Densities of the Liquid a n d Dense Phase Regions and G E O R G E THODOS T h e T e c h n o l o g i c a l Institute, Northwestern U n i v e r s i t y , Evanston,
WILLIAM J. BREBACH'
T h e expansion factor correlation introduced i n 1913 by Watson (21) h a s received considerable interest and application for t h e calculation of thermodynamic properties and d e n s i t i e s of t h e liquid s t a t e . In t h i s connection, t h e saturated liquid density data of Young (23) for isopentane and t h e high pressure data of Sage a n d L a c e y (18, 19) for propane and n-pentane were used t o c a l c u l a t e values of t h e expansion factor, defined a s :
where
7,= critical temperature, OK.
P, = critical pressure, atm. M = molecular weight p = density, grams per cc. Watson points out t h a t a correlation of t h e expansion factor with reduced temperature and pressure failed to produce a generalized relationship, as o v a l u e s a t t h e s a m e reduced conditions were found t o vary by more than 20% for different substances. T o overcome t h i s limitation, Watson proposed t o calculate d e n s i t i e s of other s u b s t a n c e s from a s i n g l e liquid density, p l , through t h e relationship,
Pl
p=o,w where o1 is the expansion factor corresponding to conditions of density pl. Equation 2 h a s proved of considerable utility for t h e calculation of liquid d e n s i t i e s over extended ranges of temperature and pressure. T h e recent introduction of t h e compressibility factor a t the critical point, z,, a s t h e third correlating parameter (7, 9, 11, 16) s u g g e s t s t h a t a correlation of t h e expansion factor with reduced temperature and pressure could become generalized if related t o t h i s parameter. Accordingly, for t h e direct calculation of densities, t h e correlation presented by Watson (21) should b e restricted t o s u b s t a n c e s having z c values comparable t o t h o s e of isopentane (2, = 0.268), n-pentane ( z , = 0.269), and propane (2, = 0.278).
111.
tures ranging from -18.3' to 200°C. T h e experimental density values of Elenedict a r e plotted in Figure 2 and cover t h e pressure range included between P, = 2.98 and PR = 174 and t h e temperature range included between TR = 0.714 and TR = 3.749. T h e density values of t h e saturated liquid s t a t e presented in Figure 1 and t h o s e of Benedict presented in Figure 2 have been converted with Equation 1 t o produce expansion factors, for t h e corresponding temperature and pressure conditions. For t h e s e calculations, t h e critical constants used for nitrogen were T, = 126.2'K. and P, = 33.5 atm (15). A c r o s s plot of t h e s e calculated o values permitted t h e construction of Figures 3 and 4. Figure 3 presents expansion factors for nitrogen a s functions of reduced temperature and pressure on rectilinear coordinates. In t h i s figure, t h e high pressure data of Benedict (5, 6 ) made possible the calculation of o values up to a reduced press u r e of PR = 180 and a reduced temperature of TR = 1.4. Figure 4 presents a n extension of t h i s temperature range up t o 7R = 4.0, on a logarithmic coordinate. G E N E R A L I Z E D A P P L I C A T I O N OF EXPANSION FACTOR CORRELATIONS
In accordance with t h e recent introduction of t h e compressibility factor, z,, a s t h e third correlating parameter, Brock a n d Bird (9) apply the principle of corresponding s t a t e s to the correlation of surface tension. Hobson and Weber (11) utilize t h i s parameter for t h e correlation of compressibility factors of t h e saturated vapor and !iquid states. Similarly, Lydersen, Greenkorn, and Hougen (16) adapt t h i s parameter for the correlation of reduced d e n s i t i e s applicable to t h e liquid and gaseous phases.
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NITROGEN
D E V E L O P M E N T OF EXPANSION F A C T O R P L O T FOR N I T R O G E N
T h e saturated liquid density data of Mathias, Kamerlingh Onnes, and Crommelin (17), van Itterbeek, d e Bock and Verhaegen (13), a n d Baly a n d Donnan (3) have been used t o e s t a b l i s h t h e saturated liquid line presented i n Figure 1. T h e density v a l u e s of t h e s e investigators a r e in good agreement a t t h e lower temperatures. At t h e higher temperatures, t h e density values of Mathias, Kamerlingh Onnes, and Crommelin (17) represent t h e only source of data which permit a n extension of t h e saturated liquid l i n e to t h e critical point. T h e critical density of nitrogen, p c = 0.311 gram per cc., reported by Kobe and Lynn (15) h a s been used t o produce t h e expansion factor for nitrogen a t t h e critical point, a, = 0.0418. T h e comprehensive experimental nitrogen density determinations of Benedict (5, 6) have proved invaluable in t h i s study. Benedict presents nitrogen d e n s i t i e s for p r e s s u r e s ranging from 100 to 5835 atm. a n d for tempera'Present Chicago, Ill.
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INDUSTRIAL AND ENGINEER1 NG CHEMISTRY
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Figure 1. Density-temperature relationship for saturated liquid nitrogen
T h e dependence of t h e expansion factor on t h e z, parameter is well illustrated in Figure 5 in which a r e presented the expansion factor l i n e s resulting for the saturated liquid data of nitrogen ( z , = 0.291) and that of isopentane T h e data for isopentane used by Watson (22) (2, = 0.268). to produce t h e original o factor correlation h a v e been utilized t o produce t h e isopentane relationship of Figure 5. T h i s relationship is found t o diverge from t h e corresponding nitrogen c u r v e with decreasing temperature. T h e disVOL. 3, NO. 2
parity of t h e s e relationships c a n be attributed to differences in critical compressibility factors. Accordingly, F i g u r e s 3 and 4 should b e capable of producing d e n s i t i e s directly for s u b s t a n c e s having t h e s a m e compressibility factor a t the critical point a s that of nitrcgen, z , = 0.291. A cursory literature examination indicates that argon, carbon disulfide, carbon monoxide, chloroform, methane, oxygen, and phosgene have critical compressibility factors near 0.291. T h e exact z c values and corresponding critical constants for t h e s e s u b s t a n c e s a r e presented in T a b l e I. A number of density values for the s u b s t a n c e s presented in T a b l e I h a v e been calculated for the saturated liquid and d e n s e p h a s e regions. T h e s e calculated values h a v e been Lompared with experimental densities reported in t h e literature to produce the deviations presented i n T a b l e I. F o r argon, carbon monoxide, methane, and oxygen, the resulting deviations were found to b e c l o s e to 1%,whereas those of chloroform and phosgene were -8.42 and -7.58%, respectively.
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