MOLECULAR A’I’TRACTIOK (THIRD P A P E R )
BY J. E. MILLS
In a preceding paper,I iiiaking use of the meastirenients of Profs. Ramsay and Young and of Prof. Young, we applied the theoretically derived equatioii, f’d -$D
= constant,
to twenty-one substances, and called particular attention to variations in the constants obtained and to the range of temperature covered by the measiirements. (In the above equation, I, denotes latent heat of vaporization, ET is energy spent in overcoming external pressure, and d and D denote density of liquid and vapor respectively.) In this paper, making use of the same measurements and the results there derived, we wish to point out some further aeplications of the theory. But first we call attention to several points bearing more directly upon the results of the last paper. T h e constant given by equation I above, as will appear later i n this article, is an important property of a substance and depends upon the attraction of one molecule for another. We have to refer to this constant so often that a inore specific designation is desirable. We have hitherto called the absolute attraction at unit distance from a iiiolecule p. T h e above constant we will call p’. (Therefore p = cp’+’v~ .) ll’e call the internal latent heat of vaporization h, and therefore have, h=p’(vd
(2)
The
aT
--
f/D
).
a t the Critical Temperature
I n the second paper we commented upon the difficulty of Jour. Phys. Cheni. June, 1904. Referred to itithis article as Paper.”
“
Second
594
J E. Mills
obtaining correctly the
aT from Riot’s formula near the critical
temperature. We entirely overlooked the fact that the constant b of the equation, p = bT - a,proposed by Profs. Ramsay and ap Young, was also a - - , and that at the critical temperature (but aT ap only at that point, see p. 623), the aT of the two equations became identical. I n work done to establish the truth of the equation,
p
= hT - a,the
ar was
obtained for three substances a t
volumes practically identical with the critical volume. T h e results are such as to confirm entirely and quantitatively the view that the divergences at this point in p’ were due to the Biot ap formula used to obtain the
n.
T h u s isopentane gives at the critical temperature (volume ap 4.266) the - = 367.8, calculated from Biot’s formula. Prof.
ar
Young’ found from drawn isochors (at the volume 4.3) the value 397 and a calculated value of 407. Therefore Biot’s formula gives results about ten percent too low, an amount just sufficient to explain the variation in p’ near that point. For noriiial pentane, Biot’s formula at the critical volume, 4.303, gives 364.8 for the ap Mr. J. Rose-Innesand Dr. Youngz aT obtained 407.3 from drawn isochors. Biot’s formula therefore shows results too low by about eleven percent, an amount which is sufficient to explain the low values obtained in the constant p’ as the critical temperature was approached. For ethyl oxide Profs. Ranisay and Young3 obtained at ap volume 4.00 the = 413.7, and it is evident from their paper a
on ethyl oxide4 that the values they used for calculating the Proc. Phys. SOC.1894-95, p. 6jo. Phil. Mag. April, 1899. Ibid. May, 1887. Phil, Trans. 1 8 8 7 6 , p. 57.
latent heat of vaporization point to a value at this point of about 490, a fact which sufficiently explains the rise noted in the value of p r . (The values Profs. Ramsay and Young used for
aT at this point are not in accord with the Biot formula they published, which prevents quantitative comparison here. See P. 6354 We have therefore direct proof that the equation,
I,--E
3JYG!---1/D
.
=constant,
is applicable in the immediate neighborhood of the critical temperature. . The Product of the Pressure and the Vapor Density I n examining the data used to discover if possible the irnmediate source of variations in p r it proved impracticable to plot either the pressure or the volume of the vapor directly against the temperature. But their product, PV, varied more slowly and the values were plotted and gave regular curves except for di-isobutyl, brom-benzene, iodo-benzene, hexamethylene, and water. This result is so interesting that the curves are given below, Diagrams I to 3. T h e numerical results are given in Tables I to 21. For water the break in the regularity of the curve occurs at 100' C, and since different formulas were used for the vapor pressure above and below that temperature it would seem certain, in view of remarks already quoted (Second paper, p. 396), that the formulas for the pressure need adjustment. For di-isobutyl, broni-benzene, iodo-benzene, and hexamethylene, the irregularities of the P V curve are more probably due to the vapor density (See second paper, p. ~ o o )and , are especially interesting because they occtir a t just the point where were obtained divergent values for p'. Reference to the preceding paper will show that di-isobutyl, brom-benzene, and iodobenzene, were the only substances, except stannic chloride and the associated substances, giving divergences (which have not been explained as due to nlultiplication of the error in calculatap ing t h e - ) greater than two percent from the mean value
ar
596 adppted for
J E. Mills Hexamethylene shows likewise a smaller
Diagram
I
Diagram
2
though well inarked divergence in p’ corresponding to the concave sink in the PV curve.
Moleculav Attractioiz
597
I t is clear therefore that these abnorinal values of the PV product innst be carefully investigated before the corresponding divergences in pf can be regarded as in anyway evidence against the theory by which that constant is derived.
Diagram 3 For water, add goo t o the ordinates shown by the diagram
Internal Heat of Vaporization T h e internal heat of vaporization was plotted against the temperature, Diagrams 8 to IO. These curves are inore fully discussed later (p. 618). W e would here call attention only to one feature of these curves, viz : Corresponding to divergences in p’ there appear irregularities i n these curves and these variations in p’ would (excepting in stannic chloride and the associated substances) for the most part disappear if the curyes were smoothed and the smoothed values thus obtained used in the calculations.
J. E. M2Z.s
598
Diagram of L - E, against the I'?/d -$YD We have plotted, Diagrams 4 to 7, the results for all of the substances examined, using the values of L - E, for ordinates and the values of $'d - I,YD for abscissz, T h i s is desirable in order to give a more exact idea of the relative ex-
e-m 2
IO
8
6
4
L
12
Diagram 4 Ordinates give internal heat of vaporization in calories. Abscisse give difference of the cube roots of the densities of liquid and vapor 2
4
6
8
10
Diagram 5 Ordinates give internal heat of vaporization in calories. Abscissze give difference of the cube roots of the detisities of liquid and vapor
tent and importance of the observations. For since neither L - E T nor f / d - YD vary uniformly with the temperature observations taken every ten degrees are consequently not taken
599
iVoZecul a / Attmciion
at equal intervals of the curve (a straight line) represented by that equation.
-
Diagram 6 Ordinates give internal heat of vaporization in calories. Abscisse give difference of the cube roots of the densities of liquid and rapor 600) 600 I I I I I
500
400
300
200
IO0
0
2
4
6
8
10
Diagram 7 Ordinates give internal heat of vaporization in calories. L4bscisse give difference of the cube roots of the densities of liquid and vapor
600 Through each set of observations, excepting for acetic acid, the niean line is drawn. T h e constants for this mean line were obtained by averaging, for any substance, all of the constants recorded i n Table I (Second paper) that were within two percent of the mean values adopted in that table. For di-isobutyl the mean value adopted appeared probably too high and we therefore choose the value 86.3 as being more nearly i n accord with the proper constant. T h e values for these constants are given in Table 2 5 under the heading p'. For ethyl oxide, di-isopropyl, di-isobutyl, isopentane, normal pentane, normal hexane, normal heptane, normal octane, benzene, hexamethylene, fluo-benzene, carbon tetrachloride, methyl alcohol, ethyl alcohol, propyl alcohol, and acetic acid, sixteen substances in all, the observations are practically complete, extending from near the freezing-point of the liquid nearly to the critical temperature. Among these sixteen substances the only divergences appearing marked to the eye are normal octane and ethyl alcohol at o o C, di-isobutyl, those for the alcohols as the lines approach the origin, and acetic acid. T h e curves for chlor-benzene, brorn-benzene, iodo-benzene, stannic chloride, and water, are not complete. All of these incomplete curves show irregularities and yet it is made most evident by the diagrams, as well as by what has already been said, that with the exception of stannic chloride, the divergences are not so pronounced as to be considered weighty evidence against the theory. I n conclusion therefore we point out that, of the twenty-one substances examined, stannic chloride and the associated substances (methyl alcohol, ethyl alcohol, propyl alcohol, and acetic acid), are the only substances that show variation i n p' without at the same temperature exhibiting irregularities in the data used. T h a t these irregularities . i n the data are due to the ineasureinents is niuch to be doubted. But if not so produced, they are significant of unknown changes taking place in the substance under examination -changes which were not taken into account in the theory of molecular attraction under discus-
sioii and to which that theory as outlined would not be strictly applicable. The Latent Heat of Vaporization I t is interesting to examine more closely and to compare the heats of yaporization calculated by use of the following equations : L = T ( Y - - v ) 3P (3) (4)
J L = p'(p/d- $'D
aT ) 4-E,.
d D ' Using the constants we have hitherto adopted, the equations become : L = 0.0~31833T ( V - v ) ap cals.
I, = 2RT loge
15)
ar
(6)
L
LZ
9. I j 2 2 d T log cals., m
m being the molecular weight, with oxygen equal to 16 as the standard, and logarithms to base ten. T h e equations are all theoretically derived. Equation 3 rests primarily upon the first and second laws of thermodynamics and is deduced therefroin by a familiar line of reasoning. No assumption is made as to the nature or cause of the latent heat, or as to the nature of the substance itself. T h e eqnation will serve as well to calculate the latent heat of fusion or the energy absorbed during the change in the crystalline form of a solid. It merely expresses the energy necessary to effect a change in volume under given conditions, and is silent as to the cause of the change or the natnre of the substance. So far as present knowledge goes there is no need for questioning the correctness of the results obtained by this equation, the data being accurate. ITe can therefore well use the latent heat so obtained as a check, either upon direct measurements of the latent heat, or upon other calculations involving relations and assumptions which perhaps are true, but which are not so fundamental.
60 2
J. E. Mills
I
\
We have already published (Second paper, Tables 2 to 2 2 the calculations for six or seven of the substances were, however, the work of others), the results obtained by the application of this equation to twenty-one substances, and only for the sake of comparison repeat a portion of the results in the tables which follow. (See Tables I to 21, under the head "her.) I t must be borne in mind that although these results are accurate where the data is correct, yet errors in the measurements may, and oftentiiiies certainly do (because of the method necessarily followed for obtaining the
ap
a?
), produce far greater proportional
errors in the result. Equation 4 is derived by a simple transposition froin equation z of the second paper. T h e assuniptions upon which that equation is founded and evidence bearing upon the equation, have been discussed in the preceding paper, and here we would oiily summarize by saying that the equation rests upon the belief that the total kinetic energy of a molecule of a liquid and of its vapor, at the saiiie temperature are the same ; and upon the further assuiiiption that the entire latent heat of vaporization is expended in overcoming the external pressure and in separating the molecules against the action of an attractive force varying inversely as the square of the distance apart of the molecules. T h e equation is riot applicable ( d # ~ i o ~ if i ) (a)the number of molecules change owing to dissociatioii or decomposition ; or if (6) the niolecules are not evenly distributed throughout the space occupied by them; or if (c) for any reason the attraction between these molecules varied with the temperature. T h e constants p' for the twenty-one substances examined are given in Table 25 of this article under the heading p', and while the constants there given were obtained by a comparison of this equation with the thermodynamical results obtained by use of equation 3, it is easily seen that such a method of obtaining the constant is, we might say, incidental, and only adopted for the sake of accuracy and convenience. One accurate measurement a t aey temperature of the latent heat of vaporization of any substance to which the equation is applicable, together with
a measurement of its vapor presslire and of the densities of liquid and vapor, would enable the constant for that substance to be calculated. T h e equation, has, therefore, no connection with the thermodynamical equation 3, but rests independently, partly upon the same and partly upon additional assumptions. T h e results obtained for the twenty-one substances are given below, Tables I to 2 1 , in the columns marked Mills. In compariiig the latent heats so calculated with those obtained from the thermodynamical equation we find that if the five associated substances be omitted, there are only four determinations in which the results as calculated by the two equations differ by so much as two calories, viz : di-isobutyl at o o , normal octane a t o o , chlor-benzene a t 270°, and broin-benzene a t 30' -in every instance the divergences being at the endpoint of the Biot curve and thus inaking it probable that all of these divergences are due to the thermodynaniical equation. Excepting staiiriic chloride, there are only twelve other instances in which the divergence is greater than one calorie. All of these divergences are marked with an asterisk in the tables.
TABLEI Ethyl Oxide Heat of vaporization Temperature 0 20
40 60 80 I00 I20
Tlier.
93-27 87.90 83.18 78.84 73.95 68.35 62.63 55.52 45.99 31.58 20. go 17.10
13.67
-
I
Mills
91.59% 87.94 83.85 79.46 74.49 68.89 62.41 55.05 45.98 32.54
20.5s 16.11 12.61:K
'
Crompton
99.42 93.42 87.62 81.95 76.03 69.76 62.79 55.04 45.71 32.19 20.25 15.84 12.36
PV/~ooo
604
J E. Mills
This comparison elliphasizes more clearly than is possible in any other way the correctness of the law of molecular attraction we have assumed. TABLE2 %
Di-isopropyl -~
I
Heat of vaporization Temperaturel
Ther.
Mills
I
IO0 I20
85.11 76.90 72.86 68.28 63.57
85.40 76.42 72.66 68.45 63.85
140
58.58
58-75 52.87
0
80
I 60 I 80 200 2 IO 220
52.70 45.86 37-15 31-09 , 22.14 , 14.57
225 227.35
-
Temperature1 I
0
IO0 I20
140 I 60 I 80 200 220 2 40 2 60
270
274 276.8
Crompton
Ther.
22 I
201
185 I59 I37 96.8
-
Mills
Crompton I
-
78.62" 67.52'3
64.15 60.70 57.01 53.10 48.51 43.09 36.39 27.08 19.29 14.22
-
PVir 000
198 234 241 243 244 242 234
45.90 37.16 31.31 22.79 15.40
-
80.99 69.25 63.79 59.84 56.30 53.05 48.83 43.80 37.37 27.93 19.54 14.24
' l-
I
60
__
i
PV/rooo
_____ ,
91.35 (69.46 64.99 60.78 56.57
52.28 47.43 41.85 35.08 25.88
18.33 13.46
-
I49 I 96I95 I97 199 201
I97 189 -175 151 I 28 115 78.8
Molccu la 9- A tiyacfion
-
___
I
TABLE 4 Isopentane -
~
I I
Heat of vaporization
Temperature1
'
Ther.
Crompton
Mills
I
1 -
0
20
40 60
88.86 82.91 78.69 74.56
87.45* 83.52 79.44 75.00
64.78 58.62 51.07 41.27 24.65 16.47 10.43
64.56 58.19 50.52 40.83 25.05 17.17 11.08 8.69
70.00
80 IO0 I20
140 I 60 I80
8.07
95.92 89.98 84.46 78.96 73.26 67.09 60.16
70.12
I
-
-
~~~
- - - ~ _ _
~
-
605
52.00
41-84 25.54 17.46 11.25 8.81
-
I
I
PV/iooo
- I-
I
1 1 ~
i
I I
236 243 252 260 265 265 259 246 223 177 I53 I35 128 107
TABLE 5
I
Normal Pentane _______
____ -~
I
Heat of vaporization _ _
Temperature -
Ther.
Mills
93.36 83.63
92.38 84.58 80.29 75.39 69.88 63.85 56.3 I
-
I
Croinptoii
~
P V, 1000
-
0
I
40 60 80
80.04
75.30
1
roo I20
140 I 60
1 I
I 80
190 195
I97 197.15 197.2
__
1
,
69.87 64.48 56.58 47.42 35.01 24.68 15.66 6.55 3. I 1
-
47.27
35.16 2 5.38
16.60 7.15 3.41
-
101.18 II I 89.47 83.98 I 78.18 71-90 65.34 57.30 47.89 35.43 25.49 16.63 7.14 3.41 ~
-
I
236 255 266 271 271
269 256
237 207 178 1.51
I25 I 16
108
f,E. Mills
606
TABLE 6 Normal Hexane
-__
-~
___.
I
i
Temperature1 __-__
1
Ther.
iP-1-
0
1
60 80
i
IO0
i
I20
140 I 60 I80 200 220
230
234 234.8
.
~
Heat of vaporization Crompton
Mills
1
~-~ --i
90.98 80.82 77.55 73.65 69.38 63.96 57.63 50.93 42.75 30.37 19.73 10.44
----
I ,
1
I I
1
,
90.33 81.09 77.43 73.37 68.91 63.75 57.78 51.04 42.78 30.82 20.56 11.26 -
1
PV/rooo
____
1 ,
100.82 84.86 79.90 74.84 69.67 63.98 57.61 50.59 42.16 30.18 20.04 10.94
1
I I ~
, , I
-
198 228 238 244 248 247 239 228 21 I
I79 I49 I23 95.7
'
TABLE 7 Normal Heptane _____--__-____-
I
~
I
Heat of vaporization
-___~ - _______ Temperature Ther. , Mills Crompton
I
~
'
I
1
0
80 IO0 120
140 I60
1
180
1
200 22 0
1
240 260 266.9
1'
89.86 79.52 75.96 71.79 67.19 62.74 58.52 53.17 46.46 37.45 21.90
, ~
1
I
1
PV~IOOO
________ ~
89.10 79.06 75.76 72.06 67.94 63.47 58.63 52.98 46.09 37.12 22.33
100.25 80.66 76.12 71.47 66.69 61.73 56.63 50.83 43.92 35.11 20.90 15.38 8.52
-
1
170
214 222
1 1
1 ~
,
226 228 229 227 220 207
185 I44
I
127
1
107 87.0
MoZecu la Y A t t r nclzb n
607
TABLE8. Normal Octane ,
Heat of vaporization Temperature
I
Ther.
0 120
89.46
140 I 60 I 80
67.56 64.82 60.99 56.87 j2.03 45.97 39. I4 28.26 19. I O
70.27
200 220
240 2 60 2 80
290 296.2
Mills
, '
-
I I
Crompton
8j.jj* 71.55% 68.38 64.96 61.07 56.71 51.72 45.65 38.57 28.13 19.47
99.98 71.58
67.52 63.45 59.06 54.38 49.20 43.10 36. I5 26.12 17.97
-
PV, IO00
I49 I97 204 2IO 211 210
204 I93 I79 152 I 28 80.5
TABLE g Benzene -
~
I
Heat of vaporization Temperature,
Ther.
1
Mills
Crompton
Pv/I000
_______._
0
80 IO0 I20
140 I 60 I 80 200 220
240
2 60 2 80
288. j
IOj.Oj
94.40 91.05 87.36 83.48 79.20 74.53 69.01 62.32 54.21 43.76 27-43
1 0 7 . 2j
95. 75* 92.07* 88.00
83.72
79.18 74.24 68.45 61.74 53.74 43.57 27-79
-
123.89 102.49 97.44 92.32 87.27 82.09 76.69 70.43 63.34 54.96 44.40 28.17
-
218 277 286 293 300
305 307 301 290 271
244 I97
102.5
J . E. Mills
608
TABLE IO Hexamethylene
~___________
-~
__
Heat of vaporization I
temperature^ , ,
o
Ther.
Mills
Crompton
96.22
97.13 82.82 78.89 74.56 70. I9 65.27 59.60 53.27 45.37 34.84 26.76 17.34 12.34
111.80
83.71
IO0 I20
78.69 73-60 69.68 65.15 59.37 53.56 45.76 35.16 26.72 16.85 1
140 I60 I 80 200 220
240 2 60
I
270
277 279 279.95
11.78
-
87.47 82.j 8 77.53 72.61 67.25 61.21 54.56 46.31 35.42 27.14 17.53 12.45
-
-
,
PV~IOOO
1
TABLE 11 Fluo-benzene
__ ______
Heat of vaporization
I
Temperature:
Ther.
Mills
Cromptoii
PV I
0
87.39
80
80.06
IO0
200 220
77.09 73.21 68.50 64.37 60.09 55.24 50.28
240
44.03
I20
140
I 60
I80
2 60
280 286.55
35.74 20.95
-
88.36 79.05 76.06* 72.68 68.91 64.96 60.6 j 55.76 50.32 43.78 35.30 21.1 j
102.66 84.62 80.38 76.02 71.46 66.92 62.17 56.89 51.18 44.34 35.59 21.18
1000
Temperature'
i
Ther.
-~
0
i
140 I 60 I 80 200 220
240
260 270 2 80
PV, I O 0 0
Cronipton
Mills
I
~
87.72 73.37 71.26 68.77 65.65 62.60 59.65 56.06 53.95
,
87.25 74.12
~
107.14 79.06 75.63
71.56
68.75 65.58 62.18 58.48* 54. 244'
1.52 218
72.08
68.34 64.46 60.30 1 55 66 1 53.10
51.88:g
--
360.7
I
226 232 235 236 235 231 --
-
223
81.3
TABLE 13 Brom-benzene _ _ _ _ _ _ _ _ _ _ _ ~ _ ___ I
-~ _
Temperature
_
-
Ther.
________
30 IO0 I 60 I 80 200 220
240
260 270
280
397.0
-
____ -
Heat of vaporization
68.68 62.58 54.69 53.80 52.27 50.41 48.29 46.30 45.03
-
,
1 I
-
I
Ilills
6j.78* 61.77 56.55" 54.80
52.82 50.61 48.24 45.72 44.32
-1
1
Crompton I - -___
79.45 68.76 60.39 58.02 55.47 52.80 50.02
47-18 45.62
1-
PVl~ooo _
__
TABLE 14 Iodo-benzene
-~ __ _____
____
___
- ~ _ _ _ _. _ _ _ .
I I
Heat of vaporization
1
Temperature
Ther.
Mills
Crompton
~-
30
56.70
55.99
IO0 200 220
53.68 45-34 44.94 43.70 42. j o 41.85
53.32 47.01* 45.64 44.02 42.25 41.27
240 260 270 280 448
Temperature
-
-
-
Ther.
~
1
I
Mills
51.87
i
IO0
44.20 42.24 40.26 37.95 35.40 32.61 29.45 25. 56
I20
140 I Go I80 200 22 0
240 260 280 283. I j
20.07
10.43 , __
~
1
i 1
I35
I47 49.7
~~/rooo
Croinpton
I 60.72 47.62 11 45.13 42.61 39.96 37.08 33.92 30.31 I 26.05
20.36 10.75
I -
92.8 114
-_ 1
i
PV,'~ooo
142 I44 146
-
I _____
0
II
68.77 60.08 49.36 47.57 45.54 43-45 42.31
, -
i
1
I11
I43 I47 150 1.51
150
I47 142 I34 119 91.2 52.3
-
61I
Heat of vaporization ___
Temperature ~
1
Ther.
-~
0
IO0
I20
140 I 60 I 80 200 220
240 2 60 280 318.7
Mills ~
1
,
35.38 , 31 * 40 30.02 28.52 26.86 1 24.89 22.97 20.89 18.60 16.03 13.08
-
-
'
Cromptoii
PV/IOOO
~~
42-19 [ 33.29 , 31 e67 30.02 28.38 26.66 24.90 22-99
35-18 30.95 29.81 28.56 27.19 25.69 24.08* 22.28* 20.25* 17.89* 15.06*
20.88
18.46 15.52
__
-
65.4 86.5 89.7 92.3 94.1 94.7 94.8 93.9 91.5
87. I 80.3 32.6
TABLE 17 Water
_~_______~
~-___-
Heat of vaporization Tenlperature
Ther.
Mills
~
Crompton
€'V/IOOO
_ ~ ~ ~____ _ _ 0
20
40 60 80 IO0 I20
140 I 60
I 80 200 220
24c 260 270
364.3
606.5 592 *6 578.6 564.7 5 50.6 536.5 522.3
574.6 571.2 565.8 558.4 549.4 538.9 526.4
508.0
512.8
493.6 479.0 464.3 449.4 423.8 394.0 374.5
498. I 481.3 463.8 445.2 423.5 399.3 385.4
-
-
738.4
965
705.8
I022
682.4 656.0 630.6 606.5 582.7 559.4 536.4 513.3 490.7 467.4 442. I 414.2 398.5
-
1082 I 142 I202 I 260
1 304 7347 1404 I435 I478
1523
1533 1514
1486 345
612
J. E. Mi/ls
-
Methyl Alcohol
TABLE18 _
I
__ _ ~ Heat of vaporization
__
_
_
I
I
Temperature'
Ther.
PV~rooo
I
289.2 284.5 277.8 269.4 259.0 246.0
0
20
40 60 80 IO0 I20
289.4 283. I 275.8 266.9 2 j6.8 245.1 231.7 1 216.6 199.4 179.3 , 154.4 , I 18.j 92.2 68.9 1
232.0
140 I 60 I80
216. I 198.3
200 220
151.8
177.2
112.5
84.5 61.7 44.2
230 236 238. j 240
jI.1
20
40
60 80 IO0 I20
,
140 I 60 I 80
I
200 220
I
I
1 I
,
658
665 664 652 629
222.7 205.0
185.8 164.9 140.0 106.2 81.9 61.0 45.0
585
494 426 372 326
--
__-
Ther.
' -I1
220.9 220.6 218.7 213.4 206.4 197.1 184.2 171.1 156.9 139.2 116.6 88.2 40.3 22. I
I
290.3 273.6 256.9 240.0
22 0
--
--
l\iIills
'
~-
Crompton
~ _ _ _---I
228.4 223 9 218.3 211.4 203.4 194.4 183.6
,
'
'
238.0 224.3 210.8 197.5 184.2 171.2
121.7
94.6
74.8
45.8
35.5
157.7 141.7
26.5
-_
I
I1
~'~/rooo
-I
157.9 144.5 130.7 115.6 97.8
171.2
,
I
Heat of vaporization
~ _ _ _ _ 0
527 561 593 62 I 643
307.2
TABLE 19 Ethyl Alcohol ____
I
Temperaturel
324.4
1
__
--
-~ - ---
240 242.5 243.6
Crompton
Mills
-1
20.3
--
369 396 423 446 467 483 490 494 491 474
437 377 265 219 167
_
TABLE 20 Propyl Alcohol ~_
_
-
____
.~
~
~
Heat of vaporization I
Teniperaturel I 0
80 IO0
I20
140
I 60
I 80 2 00 22 0
240 260 263.7
Ther. -
- - ~
,,
Mills
I
Cronipton _~
I go. 8
194.4 173.0 I 64.0 153.0 142.4 129.0 116.3
172.4 165.2 157.0 147.9 137.6 125.8
102.2
112.7
85.3 63.4 , 33.5
96.6 75.3 41.4
PI’,I O 0 0 _.
200.9 153.7 142.7 132.0 121.5 I
10.7
99.9 88.2 74.7 57.5 31.2
--
284 360
373 379 381 381 373 362 336 290 224 I37
TABLE2 1 Acetic Acid Heat of vaporization Teniperature, 20
40
60 80
IO0 I20
140 I 60 I80 200 220
240 260 280 300 310 320 321.6j
Crompton
Ther. ~-
~~
84.05
87.02 89.69 91.59 92.32 94.38 91.83 89.63 87.7 1 85-55
82.02 78.18 72.26 63.39 48.95 37.77 18.04
-
~
~~
184.80 176.94 169.46 162.05 I 54.62 147.20 139.58 131.82
123.95 115.73 106.72 97.21
86.44
Pv; I O 0 0
Accurate calorimetric measurements are exceedingly difficult even under ordinary pressures, and it is not too much to say that where equation 4 is applicable, latent heats calculated with its aid will be more accurate than direct measurements of that quantity, unless very great care is taken in the measurements. Equations 3 and 4 give with the associated substances and with stannic chloride an agreement which is partial but not complete, divergences being shown at the higher temperatures. One or more of the modifying causes mentioned on page 602 may here be operative. Equation 5 was deduced by Rlr. H. Crompton. Mr. Crompton considers the change in density as if it were due to pressure alone, then in order to keep the substance at that density without the excess of pressure doubles the amount of energy required. Thus he has, (9)
I, -=2
Ppap
L Z
= 2RT log,
d D
-~
Mr. Crompton makes no supposition as to the true came of the change of density. But he proceeds on the principle that in effecting a given change of condition the process pursued is immaterial if the total energy change is alone to be considered, the idea being that the change in density could, theoretically, have been produced by pressure. T h e law governing the change of pressure with the density is known, therefore the amount of energy involved in the change of state can be calculated. Mr. Crompton uses as the law governing the change of pressure with the volume, the gas equation, PV = RT. R u t since Mr. Crompton deals with an ideal condition, from which the action of forces other than the pressure are by assumption removed, his equation is not limited to those temperatures for which that equation holds true. I t is necessary, however, that PV = R T should represent the true law of pressure for the substance, which is ideally considered only in a limited sense. (The material size of the molecules or some effect of the temperature, etc., might, therefore, affect the exactness of the law.)
It will be further recognized that Mr. Crompton’s equation, no less than equation 4 above, involves the assumption that the only energy change is that involved in a change in density - that is, a change of potential energy, -and the total kinetic energy of the molecules of the liquid and of the gas must be the same. As a consequence it is to be expected, though not with certainty, owing to possible compensation, that the theory would not apply to substances more associated in the liquid than in the gaseous condition. I n the tables above, I to 21, in the coliimns headed ‘LCrompton”we give the results obtained from this equation for the substances under examination. For additional evidence bearing upon the theory, see Jour. Phys. Chem. April, 1902, p. 219,and Proc. Chem. SOC. 1701. 17,233,1901. It appears that at low tem@evatures, where the vajof, presszwe is small, the ?results are invariably, and usual@ very cofzsiderably, too large. But at the hzghiest tempevature examined for each substance the agreement is good, the divergence at this temperature being greater than one calorie only in th,e cases of ether, normal octane, stannic chloride, and four of the five associated substances. T h e results therefore merit detailed study. Of the twentyone substances, twelve, viz : ether, di-isopropyl, isopentane, normal pentane, normal hexane, benzene, hexainethylene, fluobenzene, chlor-benzene, brom-benzene, iodo-benzene, and carbon tetrachloride, give results that are in all respects similar. With them at the low temperatures Crompton’s theory gives too high results, but as the temperature is raised the results grow in the main continually closer to those given by the thermodynamical equation. For these substances after a vapor pressure of 7000 mms has been reached, it may be said that Crompton’s theory gives a very fair approximation, usually within one calorie, to the results obtained thermodynamically. Di-isobutyl, normal heptane, and normal octane, each show a good agreement at the lowest temperature for which the vapor pressure was measured, viz : IOO’, 80°, and 120’. Then with increasing temperature Crompton’s equation gives results lower than those obtained thermodynamically.
616 Stannic chloride is similar to the above in showing better agreement at the lower temperatures than at the higher, but i n this case Crompton’s results are uniformly the larger. I n the case of water the results of Crompton are always the larger, but had the observatioiis been continued nearer the critical temperature, it is quite possible that good agreement would have been reached. With the three alcohols, Crompton’s equation gives entirely too high results a t the lower temperatures. T h e n with rise in temperature the results from Crompton’s equation becomes decidedly the lower, but near the critical temperature the differI ence is not very marked. With acetic acid, Crompton’s equation gives results more than twice too large a t the lowest temperature. As the temperature is raised the disagreenieiit becomes continually less. I t must be borne i n mind that acetic acid vapor shows marked association. ComFaring the three equations the value of Crompton’s theory becomes doubly apparent. Crompton’s equation does not involve the vapor pressure, and therefore, if trustworthy, will act as a check upon the thermodynamical equation a t the end-points of the curve, where owing to the manner of obtaining ap the - the therniodynamical results are somewhat uncertain.
ar
On the other hand, compared with equation 4, Crompton’s theory does not depend upon the attraction and would not be affected by a variation of the attraction with the temperature. It should therefore furnish a clne to those substances i n which the molecular attraction does not remain constant with increasing temperature. At low temperatures Crompton’s equation gives values uniformly too high, and it therefore cannot be used to check the results of the other equations. Rut at the highest temperatures the evidence obtained from the results is exceedingly interesting. For ether, di-isopropyl, isopentane, normal pentane, normal hexane, benzene, hexamethylene, flno-benzene, and carbon tetra-
r’lilo Zecu la Y
A dtrnclioiz
617
chloride, Crompton’s equation gives results in better accord with the values obtained from equation 4 than with the thermodynamical results. For these substances at the highest temperatures considered, Crompton’s theory gives results differing in no case from those of equation 4 by so much as 0.4 of a calorie, and in several cases the agreement is almost exact. This is splendid confirmation of our belief that in these cases the diverL -- E, gences i n the constant of equation, y ; - - ~ u = constant, were 1
ap was obtained. 3T For di-isobutyl, normal heptane, and norrnal octane, Crompton’s equation does not confirm the results of equation 4 when the constants that we have adopted are used, but points instead to lower values for these constants, and we would here call attention to the fact that this indication meets further confirmation. (Cf. results equations 20, 21 and 25.) For chlor-benzene, brom-benzene, and iodo-benzene, Crompton’s theory points to higher constants. T h i s evidence cannot be entirely trusted since the highest measurements for these substances are considerably below the critical temperature. For stannic chloride, Crompton’s equation confirms in a measure the constant adopted. T h i s was a surprise, and suggests the possibility of an error in the Biot formula used. For the alcohols and acetic acid, Cronipton’s equation confirms the belief that in these substances the molecular attraction changes at high temperatures. T o consider the question as to why Crompton’s theory does not give correct results at low temperatures we would call attention to the fact that Mr. Cronipton could as well have taken the law of vapor pressure as PV = PIVr and ha+e obtained,
clue to the Biot formula from which the
,
(10)
L = 2P,V, log,
d D
Here VTis the volume of the liquid and PT is the theoretical pressure of the liquid. In calculating this theoretical pressure it will be seen that the equation cancels back to its original form,
61 8
J. E. Mills
. We have here called attention to the transposiD tion only that the equation might be recognized as identically the same equation with which we have to deal in the JouleThomson effect of the free expansion of gases. T h e JoixleThomson energy change is i n reality a latent heat -the very same effect of the Crompton equation, only the conipression is not carried to liquefaction. T h a t effect has been but little studied and is usually laid entirely upon cohesive forces. T h i s may not be the case, and certainly is not the case when hydrogen, which gives negative results, is considered. We here point out that zyit is exjeriineiatalGy jossi6le) a continuatioiz aizd exteizsion of lhe experiments ofJoule and Lord Kelvin i i z connectioiz with the theory of Cromjton, should eizable Cromptoiz’s theory to 6e understood aizd corvectly modzj$ed. If the PV curves, Diagrams I to 3, be examined i n connection with Croinpton’s equation, it will be noted that Crompton’s equation usually gives good agreement with the thermodynamical results at points corresponding to the descending portions of those curves. z R T log,
The Variation of the Heat of Vaporization with the Temperature T h e discussion in this and the previous paper of the data bearing upon the latent heats of vaporization obtained for the twenty-one substances examined cannot have failed to impress one with the wonderful accuracy of the measurements by Profs. Ramsay and Young and by Prof. Young, upon which that data is based. T h e data upon heats of vaporization here made available is therefore the most extensive and the most accurate yet published. T h e variation of the latent heat with the temperature has always been a question of interest, and we therefore attempt to show most clearly the manner of this variation. T h e function of a portion of the latent heat is well known. I t is expended in overcoming the external pressure. T h e portion so expended can be calculated and neither theoretically nor actually does it appear to be a simple function of the temperature. We have called the energy so expended E, and have
given its value for each substance slid temperature examined. (See Second paper, Tables 2 to 2 2 , under heading EL.) I t has been soggested that
E
-i I S
L
a constant.
Since ET is
aP 0.0~31833P(V- u)and L = 0.0~31833T-(V - ZI), this would . aT El -. aP require that - -- PT ar = constant. This relation is not con-
L
firmed. Examination shows that EI first increases and then decreases with the temperature, while the latent heat, almost invariably, decreases. E, thus varies independently of the latent heat and ranges usually between seven and fourteen percent of its value.
Diagram 8 Ordinates give internal heat of vaporization i n calories
I t was therefore thought best to subtract, from the total latent heat this variable amount of energy thus externally expended and to plot the internal latent heat of vaporization against the temperature. T h e values are given in Second
620
Diagram g Ordinates give internal heat of vaporization in calories
Diagram IO Ordinates give internal heat of vaporization in calories
AloZeczdar Attmctioiz
62 I
paper, Tables 2 to 2 2 , under the heading I, - ET. T h e curves are shown in Diagrams 8, 9, and IO. T h e observations are marked with dots, circles or crosses. T h e scale needs no explanation except that for water 300 should be added to the ordinates to make the reading as expressed in calories correct. It will be noted : I . T h a t the internal latent heat cannot be regarded as a linear function of the temperature except at low vapor pressures and for a limited range of temperature. Water does show a linear variation to 2 3 0 ° , but this is due to Regnault’s linear formula from which the values were obtained. T h e values obtained from Ramsay and Young’s observations above 230’ show beyond question that the line for water should also curve perceptibly before that temperature is reached. 2. T h e curves are all concave towards the temperature axis. Hexamethylene, di-isobutyl, broni-benzene, and iodo-beiizene would not always be concave if the observations were exactly followed. Rut the diagrams themselves add strongly to evidence already pointed out (p. 595, etc.) in indicating that these values need further study. 3. Except in the case of acetic acid, the internal latent heat always decreases with the temperature. 4. Several attempts to find a simple empirical formula connecting the internal latent heat and the temperature failed. T h e investigation was not pushed. Some Relations Resulting from the Latent Heat Equations By combining equations 5 and 7, we get : -
Equations 1 1 and 1 2 are not suitable for calculating accurately the pressure, for that value appears as the difference of two comparatively equal values. W e give as ail example of such application Table 2 2 below. Of the substances we have dis-
J. E. 1Will.S
622
cussed isopentane is one of the most carefully nieasured and the agreement is to within the limit of experimental error permitted ap by the equation. T h e - is obtained from Biot’s formula.
aT
vi%-+ 3T414 pV% ’+ VXV is given
under the heading
, a 0
11.16
20
21.04 35-66 55.73
40 60 80
81.85
3047 6165 11162 18558 28893 42783 60986 84425 114312 152163 I 69480
2742 5639 10139 16634 25541
Calculated
305 526
Biot
258 573 1131 2036 3401 5354 8040 I 1620 1628j 22262 25005
1023
I924 3359 5473 8506 1250.5 17502 19753 10060
I 14.70 37310 155.18 52480 204.42 140 71920 96810 264.0 I 60 132410 I80 335.9 187.8 159420 367.8 Equation I 2 will recall the similar equation : p = bT a , (13) ap proposed by Profs. Ranisay and Young,I where 6 =- and a = IO0 I20
aT
constant. T h e equation is applicable where the volume of the gas is kept constant. a ” has a value dependent upon the volume. ap T h e aT of equation 12 shows the variation of the vapor pressure of a liquid with a rise in temperature, the volume of the ap liquid iiieanwhile undergoing change. T h e - of equation 13 deaT Phil. Mag. May, 1887. Phil. Mag. August, 1887. Proc. Phys. SOC. 1894-95. Proc. Phys. SOC.Vol. 15. Phil. Mag. April, 1899. Proc. Phys. SOC. 1701. 17.
Mok c u In A i~7,actioiz
623
?r
notes a change in pressure of a g-as, the volume being kept constant. A liquid cannot exist above its critical temperature and at that point the liquid and its vapor are identical. T h e critical ap temperature therefore niarks the limit for which the aT of equation
12
ap can be obtained, but just at that point the -of
a r the liquid
ap
and the - of its vapor at constant volume must be identical. aT T h a t the
;
obtained from the Biot formula could not in the
nature of the case be accurate at or near the critical temperature we have already pointed out. (Second paper, p. 395.) T h a t the variation we were there led to expect is quantitatively equal to the actual variation as found for equation 13, we have subsequently shown (p. 594). I t remains to be seen if ‘ ( a” of equa31414 P‘ tion 13 corresponds to the function TJv% + v%v”3 +Fv of equa-
tion 12. At the critical temperature u = V, and therefore we have at that point,
Choosing isopentane as being one of the most carefully measured substances, we found for p’ the value 105.4 (Table 25) and V is 4.266. ((a ” therefore becomes 159,400. T h e values given by Dr. YoungL at volume 4.3 are 157,880 from drawn isochors, and 162,890 when calculated from some values of b. T h e agreement in this instance is therefore to be regarded as perfect. T h a t the laws of attraction we have assumed enable the constants of the equation of Ramsay and Young at one point to be foreseen and calculated is proof of the most convincing nature that the theory of the attraction oatlined is correct. We are led to believe that, properly modified, the same considerations Proc. Phys. SOC.1894-9j, p. 654.
will elsewhere be successful in a further calculation of these constants. T h e relation is so full of possibilities and for its adequate consideration will require so extended an investigation that we postpone the discussion for a separate paper. Again, combining equations 6 and. 8 we obtain : -
Owing to the inaccuracy of Crompton’s equation at low vapor pressures a t such points equation I j cannot give accurate results. But as the critical temperature is approached we believe that this equation offers the most accurate method yet avail-
,;:
able for finding the
giving results far better than could be
obtained from direct observations of the pressure even when the observations are afterwards smoothed. In Table 2 3 below we apply the equation to isopentane, comparing the results obtained by its aid with those obtained from Biot’s formula.
TABLE 23 Isopentan e
______ __
____ 0 20
40 60 80 IO0 I20
140 160 I80
____-
2.768 2.419 2.125 1.868 1.635 1.417 I , 206 0.9920 I , 0.7612 ’ 0.4442
187.4
187.8
I
0.1508 1
__
915.8 422.4 221. j
0.003022 0.00572j 0.009598 0.01480 0 . 0 2 147 0.02980 0.03993 0.05221 0.067 I 2
126.2 76. I ’ 47.56 30.20 19.00 11.34 5-09 0.08728 1.503 0.1003 - 0.1018
-
.__-____
12.05 22.83 38.27 59-00
85.61 18.82 159.22 208.16 267.6 348.0 399.9 405.9 I
I
11.16 21.04 35.66 55.73
81.85 114.70
1j5.18 204.42 264.0 335.9 366.4 367.8
v
log. -
" v
9 t the critical temperature the fraction -assumes the
v-v
indeterminate form
0 0
.
Evaluating by differentiating the nu-
merator and denominator we find the limit approached at the critical temperature t o be 0.4343 --, 0.4343 being the modulus of
v
the Kaperian system of logarithms. Therefore we have a t the critical temperature, a p - 124860 aT mV ' a very simple relation. For isopentane we thus get the values ap of as 405.9, a result in exact accord with the values 397 to 407
aT
as given by Dr. Young,' and thus confirming every conclusion ap we have hitherto drawn relative to the value of -at this point. aT Combining equation 16 with 12 and remembering that at the critical temperature V = zi we have, p=- 124860'I' - IO471 p'
mV
v"3
.
Applying this equation to isopentane, we have, V = 4.266, nz = 72.1, T = 460.8, /A' = 105.4, and the pressure thus calculated is 27600 against 25000 observed, an agreement well within the limit of experimental error, since the pressure is found as a difference. A more general equation is obtained by combining equations 7 and 8 to obtain
a n equation, which owing to the divergence shown by Cronipton's theory is not applicable to low pressures. We have purposely omitted all reference to those equations Proc. Phys. Soc. 1894-95, p. 650.
connecting the latent heat with the specific heat of liquid or vapor, as it is our purpose at a future time to point out a relation existing between the specific heat of solid, liquid, andvapor, a d to discuss such equations in that connection. A Further Application of Crompton’s Theory t o Verify the Proposed Law of Molecular Attraction Following a line of argument already advanced,I if we consider any gas it is reduced to the liquid state by pressure and by the molecular attraction. I n nature the two, pressure and attraction, act jointly and continuously. But theoretically we can separate their action, since mechanically all forces are independent of each other. Legitimately then, we can consider a liquid at its critical temperature as reduced to that density: First, by the action of a pressure; second, by the action of molecular attraction. Accordingly the theoretical density of the gas at its critical temperature and under its critical pressure was calculated. T h e g a s would be reduced to that condition z y there were no molecular attraction. T h e remainder of the condensation, to l‘he actual density, must be the w o r k of the attraction
alone. T h e theoretical critical density can be calculated by the equation, Pm D = 0.0,16014 - .
T
If the attraction obeys the law assumed we can use equation 2 to calculate the energy necessary to overcome the attraction and expand the gas from its observed to its theoretical density. If to the energy so calculated we add the energy necessary to overcome the external pressure during the change in volume, we have the total energy, h E,, required by the change. T h e equation will become,
+
By Crompton’s theory we can calculate the energy necesJour. Phys. Chem. 6, 223 (1902).
.,
sary to change the gas from its observed to its theoretical density as if the change were produced by pressure alone, the equation being : -
L= A
+ E, =-9 . 1 5 2 2 Tlog
d Cals.
m
In these equations T is the critical temperature, d denotes the critical density, and D is the theoretical density of the vapor at the critical point. , T h e results of equation 20 are given below i q Table 24 under heading Mills. T h e restilts from equation 2 1 are given under the heading Croinpton. T h e difference is also given. T h e agreement is as perfect as could be desired. T h e difference is usually less than one calorie and amounts to a divergence of more than four percent only in the case of normal octane and the associated substances. (To these latter neither theory is applicable.) With the three alcohols others have concluded that at the critical temperature there is 720 association. With them the molecular attraction, it w7ill be recalled, changed with the temperature. Using the values of p', obtained nearest the critical temperature, where the effect of the association could be assumed nil, we obtained the last values given, which are in good accord with the results given by Crompton. In Table 24 the critical data, except for water, are from the measurements of Profs. Ramsay and Young or Dr. Young, References have been given. (Second paper.) There is nothing in the method adopted to prevent the application of equations 20 and 21 to other points than the critical temperature. Had the equations been combined, an equation similar to equation 18 would have been produced, and the above results may be regarded as but a special application of that equation.
,."."_..
.
J. E, Mills
628
x
4
.C
c
d
o d o o o o o o d o d o o d d d o d o d o '
I
I
I --
a,
I,
.-a i I
I
Extension of the Theory to the Energy Relations a t the Critical Temperature Solving equation 6 of the first paper’ we get :
where c is the same constant for all non-associated substances, and m is the molecular weight.
L - E, $/d.-
a/D
we have shown to
be a constant for any particular substance, have called this constant p’, and have given the average constants for the substances examined. (Table 2 j q ) p represents the absolute attraction at unit distance from a molecule and must be regarded as a n exceedingly important and a constant property of the molecule. T h e values obtained for
P
are given in Table 2 j.
We would here call attention to the fact that for bodies of similar constitution and closely related chemically the values of p may be the same, though the observations are not sufficiently extended to permit of any definite conclusion. T h u s :Normal pentane, Normal hexane, Normal heptane, Normal octane, But isopentane
-
457.3
-
454.2 458.6
-
~
451.1
438.6
I t is well also to note that for the associated substances, water, the alcohols, and to a less degree for acetic acid where it is less associated, the values for p are greatly larger than for the other substances examined, arid this very large attraction is suggestive in view of the conclusion drawn in the Second paper that quite possibly the molecular association of these substances was caused by the molecular attraction. Resuming a line of argument followed in the first paper (p. 228) we can test our conclusions further. In a g a s indefinite expansion takes place as the pressure is decreased. This shows ____ Jour. Phys. Chem. 4,
209
(1go2).
Molecu In Y
Atdvn ctioiz
631
that the attraction between the molecules cannot be great enough to make the paths of the molecules closed curves. I n a liquid, while undoubtedly many molecules whose velocity is above the average molecular velocity, are continually flying away from the surface, yet i t must certainly be the case that most of the molecules are drawn back by the molecular attraction. There must be for each substance a certain temperature at which the molecular attraction, without outside pressure, is just strong enough to overbalance the kinetic translational energy of the average particle and cause i t to return to the liquid or solid substance. At this point, if the attraction varies inversely as the square of the distance between the molecules, we will have from mechanics, P , =2 -
(23)
R
where V’ is the molecular velocity and R is the distance apart of the molecules. p is the absolute attraction at unit distance. It is a common text book idea that at the critical temperature the kinetic energy of the molecules of a liquid (gas) under the critical temperature just balances the attraction. T h e idea rests on the diminution and final disappearance of surface tension at the critical temperature, and the fact, that a liquid at its critical temperature may be changed to a gas without the addition of external energy, i. e., by an infinitesimal change in pressure, the heat of vaporization being zero. I t must then be at this point that equation 2 3 will hold good. Putting therefore for the molecular velocity, V’, its value at this point,
\I3GT (derived as usual, Rc being 83,250,000) and for R its ~_ .
value c
$, the constant c being unknown, but
equal for all
substances, we get finally,
I n this equation T and d denote respectively the critical temperature and density, and cr is the same for all substances.
Using the values for the critical constants as given in Table 24, we obtain for
C'
the values given in Table 25.
Now if our ideas are correct and the absolute attraction p, given in equations 2 2 and 24 are the same, and correctly measured, we have a7ight to combine these equations and get : -
L - E,
P
"'Fd = constant,
where T must be the critical temperature and d must be the critical density.
If therefore the values of by the values of
$ given in Table
25 be divided
given in the same table, the results should
prove constant for all non-associated substances. T h e result of this division is given in Table 25. T h e mean value for the non-associated substances is 10.76. Since the values for p' are uncertain by about two percent, and since the critical data cannot be measured accurately, the close agreement can be regarded as exceedingly satisfactory. A review of the data leads the author to believe that isopentane and normal octane are the only variations that are not due largely to the values adopted for p'. Associated substances, h j ~ i o ~ could i, not agree with the equation deduced and they do not. But considering them more particularly it will be seen that if a t the critical temperature the molecular association had vanished (as is said to be the case for the alcohols), equation 24 would hold. If instead of the average value obtained for p' at the lower temperatures, we use the values for the constant obtained near the critical temperature, equation 2 2 should also hold, simultaneously with equation 24. For water the data near the critical temperature is lacking, but
making use of the proper values for the alcohols, we obtain the results given in Table 25. These results would evidently be somewhat better if the observations of p' could have been obtained yet nearer the critical point, and we are thus led to regard these associated substances as giving a very remarkable confirmation of the theory.
TABLE 2 j
-~
1
I
-
I ~-~
Ether ' Di-isopropyl Di-isobutyl Isopentane I Normal pentane 1 Normal hexane l Normal heptane Normal octane I Benzene Hexamethylene Fluo-benzene Chlor-benzene Brom-benzene I Iodo-benzene Carbon tetrachloride Stannic chloride Water Methyl alcohol Ethyl alcohol l Propyl alcohol I Acetic acid I Methyl alcohol , Ethyl alcohol 1 Propyl alcohol 1
~
l
I
1
~~~
104.4 98.08 86.30 105.4 109.9
438. 5 433.1 418.6 438.6 457.3 454.2 458.6 451.1 468.0
IO2.8j
98.75 93.00
109.5
I
,
103.6 453.8 85.60 392.3 391.9 1 81.19 56.12 302 8 , 44.40 261.3 44.09 1 236.2 1 26.04 166.4 553.3 1 1450.8 30j.o 968.6 864.5 1 241.2 199.2 780.1 I 130.0 jog. I 259.4 I 823.8 197.2 1 706.8 1 157.0 614.8 1 ~
'
I
Ratio of
42.23 41.23 37 * 7 8 43.14 44.15 42.24 40.62 39.34 43.415 44.38 35.86 36.38 27.76 23.64 22.32 15.23 123.00 78.56 61.04 53.64 55.00
-
-
10.38 ~
1 I
' ~
i
IO. 5 1 I I .08
10.17 I 0.36 10.75 11.29 11.47 10.78 IO. 23
ro.94 ~
10.91 11.05
I
I I
I
i
10.58 10.93
11.79 12.34 14.16 14-54 9.26 10.49 11.58
11.46
It should be noted that the constaiit obtained from equation 25 and given in Table 2 5 is just one-half of the constant mL obtained in Trouton's formula, T = constant, where 'I'is the boiling-point of a substance. T h a t there is a reason for this fact we propose later to show in connection with a paper applying the law of attraction to the boiling-point.
J . E. Mills
634
I n conclusion we again point out that we are indebted to Drs. Kamsay and Young and to Dr. Young, for nearly every measurement used i n this article. And we would again express our great appreciation of the accuracy of these measurements and acknowledge our obligation to them.
Summary I . Several facts bearing upon the results of the last paper are discussed. These facts confirm the law of attraction asI
sunied by making it most clear that
‘ ,$/ *’
fld -
D
does equal a con-
stant (designated P’), for normally constituted substances, and that the equation is applicable with equal exactness in the irnmediate neighborhood of the critical temperature. 2.* An
equation,
d
I, = 2RT log, D, proposed by Mr. H.
Cronipton, was investigated, and it was found that a t low teniperatures, where the vapor pressure is siuall, the results given by the equation are invariably, and usually very considerably, too large. But at higher temperatures the results are correct. 3. Crompton’s equation was shown at the critical temperature to give results confirming the law of attraction assumed. (Equations 2 0 and 21.) T T
4. It was shown that,
ap
287500 = ___
m
log
-v
,
V--v’
within certain
limits.
5. I t was shown that at the critical temperature thefollowing relations hold true : -
the last being an interesting confirmation of the law of attraction assumed.
63 5
Molecztlar Altrnction
6. I t was shown that at the critical voluine ( { a of the equation, p = 6T- a, becomes identical with the term, 10471 -V"at"' . ')
7. T h e variation of the latent heat of vaporization with the temperature is disciissed. Ciniveisity of North Carolina, Augzisl, rpog.
Addendum Since this paper was written, a letter has been received from Dr. I'ouiig, giving the values of the ap for ethyl oxide. aT T h e pressures given in the original paper are correct as are the below 180" C. T h e corrected values above aT that temperature are given below, together with the corrected values of the heat of vaporization and of p'. ~ _ _ ~ _ _ _ _ _ _ _ ~ ~ ~ ~ _ _ ~ _ _ _ _ __ __ _ -_ I
values of the
I
lap corrected
Temperature aT
l-
354.9 374.1 382.2 385.8 389.8 391.6
L
~
L-E1
_ _ _ __
26.18 19.21 14.66 11.17
22.36 16.42 12.52 9.53
-
-
Y'
1 ~~~
97.7 96.4 93.5 90.7
'
-
Dr. Young gives 194.45' as probably very nearly the true critical temperatiire, and 3.814 as the true critical volume of a gram. By interpolation of the results given by Profs. Ramsay and Young (Phil. Mag. May, 1887, p. 441) for the equation ap P = 6T- a, the true value for the - at this volume appears to
ar
be 436.
T h u s the aT from Kiot's formula at the critical tem-
perature is about ten percent too low, an amount which is not quite sufficient to explain the decrease in the value of p' at the higher temperatures. But above 180' C, owing to the hydrolysis
_ _
Moleculav Ah!vaclioiz
636
of the methyl salicylate used as a heating jacket, the data is somewhat uncertain. It should be noticed that equation 14 of the present paper ap gives 441.9 as the value of the - at the critical temperature, a
ar
result which agrees well with the value 436 given below, thus confirming what has been said as to the accuracy of that equation. Jiovenzher z, z 9 q .
