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

Are there any other ways of estimating fusion enthalpies and melting temperatures? Mobile Order and Disorder Theory. ln x = -[(  fus H /R)(1/T-1/T fus )+  (  trans H /R)(1/T-1/T trans )] – ln  ,

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

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  1. Are there any other ways of estimating fusion enthalpies and melting temperatures? Mobile Order and Disorder Theory

  2. ln x = -[(fusH/R)(1/T-1/Tfus)+(transH/R)(1/T-1/Ttrans)] – ln , where xis 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.

  3. 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 = - rSSVB/VS + OHiS(rS +bi) (6) O = Oiln[(1 + KOi(S/VS - OiB/VB)] (7) OH = OHi[ln(1 + KOHiS/VS + KBBiB/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.

  4. 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

  5. Table. Standard group interaction stability constants and related parameters at 298 Ka Term Value Comment rS 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 chains b 0 for non-aqueous solvents KOH 40 solute donor : –OH; solvent acceptor: -CN; -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: -OH KOH 2000 solute donor: –OH; solvent acceptor: ketone

  6. 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 amine KBB 1000 solute acceptor: secondary amide; solvent donor : secondary amide KBB 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

  7. 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)

  8. B = 0.5 S(VB/VS – 1) + 0.5 ln(B + SVB/VS) S = 1 - B represents a correction factor for the entropy of mixing accounting 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

  9. 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

  10. F = - rSSVB/VS + OHiS(rS +bi) represents the structuration of the solvent when the solvent is an alcohol or water b = 0 for alcoholic solvents, O = Oiln[(1 + KOi(S/VS - OiB/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.

  11. 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 solvents OH = 0

  12. Calculation of solubility of methyl hexadecanoate • The following is needed: • The melting point and the molar enthalpy of fusion in order to calculate A • The formula in order to calculate the molar volume • The values of KO,KOH • 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. .

  13. Calculation of B for methyl hexadecanoate For non-hydrogen bonded solventsKOH, KO arenot 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)/ S2 VB mol fraction XB = 0.394 ; VB = 309 cm3/mol A = -0.797 VS(hexane) = 131.6 cm3/mol S = 14.56 (J/cm3).5

  14. Calculation of solubility of methyl hexadecanoate For non-hydrogen bonded solventsKOH, KO arenot 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

  15. 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

  16. Solvent SO VSOBexpt B D F O lnBcalcd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

  17. A = - (fusH/R)(1/T-1/Tfus) RA = - fusH/T + fusS Since T = 293.2 K fusS = tpceS = 2*17.6 + 14*7.1*1.31 + 7.7 = 173 RA = (8.314)(-0.75) = -6.24 Then fusH = T(-RA + fusS) = - 293.2(6.24 + 173) = 52600 J mol-1 Tfus = 304 K Lit. fusH(304) = 55.6 kJ mol-1

  18. ; bnon-associated solvents; cassociated solvents; dcomputed using all experimental solubility data;

  19. Compound Tfus expt Tfus calcb Tfus calcdc Tfus calcdd tpceSestde tpceHcalcdd tpceHexpt

  20. Standard deviation 300-350 K  12 K 300-400 K  23 K All data (81)  39 K Figure. A comparison of fusion temperatures calculated from solubility measurements and estimated total phase change entropies with experimental values.

  21. 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

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