Phase equilibrium data shift

These considerable solvent-dependent shifts demonstrate that for molecules with such pronounced conformational ambiguity, the equilibration of conformations has to be taken into account in the calculation of thermodynamic phase-equilibrium data. In order to enable a consistent treatment, we have implemented an automated conformation equilibration scheme in COSMO therm. A compound X can be represented by a set of COSMO-files for the conformers, and a multiplicity ojx(i) can be assigned to each con-former based on geometrical degeneration aspects. Then the population of a conformer, i, in a solvent S is calculated as... 

In Figure 3, heat transfer coefficients are shown for n-pentane--C02 at 8.9 MPa and bulk fluid CO2 mole fractions of 0.830 on the liquid side of the LOST, 0.865 precisely at the LOST, and 0.876 on the vapor side. For comparison, we also show results for pure carbon dioxide at the same bulk temperature and pressure. A similar set of results is shown for n-decane--C02 for each of two pressures in Figures 4 and 5. In Figure 4, at 10.4 MPa, the LOST of 325 K occurs at a CO2 mole fraction x of 0.93 0.02 according to our Peng-Robinson fit of the phase equilibrium data. Thus, only the results for x - 0.973 are clearly on the vapor side of the LOST and only those for x - 0.867 are on the liquid side. In Figure 5, for 12.2 MPa, the LOST has shifted slightly to x - 0.91 + 0.02 and T -335 K. Therefore, we expect the data for x - 0.940 to now be on the vapor side. 

Activity coefficients, which play a central role in chemical thermodynamics, are usually obtained from the analysis of phase equilibrium measurements. However, with shifts in the chemical industry and the use of combinatorial chemistry, new chemicals are being introduced for which the needed phase equilibrium data may not be available. Therefore, predictive methods for estimating activity coefficients and phase behavior are needed. Group contribution methods, such as the ASOG [analytical solution of groups... 

The introduction of these coefficients obviously has shifted the burden from evaluating the fugacities to evaluating the activity and fugacity coefficients. These coefficients may be available in several forms. Correlations may exist for systems of interest or phase equilibrium data may be available from which the coefficients can be calculated. The following list is a representative sample of the numerous texts devoted to this. Important topic [II, 12, 18, 13, 5. ... 

The data from microwave spectroscopy have been interpreted with a dihedral angle H—O—O—H = 120.0° for the gas-phase equilibrium structure of H202. The nonplanarity of the peroxide gives rise to a stereogenic 0—0 axis . The computed total parity violating energy shift of —1.9 x 10 kJmoH between the two enantiomers, however, is too small in order to be measured with contemporary devices. ... 

Detailed measurements of the s-tetrazine gas-phase spectrum were made. With these data, measurement of the absolute Stokes shift S(t) is possible. Because the Stokes shift is zero in the absence of solvent nuclear dynamics, the magnitude of the Stokes shift at the earliest times represents the amount of relaxation within the experimental time resolution. The steady-state absorption and fluorescence spectra were also measured to provide an independent value of the equilibrium Stokes shift S< With this data, the absolute solvation response function... 

The measurement of polymer solutions with lower polymer concentrations requires very precise pressure instruments, beeause the difference in the pure solvent vapor pressure becomes very small with deereasing amount of polymer. At least, no one can really answer the question if real thermodynamie equilibrium is obtained or only a frozen non-equilibrium state. Non-equilibrium data ean be deteeted from unusual shifts of the %-function with some experience. Also, some kind of hysteresis in experimental data seems to point to non-equilibrium results. A eommon eonsisteney test on the basis of the integrated Gibbs-Duhem equation does not work for vapor pressure data of binary polymer solutions because the vapor phase is pure solvent vapor. Thus, absolute vapor pressure measurements need very careful handling, plenty of time, and an experienced experimentator. They are not the method of choiee for high-viseous polymer solutions. 

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe. 

Table 2.5 Comparison between equilibrium (eq) and nonequilibrium (neq) B3LYP/6-3IC(d) intensity shifts (km mob ) with respect to the gas phase for dimethyl ketone (DMK), methyl ethyl ketone (MEK), sec-butyl methyl ketone (SBMK) and tert-butyl methyl ketone (TBMK). Experimental data from ref [53] are also shown for comparison...

---