Infinite dilution relative volatilities

The obtained values of FX2 for these samples are plotted against time from solvent injection to establish the maximum value for the separation factor, F12 (max). Further details about the experimental technique are in the original paper (35). The larger the value of FX2 (max), the better the solvent can separate the mixture, indicating a better extractive distillation solvent. This was verified by comparing values for FX2 (max) and infinite dilution relative volatilities (a°i2) for the system n-hexane-benzene with six different solvents. The results presented in... 

Infinite Dilution Relative Volatilities through GLC. If the solvent amount injected in the column is high enough so that infinite dilution conditions for the injected solute prevail, it is readily shown (38) that the separation factor becomes equal to the infinite dilution relative volatility ... 

Doring (39) has shown that infinite dilution relative volatilities can be evaluated through GLC. He prepared a special column for each solvent under consideration, a tedious project. A year later Sheets and Marchello (38) showed that separation factors increase with increased amounts of injected solvent. Later Tassios (35) found out the same to... 

Table V. Separation Factors and Infinite Dilution Relative Volatilities for the System ft-Hexane (l)-Benzene (2) at 67°C (35)...

Figure 7. Relationship between maximum separation factors and infinite dilution relative volatilities for the system n-hexane-benzene with various solvents at 67°C (35)...

The predictive techniques are rather accurate. However, significant errors have been observed in few cases (4, 13, 27, 40). No direct comparison between the three predictive methods is available. The authors of the parachor method (27) claim that their method yields equal or better results than the PDD method for the cases considered in their study it is believed (42), however, that the latter is more reliable and it is recommended. The Weimer-Prausnitz method probably gives less accuracy than the PDD method, but it is more general. For example, Hanson and Van Winkle (40) report that their data on the hexane-hexene pair were not successfully correlated by the WP method. The Helpinstill-Van Winkle modification is recommended over the WP method. Recently, Null and Palmer (43) have presented a modification of the WP method which provides better accuracy but it is less general. The PDD method should be used cautiously when extrapolation with respect to temperature is used (27). When the GLC method is used, reliable results are expected. Evaluation of infinite dilution relative volatilities is recommended (36). 

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

Direct measurement of y would confirm whether or not the solution is infinitely dilute at saturation. Lobien and Prausnitz (23) have attempted to measure this effect in a few systems by comparing the solubility limit with measurements of y from differential ebulliometry. The systems they studied all had solubilities of a few percent, and for these systems they found significant deviations from yi = 1/xi. It would be useful to have measurements for more dilute solubilities, but in this case the limiting activity coefficient becomes very large, and ebulliometry is inapplicable for high relative volatilities. Perhaps such data could be taken by ebulliometry for systems where the solute is much less volatile than water, or by chromatographic methods. 

Equation 21 shows that the infinite dilution fugacity coefficient in liquid, (< iL)°° is identical to the relative volatility of infinitely dilute Solute 1 over Solvent 2. 

Before computing the relative volatility for the specified mixture, it is of interest to estimate the relative volatility for n-heptane and toluene at infinite dilution in phenol. Often, this represents the largest relative volatility obtainable for the given solvent at a given pressure. With essentially pure phenol, the temperature is the boiling point (819°R, 455°K) at the specified pressure of 1 atm (101.3 kPa). At this low pressure, (5-21) is applicable for the K-value. Combining this with (1-7), (5-31), and (5-34), we have... 

Use available experimental data at infinite dilution with the van Laar equations to estimate the relative volatility between n-heptane and toluene at atmospheric pressure for a liquid-phase mixture consisting of 5 mole% toluene, 15 mole% n-heptane, and 80 mole% phenol. Also compute excess enthalpy for this mixture. 

ED alters the relative volatility of a binary system when the components of the system have different polarities (Fig. 12.1). It is normal to operate at 0.8 to 0.9 mole fraction of ED entrainer in the B and C sections of the extraction column (Fig. 12.2), which can raise the relative volatility to a value at which the separation is easy. Such a high proportion of the entrainer gives activity coefficient values of components 1 and 2 which approach the activity coefficients at infinite dilution. 

In terms of the 5 2 value, an effective entrainer is capable of different types of physical interactions (polar, dispersive, hydrogen-bonding, etc.) with the two components to be separated to allow for the value to be much larger than unity to allow for a better separation by altering the relative volatility of the system, where the relative volatility at infinite dilution is ... 

In contrast to the behavior of noble gases, the radial distribution functions of water around the infinitely dilute anion (Cl ) and cations (Na" " and Li ) show a rather strong solvation, i.e., relative to pure water there is a substantial increase in the local water density around the ions due to strong ion-dipole interactions (Figures 18 and 19). From a microstructural viewpoint, the presence of an ion induces an increase in the solvent local density, relative to the pure solvent, with a consequent decrease of (dP/dxu) j (non-volatile... 

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