Line Coordinate Charts for Vapor PressureTemperature Data FRANK E. E. GERMANN AND ODONS. KNIGHT, University of Colorado, Boulder, Colo. Herein lies the greatest fault of ROBABLY the first atThe methods are briejy reviewed which have this useful method. Among the tempt to correlate vapor been used to represent vapor pressure-temperature numerous other methods which pressure data was made data. It is shoxn that this m a y best be done by have been employed are those by Dalton ( 5 ) in 1801. He atreducing the data $first to straight lines and then of Carr and Murphy (@, Cox tempted to show that the vapor by plotting these lines as points on line coordinate (S), Davis (6),Calingaert and pressure of a liquid increases in Davis ( I ) , Wilson ( I l l ) , Maxwell geometrical progression a s the charts. The literature on vapor pressures of (IS), and Wilson and Bloomtemperature increases i n organic liquids has been critically reriewed. As quist (19). arithmetic progression, and that a result, 183 organic liquids and solids were Cragoe (4) makes use of the all liquids experience an equal found whose vapor pressures are well known in integrated form of the Clausiuslowering of the boiling point if the range 500 to 900 mm. of mercury. These, Clapeyron equation. Hass and the pressure is diminished the h’ewton (8) modified Cragoe’s s a m e a m o u n t from the same as well us water, have been represented on the f o r m u l a to secure greater acinitial pressure. The statement charts. The use of these plots makes calculacuracy, but the results are still of these rules by Dalton stimutions for corrections in boiling points due io a only approximate. A personal lated a great deal of work on Tariation in pressure unnecessary, as charts 9 X communication from Hass would vapor pressures, with the result 24 inches (22.9 X 61 cm.) permit reading temindicate that boiling points near that the first of them was shown atmospheric pressure should be to be quite inexact, and only in peratures to 0.25’ C. if the pressure is known, or isolated cases, such as with the obtained with an accuracy of to 2 mm. if the temperature is known. *lo C. However, the equafattv acid series of comaounds. was“the second shown t‘o hold: tion must b e s o l v e d by the Kirchhoff (11) in 1858, and Rankine (16) in 1866 developed method of successive approximations and is accordingly what is sometimes known as the Kirchhoff formula, but more rather time-consuming. One of the most useful of vapor pressure charts yet puboften as the Rankine formula: lished is that of Ravenscroft (17). He has made use of the log P = A BIT Clog T Duhring rule and has made assumptions concerning aswhere A , B, a n d C are constants sociation in the liquid phase, different scales being used for This formula has been found to apply to a large number of associated and unassociated compounds. Since the entire substances from the freezing point to the critical tempera- matter of association is a t the present time in a rather unture, with a maximum error of 3 per cent. It has been modi- settled state, it would seem well, if possible, to avoid any fied by Nernst (14) who attempted to put it on a better reference to it. theoretical basis. DRAWIXG OF LINE COORDINATE CHART Ramsay and Young (15) in 1885, suggested the relation: There has been a great desire on the part of chemists to T A / T B = T’A/T’B = a constant find some rapid, accurate method of determining the boiling where T A and T B = the boiling points, on the absolute scale, of two points of compounds at various atmospheric pressures, such sub4tances under pressure p as are encountered in laboratories a t various altitudes, as T’A and 2 ” ~= their boiling points under another pressure, p’ well as to determine the temperatures a t which these comThe law holds for closely related substances, but for widely pounds mould boil a t various pressures artificially created. Tables are available giving values of the variation in temdifferent substances another term must be added, thus: perature per centimeter variation in pressure for many subT A I T B= T‘A/T‘B C ( T A- T ’ A ) stances, but, unless the laboratory is located near sea level, these tables are of no value. A t the University of Colorado The integrated form of the Clausius-Clapeyron equation the barometer averages about 62 em., so that the above may be written in the form: mentioned tables are useless. I t mas with the idea of filling this need that the present plots were devised. k / T C log p = Using the integrated form of the ClauFius-Clapeyron This equation has been modified by Henglein (9) and Hilde- equation as the basis for the work, the reciprocals of the brand (IO),so as to be valid over a larger pressure range, absolute temperatures were plotted against the logarithms The most serious objection t o the use of Hildebrand’s equation of the pressures, over the range of 500 to 900 mm. of mercury, would seem to be the fact that it applies only to liquids Over this range the resulting curves were straight lines. which we have thought of as being nonassociated. The more accurate the data, the more nearly all the points Many attempts have been made to correlate vapor pres- fell on the straight line. A critical review of all existing sures and temperatures by graphical methods. Perhaps the literature on vapor pressures of organic liquids and some oldest well-known method is that known as Duhring’s rule solids resulted in the establishing of such straight lines for ( 7 ) . Mathematically, Diihring’s rule is nothing but a graphi183 organic compounds. In cases where various workers cal representation of the simplified Ramsay and Young law. had reported vapor pressures on the same compound, the Since this law is not exact, Duhring’s lines are not straight. relative merits of the methods used were studied, and weighted
P
+
+
+
+
467
INDUSTRIAL AND E N G I N EE R I N G CHEMISTRY
468
BOILING POINTS OF
BO1LING POINTS OF
CHAIN COMPOUNDS
RING COM POUNDS SCALC C 'C
Vol. 26, No. 4
SCALE
SOIL€
C
6
D
r
"i
HG
900
850
7.50
40F2' -31
Z'BO
2.75 ~
to /Z
'2s
2.50
1
I
L mP
curves were drawn. I n all cases, individual variations among the results were greater than the possible error in assuming the lines to be straight. I n other words, the straight lines drawn represent improvements over the original data, within the range considered.
IOOO/K
/Ow/%
tL O G P
These straight lines were then reduced to points on line coordinate charts (0 X 24 inches, or 22.9 X 61 em.), each point being assigned a number corresponding to a given compound. For convenience the compounds were separated into chain and ring compounds, the only reason for this
'
I N D U S T R I A L A N D E N G I N E E R 1N G C H E M I S T R Y
April, 1934
TABLEI.
ALPHABETICAL INDEX TO
BOILIXGP O I N T
469
CHaRTS
( A , B. C , and D refer to groups of compounds on the charts: numbers refer t o compounds within these groups) Acenauhthene. D-26 hcetal?iehyde,'A-13 Acetio acid, A-72 Acetone, A-28 Acetophenone C-46 n-Amyl alcohdl, B-20 n-Amyl n-butyrate, B-44 n-Amyl formate, B-13 n-Amyl isobutyrate, B-42 n-Amyl n-propionate. B-36 Aniline, C-34 Anthracene, D-35 .4nthraauinone. D-37 ~
Benzaldeh de C-29 Benzene, 6-16 Benzoic acid, C-37 D-21 Beneonitrile, Benzophenone Benzoyl chloriheD-32 C-41 Benzvl alcohol, 6-51 Bromobenzene. (2-22 a-Bromonaphthalene D-27 rn-Bromotoluene, C-3'3 o-Bromotoluene, C-30 p-Bromotoluene, C-31 o-Bromo-p-xylene D-10 n-Butyl alcohol, k-73 tert-Butyl alcohol A-47 sec-Butyl chloroaEetate, B-40 n-Butyl formate, A-63 see-Butyl formate, A-53 n-Butyric acid, B-38 Camphor C-52 Carbazod D-36 Carbon dibulfide A-25 Carbon tetrabromide. B-48
o-Cresol. '2-38 p-Cresoi C-48 Cycloheiane, C-11 Cymene, C-28 n-Decane B-35 Dibenzylketone, D-33 1,3-Dibromopropane, B-39 2 3-Dibromopropylene, B-26 l:Z-Dichloroethane, A-45 Diethylaniline, C-55 Diethyl ether A-17 Dilsobutvl. A h 4 Dilsopro- yl A-31 Dimethyyadline, C-39 Dimethyl-o-toluidine, C-35 Dimethyl-p-toluidine, (2-54 Diphenyl, D-22 Diphenylmethane, D-25 Dipropyl ether, A-50 Durene, C-40 Ethyl Ethyl Ethyl Ethvl
acetate, A-40 alcohol A-42 aniline ' C-50 benzenk. (2-16
Ethilene elvcol. B-50 Eth>lene &de,' A-1 1 Ethyl formate, A-27 Ethylidene chloride, A-29 Ethyl iodide, A-37 Ethyl isobutyrate, A-65 Ethvl mercautan. A-18 E t h i l propidnate, A-56 Ethyl sulfide A-51 Ethyl-n-vale;ate, B-23 Fluorene, D-31 Fluorobenzene. C-12 Formic acid, A-58 Glycol diacetate, B-49 n-Heptane A-55 n-Heptylic'acid, B-52
being to scatter the points over a larger area. I n order to increase the accuracy of the temperature reading, the chain compounds were separated into compounds A with a temperature scale reading from 0" to 125' C., and compounds B with a temperature scale from 105" to 230" C. Similarly, the ring compounds were separated into compounds C with a temperature scale from 65" to 225" C. and compounds D with a temperature scale from 185" to 390" C. With compounds -4,scales A and PI are used; with compounds B , scales B and P1; with compounds C, scales C and P z ;and with compounds D, scales D and P P . On the right-hand side of scales A , B, C, and D is the original uniform scale of 1000 times the reciprocal of the absolute temperature, while on the left of scales P I and P z is the uniform scale of the common logarithm of the pressure in millimeters. These fundamental scales are then made directand PZscales. Having thus reading in the A , B , C, D, P1, established nonuniform temperature and pressure scales, the uniform scales are no longer necessary. If, for example, we wish to know the boiling point of water when the barometer reads 620 mm., we note from Table I that water is listed as A-61. Therefore, place a straightedge a t 620 mm. on P I scale, and pass it through the center of circle 61 under compounds A. On scale A we read 94.4" C., which is the value given by the International Critical Tables for a pressure of 620.01 mm. mercury. It is safe to state that within the pressure range of 500 to 900 mm. the chart will give boiling points within 0.25" C. and pressures within 2 mni. This accuracy is sufficient for most work in the organic laboratory where temperatures of boiling are used as criteria for the purity of compounds. Where vapor pressures are more accurately known, as in the case of water, more accurate readings are easily possible. I n other words,
Hexachloroethane, B-46 Hexamethyl benzene, D-24 n-Hexane A-36 1-Hexene' A-33 Hydroper; cyanide, A-14
Nitromethane, A-59 m-Nitrotoluene D-16 o-Nitrotoluene,'D-13 p-Nitrotoluene, D-19 Nitro-rn-xylene, D-20
Iodobenzene. C-36 Isoamyl alcohol, B-19 Isoamyl formate, B-14 Isobutyl acetate A-69 Isobutyl alcohol' A-66 Isobutyl benzenk, C-26 Isobutyl-n-butyrate B-34 Isobutyl formate A's4 Isobutyl isobutyiate, B-30 Isobutyl-n-propionate, B-24 Isobutyl-n-valerate B-41 Isobutyric acid B-62 Isocaproic acid,' B-51 Isodurene, C-42 Isopentane, A-15 Isopropyl acetate 4-49 Isourouvl alcohol.' k-46 Isopropyl benzene (2-19 Isopropyl chloride: A-19 Isopropyl chloroacetate. B-31 Isopropyl formate A-35 Isopropyl isobutyiate, B-10 Isovaleric acid, B-43
n-Octane, B-16 Pentachloroethane, B-37 Pentamethylbenzene, D-17 n-Pentane, A-21 Phenanthrene, D-34 Phenol, C-32 Phthalicanhydride, D-28 Prehnitene D-11 n-ProDionib acid. B-25
n-Propyl formate, A-43 n-Propyl isobutyrate B-22 n-Propyl n-propionatk, B-12 n-Propyl n-valerate, B-33 Paeudocumene, C-27 Pyridine, C-14 Quinoline, D-18 1,l.l,?-Tetrachloroetha~le, B.-18 durn-Tetrachloroethane, B-29 Tetrachloroethylene. A-71 Tetranitromethane, B-15 Toluene. C-13 m-Tolui$ne C-49 o-Toluidine 'C-44 p-Toluidine: '2-45 1 1 1-Trichloroethane A-38 1'1'2-Trichloroethane: A-68 T'ri'chloroethylene, A-48
Methll butyrate' A-62 Methyl chloroacktate, B-17 Methylene chloride A-24 Methyl ethyl ether,' A-10 Methyl formate A-I6 Methvl isobutv;ate. A-52 Methil n-proGionate, A-41 Methyl propyl ether, A-25 Methyl salicylate D-14 Methyl sulfide, A120 Methyl n-valerate, A-70
Urethane, B-45 n-Valeric acid, B-47 Water. A-61
Naphthalene, (2-56 a-Naphthol D-29 &Naphthol,' D-30 Nitrobenzene, D-l?
m-Xylene, C-18 a-Xylene, C-18.3 p-Xylene, '2-17
the charts have about the same degree of accuracy a5 the best vapor pressure data for the compound in question. INSERTION
OF
NEW DATA
S e w points may be inserted on the chart as the data become available. Thus Lenth (1.2) has just published data on the vapor pressures of n-butyl chloride. Plot a curve of the reciprocal of the absolute temperature against the logarithm of the pressure and draw the best straight line through the points. Let us assume that the data of Lenth have been represented by such a line. Then a t 66.0" C. the pressure would be 50.5 cm., and a t 77.5" C., 76 cm. Lay a straightedge from 66.0" C. on scale A to 505 mm. on scale P and draw a light line. Then lay the straightedge on 77.5" C. on scale A and 760 mm. on scale P and draw another light line. At the point of intersection of the two lines draw a small circle and number it 40.3, indicating that it lies about one-third of the way between 40 and 41. It would be listed in the table as n-butyl chloride, A-40.3. If then we wish to know the pressure a t 73", we read the value 649 mm. from the chart. Lenth gives the experimental value of 650 mm. and the calculated value of 649 mm. The charts should be of value in all laboratories, whether they be at sea level or higher, since all calculations are avoided ; it is necessary to know only the barometric pressure. Similar charts are being constructed for inorganic substances, as well as for other pressure ranges.
(1)
LITERATURE CITED Calingaert and Davis, IND. ENG.CHEM., 17, 1287
(1925).
(2) Carr and Murphy, J . Am. Chem. Sot., 51, 116 (1929). (3) Cox, IND.ENQ.CHEM.,15, 592 (1923).
INDUSTRIAL
AND ENGINEERING
Cragoe, International Critical Tables, Vol. 111,p. 246, McGrawHill, 1926. Manchester, 5, 550 (1801). Dalton, Mem. Literary Phil. SOC. Davis, IND.ENQ.CHEM.,17, 735 (1925); Chemist-Analyst, 20, No. 3, 7 (1931). Duhring, “Neue Grundgesetse zur rationellen Physik und Chemie,” Erste Folge, Leipsig, 1878. Hass and Newton, “Handbook of Chemistry and Physics,” 17th ed., p. 1039, Chemical Rubber Publishing Co., Cleveland, 1932. Henglein, 2. physik. Chem., 98, 1 (1921). Hildebrand, J . Am. Chem. Soc., 37, 970 (1915).
CHEMISTRY
Vol. 26, No, 4
Kirchhoff, Ann. Physik, 103, 186 (1868). Lenth, J. Am. Chem. SOC.,55, 3283 (1933). Maxwell, IND. ENQ.CHEM.,24, 502 (1932). Nernst, “Theoretical Chemistry,” Codd’s English Ed., p, 816, Macmillan, 1923. (15) Ramsay and Young, Phil. -lZag., [ 5 ] 20, 515 (1885); 21, 33, 22, 37 (1886). [4] 2oo (1866). (16) (I7) Ravenscroft~IND.EsG. 21i 1203 (Ig2’). (18) Wilson, Ibid., 20, 1363 (1928). (19) Wilson and Bloomquist, Ibid., Anal. Ed., 4, 136 (1932). (11) (12) (13) (14)
313
RECEIVED October 23. 1933.
Heat Content of Gases from 0” to 1900” C. GUY €3. TAYLOR, E. I. d u P o n t d e N e m o u r s & Company, Inc., Wilmington, Del, ALCLL.1 TIOSS for processes involving heating or cooling by or with gases ordinarily require a knowledge of the heat content-. g., how many calories or pound Centigrade units (P. C. U.) are required to heat a given quantity of some gas mixture from t 1 ° to 12’. Except for the case of saturated steam, reference books give no tables for heat content but supply instead data or formulas for specific heat. In engineering calculations specific heat values are not useful as such but must be translated into terms of heat content. The tables given here are convenient for heat calculations. The heat contents for the individual gases were calculated by integrating Bryant’s’ equations for specific heat a t constant pressure. The specific heat equations are all given in the form: C, = A BT + CT2 (1) where A, B, and C are constants
C
+
which upon integration becomes, between the limits’ TI
Tz
=
H
TABLE
TEMP,
c. 0
--COn-H
0 935
+ BT dT + CT2.dT
300
3000
400
4120
500
5292
600
6512
A
700
7773
688
800
9072
705
900
10403
722
1000
1176 1
737
1100
13142
752
1200
14539
766
1300
15950
779
1400
17368
791
1500
18788
802
1600
20206
812
1700
21616
82 1
1800
23015
xRn _._
1900
24395
TEMP
c. 0
-H?H
0
100
693
200
1388
300
2088
400
2791
500
3498
600
4210
io0
4928
800
900 1000
5652 6383 7121
1100
7866
1200
8620
1300
9383
1400
10155
1500
10937
1600
11730
1700
12534
1800
13349
1900
14177
1
IND.
DX.%TohfIc GASES
(Calories per gram mole) ,-----O?--,----NzH A €1 A 0 0 707 693 707 685 728 695 1386 1435 749 700 2102 2184 767 703 283 1 2951 784 707 3735 3575 800 712 4535 4331 814 718 5349 5100 826 724 6175 5879 837 73 1 7012 6670 847 73s 7859 7471 854 745 8713 8281
__
7.54 .
763 772 782 793 804 815 828
___ Xfi 1
9574 10439 11308 12178 13049 13918 14785 15646
ENG.C H E M . , as, 820 (1933)
865 869 870 871 869
867 861
9100 9926 10761 11602
12448 13300 14157 15017
A 685 701 716 729 744 756 769 779 791
so1 810
___ x19
826 835 84 1 846 852 857 860
,--COP H 0 688 1393 2115 2852 3604 4370 5149 5940 6742 7554 8375 9205 10041 10885 11734 12588 13445 14305 15167
*
836 844 849 854 857
860 862
-CHIA
1936
TABLEI. HEATCOXTEXTS OF
+ B/2T2 + C/3T3
AT
O F POLYATONIC
G~SES
(In calories per gram mole)
100
A.dT
=
11. HEATCONTENTS
200
= JlT2
0,
Tables I amd I1 give heat contents in calories per gram mole (P. C. U.per pound mole) from 0 ” C. to the indicated temperature. Differences for each 100” are given for interpolation purposes. The calculations were made by using five-place log tables. The constants are given in Table 111. The formulas, and consequently the values above 1500” C., are less reliable than below this temperature.
The heat content from this form of equation is: H
=
T:
H
0
935
873
1001 1064 1120 1172 1220
1261 1299 1331 1358 1381 1397 1411 1418 1420 1418 1410 1399 1380
1893 3053 4344 5756 7284 8917 10648 12469 14370 16343 18380 20474 22615 24793 27003 29236 31482 33733
--HL--
‘-C?Hz-A
H
0
873
1141
1020
2365
1160
3669
1291
5049
1412
6497
1528
8010
1633
9582
1731
11208
1821
12881
1901
14597
1973
16352
2037
18138
2094
19953
2141 2178 2210
A
21789 23641
2233 2246 2251
25505 27374 29244 31110
II
A
0
1141 1224 1304 1380 1448 1513 1572 1626 1673 1716 1755 1786 1815 1836 1852 1864 1869 1870 1866
791 1613 2465 3345 4253 5189 6152 7141 8155 9194 10258 11344 12453 13585 14738 15911 17105 18318 19549
79 1 8 22
852 880 908 936 963 989 1014 1039 1064 1086 1109 1133 1153 1173 1194 1213 1231
TABLE 111. CONSTANTS USED IN FORMCLAS GAS Ha 0%
N2
co coz
HzO
CHI CzHz
A 6.88 6.26 6.30 6.25 6.85 6.89 3.38 8.28
66 2746 1819 2091
XSRR ....
3283 17905 10501
f 279 770 345 459 -2475 ~. 343 -4188 -2644
-
33.0 1373.0 909.5 1045.5 4266.5
iSii.5
8952.5 5250.0
+- 256.67 93.00
- 115.00 -- X25.00 153.00 - ii4.33 -1396.00 881.00
-
RECEWEDDecember 6, 1933. This paper is Contribution 135 from the Experimental Station of E. I. du Pont de Nemours & Company.
