THE RELATIONSHIP OF THE HEAT OF VAPORIZATION OF GASES TO THEIR DENSITY AND ALSO TO THEIR BOILINO-POINT. BY W M .
L.DUDLEY.
Received September
v , I@$.
I
N studying the heat of vaporization or latent heat of various gases it soon became apparent that this constant bore an interesting relationship to their density and boiling-point. To trace out:this relationship I have endeavored to obtain the latest and best latent heat determinations, as well as the specific gravity of the liquids at the boiling-point. Accurate data of this kind are scarce, and there are few homologous series in which these constants have been determined for many members. However, I have obtained a sufficient number of trustworthy determinations to show some results, which seem to be worth recording. T h e amount of heat absorbed by one cc. of vapor (reduced to oo and 760 mm. pressure) in the passage of the liquid to the gaseous state, is taken as the standard for comparison. T h i s constant is found by the formula
= the heat of vaporization in one cc. of vapor, W= the weight of one cc. of the liquid at its boiling-
where L
point,
W = the heat of vaporization, and w = the weight of one cc. of the vapor at oo and 760 mm. pressure. Until the latent heat researches made by R. Schiff' these constants were determined wikhout any special reference to the relationship of the compounds to one another, and, therefore, not inany series can be found complete enough to make a comparison. I believe, however, that I have gathered the data quite completely and I give in this paper all the series in which the data are complete for as many as three members. I n the following tables the columns marked 1Ann.
Chenr. (Liebig), 134, 338, 1886.
u-11. I..
9;o
rii
DLEI
D = the vapor density, B. I-'. = Boiling-point in absolute temperature, S. G . = Specific gravity at the boiling-point, H. I-.= Heat of vaporization in calories. 1- = Yolunie of vapor, i n cubic centimeters (reduced to 0' and :Go mni. pressure), produced from one cc. of liquid a t the boiling-point. L = Heat of vaporization in a unit of volume (one cc.) of gas reduced to on and 760 nini. pressure. T h e specific grayit). of liquids at the boiling-point is taken from Clarke's tables of Constants of Nature." where the references are fully given T h e boiling-point iq obtained from Carnelley's tablei. I will first show the results obtained froni some of the fatty acids arid their alkyl compounds. FoR3laTr:s.
v I, 542.26 0.2226 I I7 . 1 0 ~ 0.3306 X e t h y l formate CH,$CHO, 30 3Oj.3- 0.95196 102.70' 353.'5 0.2900 E t h y l formate C,H.,CHO, 37 326. j - 0.86667 92.1j4 263.36 0,3499 Propyl formate C,,HiCHOI 44 351.2 0.82146 85.25' 208.37 0.4091 7 7 . 0 ~ 170.34 0.4520 I s o l i ~ i t y formate l C,H,,CHO, j I 371.0. 0.7784 71.6j4 13j.3j 0.4929 Isoamyl formate C , H 1 , C H O , j8 397."- 0 . 7 j j j 9a111e
Formic acid
P'oriii~ila,
IICHO:
I).
23
I( I'
S.G.
373.8- 1.1175
I$
v
120.72~
Fig. I represents the curves of the formates, the density and boiling-point curves being shown on the same sheet. In all cases the corresponding acids fall in line in the density curves but iiot in the boiling-point curves. T h e acids! however, form both density and boiling-point curves of their own, a s ill be shown later on. It will be seen from Fig. I that the heat of vaporization per unit of volume (1%. V . ) of methyl formate obtained from the result of Andrews' determination is too high. T o conform to the curve it should be 0 . 2 9 0 0 which would give 1 0 2 . j o as the heat of vaporization ( H . V . ) instead of 1 1 7 . 1 0 as given by Andrews. whose determination has never be'eii verified. But 1 Farre aiid Silbermau : A n n . chzm.phys. [ J ] , 37, 464-470. 2 A i i d r e w s : C h e m . SOC.Qunr. J . , I , 2 7 .
3 4
Calculated froin the data furnished by the curves showii Schiff' A n n . C/l?nr. (Liebig), 234, 338.
iii
this paper.
I
I
M
0 FIC;.I
973
HEAT OF VAPORIZATION.
since many of Andrews' determinations have been found by later investigators to be considerably too high, it is reasonable to suppose under the circumstances that this one is too high also. To substantiate this I will give the following instances, which may be cited from determinations made by A n d r e w and Schiff : Andrews, I 10.20 Methyl acetate Schiff, Ethyl acetate
{ { Andrews, Schiff,
Ethyl formate
93.90-94.0 92.68 I 83.0-83.1-83. 105.30 92.2-92.1
Schiff, Andrews,
ACETATES. Name.
Formula.
Acetic acid HC,H,O, Methyl acetate CH,C,H30, Ethyl acetate C,H,C,H,O, Propyl acetate CIH,C,H,O, Isobutyl acetate C,H,C,H,O, Isoamyl acetate CjH,,C,H30,
D.
B.P.
S.G.
H.V.
V.
L.
30 3 9 1 . 1 ~0.9372 101.91' 348.66 0.2923 93.95' 265.68 0.3536 37 330.3" 0.8808 44 350.0~ 0.82673 83. I? 209.70 0.3961 5 1 3 7 ~ . 3 0,7917 ~ 77.3? 173.25 0.4462 69.9' 58 389.8O 0.7708 148.32 0.4713 127.56 0.5201 65 415.0" 0.74295 66.35'
The acetates form very good curves, a s will be seen in Fig. 2 . T h e boiling-point curve is almost a straight line. I t has been shown above that Schiff's determinations of the heats of vaporization (H. V.) of methyl and ethyl acetates are much lower than those of Andrews. Favre and Silbernian's determinatiou gives a number for ethyl acetate much higher than that of either of the other investigators, it being 105.8. T h e results of Schiff are taken as being more riearly correct. PROPIONATES. Name.
Formula.
D.
Propionic acid H.C3H,0, 37 Methyl propiouate CH3.C3H,0z4 Ethyl I' C,Hj.C3H,0,5~ Propyl '' C3H,.C,H,0, 58 Isobutyl 'I C,H9.C3HSOz 65 Isoamyl 'I CJHI1.CYHjOP 72
B.P.
S.G.
413.70 0.8589 353.0" 0.836798 371.7" 0.7962 395.6" 0.76815 4 0 9 . 8 ~ 0.7424 433.5" 0.7295
H.V.
V.
90.42:' 259.08 84.15' 212.25 7 7 . 1 ~ 174.64 71.5' 147.81 6 6 . 0 ~ 127.78 6 3 . 0 5 ~ 113.08
..I
0.349 0.3965 0.4415 o.@~z
0.5165 0.5576
T h e curves representing the propionates are shown in Fig. 3> a n d it will be seen that they are quite regular. T h e heat of vaporization (H. V.) of propionic acid has never been deterand Silbennan : AI!?!.d r r a r . ph.1.s. [3], 37, 464-470. Schiff: A m i . Chetn. (Liebig), a94,336. 8 Calculated by the data furuished by the curves shown iu this paper. 4 Schiff : A n n Chem. (Liebig), 034, 338. 1 Favre
2
&AT 0
0
QPVAPORIZATION. 0
3
0
97s
HEAT OF VAPORIZATION.
mined ; but according to the density curve of the propionates, its heat per unit of volume of vapor (L.) should be 0.3490, which would give for the heat of vaporization ( H . V.) the number 90.42. BUTYRATES. Name.
Formula.
Butyric acid
H.C,H,O,
D.
B. P.
S. G .
4 435.5" 0.8120
Methyl butyrates CH3C,Hi0, 51 Ethyl " C,H5C,Hi0,58 I' C3HiC4H,0,65 Propyl '' C,HgC4H,0, 72 Isobutyl " CjHl,C,H,O, 79 Isoamyl
375.3' 0.80261 392.0' 0.7694 4 1 6 . 4 ~ 0.745694 4 q . f 0.7163 451.0' 0.71148
H. V.
V.
L.
114'671 205.96 0'5567 82.79* 0.4020
87*93' 77.25 71.5" 66.23 61.9~ ~ 9 . 4
175.64 148.05 128.03 111.03 10o.51 ~
::::$ 0.4829 0.5170 0.5575 0.5910
T h e curves of the butyrates are shown in Fig. 4 . T h e density curve is alniost a straight line, while the boiling-point curve breaks badly at propyl butyrate. This would indicate that its boiling-point, as determined, is too high and should be 408' (absolute temperature) instead of 416.4', as determined by Linneman, which is given the preference by Carnelley over other determinations. T h e recorded results of the determinations of the boiling-point of propyl butyrate are as follows : 144.3' c. Pawlewski. 143.42' C. Linneman. 142.7' c. Elsasser. 139'--141' C. Chancel. 137.25' (765) Pierre and Puchot. T h e last result would agree very well with that deduced from the curve, viz., 135' C. T h e heat of vaporization ( H . V . ) of butyric acid has only been determined by Favre and Silberman. Their result is I 14.67 cal., which is probably too high. I t gives the heat per unit of volume (L.) 0.5567, which throws it entirely out of the curve shown in Fig. 4, according to which the number should be about 0 . 4 0 2 0 ; this would give 82.79 cal. as the heat of vaporization ( H . V.) of butyric acid. As will be seen in the table above F'avre and Silberman's result for methyl butyrate is much higher than Schiff's. and Silberman : A n n . chim.phys. 1.33. 57,461-470. Calculated by the data furnished by the curves shown in this paper. Schiff : A n n . Chem. (Liebig), a34,338.
1 Favre 2 8
.-
BF!ABSOLUTETCMP.
FIG. 4 .
977
HEAT OF VAPORIZITION.
ISOBUTYRATES. Name.
D.
Formula.
Isobutyric acid H.C4H10, 44 Methyl isobutyrate CH,.C,H,O, 5 1 Ethyl " CzH6.C4H,02 58 Propyl " CsH7.C,H70, 65 ISObUtyl " C4H,.C4H70,72 Isoamyl " C6H,,C,H,0279
B. P.
S. G.
H.V.
428.5" 0.8054 76.67' 365.5" 0.80397 75.5* 383.0~ 0.7681 69.2* 407.0' 0.74647 63.yz 421.6~0.73281 59.95' 441.0~ 0.70662'57.65%
v. 204.29 175.93 147.80 128.17 113.59 99.82
L.
0.3900 0.4291 0.4682 0.4985 0.5278 0.5775
T h e isobutyrate curves (Fig. 5 ) seen1 to indicate that the heats of vaporization (H.V.) of the propyl and isobutyl isobutyric rates as determined are a trifle too low. From the density curve it will be seen t h t the heat per unit of volume (I,.)ofisobutyric acid should be 0.3900 which would give 76.67 cal. for the heat of vaporization ( H . V.). No determination of this constant has been recorded. VALERATES. Name.
Formula.
D.
v. I.. 0.6042 4 ~ 8 . 40.7828 ~ 103*523 171.30 0.4310 73.834 389.3' 0.77518 6 9 . 9 ~ 149.16 ~ 0.4684 407.0~ 0.74764 64.69 128.37 0.5036 428.5" 0.727405 61.2~ 112.75 0.5427 442.0' 0.70549 5 7 . 8 ~ ~99.66 0.5805 460.5' 0.698435 ~ 6 . 2 ~90.64 0.6200 B . P.
S. G.
H . V.
H.CSHgO, 51 CH,C,H,O, 58 C,H,C5H,0, 65 C,H,C,H,O, 72 C,H,C5Hg0,79 C5H11CSHBOZ 86 T h e curves representing the valerates are shown in Fig. 6. T h e density curve is quite uniform. Schiff finds the heat of vaporization ( H . V.) of isoamyl valerate to be 56.2 cal. and from the curve it will be seen that the heat per unit of volume (L.) should be 0.6200, but this constant could not be calculated since no determination of the specific gravity of this compound at its boiling-point has been made. However, assuming the curve to be correct, the specific gravity at the boiling-point becomes 0.698435. T h e only determination of the heat of vaporization ( H . V . ) of valeric acid on record is that of Favre and Silberman, which places it at 103.52 cal. This would give 0.6042 as the heat per unit of volume (I,..),while according to the curve it should be 0.4310,which gives 73.83 cal. as the heat of vaporization ( H . V . ) ,
Valeric acid
Methyl valerate Ethyl I' Propyl " Isobutyl " Isoamyl ''
1 Calculated b y the data furnished by the curves shown in this paper. Schiff: A n n . Chem. (Liebig). 134, 238.
2
8
4 6
F a n e and Silbermau : A n n . r h i w . plays. 131. 37. 464-470. Calculated by the data furnished by the curves shown in this paper, Schiff: A n n . Chem. (Liebig). 1 3 4 , 338.
HEATOF V~POPIZATION
f
I(.
979
HEAT O F VAPORIZATION.
According to the boiling-point curve the boiling-point of propyl valerate 428.5' (absolutetemperature) or 155.5OC.isatrifle too high. Fig. 7 gives all of the density curves of the compounds above mentioned, in one diagram, showing that the relationship between theni is very close and that the uniformity of the curves is very striking. Fig. 8 is a siniilar combination of the boiling-point curves, showing the general tread of them to be almost that of a straight line. ACIDS. Name.
Formula.
Forniic
H.CHO,
Acetic Propionic Isobutyric Butyric Valeric
H.C,H,O, H.C3H50, H.C,H,O, H.C,H,O, H.CjH,O,
S.G.
D.B.P.
30 37 44 44 51
391.1~ 0.9372 413.7' 0.8589 4 ~ 8 . 5 0.8054 ~ 435.5' 0.8120 458.4' 0.7828
H.V.
V.
I O I . ~ I ~348.66
90.49 79.673 82.7g3 73.833
259.08 204.29 205.96 171.30
L.
0.2923 0.3490 0.3900 0.4020 0.4310
T h e curves of the acids (Fig. 9 ) are constructed as far as possible from their constants, as determined and recorded by the various observers, but otherwise the data used have been derived from the curves formed by their corresponding compounds. T h e heat of vaporization ( H . V.) of aceticacid as determined by Ranisey and Young seems to be too low as it does not conform to either the density or boiling-point curve. ALCOHOLS. Name.
Formula.
D.
B. P.
S. G.
Water H.OH 9 373.0~ 0.9589 16 339.2' 0.7483 M e t h y l alcohol CH,OH Ethyl " C,HjOH 23 351.3' 0.74035 Isopropyl I ' C,H,OH 30 355.8' 0.7413 Propyl '' (nor.) C,H,OH 30 370.1' 0.7366 C,H,OH Isobutyl 37 381.4~ 0.7265 I ' ( n o r . ) C,H,OH Butyl 37 389.96O 0.7269 Amyl CjH,,OH 44 404.4' 0.7154 1 Ramsey and Young : /. Chena. SOL.. Lond., 49, 790. ('
2 8
4 5
H. V.
v.
536.0' 1;189.11 263.W 521.97 201.425 359.25 159.72' 275.78 164.07: 274.03 136.16~ 219.14 138.1Sj 219.26 1 1 8 . 1 5 ~ 181.46
Favre and Silberman : A n n . chim. # h p . [3], 3 7 , 464-470. Calculated by t h e data furnished by t h e curves showii iu this paper. Regnault : Mem. Acad. Sci.. 21,638. Louguiuine : Compf. rend.. 119, 601.
L.
0.4507
0.5055 0.5607 0.5791 0.5987 0.6213 0.6298 0.6511
HEAT or VAPDRIZATKN,
FIG. R
HE~ O fT VAPORlJ A T I O N 0
0
0
983
HEAT OF VAPORIZATION.
T h e normal alcohols form quite symmetrical curves, as is shown in Fig. IO. I n the density curve, water, as the type, falls in with the alcohols as the acids do with their corresponding compounds. It will be noticed that isopropyl and isoamyl alcohols do not fall into line with the normal alcohols, but, as iiiight be expected, they form a portion of a curve for which the data relating to the remaining members of the series are not to be had at present. In constructing the alcohol curves, the heat of vaporization ( H . V . ) of methyl alcohol, as determined by Favre and Silberman, was taken in preference to that of Diakonoff, which is believed to be an impossible value. These determinations are as follows : Favre and Silbernian. ........................... Diakoiloff .......................................
263.86 cal. 123.79 "
I n the case of ethyl alcohol the determination of Longuinine was used, although three determinations are recorded as follows : Favre and Silbernian.. .......................... A n d r e a s ........................................ Longuinine .....................................
208.92 cal.
202.40 201.42
I '
Of the two determinations of propyl alcohol (normal) Diakonoff ....................................... Longuinine .....................................
165.92tal. 164.07 '
