MOLECULAR ATTRACTION, VII. AN EXAMINATION OF SEVEN ESTERS BY J.
E. MILLS
In previous papers’ we derived and discussed the equation : I.
Here 1, is the heat of vaporization of a liquid, E, is the energy spent in overcoming external pressure, I,--E, is, therefore, the internal heat of vaporization, d and D are the density of liquid and vapor respectively, and the constant we have called p’. For a more complete discussion of the ideas underlying this equation, and its limitations, the reader is referred to the second and sixth papers t o which references are given above. It is sufficient to repeat here that the equation was deduced upon the assumption that the molecular attraction varied inversely as the square of the distance apart of the molecules. If the equation is finally proved true it will indicate that the molecular attraction varies according t o the same law as does the gravitational attraction so far as the variation with the distance is concerned, and will also show that this attraction alone is sufficient t o account for, and is a measure of, the cohesion between the molecules of a liquid. In the second paper above cited, the equation is applied. to twenty-one substances, in most cases over a range of temperature extending from near the freezing-point of the liquid nearly t o the critical temperature itself, the excellent measurements of Drs. Ramsay and Young, and of Dr. Young, being used. In the fifth paper the equation was applied to ten additional substances, three of these ten being esters which had been measured by Prof. Young and Mr. Thomas. The results obtained from the thirty-one substances previously Jour. Phys. Chem., 6, 209 (1902);8, 383 (1904);8, 593 (1904);g, 402 (1905);IO, I (1906); 1 1 1 I32 (1907).
595
Molecular Attrnction
examined and reported upon have confirmed in the most satisfactory manner the truth of the equation above cited. The present paper deals with seven esters measured by Prof. Young and Mr. Thomas and therefore concludes the examination of the ten esters measured by them. We may add further, that so far as we are aware, the present paper concludes the study of all of the liquids for which the necessary measurements are available. In the work which follows the heat of vaporization was calculated by using the well-known thermodynamical equation : dP dP L= T - - (V-V) = 0.0,31833T - ( V - v ) . 2.
J dT
dT
e
dP dT
The - was obtained by first calculating the constants for an equation of the form proposed by Biot, viz.: 3.
log P = A
+ 6 0 1 ~+ c P t .
The smoothed pressures as observed by Young and Thomas were used for the calculation. If now we let, 4.
A = 168.775 (6. log. a. a t
+ c. log P. p i ) , then,
dP
5.
iT = 0.031414P A ,
and
6.
Por calculating E, we used, as in previous papers, the formula, 7. E, = 0.0~31833P(V--v). The density (volume) of the liquid up to the critical temperature is in every case obtained from the measurements of Prof. Young and Mr. Thomas1 as is also the density of the vapor, except a t o o C where it was calculated from the formula, 8.
P??Z D = o.04160r4-.
T
Jour. Chem. SOC., 63, 1191(1893).
I
J. E.
596
MiZZS
The data a t the critical temperature was taken from a paper by Dr. Young.' The constants for the Biot formula, equation 3, are given below in Table I . The observed vapor pressures, and the calculated vapor pressures making use of the above constants, are given below, Tables 2 t o 5 inclusive. We have already shown2 that Biot's formula does not, and cannot by any recalculation of the constants be made to, fit the vapor pressure curve exactly, in the neighborhood of the critical temperature. As will be seen,, the comparison given below is further evidence upon this point, the divergence being even more marked in the case of the esters than with the ordinary substances. Hence the
dP
--
dT
and consequently the heat of vaporization calculated
with its aid, will both be too small in the neighborhood of the critical temperature. This will make the constant found for equation I , that is p', decrease as the critical temperature is approached, a result not wholly, if at all, due t o an actual departure of tF.e substance from the law, but merely to the error thus introduced by the Biot formula. Needless to say, were a perfect formula for representing the vapor pressure curve known to us, we would use it, but as the error in the Biot formula does not appear appreciably large until within 20°, or less, of the critical temperature, and elsewhere its behavior seems perfect, we have thought it best to continue the use of the formula. As a check upon the results in the immediate neighborhood of the critical temperature, we have obtained the
dP dT
directly from the observations, and also by
another method from the theory of Crompton alluded t o later in this paper. These results in most cases confirm the belief that the entire divergence near the critical temperature is introduced by the Biot formula. But with the ten esters there seems usually to be a greater divergence than can be Phil. Mag. [5], 50, 291 (1900). Jour. Phys. Chem., 9,402 (1905).
Moleczslar Attractioyz
59 7
598
1.E.
Mih
accounted for as above. We hope durini the coming year P to be able to investigate the dat the critical temperature
dT
experimentally, and therefore will not give here the detailed data upon this subject. The calculations involved in all of the tables given in this paper were checked and were carried t o that degree of accuracy warranted by the measurements. We give below the equations for calculating A, and also the detailed results of the calculations, Tables 6 t o 1,2, inclusive. For propyl formate, A = antilog (?.2490105 0.000774195t ) aiitilog (0.1g4007o - 0.003g2179 t ) , t = ToC - IO.
+
For ethyl acetate,
+
+
A = antilog (1.6342371- 0.00035554 t ) antilog (0.1681675 -0.00466474 t ) , t = ToC .
For methyl propionate,
+
A = antilog (1.6069817- 0.0003oog3 t ) antilog (0.1772937 -0.00452811 t ) , t == ToC.
For propyl acetate,
+
+
A = antilog (i.4610421 0.00014984t ) antilog (0.2594356 -0.00419859 t ) , t = To C.
For ethyl propionate, A = antilog (1.4369301-I- 0.000282082 I ) antilog (0.2648128 -0.00427465 t ) , t = ToC.
+
,
For methyl butyrate,
+
A = antilog (y.6121551-0.ooo2j106 t ) antilog (0.2344221 - 0.00456542 t ) , t ToC.
For methyl isobutyrate,
+
A = antilog (Y.6085499 - 0.00029267t ) aiitilog (0.2061414 - 0.00455208 t ) , t = ToC.
Molecular Attrnctioiz
599
TABLE 2 ~~
~
-
~~
~~
Propyl formate Temperature
Pressure Pressure calculated observed
Pressure :alculatec
~
~
~-
~
Ethyl acetate A
Pressure observed
~~~~~
-zoo
c
-
0 IO
20
30 40 50 60 70 80 90 IO0 I IO
I20
130 140 150 I 60 170 I 80 r9o 200 2IO 22 0
230
240 245 247 249 250
250.1 2 60
264.85
i
-
11.56 21.42 37.85
-10
1
11.4' 21.4( 37.8, 63.9 104.1: 104. I 1 6 3 . 3 ~ 163.6 247.9: 249.4 365.3; 364.9 523.9 523.9 732.9 734.5 1002.5 1004 1343.6 I345 1767'7 I770 2286.9 2288 2914 . O 2915 3662. I 3676 4545.4 4558 5578.4 5605 6777 1 6797 8158.3 8177 9740.9 9734 [ 1560 I545 3594 i3.575 :5870 5912 8529 ,8465 !1425 I477 '
-
-
4792
!4693
-
8519 0488
-
-
0.16
6.55 13.02
6.55 12.95 24.3 42.7 72.8 118.7 186.2 282.2 415.4 596.3 832.7 I 130 1517 2001.5 2586 3298 4166 5168 6369 7742 9318 1125
24.3c 43.12 0.13 73.09 118.88 0.03 186.33 - 0.26 - 1 . 4 3 282.42 415.37 0.47 0 .o 594.53 - 1.6 830 37 - 1 . 5 1134.4 1519.2 - 1.4 - 2 . 3 1998. I - 1.1 2585 7 - 1 . 0 3297.0 4148.6 -13.9 -12.6 5157.5 -26.6 6342.4 7722.6 -19.9 -18.7 9319.1 1I54 6.9 3200 3253 -15 5539 5565 I9 8343 42 8255 1270 I393 64 52 4825 4807 5 6740 6693 7471 7535 8266 8370 8671 8800 99 87iI 28877.5 0.02 0 .o
'
'
0.04 0.07 0.0
0.42 0.29 0.18 0.13 0.22
- 0.03 - 1.77 - 2'33 4.4 2.2
3'4 - 0.3 -
.o
- 26.6
- 19.4 1.1
29 53 74 88 123
17.5
'
- I -
I
- 17.4 - 10.5
- 47 - 64
-104 29 -166.5
-1
-
-
J. E. MiZ2.s
600
TABLE3 ~-
-
.
~~
Propyl acetate
Methyl propionate Temperature
-200
-10
0 IO 20
30 40 50 60
70
80 90 IO0
1\10 I20
130
140 150 I 60 Ijo
I80 190 200 2 IO 22 0
230 240 245 250 253 255 256
r\ L
I
A
A
Pressure Pressure -alculated observed ~__-
5.931 5.65 11.721 11.55 21.90' 21.9 38.85 38.93 66.2 66.15 107.89 107.8 169,58 169.3 256.7 257.8 380.3 380.3 545.94 548 .o 764.65 7 7 1 . 0 1047.4 1045 1406.2 I 406 1853.8 I854 2404 .O 2406 3071.2 3071 3871. I 3888 4819.6 4830 5934.5 595 7 7233.7 7245 8737 .o 8737 10420 10465 12380 112441 114687 1462.5 '17160 17231 20101
~20000
23325 25080
23325
26937
126997.5 2820j 29055 129445 30032.5
28 102 28900
0.28 0.1; 0 .o 0.02 0.05
-
0 .os 0.22 1.1 0.0
1-
-
2.06
6.35 2.4 0.2
-
0.2 2 .o 0.2
16.9
-
- 10.4 - 22.5
11.3
-
0
IOI 0.0
-
Pressure observed
-
-
3.70 7.38 13.92 25 .oo 42.71 70.67
0 .I 3.60 7.4 - 0 . 0 2 0.02 13.9 25.1 - 0 .I 0.01 42.7 70.8 - 0.13
112.2
112.2
172. I 255.9 370.7 523.2 721.9 975.5 I294 I 687 2166 2 743 3432 4240 5190 6287 7556 901 I 10673 12563 14704
171.8 257.3 372.8 524.8 723.6 976 '293 168j 2171 2 747 3441 4269 5189 6275 7543 8973 0620 2 505 4675
35 - 6 0 . 5 17123 -103 -155 -139 -150.5 19849 21645 22913 23903 - 24584 24998 -
1 l --
.o
45 61 62 71
Pressure calculated
-
0.0
0.3
- 1.4 -. 2.1 -
I
.6
- 1.7 0.5 I 2
- 5 - 4 -
9
- 29 I I2
I3 38 53 58 29
-
-
7090
-
-
-
9855 1685 2980 4060 4750 5227.5
33
-
-
- 6 - 40 - 67 --I 57 -166 -229.
j
MoZeczi Zar Attraction
60 I
TABLE4
1 Temperature
0
IO 20
30 40 50
60 70 80 90 IO0 I IO I20
130 140 150 I 60 170 I 80
190 200 2 IO 220
230 240 250 2 60 265 268 2 70 275 2 78 280
281.3
~~
~
Methyl butyrate
Ethyl propionate A
8.10 15.31 27.50 47.16 77. 58 122.8
188 .o 279 .o 402.5 566.2 778.4 I 048 1386 1801 2305 2911 3630 4476 5465 6611 7934 9452 111186 113161 1.5402 17941 2081 I 22381 23370 124050
4 .o: 8.3 15.5: 27.7: 47.7: 77.9 123 .o 188 .o 279.9 403.6 569.5 785 .o 1048 1386 1801 2316 2920 3657 4505 548 7 6619 7934 9456 11195 13145 15425 17970 20825 22400 23415 24105 24660 25217.5 -
-
A
Pressure Pressure :alculated observed
Pressure Pressure calculated observed
.o
3.55 7.13 - 0.2r 13.52 - 0.2; 24.34 - 0.55 41.82 - 0.3: 68.90 - 0.2 109.28 0.0 167.5 - 0.9 248,9 - 1 . 1 359.7 - 3.3 507 .o - 6 . 6 698.4 0.0 942.6 0.0 I249 1627 0 .o - I1 2088 2643 - 9 - 27 3304 4085 - 29 - 22 4998 - 8 606 I 0 .o 7287 8696 - 4 0306 - 9 16 2137 - 23 4213 - 29 6557 - I4 9197 - I9 - 45 2161 - 55 - 90 -153 3774 4787 5482 5942
~-
0
0.2
3.55 7.3 13.8 24.55 41.95 69.2 109.65 167.5 250.3 361.4 507 .o 700.7 941 1248 1627
0.0
- 0.17 - 0.28 -
0.21
- 0.13 - 0.30 - 0.37 0 .o
-
-
1.4 1.7 0 .o
2.3 I .6 1 0 .o
2 IO0
-
2657 3328 4111 5020 6063 7287 8684 028j 2105 4230 6550 9185
- I4
-
-
2160
-
3795 4820 5560 6055
I2
- 24 - 26
-
22 2 0 .o 12 21
32
- I7
7 12
1
- 21 - 33 - 78 -1
13
J, E. MiZh
602
_ ____
TABLE5 -
~
~~
-~
~
Methyl isobutyrate Pressure calculated
Pressure observed
-
-IO0
c.
0
IO 20
30 40 50 60 70 80 90 IO0 IIO I20
130 140 150 I 60 170 I 80
I90 200 2IO 22 0
230 240 2 50 256 260 263 265 266.5 267,55
6.28 12.1.5 22.28 38.93 65.10 104.6 162.3 243.8 355.7 505.5 701.5 952.8 1269 1662 2141.6 2720
3411 4226 5180 6291 7571 . 9040 107I 5 12617 14768 17190 19910 2 I695 22954 23935 24608 25121 25486
6.22 12.15 22.4 38.9 65.45 104.7 162 .o 243.8 355.2 505 .o 707 .o 952 1270 1662 2142.5 2733 3418 4248 5196 6291
7557 go1 I 10690 12570 14700 17190 19925 2 I740 23030 24080 24780 2 5 345 25740
0.06 0.0
I
- 0.I2
.o .03
- 0.35 - 0.1
0.3 0
.o
0.5 0.5
- 5.5 0.8
-
I .o 0
.o
- 0.9 - I3
- 7 - 22
- 16 0
-
.o
14 29 25 47 2 0
- I5 - 45 - 76
-145 -172 -224 -254
.o
Molecu jar A ttractioz
60 3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Q
0
3
h W v ) c o OI h
0
U 3
mHQ 9 0 hOhQ
* o
u -00 h M mMNQ h W m m W O W u * h U Q N 0 0 h Q O O
u M*WhOO
m O 0 0
0
13
3
u N
N
mmo
* 0* Moo **
Mrc)*mQOO
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? V U
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 o 0 0 0 0 0 0 0 0 0 0 0 d 0 0 0 0 o
-I
% & W Q
h m o
13
* * H
mm
J. E. Mills
604
0 0 3 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0
. . . . . . . . . . o o o o o o o o o o o o o o o o o o o c o O
h
MM*N
____
I h O Q. m. e. w.
-
.
y
MoZecit Zar A t tvnct l b r z
4
605
606
c N O O O O 0 0 0 0 0 0 0 0 0 0 0
n
I o o o o o o o o o o o o o o P
000000
o o o o
0 0-0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0000000
608
J. E. Mills w
x w
4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Mobcular Attraction
609
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 I
!J
0 0 0 0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -
~_
v)
H
v)W
-~
___
~_
-_
.
610
/.
E. MiZZs
The mean value for p’, which we have adopted for the different esters, is given at the top of Table 13. The average value of the uncrossed results is shown a t the bottom of the table. In the summary shown in this table the results given by the three esters previously examinedl are also shown in order that the behavior of the ten esters may be seen at a glance. We have already critically discussed* the extent to which errors of observation occurring in the various measurements used will affect the value of the constant given by the ratio, L-El From that discussion, we concluded, that since the ~ ~QD. - errors of measurement were always compounded and were often multiplied in their proportionate effect upon the constant, that a divergence from the mean values of the constant of less than 2 percent could be regarded as within the limit of error of observation, even when using measurements that had been most carefully carried out. In the tables all values that differ from these mean values by more than 2 percent are marked with an asterisk. All values that differ by more than 5 percent with a double asterisk. Examining the results it will be noted that always there is a divergence from the mean value-the results being too low-as the critical temperature is approached. We have already recalled, in this paper, the fact previously established, that this was due largely, if not wholly, to an error introduced dP by using the Biot formula from which to obtain the dT.
There are also four substances which show a considerable divergence a t o o C. While we are quite unable to explain that divergence, yet we would call attention to the fact that the density of the vapor used at that temperature was calculated, assuming the gas laws to hold. Ordinarily we would have expected them to hold, but as Lord Rayleigh has pointed out within recent years, it is quite possible that the gas laws Jour. Phys. Chem., IO, I (1906). Ibid., 8, 392, etc. (1904).
MoZecu Znr A ttrnct io?z
N
Q m
WP
w w Pcn
N 001
Q
. .O
W H H
O
N 000,
.wacn .u ' Ucn
0
61I
61 2
J. E. MiZZs
may not hold always, even at low temperatures and pressures. We hope to make these divergences the subject of investigation in the laboratory later, and in the meanwhile, since a calculated factor does enter into the result, we would not consider the divergence of serious moment. Excepting these divergences at oo C, therefore, because of uncertain data, and those near the critical temperature for reasons’ given, there are only three results throughout the entire series of measurements of esters that differ from the chosen mean value by more than 2 percent. Comment is almost unnecessary. Such a result could not possibly happen unless the equation represented the facts with the greatest accuracy, and assuming its accuracy, the fact that there are only there divergences of more than 2 percent among 163 tests, each test involving a measurement of four different quantities, speaks in the highest degree for the wonderful skill and accuracy of theexperimenters, Professor Young and Mr. Thomas, for the errors introduced by the measurements are, as we have in previous papers carefully pointed out, not only compounded but in ceftain portions of the temperature scale greatly multiplied proportionately in their effect upon the constant by the method of calculation. The service which Professor Young and his co-workers have rendered to science by such a series of measurements, carried out for thirty-one substances, is simply incalculable, and it gives me the greatest pleasure not only t o express my own indebtedness t o their work, but to hope that their work will meet with that universal recognition and praise which is its due. The substantial accuracy of the equation can be again illustrated, and its mqaning emphasized, by solving the equation for I.,thus giving, 9.
L = p’ ( 42-- Yij)
+ E,.
The values of p’ used in calculating I, from this equation are the “average” values given a t the bottom of Table 1 3 above. The results of this equation are given in Tables 14 to 2 0 inclusive, where they are compared with the heats of
MoZecu Zar A ttract ioIZ
613
vaporization calculated thermodynamically. We have marked all divergences of more than, one calorie between the two sets of values with an asterisk. It is clearly apparent that the theory proposed does adequately account for the heat of vaporization. In previous papers we have already had much to say of a theory by Mr. H. Crompton and have given a considerable amount of investigation to his equation for calculating the heat of vaporization. His equation reads : IO.
We have extended the investigation of this equation to the seven esters examined in this paper and give the results likewise in Tables 14 to 2 0 , under the heading “Crompton,” for comparison with the heats of vaporization as calculated by equations z and 9. It will be seen that the conclusion previously drawn regarding the equation of Mr. Crompton is further confirmed, viz., a t the lowest temperatures, where the vapor pressure is small, the results obtained from his equation are uniformly too high. But a t higher temperatures, with increasing pressure, the results become more nearly correct, and near the critical temperature we believe them to be practically correct. It will be noted that usually just as the critical temperature is approached the results from Crompton’s equation more nearly agree with the values from equation 9 than with the values from equation 2, a fact due to the faulty Biot formula involved in the results from equation 2 , as already pointed out. We would here repeat our opinion that this theory and equation of Mr. Crompton’s is important, and deserving of further recognition and study. In spite of our work upon the equation we are yet quite a t a loss to account for the too high values obtained from it at low vapor pressures.
J. E. Mills TABLE14 Propyl formate . ~ _ _
~
I ~
I
__
~
~
Heat of vaporization
Temperature Ther.
Mills
Crompton ~-
oo
c
80
IO0
I20
140 I60 I 80 200 220
240 2 50
260 264.85
99.63 86.42 82.61 78.71 73.84 68.29 62.80 56.91 49.62 39.45 31.99
97.75* 86.14 82.43 78.43 73.94 68.86 63.32 57.03 49.40 39.36 32.29
21.02 0.0
21.73
111.35
89.28 84.22 79.25 74.01 68.41 62.48 55.97 48.23 38.20 31.20
20.89 0.0
0.0
TABLE15 Ethyl acetate
_~__
~
~
~
Heat of vaporization Temperature
ooc
1 ,
-
~
Ther.
Mills
~
IO0
100.61 85.45 81.95
97.92* 85.53 81.64
I60 I80
65.91 59 * 87
200 220
52.71
66* 53 60.26 52.90
20.79 17.12 12.03
22.24* 18,61* J3.40"
240 245 247 249 250.I
0.o
~
0.0
1
Crompton
109.74 87.oo 81.86 76.49 70.85 64.63 58.IO 50.64 41.11 26.84 20.88
17.44 12.52 0
.o
h'olecu tar A ttlract ion
615
TABLE 16 Methyl propionate ~ _ _ .~ _
Heat of vaporization Temperature Ther.
1
oo
c
80 IO0 I20
140 I 60 I 80 200 220
240 2 50 253 255 256 257.4
100.87 87.32 83.22 78.27 73.42 68.22 62.05 55.67 47 * I 4 34.41 24.30 19.94 15.67 12.70 0.0
Crompton
Mills __
-----
102.09"
86.49 82.84 78.24 73.51 68.24 62.19 55.44 47 .oo 34.99 25.44" 21.20"
16.96" 13.95" 0
.o
111.20 88.83 83.65 78. I9 72.71 66.92 60.53 53.60 45. I4 33.36 24. I 3 20.07 16.03 13.18 0
.o
TABLE17 Propyl acetate Heat of vaporization Temperature
oo
c.
IO0 I20
140 I 60 I 80 200 220
240 2 60 2 70 273 275 276.2
Ther.
Mills
96.03 79.92 76.26 72 * 34 67.70 62.94 57.23 50.78 42 .40 30.70 20.57 16.17 11.73
92.31" 79 * 32 75.78 71.91 67.57 62.78 57.22 50.78 42.65 31.43 21.95" 17.44"
105.59 79.58 74.92 70.23 65.30 60.13 54.36 47.89 39.91 29. I 5
0.0
0.0
0 .o
12.85"
Crompton
20.27
16.04 11.79 '
J. E. MiZZs
616
Temperature
oo
c.
IO0
I20
140 I 60 I 80 200 22 0 '
48.59 40.23 27.75 23.06
240 260 265 268
28,11 I
270
15.57
~
272.9
0
I
46.20 37.95 26.29 21.97 18.56 15.21
40.21
I
.o
23.57 19'96 16.39 0
.o
0.0
-
~
~
~
~~~~~
Heat of vaporization Temperature
I
~
Ther. 00
Croinptoii
I
c.
I20
140 I 60 I 80 200 220
240 2 60 2 70 275 278 2 80 281.3
-
Mills
,
96.87 74.39 70,63 66.85 62.32 57.59 51.45 44.19 34.34 26.79 21.07
~
i
91.16" 74.93 71.17 67.09 62.45 57.31, 51 I9 43.80 34. I4 27.05 '
21.70
16.32 11 .04
0.0
0 .o
1
1
106.08 75.36 70.70 66 .oo 60.89 55.44 49. I5 41.75 32.28 25.44 20.36 16.04 11.18 0
.o
TABLE 20 Methyl isobutyrate ~ ~
~
~
~~
~~
~
-
-.
Heat of vaporization Temperature
oo c. IO0
I20
140 I 60 I80 200 220
240 260 263 265 266.5 267.55
8.7 ’ 43* 74.13 70.49 66.56 62.22 57.31 51.84 45 .oo 36. I3 22.39 18.61* 15,27*
91.78 74.47 70.38 66.62 62.34 57.44 5 2 . I9 45.13 35.79 21.49 17.53 14.21 10.51 0
Crompton
Mills
Ther.
*
I 1 .SO
.o
0
.o
100.31 75.24 70.57 65.92 61 .os 55.78 50.07 43.18 34.42 21.14 17.53 14.37 10.79 0
.o
Some Rela ions at the Critieal Temper ture In the third paper, p. 626, we deduced, by an extension of the principles underlying the theory of molecular attraction we have outlined the equation : I
11.
’
I, = p‘
(qd -
qD)
+ 0.0~31833P
where d is the actual and D the theoretical critical density. Also in that paper by a similar application of Crompton’s theory we deduced the result : 12.
I,
=
d ~ m z log Qcals. D
,
The two equations should give values in agreement if both theories are correct. We show the results obtained from equation 11 in Table 2 1 under the heading “Mills,” and the results obtained from equation 12 under the heading “ Crompton. ” The difference is shown. The divergence never exceeds 4, and seldom exceeds 3 percent, and the,agreement is therefore very satisfactory.
J E. MiZh
618
s
0 0 0 0 0 0 0 0 0 0 H
*w
N
0 0 0\0000 h h W h
u
N
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The critical data used is shown in the same table, as is also the similar data for the three esters previously investigated. The critical data is taken from a paper by Prof. Y0ung.l A in the table denotes the internal heat of vaporization to which E, must be added to give I,. We also .discussed in the third paper an equation (25) holding true for all substances at the critical temperature, that takes the form :
mnye
13.
T
=
constant,
The mean value of this constant as deduced in that paper for the non-associated substances was 10.76. The values for the constant for the substances now under consideration are given in Table 2 1 under the heading “Ratio !! to
C
7.’’The C
average value of the constant for the ten
esters now considered is 1 1 . 1 0 , or about 3 percent higher than the previously obtained value. We consider this agreement satisfactory. In the fourth paper, p. 415, we showed that it followed from the theories discussed that, 14.
where P, V, and T are the critical volume, pressure and temperature, and rn is the molecular weight. The average value of the constant for the substances there examined was 16293. The values for the esters now considered are shown in the last column of Table 2 1 . The average value is I 5920 or less than 3 percent lower than the average value previously obtained. We regard this agreement as satisfactory. A slight divergence in the results obtained from the three previously cited equations bearing upon the critical temperature we do not consider surprising, for we know that the molecular attraction is dependent upon the constitution of the’body, and with large changes of temperature Phil. Mag.
[SI, 50, 291 (1900).
.
there must undoubtedly be incipient ' changes in the constitution of the substance even before these changes commence to manifest themselves in the decomposition of the body. We think the slight changes so caused in the molecular attraction would be sufficient to account for the variations above noted, which only rarely exceed 3 percent. Summary ( I ) In this paper as in previous papers of this series, our endeavor has been t o show that the attraction between the molecules of a liquid varies inversely as the square of their distance apart. For this purpose we further studied the equation previously deduced, - dD
=
constant,
applying the equation to seven esters not previously studied. The results indicate beyond any doubt the truth of the equation, and it is therefore reasonable to suppose that the assumption upon which the above equation was founded is the true one, and that the molecular force does vary inversely as the square of the distance from the attracting particle. ( 2 ) In this paper an equation given by Crompton, I, = d
zRT loge - , was further examined and the conclusion hitherD
to reached was confirmed, viz., this relation gives results for the heat of vaporization uniformly too high a t low vapor pressures, but at high vapor pressures, in the neighborhood of the critical temperature, the equation is accurate. ( 3 ) Some relations at the critical temperature, already pointed out, are examined further for the seven esters under consideration and the relations are confirmed. Addendum Regarding the divergence shown by methyl isobutyrate at 130' C., see Table 1 2 , it seemed to me after inspecting the data, that the cause of the divergence shown at this temperature lay with the value used for the volume of the vapor. On looking up the original data as published, we found the smoothed value
1.E.
622
Mills
given at the temperature, which was the value used, to be 105 and the observed value 103. Thinking it possible that a misprint had occurred, we wrote Prof. Young asking him to look up the value as given in his original note book. This Prof. Young very kindly did, and in his reply just received states: The volume of a gram of methyl isobutyrate read from the curve a t 130’ should be 103, not 105; in fact it is barely 103, more like 102.8, but I have not trusted the first decimal a t these comparatively low temperatures. The 105 is evidently a misprint or a mistake in the original manuscript.” Making the necessary corrections, the values in Table 1 2 , using 103 for the volume of the vapor should be: E, = 6.93, P. A V. T -87.77; Latent heat =68.76, L-E, =61.83, 42-46 = I o6 0.6968,
-L-E1
42-
- 88.76, a value in excellent accord with the 45 -
average value of the ratio which was 88.5 I . The fact that the misprint of 105 for 103 was discovered by means of the theory which we have advanced goes to show that we have not claimed too much for the relation we have discovered in saying that it represents the facts accurately, and is not a mere approximation.-October 5, 1907. University of North Carolina, August 16; 1907.
