VAPOR PHEjSURE-TEIIPER1TURE
(24) (25) (26) (27) (28)
RELATIOSSHIPS
425
T - o ~ ~ o vZ.: a , Acta Physicochim. U.R.S.S. 21, 563 (1946). WARK,I. IT.: J. Phys. Chem. 40, 663 (1936).
WARK, I. W.:J. Phys. Chem. 37, 639 (1933). DE KITT, C. C.: J. Am. Chem. Soc. 57, 775 (1935). Z ~ X I G AH. , G. : Bol. minero soc. nacl. mineria (Santiago, Chile) 47, 83 (1935); Chem. Abstracts 30, 75116 (1936).
Y=1POR PRESSLRE-TE1\IPERA4TURE RELhTIOSSHIPS A M O S G T H E BR-4SCHED PAR-kFFIS HTDROC-4RBOKS HARRY W I E K E R D e p a r t m e n t of Chemistry, Brooklyn College, Brooklyn, Mew Yo&
Receixed July 24, 1947 ISTRODCCTIOS
The difference in normal boiling point betn-een a branched-chain paraffin and its straight-chain isomer can be expressed (4) as a function of two structural variables by the equation' 98 At = - AW f 5.5Ap n2 In this paper, it is shon-n that the boiling points of branched-chain paraffins also obey this law a t pressures other than 7GO mm. of mercury, with only the empirical constants changed. In any equation relating the vapor pressures and temperatures of paraffins, the constants involved \Till differ for individual isomers, and are therefore functions of molecular structure. If the boiling points of isomeric paraffins at different pressures are linear functions of the strirctural parameters I w and A p , it is probable that the constants of temperature-pressure equations will be represented by similar functions of these til-o variables. For the ,Intohe vaporpressure equation this rule holds, and the constants can be correlated by such functions. BOILISG P O I S T S .1T D I F F E R C S T PRESSURES
The general form of equation 1, a t pressures other than TGO mm. of mercury, is k
A! = - AW n2
For a single group of isomers
tz
It
+ bAp
is constant, and equation 2 hecomes =
alu:
+ hIp
(3)
w is the sum of the distances, in terms of carbon-carbon bonds, betxeen the members of all pairs of carbon atoms in the molecule; p is t h e number of pairs of carbon atoms separated by three bonds; I t = f , - t,,,; l i o = zcn - tulso;I p = p n - p l s 0 .
426
H h R R Y \VIENER
-kccurate values for the boiling points of many hranched-chain paraffins a t pressures other than 760 mm. of mercury are available, as a result of experiments carried out a t the Sational Bureau of Standards, and may be used t o determine whether equations 2 and 3 hold at different pressures. In these experiments, Willingham, Taylor, Pignocco, and Rossini (5) determined the temperatures of the liquid-vapor equilibrium for numerous hydrocarbons over a wide range of pressures, including the boiling points of seventeen octanes (all except 2,2,3,3-tetramethylbutane) at tn-enty fixed pressures ranging from 47.7 t o 779.3 mm. of mercury, above about 12OC. Equation 3 was fitted to the observed boiling points of these seventeen octanes at three pressures,-779.3, 402.4,and 57.5 mm. of mercury,-by the method of least squares. The values of the two constants of equation 3, obtained in this manner, are: at 779.3 mm., a = 1.520, b = 5.56; a t 402.4 mm., n = 1.485, b = 5.31; at 57.5 mm., a = 1.386, b = 4.68. The variation of the two constants with pressure is v-ell represented by the equations CI
=
0.118 log P
1) = 0.77 log P
4-1.178
(4)
+ 3.32
(5)
&isk = G4a for the octanes, the general equation for the difference in boiling points of tivo isomers, as a function of their structure and of pressure, becomes
Af
=
(7.55 log P f 75.39)
/L2
+ (0.77 log I' + 3 . 3 2 ) A p
(6)
The manner in which thi5 equation reproduces the observed values ir shown in table 1. The average deviations for the sel-enteen octanes are f 0.59"C. a t 779.3 mm., =t 0.53"C. a t 402.4 mm., and f 0.49"C. at 57.5 mm. of mercury. Equation 6,therefore, appears to be applicable about equally well over the pressure range from 50 to 800 mm. of mercury. Comparison of values calculated from this equation rvith observed boiling points for some lower paraffins a t other pressures supports this conclusion, the average deviations being well below 0.5"C. The ratio of the constants a and b of equation 3 varies with pressure. The fraction b / a decreases from 3.66 at 779.3 mm. to 3.58 at 402.4 mm. and to f3.37 a t 57.5 mm. of mercury. This indicates that a t lon- temperatures, the relative importance of the structural factor, compactness (w), becomes somewhat increased over that of the parameter representing interatomic attraction forces ( p ) . Inspection of table 1 also shows that compounds for which A p = -4 have increasing values of Af at decreasing pressures, while for compounds which have Ap = 0, Af falls rapidly with decreasing pressure.? Other factors being equal, the separation by distillation of a branched-chain from a normal paraffin isomer, or of two branched-chain isomers, is therefore best performed a t low pressures if the t x o compounds have widely different values of Ap, while better results are 2
For values of Iw and I p s see table 3
VAPOR PRESSURE-TE,MPERhTTRE
42i
REL.1TIOSSHIPS
obtained a t higher pressures for substances I\-hich have the same, or only slightly different, values of' A p . C O S S T A S T S O F THE . I S T O I S E EQUA%TIOS
The -1ntoine equation (2)
R
t
- log P
-c'
(7)
TABIX 1 Boiling points of octanes
224hl5 233115
24 95 11 81
24 64 12 03
-0 31
+o
22
26 7 3 11 35
26 00 11 30
-0 73 -0 05
27 34 I 1 22
26 11 10 hY
-0 (30 -0 34
428
HARRY \T'IESEII
The variation of tliese constants with cliaiiges in isomeric structure can be represented by relations similar t o ecpatioii 2 . Equation 2 vas therefore fitted t o the data for-1 and B. given in the A.P.1. tables. by the nietliod of least squares. leading t o equations 8 and 0 . The constant C is calculated by substituting into TABLE 3 Constatits of thr d n t o z n e cquution COUPOUKD
AP
AW
_
_
_
~
2113. . . . . . . . . . . . .
1
1
6.748
2314 . . . . . . . . . . . . . 22313 . . . . . . . . . . . .
2 4
0 2
3
0
4
6
-1 0 -1
4 6 8 10 10 8 12 14
0 -1 -2 0 -2 0 -2 -2
5 8 9 12 13
0 -1 -1
14 13 10 17 16 17
-2
'0
-4
21 IS 22 19
-3
2115 . . . . . . . . . . . . . 3115 . . . . . . . . . . . . . 22114 . . . . . . . . . . . . 23114 . . . . . . . . . . . .
. I
2116 . . . . . . . . . . . . . 3116 . . . . . . . . . . . . . 3E5 . . . . . . . . . . . . . 22115. . . . . . . . . . 23AIj . . . . . . . . . . . . 24h15 . . . . . . . . . . . 33A15 . . . . . . . . . . . 223114
2117 . . . . . . . . . . . . . 3117. . . . . . . . . . . . . 4117 . . . . . . . . . . . . . 3E6 . . . . . . . . . . . . . 22bIG . . . . . . . . . . . . 23m. . . . . . . . . 241\16 . . . . . . . . . . 2316. . . . . . . . . 331IG . . . . . . 34116 . . . . . . . . 2113E5 . . . . . . . 3113L3 . . . . . . . 223% . . . . . . . . .
224x5. . . . . . . . 333115 . . . . . . . . 234% . . 2233314 -___
~
' ~
....
-_
. .
-2
0 -1 0 . .>
.
. 3
-3
0
6.780
893.9
235.81
6 .804 6.738
1027.3 6.816 950.8 6.736
1032.6 946.6
234.56 236.05
0.02
6.839 6.849 6.755 6.810
1135.4 6.841 1132.4 6.850 1081.2 6.791 1127.2 6.825
1138.2 1154.1 1093.7 1131.8
227.15 227.50 229.98 228.98
0.03 0.03 0.08
6.880 6.862 6.873 6 . 815 6.858
1240 . 1238. 1249.8 1190.3 1240 . 1904 . 1223.5 1205.0
6.866 6.870 6.874 6.811 6.855 6.830 6.837 6.818
1236.0 1246.6
220.11 220.56
1337.5 1331. 5 lS27 . 7 1327.9 1273.6 1313.5 1287.0 1%; . 3 1307 . 9 I330 . I) 1 s i x. I 1247. 2 1291.9 1262.5
6.8bY 6.890 6.8b3
6.848 6.818 6 . 800
6.917 6.899 G . (301 6. 5'31 6.837 ti . S i 0 6.833 6 . 560 G.S.31 0 .sso G.dti4 Li . S i 7
6.525 ti.SS0
Zi .
.
882.8
....
__
.
1203.3 224.20 1224.6 223.49 1208.3 223.26 212.66 213.35 213.60 214.74 215.50 215.70 13OU.O 217.92 1992.6 216.2+ 1302. (3 216.46 133G . 1 "15 63 1329.9 217.74 133'3.1 217 10 13ci4.If L'l9.60 l242.G ' 2lId.O; 1325.6 2lS.04 1317.3 217.93 1::OJ.G '"3.13
1323.9 1332.1 1325.9 1334.1 12773.9 1321.6
6.8bl 6 . 833
0. 870
.\ ...
~
6 . S55 G.85k 6 . S4S 6 . 877 G . S7cI li. S i 1 tj.s12 G.7!17 37 56 G.I.?!!, _
.
~~~~
0.05
0.26 I
~
~
'
.
0.11 0.18 0.24 0.27 0.07 0.17 0.32 0.28 0.06 0.20 0.20 0.30 0.25 0.18 0.34
0.01
______ .
the An1oine eqiiatiori tlie value. of 1 ::ill1 I< ol)t :~irletIin t 111- I\ .q. . togetlwi* itli the normal h i l i n g points. IT hen av~~11~11)lo If the 1101 mal h i l i n g point i. not recorded in tlw lite] atiue. C' may lie ohtaiiircl l)y iibing t h e boiling temperature calculated from equation 1. For talile 4. thrl h i l i n g pointy ut yome of the iionniies 11 ere estimated. coii*idering both e.\perimental and calculated values . The equations t o be used for the cnlculation of 1-1 and AB. with the lea-t~
3RIb 4hIb 3E7 4C7 22117 23117 24117 25AI7 26117 33hI7
lb
34117 35117 44117 2113Lb
2h11E6 3h13E6 3hI4E6 223316 224116 225116 233AI6 234AI6 235116 244116 334A16 33L5 22113E:5 23313E5 24113E5 2233115 2234115 224.1115 2331115
0 -1 -1 -2 -2 0 -2 -1 -1 0 -2 -3 -2 -2 -3 -2 -4 -4
6 10 12 16
2A18
I
I
16 lb 18 16 12 22 22 20 24 24 22 28 26 2b 26 22 30 28 24 28 32 32 32 34
-3 -1 0 -4
-4
~
-2 -2 -5 -6 -4
-6 -4 -6
30 38
.4
143 3 141 2 142 5 143 0 141 2 130 3 110 5 133 6 136 5 135 2 137 3 110 5 137 0 135 0 138 6 134 4 140 0 141 0 133 4 126 6 124 1 137 2 139 0 131 1 130 0 139 6 146 5 133 b
6 912 6 . (311 6 900 6 900 6 b89 6 856 6 889 b 867 6 bib 6 bib 6 867 6 bb9
1
142
1
136 7 140 2
I
-4 0
34 32 36
(ahd
4
133 0 122 3 1-11 5
-6
C
b bib
6 856 G b7H 6 867 6 877 6 88'1 b 855 6 823 6 823 6 866 6 877 6 856 6 833
6 6 6 6 6 6
877 899 855 888 866 866 6 811 6 8ll* 6 877
1
~
1
! 1
1'
1405 6 1412. 8 I 1402 9 1410 2 1400 3 1366 2 1100 3 I373 3 1383 2 1 1375 9 1380 6 1107 6 l 1390 4 1370 7 1397 7 13b0 6 1104 (1 1414 b 13i7 9 I 1 1333 h 1326 6 1393 1 I 1404 9 1370 7 1350.9 1412 2 1 1.130 2 1385 2 1429 1 1 1396 1 1 1409 6 1375 3 1316 7* 1 1419 4
I
1
205 206 206 207 20b 210 208 210 209 209 209 210 210 LOO 211 212 211 212 213 211 212 212 212 213 211 213 211 214 214 213 213 214 212 213
4 4
6 9 L
i 9 9 6 0 1 7 9 h 1 0
6 0 3 9
1 9 6
+
h h
7 h
3 1 5 I h
7
* For 2,2,4.4-tetranieth?.Ipeiitarie, 9 of A . i c l l c d and of M e n l e d wcsre used, iri order t o give partial correction t o a large e r i o r charxc*tcristic of t h i s compound squares constants reduced to the minimum number of signifhaant figureL. (' C ' I J I I I ~ ~ itfind 107, d h l t I'SXS) TIio\rio,,. ( ; \V ( ' I i ~ ~ i i iI ~ C 38, ~ L 1 (1946~ WIIXLR II ,J 1111 ('llciu bo( 69, I T tIQ471 \VILIIV(,III\I C' 15 . T ~ IoIt. I \I-. ,J . l'rc,\occ.o. I \ I , \ \ I ] I t c > s s ~ \ t 1. I) I l ? t > ~ e w ~ c h \'at1 13111 htniidnrd- 35, ?l(+ (1045 \ I I ~ P I I I ~ : L I iJi I i I i l l ( L I I I I l i i ~ t i ~ u lii cc~~, t ~ , i i ( - I iI'iojert
aids
(2) (3) (4) (.51
