Vapor pressure determination by differential thermal analysis

Abstract

The ordinate of the frequency distribution is obtained by substitution of Equations 5 and 7 into 4:The beta distribution least squares fit to the cumulative distribution is given in Figure 1. The frequency distribution represented by Equation 10 is given in Figure 2.As a means of checking the procedure used in fitting the density distribution, the average density, 6, is calculated.Only the total volume, V , of the particles must be calculated from the frequency distribution since the total weight, W , was obtained experimentally:It is assumed that an infinitesimal interval change in the volume is given as :The right hand side of Equation 12 may be obtained by equating the right hand sides of Equation 10 and Equation 4. Then the relationship in Equation 7 is used. The final result is writtenThis equation was solved with the aid of the 16 point Gaussian quadrature formula (5,9).To check the values of the shape parameters, p and q, as obtained from least squares fitting of the experimental cumulative density distribution to the cumulative beta distribution, the values of p and q were changed by & 1 %, i 5 %, and =klOx, The average density was recalculated with the new values of p and q. With a change of + 1 % in p and q the calculated density remained unchanged. All calculations were performed on an IBM S/360, Model 44 computer. Double precision (16 significant figures) was used and was necessary for the evaluation of the beta function, the least squares procedure, and the evaluation of the integral in Equation 13. The pertinent data for two independent determinations on the same lot of glass beads are given in Table 111.From the results summarized in Table 111, it is clear that the least squares cumulative and frequency distributions, when used to calculate a mean density of the glass beads, give results in good agreement with the pycnometer results. The error in the calculated mean densities is comparable to that expected when densities are determined by Equation 1. Also, examination of Figure 1 indicates rather good agreement between the calculated and experimental distributions.Comparison of the results for the two independent determinations indicates good agreement between these two sets of measurements.

Measurements of isobaric LLV equilibria of the 1,1,4,4-tetramethyl-2-tetrazene-water binary system: novel experimental approach and modeling essays

“…It is very suitable for the study of melting temperature and enthalpy measurements. More rarely, it can also be used to characterize LV equilibrium from the onset temperature of the endothermic peak corresponding to the vaporization [16][17]. Moreover, methods have been recently developed for the determination of vaporization phenomena of binary mixtures [18].…”