HYDROCARBON VAPOR
where F
The saturated vapor pressures of all hydrocarbons with molecular weights over 30, whose data are available, can be correlated by three equations, if boiling point and critical temperature and pressure are known; and the latter can be calculated for the normal paraffin series.
- b)/T
= A(l
-B/T)
(2)
E = 0.0008B - 0.04895 loglo A, = 0.61076 0.0005~~
(3)
+
(4)
Another equation which helped to correlate the critical points was : logi,(mP,/C) = 0.766484 - 0.0000842m - 0.030506 logiom (5) where m = approx. mol. weight (whole numbers) P, = critical pressure, atm. C = critical temp., K. O
+
TABLE I lists values calculated from these equations for Y the series propane to n-octane; important observed values are also included for comparison. Table I1 gives
HE general equation chosen is = A(l
log,o(A/A,) = E(1 - T R ) ( F - T R ) 0.85 for the scope noted
These equations fix P, and C, which were calculated by trial and error. The equation for normal boiling ppints was derived in a previous survey ( 8 ) : log,& = 1.07575 0.949128 lOgioWZ - 0.101 10gi,zfiZ (6)
EDWIN R. COX The Texas Company, Long Beach, Calif.
log10 P
=
The evaluation of E was effected by taking temperatures at which p = 15 mm. mercury and plotting log (B/TI6) against B. This proved to be linear even up to heptadecane. Using these values of T15,two concordant equations were obtained for E and A, which satisfied Equation 2:
PRESSURES
@T
paraffin series, the first to be considered. Accordingly, log (A/&) was plotted against TR(T/T,)for propane, using the data named on Figure 1 and for pentane to octane, using Young's data (17). Each of these curves was found to be parabolic with log (AIA,) = 0 a t T R = 1 and a t T R = 0.85. The fact that all the curves crossed the zero line a t 0.85, as closely as could be detected, was particularly significant and indicated the equation,
(1)
where P = pressure, t, b = temp. and boiling point, O C., T , B = the same, O K. (0" C. = 273.16' K.). A varies through a relatively short range. The equation can be derived from an approximate integration of the Clapeyron equation and has been used extensively. Thiesen (14) used a formula for steam pressures which is equivalent to Equation 1 with A = 5.409 f ( t - b). A formula equivalent to Equation l is used in International Critical Tables (6) with -4constant for low pressures. The evidence indicates that A varies uniformly from the triple point to the critical point but is approximately constant for the vapor pressure of solids in the crystalline state. Cragoe (4) plots curves of A (a) against T / B for a number of substances. Since normal boiling point is arbitrarily selected, whereas critical temperature is a natural datum point, it was thought best to utilize the theorem of corresponding states and plot A against reduced temperature, T/T,, where T , is the critical temperature in O K. Then the obvious values to correlate for different members of a series would be A a t the c r i t i c a l t e m perature, or A,, and the values to correlate for each member of the series would be A/A,. Log A, was found to be preferable as the subs t a n c e characteristic, since it proved to be linear with molecular weight for the normal
values of A for T R = 0.4, 0.5, 0.6, 0.7, 0.78, 0.925, and 1.0, calculated from Equations 2 and 3. These points are used in plotting the curves in Figures 1 to 6. The observed points were calculated from the data noted. The agreement is
LOG,A- 0.63266 t 0.1355 ( I-T.) (0.85-T,/
+
0
DANA SAGE
-
P
FIG.1, PROPANE 1
1
0.6
l
1
1
l
1
0.7
1
1
1
l
I
'
-T
I
I
"" I
1
I
I
l
,
I
I
I
I .O
0.9
0.8 T~= T/T~ 1
I
0 00
1
-
-
CALCULATED FROM :LOG,A=0.64676+
0.19691 (t-T,)
0
4.6
c
4.5
/-
\ o
(0.85-T')
YOUNG
4
1
INDUSTRIAL AND ENGINEERING CHEMISTRY
614
VOL. 28, NO. 5
A CALCULATED FROM :LOG,, A s 0.66076 t 0.24628 (I-T-1
I
AA
5.0
4.6
B'P \ O
t
0
0
4.5
1
1
1
0.4
I
1
l
l
1
I
l
l
1
I
l
l
0.7 , T ~ T/T~ =
0.6
0.5
1
1.0
0.9
0.8
particularly good, when compared with plots of older data where the points would fall entirely off the charts as drawn or were so scattered that not even the shape of the curves could be determined. PRINCIPAL
n =
FOR
230.57 373.27 373. 27a 43.77 43.78a 0.63276' 0 63268a 0.71264 0.71264" 0.13551 b Seibert
TR
0.78
0.925 0.86. 1.0
.. b'
t
0.4
I
I
I
I
I
I
I
I
I
I
0.6
0.5
I
I
I
I
I
l
l
l
0.7
1 1 1 1 1 1 1 1 1 1 1 1 1 0.8 0.9 L.0
A
F IG.6 .O C T A N E
PARAFFIN
4 5 6 7 8 398.75 341.87 371.54 272.51 309.16 669.00 540.20 507.64 426.34 470.24 426.36b 470,360 507.96C 540.01C 569.36C 26,89 24.68 37.51 33.02 29.60 24.70C 26.90C 29.640 37.5d 33.04C 0,63976 0.64676 0.65376 0.66076 0.66776 0.64704 0 0.653710 0.66105C 0.66720C 0:70780 0.70376 0.70023 0.69705 0.69414 . . . . 0.70376C 0.70023c 0.69705" 0.693246 0.16907 0.19837 0.22466 0.24828 0.27005 (15). 0 Young ( 1 7 ) . d Kuenen (according t o
.
5.2
YOUNG LESLIE & C A M A MUNDELL x WORINGER 0
A -
-
0
VALUESOF A TABLE 11. CALCULATED SERIES 0.4 0.5 0.6 0.7
NORM.4L
-
o YOUNG MATHEWS X LESLIE & C A R R A ORMANDY 8. CRAVEN 0 MUNDELL
SERIES 3
Calcd. B , K. Calcd C K Obsvd. d K. Calcd. P i , atm. Obavd. PO,atm. Calcd. logla Ao Obsvd. logio Ac Calcd. mPc/C Obsvd. mPc/C Calcd. E 4 Sage (1)). Onmard) ( 7 ) .
CONSTANTS
x
4.7
5.4
TABLEI.
(0.85-TR)
n = 3
4
4.670 4.534 4.429 4.354 4.314 4.285 4.293
4.846 4.670 4.536 4.440 4.389 4.353 4.363
5 5.016 4.803 4.641 4.526 4.465 4.422 4.434
FOR
NORMAL PARAFFIN
6 5.181 4.932 4.745 4.612 4.642 4.493 4.606
7 5.343 5.061 4.848 4.698 4.619 4.564 4.579
8 5.504 5.188 4.952 4.785 4.698 4.637 4.653
This calculation of A and plotting of the points to the sensitive scales used, is a severe test of accuracy. Without Young's classical work, it would be impossible to coordinate the curves. Assuming that F = 0.85 and that E could be determined from Equation 3, the isomers were plotted in Figures 7 to 10 and showed equally good accord. This was not unexpected, since E depends only upon boiling point. That cyclohexane and benzene (Figures 11and 12) also fell in line, was a distinct surprise, since they are members of quite different series. Propylene also agreed, though the points were so scattered (indicating such large experimental errors) that the plot was not conclusive and is omit,ted. On the whole, the indications are that the rules for E and F apply to all hydrocarbons with n > 2, though this must be verified by further research. METHANE, ethane, ethylene, and acetylene show no 4 6 accordance with the rest of the hydrocarbons as regards E and F, although the parabolic relation between log A
T,= T/T~
and T i s maintained. This relation was also found to be valid for all vapor pressure data analyzed, including hydrogen, oxygen, nitrogen, carbon dioxide, water, ammonia, and several alcohols and ethers. Since no coordination has yet developed for this group, they seem properly to belong to a separate survey. Steam in particular is well worth a separate survey. The preliminary analysis shows such smooth alignment of points and close adherence to the parabolic relation that it tends to verify Equation 2 for vapors in general. It also emphasizes the need for purity of sample. The data on steam
MAY. 1936
INDUSTRIAL AND ENGINEERING CHEMISTRY
seem to show almost a higher order of precision. Part of this is no doubt due to its .industrial importance and t,he amount of labor involved in its investiaation, but part is also due to the wyth which pure samples can be obtained. Impurity of sample has so far been the greatest-handicap to securing concordant vapor pressure data for the hydrocarbons. The importance of purity is also emphasized by the findings in regard to b o i l i n g points (g), The latter were correlated to 0.01" C . from propane to
615
TABLE111. CALCULATIOXS FOR MISCELLANEOUS HYDROCARBONS Obsvd. B Obsvd. C," Obsvd. P o
K. K.
E::Calod. ; POAc A: TR = TR = TR = TR = TR = TR = TR =
5
Iaobutane Isopentane Diisopropyl 261. OSo 301.Olc 331.25C 406.86b 460.960 500.51C 36.54 atm.b 25018 mm.c 23360 mm. 0 0.63578 0.64079 0.64335 0.15990 0.19185 0.21605
.....
0.4 0.5 4.611 0.6 4.485 0.7 4,395 4.347 0.78 4.314 0.925 0.85 & 1.0 4.323 Dana ( 6 ) . b Seibert (18).
.....
.....
4.725 4.571 4.461 4.403 4.362 4.373 Young (27).
4.7
1
1
Diisobutyl Cyclohexane Benzene 382.37C 353. 9Sc 353.370 549.96C 553.110 561.660 18660 mm. 0 30260 mm. C 36395 mm. c 0.65913 0.64781 0.65620 0.25695 0.23423 0.23375 5.352 5.060 4.840 4.685 4.604 4.547 4.562
4.791 4.623 4.496 4.433 4.387 4.399
1
,
(
1
/
1
I
I
,
5.141 4.884 4.691 4.654 4.481 4.431 4.444
I
(
1
1
5.240 4.979 4.782 4.642 4.569 4.517 4.531
1
1
I
I
I
CALCULATED FROM :LOG,, A-0.64079 t 0.19185 (I-T,) (0.85-7,)
4.5 4.6
OG,, A=0.63578+ 0.1599
0
