INDUSTRIAL A N D ENGINEERING CHEiVISTRY
December, 1925
1287
Pressure-Temperature Charts-Extended
Ranges’
By George Calingaert and D. S. Davis MAS~ACHUSETTS INSTITUTE OF
%CHNOLOGY,
CAMBRIDGE,
T HAS been shown2 that the empirical method of Coxs of plotting vapor pressure data was suitable for the range of 0” to 300” C. in the case of several vapors. It is the purpose of the present paper to show that this method is applicable over very much greater ranges. The usual straight-line plot, based on the Clausius-Clapeyron equation, is a plot of the logarithm of the vapor pressure versus the reciprocal of the absolute temperature. Over short ranges the data for a wide variety of substances fall on straight lines and the lines
I
MASS., AND UNIVERSITY OF VERXONT,
BURLINGTON, VT.
paraffin series, which has been shown by one of the authorss to be applicable as well in the cases of the alcohols, halogensubstituted benzenes, and organic acids, appears to be accurate enough for many purposes and is the most convenient. By the Cox method, the nonuniform temperature scale is laid off from a straight line drawn a t any convenient angle with the logarithmic pressure abscissas. The straight line is taken- as the vapor pressure curve for water and the temperature ordinates may be marked off along it with the assistance of a steam table. This suffices very well for the range from the freezing point to the critical temperature of water. For temperatures above the critical (370” C.) a method has been developed for laying off the temperature scale, making use of the equation empirically derived in the previous b/t, where y is the distance from 0” to paper, l / y = a t o C., the constants depending upon the scale and units chosen. The same equation may be used in locating the lowtemperature ordinates, and the validity for both low-temperature and high-temperature work is substantiated by the plots presented here. It will be shown that Cox’s method may be regarded as being based upon the assumption that the vapor pressure of a substance can be expressed by an equation of the form
+
b
$ -7
8k
R
PRESSURE MM HG
Figure 1-Normal
Paraffin Hydrocarbons. Numbers Are Values of n i n Formula, CtrHin+z6B, Benzene
for related substances are reasonably parallel. However, the log p vs. 1/T plot does not usually give straight lines for data covering large temperature ranges. A se:ond fairly simple method is that of plotting log p against l / ( t c ) , but it is difficult to choose a value of c suitable for a wide range of substances. The value 260, which occurs in the Antoine equation4 for water vapor,
+
logp
A-
B + 260
t
where p is in millimeters of mercury and t is in degrees1Centigrade, will be shown to be not entirely satisfactory. Still another, that of A ~ h w o r t hmay , ~ be considered. He points out that the form log
fi
= A-
G +f
B
does not lead to exactly straight lines, and makes use ofyan empirically derived equation in which the T of the van’t Hoff equation is replaced by f ( T )=
d W - c
His plot gives rise to very good straight lines but has the disadvantage of being somewhat complicated. The empirical method of Cox for hydrocarbons of the Received July 17, 1925. THISJOURNAL, 17, 7, 736 (1925). * Ibid., 15, 6 , 692 (1923). 4 Chwolson. “Physik,” Vol. 111, 3rd German ed., 1906, p. 741. 6 J . Inst. Petroleum Tech., 10, 787 (1924). 1
2
PRESSURE MM HG
Figure 2
It is evident that a plot of l/y vs. l / t is a straight line, and the “zero ordinate” for this work may be found by solvTHISJOURNAL, 17, 735 (1925).
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1288
ing the equation for t when l/y is set equal to zero. value is - 230 " C. Antoine's equation is given as logp = 8.3118 -
This
1956 + 260
t
Vol. 17, No. 12
a given family of substances intersect at a common point. Thus only a single experimental point is required to enable one to draw a fairly satisfactory curve, once the point of convergence is known. Such curvature as does exist in some of the lines plotted by the Cox method invariably occurs toward
but since 230" C. is to be used instead of 260" C. it will be necessary to choose new,values for A and B. These constants may be evaluated by substituting the vapor pressure data for water at, say, 100" and 300" C., which is 760 mm. and 64,290 mm., respectively. The equation becomes log f~ = 7.991
1687 - t+ 230
Figure 3
TabIe I shows a comparison of values of the vapor pressure of water calculated from Equation 1 with the actual values and with the values calculated from Antoine's equation. 1(O
C.)
0 40
IO0 200 300
Table I -----Vapor Pressure (Mm.)--Antoine Actual Eauation 1 6.18 4.58 4.63 61.9 55.3 55.7 757 760 759 11,500 11,600 11,800 66,100 64,300 64,400
Figure 5
Bearing in mind that the "zero ordinate," -230" C., was obtained from an analysis of Cox's temperature scale only, inspection of this table shows (1) that the nonuniform scale of temperature ordinates as given by the Cox method is the equivalent of a reciprocal temperature scale, the reciprocal being l / ( t 230) instead of the usual l / ( t 273) commonly designated as 1/T, and (2) that Equation 1 represents the data somewhat better than does the Antoine equation, indicating that the Cox method is superior t o a log p vs. l / ( t 260) plot.
+
PRESSURE MM HG
+
the low-temperature ends, which are generally the least important ends and where the data are least reliable. Although covering the range of only 0" to 370" C., Cox's paraffin hydrocarbon plot (Figure 1) has been redrawn from the data compiled by Wilson and Bahlke,' which is thought to be more reliable than the data originally used by Cox. Figure 2 is a paraffin hydrocarbon plot which covers a much greater temperature range-i. e., from -130' C. to convergence. It will be noted that this plot includes the graphs for
+
PRfSSURC MM HG
Figure 4
Figures 1 to 6, inclusive, give the pressure-temperature data plotted according to the Cox method. It will be noted that this method of graphical representation gives very fair straight lines with the additional advantage that the lines c
given in Figure 1. Figures 3 and 4 are plots for the halogen-substituted benzene and the alcohol series, r e s p e ctively, and are a like those prePRPJSUG MM HG sented before but Figure 6-Metal Series with the addition of the range below 0 ' C. Figure 5, the silicon hydride series, includes various substituted halogen and methyl hydrides. l i ' i m w 6 is a high-temperature plot for metals and shows that
' ''
---
'
_I
'NAL,
16, 115 (1924).
