a d GEORGE THODOS iA'orthwestei-n Technological Institute, Evanston, Ill.
A
critical literature survey of experimental vapor pressure data for the light normal saturated aliphatic hydrocarbons has made possible the development of an empirical vapor pressure equation accurate over the entire range between the triple and critical points. An accurate representation of the vapor pressure curve necessitated separate treatments of the inherently different high and low vapor pressure regions. The point at which these regions merge has been arbitrarily defined as the divergence point. A generalized equation of the form : logP = A + B
(9 (i)' +
represents accurately all vapor pressure data below the divergence point. By the addition of a graphical residual
EXACT mathematical representation of the vapor pressure of hydrocarbons over the complete range included between the triple and critical points has long been the object of considerable study. The difficulties encountered in expressing such a representation are due to the inherent irregularities associated with the vapor pressure curve. I n the past, attempts have been made to define this function over the entire range by integrating the simplified Clapeyron equation t o produce the following expression: log P = A B/T (1)
+
where P = vapor pressure, T = absolute temperature, and A and B = empirically determined constants. Experimental evidence has proved conclusively that this simplified expression is applicable within relatively narrow limits of temperatures. I n 1936, Cox (15) attempted to represent accurately the vapor pressures of all the hydrocarbons with a molecular weight greater than 30 over the complete range between the triple and critical points by a simple modification of the above equation. Cox's proposed equation is of the form:
l 0 g P = A (1 -
$)
where T Bis the absolute boiling point and P is the vapor pressure in atmospheres. A is a function of temperature which was found to have the same general shape for all compounds tested. Cox showed that log A was parabolic in T or, in terms of reduced temperature: log A = log A , E(1 - TR)(F - T R ) @a) log Po where A, is the value of A at the critical point, A , = T,T,-,
+
and E and F are characteristic of the compound. Inasmuch as F was found to be 0.85 for all hydrocarbons, there is only a single empirical constant left, E, which Cox correlated with the boiling point. Gamson and Watson (29) proposed to define the vapor pressure function over its complete range with the following vapor pressure equation:
applicable above the divergence point, the generalized equation may be used over the entire range of vapor pressures. The graphical residual has heen expressed mathematically as: A = D
($ - l ) n
All the constants, A , B , C, D , and n , have been uniquely determined for each hydrocarbon and have been expressed as functions of the normal boiling point. A large number of vapor pressures calculated for each of the hydrocarbons by the above method produced an average absolute error of 0.29'~. This indicates a marked improvement in accuracy over past vapor pressure equations proposed for similar compounds.
where A , R, and b are constants characteristic of the substance, and T , is the reduced temperature. In this equation, the exponential term accounts for deviations from a straight-line relationship in the loiv pressure region and becomes insignificant a t elevated temperatures. The introduction of the graphical residual in analyzing vapor pressure data represents an empirical approach which has made possible an accurate graphical evaluation of vapor pressure data over the complete range. This method involves the establishment of a straight line of the form represented by Equation 1 between any two convenient vapor pressure reference points. The commonly used references are the boiling and critical points. The deviation of the logarithm of the experimental vapor pressure from the calculated value, a t a given temperature, is defined as the graphical residual. This approach has been successfully employed by Hachmuth, Hanson, and Smith ( S I ) , Kay (SQ), and Williams and Koch (87) and proves satisfactory for a number of specific cases. The graphical residual, although accurate and significant in defining the vapor pressure relationship near the critical point, fails from a standpoint of convenience and accuracy in the region of lower vapor pressures. An attempt to obtain a correlation of graphical residuals near the critical point for the normal saturated aliphatic hydrocarbons has thus far proved unsuccessful. Using the best available literature data, Solari (80) calculated the graphical residuals for the light normal saturated aliphatic hydrocarbons up to and including n-octane. The resulting graphical residuals failed to produce an adequate quantitative pattern for this homologous series. Upon analyzing these inconsistencies, it m-as concluded that the graphical residual was extremely sensitive and required precise data for its proper application. Although the boiling points of the normal saturated hydrocarbons are well established, the critical points for the majority of these have not been determined with the same degree of accuracy. Errors as small as +=0.5" C. in the critical temperature are sufficient t o mask the analysis and 1514
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1950
1515
Lto3 ( T = 'KELVIN) T Figure 1.
Vapor Pressure-Temperature Relationships for Normal Saturated Hydrocarbons
preclude a generalized correlation of graphical residuals for the hydrocarbons of this homologous series. GENERALIZED PROPERTIES OF VAPOR PRESSURE CURVE
An extensive literature search has been made for all data on the vapor pressures of the normal saturated aliphatic hydrocarbons published t o date. Young (92-94) was able to produce remarkably good vapor pressure data a t the turn of the century. The recent contributions of Aston ( I ) , Smith (77), and Rossini and co-workers (88) have provided ample accurate vapor pressure information in the low pressure region to make possible a study of certain fundamental properties associated with the vapor pressure curve. I n order to obtain a comprehensive insight into the vapor pressure relationships of the normal saturated aliphatic hydrocarbons, all the available vapor pressure data between the triple and critical points were considered. A screening process was ,then instigated objectively to select the more accurate data on which further studies were t o be made. This was accomplished on a large plot using logarithmic pressure in millimeters of mercury as ordinate and reciprocal absolute temperature in degrees Kelvin as abscissa. For this plot, an ice point of 273.165' K. was used throughout. Inconsistencies within a group of vapor pressure determinations by a single investigator were considered grounds
for discarding these data. Also, all data obtained using questionable experimental techniques and which were not in agreement with the general over-all pattern of the curves were deleted. The over-all effect of the screening process was to eliminate unreliable data. The vapor pressure curves included in Figure 1 represent the results of the screening process. All the references compiled from the literature and the selection utilized for the development of Figure 1are presented in Table I. For the normal saturated hydrocarbons between methane and n-octane, inclusive, adequate critical data were available to establish a critical locus. These values are presented in a s u m & rized form in Table 11. Unfortunately, no experimental critical data were available for normal saturated hydrocarbons above moctane. Critical constants for the higher homologs appearing in Table I1 were obtained by extrapolation of the critical locus appearing in Figure 8. A review of the curve pattern indicated in Figure 1reveals some interesting characteristic properties associated with these vapor pressure curves. Methane exhibits a nearly linear vapor pressure relationship between its triple and critical points. With increasing molecular weight the vapor pressure relationships show increased curvature in the low pressure region. This effect is most pronounced with n-dodecane. As pressure increases, the logarithmic vapor pressure-recipro-
INDUSTRIAL AND ENGINEERING CHEMISTRY
1516
Vol. 42, No. 8
TABLE I. DISPOSITIOK OF AVAILABLEVAPORPRESSURE DATA References Cited - - -. -. SIethaiie
Henning and Stock (34) Karwat (36) Keyes, Taylor, and Smith
Pieliniinars Selection Used in Figure 1
Cardoso ( 1 3 ) Cronimelin (16) Dewar ($2) Eucken and B c r v r ( 2 4 ) Viseher and K l o k m ( 2 6 ) Freeth a n d Versclioyle (2s)
Olsoewski (64) Volora (84)
Beattie. Tfadlork and Poffenberger (8) Beattie, Sn, and Siniard (7) Burrell and Robertson (10) Cardoso and Hell (/4) Delaplace (19) Fischer and Kleinm (2G) Hainlen (32) Kay ( 3 7 ) Kharakorin (45) Kuenen (46) Kuenen and Robson (46) Lamb and Roper (48) Looinis and Waiters (68)
Lu, Newitt, and Riiliemann Beattie, Hadlock. and Pof(53) fenberger (5) M a a s s and McIntosh ( 6 4 ) Beattie. Bn, and Siniard 17) hIaa*s and Wright ( 5 6 ) Alchlillan (66) K&' ( 3 7 ) K&'(37> Mason, Yaldrrtt, and Kharakoiin Kharakorin (43) iL3) Maass 167) Kurnen i(46) Kuenen L6) &yer (60) Iiuenen a& and Robson (46) Olbzewski ( 6 2 ) Lanmh and Roper (48) Olszeaski (63') Loonii. and \?'alters (62) (62) Porter (66) 1.11 Vpvitt, Vpvitt a n d RiiheSage, Webster, a n d Lnccy iiianii (59) (rii Porter (66) W'iit ( O D )
cal absolut'e temperature relai ionship k n d s to become linear, UIItil a t moderate pressures a reversal of curvature is observed. The typical relationship may be characterized by the elongated S shaped curve presented in Figure 2. The point at m-hich the curvature changes is here referred to as the inflection point. This behavior was noted for all hydrocarbons for which data near thci critical point were available. The effective reversal of the vapor pressure curves in the critical region becomes somewhat obscure in Figure 1 because of a necessary size reduction of the original plot. The reversal, however, is apparent in the enlarged plot of this region presented in Figure 3. An exact mathematical representat,ion of such a function is complicated and would prove rather difficult to present analytically over the entire vapor pressure curve in a simple expression. Because of t'his limit,ation, it, was considered advisable to anttlyze the exact nature of the upper and lower curved sections of the vapor pressure curve sep:iratelg- for the possible existence of basic
. Figure 2. Typical Vapor PressureTemperature Relationship A . Critical point B. Inflection point C. Boiling point
August 1950
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
TABLE I.
nISPOSITION O F
AVAILABLEV.4POR
References Cited ,
