Enthalpies of dimerization

The total enthalpy correction due to chemical reactions is the sum of all the enthalpies of dimerization for each i-j pair multiplied by the mole fraction of dimer i-j. Since this gives the enthalpy correction for one mole of true species, we multiply this quantity by the ratio of the true number of moles to the stoichiometric number of moles. This gives... 

A very interesting system which serves as a splendid example of many of the points made so far concerns the acid methylcobaloxime. Methylcobaloxime is a dimer in non-basic solvents. The solvation minimized enthalpies of adduct formation corrected for the enthalpy of dimerization of methylcobaloxime (55) are presented in Table 6. 

Accepting the enthalpy of dimerization for reaction 22 of ca 21 10 kJmol (an averaged value from results in two nonpolar solvents ) to apply to the gas phase. 

Dithiazolyl radicals (58) do not dimerize at low temperatures in diluted solutions, do not react with O2, are stable to photolysis (at 350 nm), heat and in aqueous solutions at or above pH8 <83JCS(F1)925>. This makes them different from 1,3,2-dithiazolidinyl radicals. In 1987 <87CC66> solutions of (58 R = CF3) have been shown to contain 65% of the free radical and 35% of the diamagnetic dimer the concentration of the radical in concentrated solutions does not change with temperature indicating an almost zero enthalpy of dimerization. The latter in neat liquid is —3.5... 

The value 2.70 A for the O—H- O distance in this substance is smaller than that in ice, 2.76 A, as expected for this stronger bond. From the enthalpy of dimerization, 14.12 kcal/mole, the O—H O bond energy is found to have the value 7.06 kcal/mole. The value 7.6 kcal/mole is similarly found for the hydrogen-bond energy in acetic acid. 4 These values are about 50 percent greater than those for ice. 

Below 700 K, CsN02 evaporates without decomposition and the vapor contains both monomers and dimers. AH of sublimation is 161.5 kJ, and 208.8 kJ for the dimer, recalculated to 298 K. The enthalpy of dimerization is 477 kJ.38... 

Let us assume for a moment, however, that we had reliable (and direct) thermochemical information about trimethylarsine and tetramethyldiarsine. How valid is it to assume all As—As bonds have comparable dissociation enthalpies Clearly we know enough not to assume the As—As bond in AS4 is the same as in tetramethyldiarsine. The former is immediately identified as strained and so we are to use the more stable allotrope with an infinite network of nonplanar hexagons. What about Sb—Sb bonds If we assume constancy of the dissociation enthalpies of these bonds (excepting the strained Sb4), how about using the bond enthalpy from elemental solid antimony The enthalpy of dimerization of antimonin. CsHjSb, to form the tricyclic Diels-Alder or [4-1-2] cycloaddition product has been determined to be — 30.5 +1.3 kJ mol by a careful study of the monomer-dimer equilibrium (equation 19). 

References relative to the monomer-dimer ratio in magnesium chloride vapor are given in the discussion for monomeric ideal gas. The selected best value for the enthalpy of dimerization at 900 K is -39.2 kcal mol". Combined with enthalpy of formation data for the monomer and the heat capacity of the dimer, this yields A H (298.15 K) - -228.10 kcal mol". ... 

Schoonmaker and Porter ( ) analyzed the vapors in equilibrium with liquid CsOH and mixed KOH-CsOH condensed phases with a mass spectrometer and reported the presence of appreciable concentrations of dimer in the temperature range 650-700 K. By applying the method of relative equilibrium constants, these workers calculated the difference in the free energies of dimerization for KOH-CsOH. A 3rd law analysis of their free energy data for this pair leads to a difference in the enthalpies of dimerization of 4.9 kcal mol at 298.15 K for CsOH and KOH. Based upon the adopted value for KOH(g), AjH (dimerization, 298. 15 K) = -45.3 3.0 kcal mol" (2), we derive A H (dimerization, 298.15 K) -40.4 4.0 kcal mol" for 2 CsOH(g) = Cs2(0H)2(g). Combining this result with the enthalpy of formation for the gaseous monomer (3), that for the dimer is AjH (CS2(0H)2, g. 298.15 K) = -164.4+10.0 kcal mol" (-687.8+41.8 kJ mol" ). 

Mass spectrometric studies (1.-5) of the equilibrium gases over pure KOH(cr, t) and mixed KOH-NaOH condensed phases have unequivocally identified the vapor species as monomer and dimer in the temperature range 600-700 K. Absolute partial pressures for KOH(g) and K2(OH)2 (g) have been determined from peak intensity data by Porter and Schoonmaker (3 ) and Gusarov and Gorokhov (5). These data are analyzed by the 3rd law method with JANAF Gibbs energy functions (6) in order to evaluate an enthalpy of dimerization at 298 K. The adopted value is A H (298.15 K) = -45.3 t 3.0 kcal mol" for the reaction 2 KOH(g) = K2(0H)2 (g). 

Vapor pressures for liquid KOH have been determined by static (1443-1600 K) (7) and transpiration (873-1323 K) (8 ) methods. In order to evaluate Ay pH (K0H, t, 298.15 K) we have used a trial and error variation of A pH (298.15 K) for the monomer and dimer, such that these values are in accordance with the adopted enthalpy of dimerization given above, and the sum of the calculated partial pressures for KOH(g) and [KOH] (g) is in good agreement with the experimental vapor pressure data. Since the... 

Trends in the dimerization energies for the higher alkali metal hydroxides, as well as for the dimeric alkali fluorides and chlorides, suggest that the enthalpy of dimerization for LiOH from the work of Berkowitz et al. (2) may be slightly high. Such a comparison results in A H (dimerization, 298.15 K) values in the range -(52-61) kcal mol". Further support for a lower value comes from the mass spectral work of Porter and Schoonmaker (JL). They investigated the reaction of H 0(g) with a mixture of... 

Since HLiCO and LiCOH are intramolecular solvated organolithium species - in contrast to LiH - it is a question of interest, whether oligomerization is still a strongly exothermic process. Therefore again ab initio calculations on HF/6-3 IG level of theory are used to explore geometries and reaction enthalpies of dimers and tetramers, when the lithium to carbon monoxide ratio is 1 1. 

The vaporization of CsN03 has been investigated by mass spectrometry. The enthalpies of vaporization of monomeric CsN03(g) and dimeric (CsN03)2 are 28.2 and 29.3 kcal mol"1, respectively, at 298 K. The enthalpy of dimerization of caesium nitrate is -27.1 kcal mol"1 at 298 K.281 The thermal decomposition of potassium oxalate in molten KN03 at 350 °C yields K2C03, KNOz, and C02. There was no trace of carbon monoxide.282 The extraction of Co11 and some 4f (Pr, Eu, Tm) and 5f (Am, Cm, Cf)... 

The data for the hetero-complexes in Table 24 were obtained by a second-law evaluation. The accuracy of these data is checked by the computation of second-law dissociation enthalpies of dimer homo-complexes additionally present in the vapor of the quasi-binary systems. The dissociation enthalpies obtained in this way in general agree very well with the data in Table 23 resulting by vaporizing pure metail halides (cf e.g. Ref 61). 

Controversy has arisen over the years as to the exact interpretation of the infrared spectra in terms of the type of dimer formed. Van Thiel, Becker, and Pimentel (29) have shown that a cyclic dimer occurs in the solid state of methanol at low temperatures. Quantitative infrared (18) and NMR (2) measurements in dilute solutions have enabled the enthalpy of dimer formation to be calculated if certain assumptions are made. The high value of the enthalpy—9.2 kcal. per mole in the case of methanol— again suggests that cyclic dimers are formed since this is a rather high value for a single hydrogen bond. 

For 2-methyl-2-propanol, 3-ethyl-3-pentanol, 3-ethyl-2,4-dimethyl-3-pentanol, and 2,2,4,4-tetramethyl-3-pentanol, the curves are superposable while for 3-methyl-3-pentanol, 2,2,4-trimethyl-3-pentanol, and 1-butanol there is an appreciable separation between the curves. As Josien points out, the formation of open dimers in 2-methyl-2-propanol is in agreement with the low enthalpy of dimer formation, 4.8 kcal., obtained by Liddel and Becker (18). 

Because of this behavior we have been able to obtain values for the enthalpy of dimerization from infrared data by the method of Liddel and Becker (18) and from NMR data by the method of Davis, Pitzer, and Rao ( ) without having to resort to such low concentrations as usual. Extrapolated values of the infrared molar extinction coefficients, em, of the monomer OH band at zero concentration were obtained from curves of em vs. concentration at 25° and 50°C., and from these a value of 5.4 kcal. per mole was obtained for the enthalpy of dimerization. The limiting slopes of the curves of NMR chemical shift vs. concentration at 0° and 35°C. gave a value of 6.1 kcal. per mole. These values are in reasonable agreement with each other and significantly lower than the values of 8 kcal. for 1-heptanol and 7.9 kcal. for 2,4-dimethyl-3-pentanol, obtained from NMR data only. 

The enthalpy of dimerization was determined from the dimerization constants measured at different temperatures between 5 and 50 C. The spectral and thermodynamic data are summarized in Table 5.3. 

N-methy lacetamide is known to exist almost exclusively in the irons form whereas N-phenylurethane is found to be 95 % cis and 5 % irons (Russell and Thompson, 1956). Bhaskar and Rao (1967) studied the dimerization equilibria of N-methylaceta-mide and A -phenylurethane by measuring the concentration dependence of the first N—H overtone band. The procedure for determining the dimerization equilibrium constant was similar to that of Liddel and Becker (1957). The enthalpy of dimerization was evaluated from values of at different temperatures. The details of the procedure and uncertainties in the determination of Kj have been described in the paper by Singh and Rao (1967). The values of (liters/mole) at 26 C were 5.4 for N-methylacetamide in CCI4. and 1.5 for N-phenylurethane. The values of —AH were 4.7 and <3.0 kcal/mole, respectively. The values of and — A// for each of these compounds with various bases, e.g., pyridine and benzophenone, were also determined by a method similar to Becker s (1961). The and A// values did not show a clear-cut dependence on the configuration of the N—H bond of the secondary amide. 

CNDO/2 calculations of spin densities. ) Tentative assignment of structure. McLachlan calculation of spin densities. From [79Gerl]. Replaced by a(D) = 0.046 mT upon deuteration at positions 6 and 8. Determination of dissociation enthalpy of dimer. ) McLachlan calculation of spin densities. Radical generated by thermolysis of l,6-methano[10]annulene-ll-t-butylperoxy ester. ... 

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