314)(-0.75) = -6.24

ThenfusH = T(-RA + fusS) = - 293.2(6.24 + 173) = 52600 J mol-1

Tfus = 304 K

Lit. fusH(304) = 55.6 kJ mol-1

Compound Tfus

expt Tfus

calcb Tfus

calcdc Tfus

calcdd

tpceS

estde

tpceH

calcdd

tpceH

expt

p-benzoquinone 388 412 29.4 12.1 18.5 methyl 4-hydroxybenzoate

400

403

60.2

24.3

22.6

acetanilide 386 402 48.6 19.5 22.0 4-hydroxyacetanilide 442 502 54 27.1 27.0 Nipagin A 389 387 67.3 26.0 25.5 benzocaine 363 401 68.5 27.5 23.6 naphthalene 353 348 371 365 44.4 16.2 19,1 camphor 452 309 38.0 11.7 21.5 acenaphthene 367 442 41.0 18.1 21.5 propyl 4-hydroxybenzoate

369

366

74.5

27.3

28.0

risocaine 347 337 75.6 25.5 20.5 phenacetin 407 422 63.1 26.6 31.3 ephedrine 312 344 55.3 19.0 20.4 ; bnon-associated solvents; cassociated solvents; dcomputed using all experimentalsolubility data;

adamantane 541 486 44.9 20.7 14.3 antipyrine 386 479 49.1 23.5 24.5 butyl 4-hydroxybenzoate

343

337

81.6

27.5

26.8

n-butyl 4-aminobenzoate

331

344

82.7

28.4

20.5

thianthrene 428 481 60.5 29.1 25.4 1-dodecanol 300 302 302 302 122 36.8 40.2 biphenyl 343 338 59.2 20.0 18.7 thioxanthen-9-one 488 563 56.0 31.1 35.5 aminophenazone 382 516 52.9 27.3 26.9 anthracene 490 566 568 568 44.2 25.1 28.8 phenanthrene 369 385 393 388 44.2 17.1 18.6 benzil 368 347 68.4 23.7 23.6 trans stilbene 398 397 69.7 27.7 27.4 lidocaine 340 339 66.5 22.5 15.3 1-tetradecanol 311 315 304 309 141 44.1 49.4 pyrene 424 432 471 442 43.8 19.4 17.1 1-hexadecanol 322 337 324 334 159 53.2 58.4 methyl hexadecanoate 304 304 301 304 174 52.7 55.6 diethylstilbestrol 442 402 97.8 39.3 28.8 estradiol 452 467 520 491 67.3 33.1 40.6 estriol 555 638 67.9 43.3 42.7 n-octadecane 301 302 185 55.7 61.4

Compound Tfus

expt

Tfus

calcb

Tfus

calcdc

Tfus

calcdd

tpceS

estde

tpce

H

calcdd

tpce

H

expt

Tfus (experimental), K

250 300 350 400 450 500 550 600

Tfu

s (ca

lcul

ated

), K

250

300

350

400

450

500

550

600

650

700

Figure. A comparison of fusion temperatures calculated from solubility measurements and estimated total phase change entropies with experimental values.  

Standard deviation

300-350 K 12 K

300-400 K 23 K

All data (81) 39 K

Figure 2. A comparison of calculated and experimental total phase change enthalpies.

Experimental Total Phase Change Enthalpies (J)

0e+0 2e+4 4e+4 6e+4 8e+4 1e+5

Cal

cula

ted

Tot

al P

hase

Cha

nge

Ent

halp

ies

(J)

0.0e+0

2.0e+4

4.0e+4

6.0e+4

8.0e+4

1.0e+5

1.2e+5

Figure. A comparison of calculated total phase change enthalpies with experimental values for all 81 compounds in the data base.

Standard deviation

6.4 kJ mol-1