CORRESPONDENCE pubs.acs.org/IECR
Comments on “Experimental Measurement of Vapor Pressures and Densities at Saturation of Pure Hexafluoropropylene Oxide: Modeling Using a Crossover Equation of State” Serge Laugier*,† and Dominique Richon‡ † ‡
I2M, UMR CNRS 5295 ENSCBP, 16 Avenue Pey Berland, 33607 Pessac, France nergetique et Procedes, 35 Rue Saint Honore, 77305 Fontainebleau, France MINES ParisTech, CEP/TEP—Centre E
ir: In the paper under consideration,1 the reported vapor densities are not as accurate as expected by their authors, especially at the lowest pressures, where the perfect gas law must be respected. At the lowest pressures, uncertainties on densities are underestimated by a factor of at least 3. For vapor-phase calculations, the virial equation is a convenient tool:
S
Z¼
Pv B C ¼ 1+ + 2 RT v v
ð1Þ
Furthermore, at pressures below 0.3 MPa (at temperatures of T ∈ [263273 K]), one is justified to set a value of C = 0. Consequently, eq 1 becomes Z¼
Pv B ¼ 1+ RT v
ð2Þ
By plotting Pv/(RT) as a function of 1/v, we can check for linearity of this expression, with respect to experimental values, and have a means to determine the value of B. For pressures of P > 0.8 MPa (T ∈ [323358 K]), C is a nonzero value. Then, eq 1 is written as Pv C 1 v ¼ B+ ð3Þ RT v By plotting Pv/(RT) as a function of 1/v, we can determine both B and C. For intermediate pressures (P = 0.30.8 MPa), two tests have been performed in order to verify if using a value of C = 0 is a reasonable approximation. These test results are presented in Figures 15. At 263 and 273 K, we observe singularities as displayed in Figure 1. The experimental points are satisfactorily represented by linear functions; however, the latter plots do not pass through the coordinates (1/v = 0, Z = 1). This observation suggests systematic error in these datasets. At temperatures of T = 283303 K, the hypothesis of neglecting the third virial coefficient is justified. Indeed, at each of these temperatures, the curve (where the slope is equal to B) representing Z = f(1/v) is linear (see Figure 2) and the curve representing (Z 1)v = f(1/v) is linear, with slope C = 0 and the ordinate at the origin being B (see Figure 3). There are considerable deviations for low abscissas values, but the Z = f(1/v) curves go through coordinates (1/v = 0, Z = 1), contrary to that which was observed in Figure 1. At T = 323358 K, we need to introduce a third virial coefficient, because Z = f(1/v) is not linear anymore (see Figure 4), r 2011 American Chemical Society
Figure 1. Compressibility factor as a function of inverse volume at 263 K: experimental value (represented by a black cross (+)) and linear tendency line (represented by a solid black line (—)).
Figure 2. Compressibility factor, as a function of inverse volume at 283 K: experimental value (represented by a black cross (+)) and linear tendency line (represented by a solid black line (—)).
over a wide pressure range. Figure 5 allows one to determine the value of the third virial coefficient (C). This figure shows high inaccuracy for the smallest density values. At ∼0.5 kmol m3 (see Figure 5), we observe surprising discontinuity. To display the inaccuracies in the measurements, density values were calculated from the virial equation using the values of B and C obtained by linear regression of the experimental data.
Published: July 05, 2011 9473
dx.doi.org/10.1021/ie2011559 | Ind. Eng. Chem. Res. 2011, 50, 9473–9475
Industrial & Engineering Chemistry Research
Figure 3. (Z 1)/v, as a function of inverse volume at 283 K: experimental value (represented by a black cross (+)) and linear tendency line (represented by a solid black line (—)).
CORRESPONDENCE
Figure 6. Second virial coefficient, as a function of temperature: data determined from experimental density values (represented by solid circles (b)) and extrapolated values (represented by blue open boxes (0)).
Table 1. Second and Third Virial Coefficients at Various Temperatures
a
Figure 4. Compressibility factor, as a function of inverse volume at 353 K: experimental value (represented by a black cross (+)) and linear tendency line (represented by a solid black line (—)).
Figure 5. Plot of (Z 1)/v, as a function of inverse volume at 353 K: experimental value (represented by a black cross (+)) and linear tendency line (represented by a solid black line (—)).
At 263 and 273 K, since the measures showed systematic errors, values of B were estimated by extrapolating the values at higher temperatures (see Figure 6 and Table 1). The relative density deviations, as a function of density, are shown in Figures 79 for three temperatures. The error limits estimated by the authors of the experimental data are shown in these graphs as red lines. In Figure 7, we have drawn systematic errors associated to the data (∼2.1%). For almost all other temperatures, for densities
temperature, T (K)
B (m3 kmol1)
C (m6 kmol2)
263.27
0.8036a
273.21
0.7158a
283.17
0.6330
293.22
0.5748
303.15
0.5085
323.22 343.26
0.4137 0.3645
0.015 0.028
353.06
0.3583
0.041
357.92
0.3487
0.041
Estimated value.
Figure 7. Relative deviation in density, as a function of density at 263 K: experimental data (shown by a black cross (+)) and the estimated deviation boundary1 (represented by the red lines).
values of
