MOLECULAR ATTRACTION (SECOND PAPER)
BY J. E. MILLS
Review of the Theory This paper presents additional evidence tending to show that the attraction between molecules varies inversely as the square of their distance apart and does not vary with the temperature. Considering the attraction as a property belonging to each molecule, or to be more exact, a mutual property of each pair of ~nolecules,it must vary as the inass, large numbers of similar molecules being here considered. Briefly therefore this paper is an attempt to show that the law of gravitatioiz holds, not only between masses, but between the molecules of a substance, and that this law is alone sufficient to account for the phenomena of the internal latent heat of vaporization. T h e assumptions upon which the present work is based are stated in the original paper,I and it would not be necessary here specifically to call attention to them were it not for the fact that certain reviews have overlooked the significance of the preliminary statements to that paper. We may say that the steps leading up to the present work are briefly : I. T h e kinetic theory of gases and v a n 9 Hoff’s application of the gas law PV = R T to solutions. 2. T h e conclusion from the above theories and related work ;hat the average translational energy of gaseous and liquid molecules must at the same temperature be equal. 3. T h e belief based on the study of the specific heat of gases, that the total energy of a gaseous molecule, exclusive of the energy which holds the molecule together and of extraneous forces, is proportional to tlie translational energy. 4. T h e inference, for it is somewhat more than a mere assumption, the causes for 3 being considered, that the total energy Jour. Phys. Cheni. 6, 209 (1902).
I ,
J. E. Mills
384
of a molecule of a liquid would siniilarly be found to be proportional to its translational energy. These four preliminary steps may be summed up by the statement that the total energy per se of a molecule must be the same in the liquid as in the gaseous state, the temperature being the same. If at a given temperature a given weight of gas represents more energy than the same weight of the substance as a liquid, the extra energy of the gas must be energy of position only (assuming no intramolecular change). We made no attempt in the former paper, and we make none in this, to prove the last statement above, or to give the evidence for it. To do so even cursorily would require a discussion of the kinetic theory of gases, their specific heats more particularly, and the modern theories of solution. T h e statement is here made only as the belief of the author upon which the present work is based. Many citations of closely related belief might be given. Ostwald' gives a clear and succint statement of I and 2. 0. E. Meyer' shows the grounds for 3. T h e author has published3 the study which,led him to conclude that 4 was a reasonable supposition. So long ago as 1885, Ramsay and Young made practically the same statement.4 Expressing the above belief in a different form, we may say that the energy necessary to change a liquid into a gas must then be spent solely in overcoming the external pressure and in altering the distance apart of the molecules. (Unless the molecule breaks apart also or nears the point of disruption.) Denoting the energy spent in overconiing the external pressure by E,, this energy can be calculated from the equation,
E, = 0.0~31833P ( V - v ) cals, where the unit calorie is from 15" to 16" C, P is the pressure (1)
Solutions, pp. 147, 148. Kinetic Theory of Gases, p. 117. Journal of the Elisha Mitchell Scientific Society, Vol. IS (1902). Phil. Trans, 18868,Evaporation and Dissociation, y. 72, Section 4 ; c and d of that section not being necessary under the limitation imposed above that there should be no intramolecular change, and e and the footnote being unnecessary in the light of the later work of van 't Hoff. e
MoGecuZaY A ttTaction
385
in millimeters of mercury, V and are the volumes before and after expansion. To obtain the constant, 0.0~31833,we used the values : density of mercury, 13.5956; Rowland's value of the therm, corrected by Day, at 15' to 16' C, 41880000 ergs, as unit ; and gravity taken as 980.5966. Denoting the total latent heat by I,, we have I, - Er as the energy spent in overcoming the molecular attraction at any particular temperature. On the further assumption : 5. That the molecular attraction varies inversely as the square of the distance apart of the molecules, the equation 7 (p. 212) of the original paper was derived, which equation readily takes the more convenient form, -_ E,_ = constant, vz_L_
for any particular substance, where I, - E, is the internal latent heat of vaporization, and d and D are the densities of liquid and vapor at any particular temperature. With regard to this equation, we will here say that it was designed to test the assumption advanced in 5. Had it failed to produce a constant or some function of the temperature, the author hoped to substitute 5 by some other distance function of the attraction, obtain the formula similarly, and thus repeat until the correct assumption was made. As to the mathematics by which it was derived, the vagaries of a particular molecule cannot of course be followed. But in considering energy relations we commit no error by considering the average molecule as was done. T h e formula should therefore hold strictly true provided : (a) T h e molecules are evenly distributed. (b) T h e number of molecules does not change. (c) No energy is spent in intramolecular work. (d)T h e attraction does not vary with the temperature. Or, we might sum up a , b, c, and d, by saying that formula 2 should hold! provided we are dealing with a stable chemical compound whose molecules are not associated.
-
386
J. E. Mills
T h e first paper tested the formula so far as the direct measurements of latent heat and the related data permitted. T h e agreement appeared to be much too close to be the result of accident, but where variations in the data as given by different observers amounted often to five and ten percent, any close agreement was impossible. It being impracticable to make direct measurements of the latent heat at widely different temperatures, attention was called to the measurements of Ramsay a d Young and of Dr. Young. These measurements give the vapor pressure and density of liquid and vapor, at arresponding temperatures over a wide range of temperature for thirty-one substances. T h e present paper deals with twenty-one of these substances, the calculations for the ten esters being not yet completed. The Measurements. T h e complete measurements used are given in the appended tables. T h e few exceptions to the following general statements are noted below. ( a ) T h e vapor pressure, density of the liquid, and density of the vapor, are from the measurements, references given below, by Professors Ramsay and Young, or Young. (6) T h e vapor pressures from Biot's formula were used in preference to the observed values. (c) Where calculated the density of the vapor was obtained from the formula. (3)
P??Z D = 0.0,16016 __
T ' where P is the pressure in millimeters of mercury, w is the molecular weight, oxygen equal to 16 as standard, and T is the absolute temperatixre. T h e constant 0.0~16016was obtained by the use of the values 0.0~89873for the density of hydrogen at oo C, 760 mm pressure, latitude 45" and sea level, and oo C = 273' absolute. (dj T h e densities of the vapor given are often carried one place further than the accuracy of the measurements would war-
'
387
iVoZecuZay Attvaciion
rant. This was because the density of the vapor was not always given directly in the original paper, and in the necessary transposition the additional figure of the calculation was retained. ( e ) Making use of the well-known thermodynamic equation, (4)
the latent heat of vaporization for methyl, ethyl and propyl alcohols, acetic acid, and ether, were calculated and given in the original papers, where the method in detail may be obtained. T h e latent heat for water, oo to 230' C, is from Regnault. T h e latent heat for benzene, oo to 270' C, is from Tsuruta,I using measurements of Young. (f)I n all other cases the latent heats were calculated by the author, the following method being used. Biot's general formula for the vapor pressure, log P = a
(5)
+ bat + cp",
has been found with properly chosen constants accurately to represent the vapor pressure. Differentiating and changing base of the logarithms from natural to Naperian we get : a P ( b log - p_- at wr2
aa'
+ c l o g pp'), ap
where m = 0,434294. Substituting this value of --inequation
aT
4)we get *
and using values for P and J already adopted (p. 385) we have finally : L=o.o3r68775 P . A v . T ( b log aa' + c log pp') cals ; or (8) (9)
Phys. Rev,
IO, z
(1900)
J. E. Mills
388
In this form the calculation of the latent heat is not only theoretically correct, but is much shortened in comparison with the usually adopted methods. T h e values for A were obtained from the constants for Biot's formula given in the original papers, and the equatious thus derived for each substance are given below under that substance. (9) All calculations in this paper were checked and every effort was made to make the calculations as accurate as the data from which they were derived. Ether. See Table 2. Data from Phil. Trans. 18878, p. 57 ; except density of liquid at IO', 20' and 30' C, where the values are from Oudetnans. Molecular weight used 74.08. Di-isopropyl. See Table 3. Data from Jour. Chem. SOC. 1900, p. 1126,except vapor pressure at 216' and 225' C (calculated from Biot's formula) ; and vapor density at oo C which is theoretical. Molecular weight used, 86.I I 2. For calculation of the latent heat,
A
= antilog (1.572552- 0.00020800t)
+ antilog (0.1268648- o.o0466932t),
+
where t = t o C IO. Di-isob~ttyl. See Table 4. Data from Jour. Chem. SOC. 1900, p. 1136,except vapor pressure at 274" C (calculated from Biot's formula); and vapor density at oo C which is thebretical. Molecular weight used, I 14.144. For calculation of the latent heat,
-
A ==antilog
+ 0.00104426i) + antilog (0.2271234- o.o0380225S),
(I. 1739925
where t = t o C - IO. Isopentune. See Table 5. Data from Proc. Phys. SOC. 1895,p. 602 ; except vapor density at oo C which is theoretical. Molecular weight used, 72.10. For calculation of the latent heat we have, -
A = antilog (1.6310169- o.ooo3154gt) antilog (0.1373762-0.00515903t), where 1 = t o C 30. I
+
+
MoZecu la Y A t t ra ctio n
389
Normal Pentane. See Table 6. Data from Jour. Chem. SOC.21, 1897,p. 446; except vapor density at 0" C which is theoretical. Molecular weight used is 72.IO. For calculation of the latent heat, we have, -
A = antilog (I .7496468- o.ooo73363f) antilog (0.0668185-- o.oojj1392t), where t = t o C -1 20. NormalHexnne. See Table 7. Data from Jour. Chem. SOC.1895, p. 1071; except vapor density at 0" C which is theoretical. Molecular weight used is 86.I I. For calculating the latent heat, we have,
+
-
A = antilog (I .3604438
+ 0.000423j5t) + antilog (0.20293jg -0.004I I
2jjt),
where t = t o C -/ IO. Normal Heptane. See Table 8. Data from Jour. Cheni. Soc. 74, 1898; except vapor density at 0" C which is theoretical, and vapor pressureat 266' and 266.5"C which is calculated from Riot's formula. T h e molecular weight used is 100.13. For calculation of the latent heat, we have,
A = antilog
( I ,340707I
+ o.ooo53408t) + antilog (0.2342860-0,oo403623t),
where t = t o C. Normal Octane. See Table 9. Data from Jour. Chem. SOC.1900,p. 1145;except vapor density at oo C which is theoretical. T h e molecular weight used is 114.144. For calculation of the latent heat, we have, -
+
A = antilog (1.3927781 o.ooo342913t) 4-antilog (0.2497609- o.o04006534t), where t = t o C - IO. Benzene. See Table IO. Data from Jour. Chem. SOC. 1889, p. 501 ; except density of vapor at 0' C which is theoretical. Molecular weight used is 78.05. Latent heats were except at 0" C, calculated by Tsuruta (Phys. Rev., 1900,p. II~), where the value found by Griffiths and Marshall is used, and at 280" C where the calculation was made by the author.
J E. Mills
390 Hexametliybne.
See Table
11.
Data from Jour. Chem.
SOC.1899, p. 873 ; except vapor density at o o C which is theoretical. Molecular weight used is 84.096. the latent heat, we have,
For calculation of
+ 0.0004971jt)
A =antilog (1.295611 j
f antilog (0.1878242- o.o0391252t), where t = t o C. Fho-benzene. See Table 12. Data from Jour. Cheni. Soc. 21, 1889, p. 505 ; except the vapor density at oo C which was calculated. Molecular weight used is 96.09. For calculation of the latent heat, we have, c
A = antilog
(I,
131 57974
+ o.ooo942654t) + antilog (0.2224140
-
o.o0363024f),
where t = to C. Chlov-benzene. See Table 13. Data from Jour. Chem. SOC.1889, p. 502 ; except vapor density at oo C which is theoretical. Tlie molecular weight used is 112.5. For calculating the latent heat, we have, -
+ o.ooo7j84jt) + antilog (0.1846519-o.o03j9227t),
A =antilog (1.2268791
where t = t o C - 30. lodo-benzene. See Table 14. Data from Jour. Chem. SOC. 1889, p. 506 ; except vapor density at 30' and 100' C which is theoretical. Molecular weight used was 203.9. For calculating the latent heat, we have, A = 0.09891873{ antilog 0.001421982t antilog 1.287j9778- 0.00324574t) } , where t = io C - 30, a form of the equation less convenient for calculation than the one usually adopted. Blow-benzene. See Table I 5. Data from Jour. Chem. SOC. 1891, p. 134 ; except vapor density at 30' and 100' C which is theoretical. Molecular weight used was I 57.0. For calculation of the latent heat, we have,
+
-
A =antilog (1.8373717- 0.0009j092f) antilog 0.0763464 -- 0.0048946jt)
where t
= to
C - 30.
+
~
Molecu lar Attrnclion
391
Cavdon Tetrachdoride. See Table 16. Data from Jour. Chem. SOC.1891, p. 911 ; except vapor density at oo C which is theoretical. Molecular weight used was I 53.8. For calculation of the latent heat, we have, A = 0.23j8 { antilog 0.0002685jt antilog (0.7970j07- o.oo402434t) } , where t = t o C, a less satisfactory form of the equation than the one usually adopted. Slannic Chloride. See Table 17. Data from Jour. Chem. SOC.1891, p. 911 ; except density of the vapor at oo C which is theoretical, t h e molecular weight used being 260.8. For calculating the latent heat, we have,
+
A =antilog (1.3282379+ 0.00026212t)
+ antilog (0.2481708-oo.oo368282t), where t = t o C. Wder. See Table 18. See Phil. Trans. 1892, p. 107. Vapor pressures, oo to rooo C, are Broch's calciilations from Regnault's measurements, and other values are from Ramsay and Young. Density of the liquid, oo to 100' C are from values in Landolt and Bornstein's tables, p. 39, and rooo to 270' C are from Ramsay and Young. Density of vapor, oo to 220' C are as given by Ramsay and Young from Regnault's heats of vaporization, and 230' to 270' are recalcnlated " values from their own measurements. Latent heats, oo to 230' C are from Regnault, and 240' to 270' C were calculated by the author from the formula, A =antilog (o.1416j14-0.0059j0708t) antilog (0.13884017-- o.o016j6138t), where t = t o C 2 0 , the constants used for Biot's formula being given by Regnault. iMethyZAZcohoZ. See Table 19. Data from Phil. Trans. 18878, p. 313 ; except density of liquid at oo C from Dittiiiar and Fawsitt, and at 10' C average value of oo and 20°. Inadvertently the observed pressures were used for the calculation of EI, but the difference thus made is never more than 0.1 to 0.2 calorie, and the error thus introduced into the constant of equation 2 could never exceed one-tenth of one percent.
+
+
1.E. Mills
392
Ethyl AZcohoZ. See Table 20. Data from Phil. Trans. 188gA, p. 1 2 3 ; except vapor pressure at 241", 242", and 2q2.5" C (calculated from Biot's formula) ; density of liquid 0" to 30" and at 100"Mendelejeff, 40" to 80" from Kopp's formula, and at 90' C estimated value. Pro~yZAZcohoZ. See Table 21. Data from Phil. Trans. 18898, p. 137. Observed vapor pressures were used to calculate E,. Density at 0" C is theoretical, the molecular weight used being 60.06. * Acetic Acid. See Table 22. Data from Jour. Chem. SOC. 49, 1886, p. 790, and in 1891, Vol. 59, p. 903, preference being given in all cases to the later measurements. For calculating the latent heat, we have, i
-
A = antilog (1.9257964 - o.oo149898t)
-
+antilog (1.1390566 -o.o130424t), where t = t o C - 120. Application of the Theory For details of the calculations involved the appended tables, 2 to 22, must be consulted. A summary of the results obtained for the constant by the use of the equation
Ld- E, 3,= constant, is given below in Table 1/. vn
I.
Certain mean
values of this constant somewhat arbitrarily chosen are given at the top of each column. All results not in agreement with this mean value of the constant by as much as two percent are in italics. Since from 0" C to within IO" of the critical temperature eleven of the substances show altogether, out of two hundred and seventeen observations, only two divergences greater than two percent from the average values, it is clearly evident that the relation given by the equation cannot possibly be accidental. But is the relation in these a n d i n the other cases as accurate as the excellent experimextaZ data will permit ? Only by such an agreement could the theory be finally established. T o answer this question we must examine the manner and ex-
MoIecuZar Attraction
393
tent to which errors in the observations will affect the constant.
L-E = co n f?T- #%i stant, would make it appear that as the critical temperature is approached and d approaches D in value, the diminishing difference of their respective cube roots would enormously increase the proportional errors of the observations. This is however not the case. Substituting for I, its value from equation 4 and for EI its value from equation I, we have, 0.0JI833 (V-ZJ) (-T-P) ap A cursory examination of the equation
ar
$/r-#/E-
(11)
= constant.
Next putting d = I / V and D = r/V, and simplifying, we get,
+ V%J%+ VXv) ( Z T- P) =constant.
(12) 0.0~31833(Vv%
On inspection of the factor, VvX
+ V%% + VXv, we see :
I. That errors of observation occurring in the density o f the liquid have at low temperatures little effect on the constant, but as the critical temperature is approached and v approaches V in value, a percentage error in the density of the liquid will of the same percentage error in the constant. cause about 2. That errors of observation occurring in the density of’ the vajoy cause at low temperatures about the same percentage errors in the constant, but as V approaches v the percentage error caused in the constant is decreased to about 5 of the error of the observation. T o determine the error caused by an error in the vapor pressure, we transform equation 1 2 into the form
T h e right-hand side of the equation is very small at low temperatures, but increases with rise of temperature until as the critical temperature is approached the function of the volumes approaches 3V3. T h e relative magnitude of the terms on the left-hand side of
%
J. E. Mills
394
the equation niust be considered. Taking water at no C as typical of a low vapor pressure (that it is typical will be: seen if ap
other substances are examined), we have - = 0.329, T = 273, aT P = 4.600, V = 211131, z, = I , and the equation takes the form Constant 0.329 x 273--'4.600 = Since 0.329 x 273 0,0431833X 214737'
= 89.80,
the influence upon the constant of an error in the vapor pressure is relatively very small. T may be assumed correct, and the determining error therefore rests with the
ap
-.
a'r'
It is exceed-
ingly important to note that while an error of 0.01 millimeter in the vapor pressure is an error of only two-tenths of 0i2e percent in that observation, yet if the same error exists in the
aT
the error so caused in the constant is threepercent. For high vapor pressure considering water at
a typical case) we have
ap
614, T = 543, P a-- r -
270'
C (also
= 40570 (from
Biot's formula as given by Regnault), and the equation takes the form 614 X 543 - 40570 = etc. And since 614 X 573 = 351800, it again appears that an error in the pressure produces only a very greatly diminished proportional error in the constant. It is again important to note that while an error of 2 0 millimeters in the pressure means an error of only 0.,005 of one percent in that measurement, yet this error occurring in the would produce an error of moYe than three percent in that aT constant. ap T h e function ar was obtained from Biot's formula (see equation 5). Biot's formula has stood the most severe tests, and I do not believe the accuracy of that formula f e r se can now be qaestioned.' But it is a purely empirical formula jilted to the observations. It represents a curve and primarily is but a more refined method of drawing a curve through the observations. 1
____ See Ramsay and Young.
Phil. Trans. 1887A, p. Sz.
MoZecuZar Attraction
395
For all points along the line of this curve one is guided by the observations on either side until the ends of the curve are approached, Eut as the ends of the curve are approached one has to be guided more and more by the trend of the curve already established. That is, along interior portions of the curve individual eyroFrs i i z the measum-ement o f the p r e s s w e are smoothed out and Biot's foymula is f a r more accurate than the individual nzeasurenzenis, but at the ends o f fhe cziyve thzs smoothkg is necessarily f a y more iw$erfect and Riot's formula cannot give greatZy more accurate reszt Its than the individual observations. (The fact that the constants for the formula are mathematically calculated makes this observation of course none the less, true.) Individual observations of vapor pressure could not be used to obtain a correct idea of the
ap
aT because an error i n these 06-
-
sevvaiions is muZtz&ied pyoportionately aizywhere from ten to ap s c v ~ n t ytimes in the --. T h e method adopted tyill keep this
ar
enormous multiplication of error from being greatly apparent, except as either end of the Biot formula curve is approached. But throughout the entire range of the observations it is doubtap
that is most often reaT sponsible for the variation in the constant. Many illustrations taken directly from the nieasurements enforcing the above remarks might be given, but attention will only be called to the case of water. Ramsay and Young's observations of the vapor pressure of water are in beautiful accord (0' to 230' C) with the Regnault-Biot formula, whose results they quote. But when this formula is forced past the temperature (230' C) for which it was calculated, an error in the trend less this multiplication of error in the
(g)
--
of the formula is at once apparent.'
This error could
neither have been suspected nor provided for, had either set of observations below 230' C been used to calculate the formula. ' S e e Phil. Trans. 18928,p.
112
.I. E. MiiZs
396
I n this connection Prof. Young calls my attention to Broch’s calculations of the vapor pressure of water, 0’ to Broch used the formula, 100’ C. P =A,,
bt
+ ct2 + dt3+ et4 +f t 5
+at and made exceedingly careful and laborious calculations. But unfortunately ifi obtaining his constants he used Regnault’s data from -32’ to 100’ and the vapor pressures at the lower temperatures were for the most part those of ice, not water. Hence, remarks of Prof. Young, “ I t is interesting to notice that below 0’ his calculated pressures are with trifling exceptions, higher than the vapor pressures of ice observed by Regnault-a striking proof, if such were needed, that the vapor pressures of water are really higher than those of ice at the same temperatures. Moreover, Broch makes the vapor pressure of water at oo = 4.569, whereas the mean of Regnault’s actual observations, 1 2 in number, is 4.608.” Again at 100’ C, Prof. Young points out that the trend of Broch’s curve is certainly wrong, and in proof of this he sends, and kindly permits me to publish, the following calculations upon the vapor pressure of water, made some years ago but never published. 3
I
____
From Regnault’s From Broch’s formula
curve
Temperatures
760.00 760.00 0.00 1489.0 1544.7 55.7 3572.0 4244.3 672.3 150 20201.0 11660.0 31861.0 200 Corrected for latitude, etc. and normal degrees C. I ooo I20
~~~
~
I 11660.0
-
1
31839.0 1 20179.0 Preliminary constants before employment of method of least squares 200°
’
11660.0 I 40547.0 1 28887.0 I t surely cannot be necessary to give further illustrations of the fact that the trend of no empirical curve can be trustworthy near its end point. 200°
397
Molecular Attraction
In conclusion therefore :3. Errors of observation occurring in the vapor pressure will exert per se little effect upon the constant of formula 2. 4. Errors in the vapor pressure may cause greatly multiplied error in the constant by affecting Biot's forniula used for
ar
the calculation of the -
aT *
This source of error will be greatly
more apparent at the end points for which the Biot formula was calculated. The Evidence for the Theory T h e measurements considered in calculating the constants, of which Table I gives a summary, include thirty-one substances, TABLEI
9-
b,lP
~
"?
Mean value
104.4
4
88.7
109.0
101.7
89.1 .... ... ... .... .... .... .... .... .... 98.6 .... 98.7 ... 99.0 .... 98.4
107.2 111.1 104.8 104,s 104.1 107.6 104.3 108.5
.... ....
105.6
98.0
103.6
~
1065 973 105.6 104.4
0.
IO 20
30 40
50
60
70 80 90 Io0
130
140
I
104.9
,
105.5
105.3 104.4 103 o ZOI.0 106.3 98. I
150
I60
170 180
190
220
98.2 97.8 97.4 97.6 97.7 97.7 99.7 97.7 97.7 98.0
I
1 ....
98.I 97.3
94.8 .... r 225'
230 I
(92.0
. . . .... .... .... .... ....
104.5
109.3
104.7 1046 105.2 105.5 105.8 106.0
109.5 '09 6 109.7 19.9 109.9 110.4
Critic'l temp.
'940
8
90.4 8R.7 87.0 106.3 111.1 85.8 111.0 IO6.j 85.0 106.7 110.5 84.9 84.6 106.9 110.5 106.7 110.3 85.1 105.5 I103 85.7 86.2 103.4 1093 187.401 r06.3 86.8 I 96.6 197.15 87.0 98.8 57.3 87.9 88.6 89.0 89.5 89.4 87.6
-
__
227.35 276.8' 187.80 197.2'
- -
-
~
1
.
1
91.2
102.5 102.4 102.6
109.1
1095 109.8
.... .... .... .... .... .... ... ....
105.6 104.8 104.I 103.3 102.5 102.1 102.2
92.8 928 92.9 93.I
99.2 99.7 99.7
103.1
110.5
103.5
98.0
99.8
93.3 93.9 93.6 93.9
110.5
102.1 101.1
93.7 94.2 94.6 94.3
110.6 104.6 110.3 104.9 110.0 104.7 110.0 103.4 107.8 "2.79'
102.7
I234O
i
I
102.6
97.5 97.7 98.5 98.9
102.8
.... ....
.... .... .... ... .... .... .... .... .... .... ....
.
~
108.1
1
.... .... .... .... ... .... .... .... , m0 64 .... .... ... .... 8.... __
109.3 .99.6 . . . . 97.5 . . . I .... .... .... :::: 1 .... I .... .... .... 1 .... .... 1 .... I .... 102.4 .... I . . . . . . . . . 102.7 100.3 , .... , .... 103.0 99.4 .... 107.8 103.0 99.1 1 .... j 107.8 99.0 ..... 103.3 98.9 ' .... 103.7 103.6 6 S . i 1 108.3 108.6 91,4 108.8 103.5 103,~ zi:: 109.4 103.1 97.2
.... .... .... ....
99.6 99.3 96.6
942 .... ....
....
266.5'
....
... ....
90.8
.... ~
234.8C
93.4 91.0
, ,
102.7 103.1
103.4 110.4 102.9 110.0
110.7 111.1
104.2
104.6
98.1 .... ....
__ __ __
266.9O 296.20 288.50 r79.950
--
J. E. MiZZs
398
TABLEI.-(
Continued)
~.
81.0
85.7
0
10 20
30 40
50 60
70
80 90
100 I10 I20
130 140
150 160 170
180 190 200 210 220
230
240 250 260
270
280
290
I
1
56.1
43.53 44 99
.... .... .... ....
86.6 86.8 86.3 84.7
1
.... 44 65 .... .... .... .... ... ....
1 '
56.44 56 92 5.t.15
I
I
585.7
.... ....
580.2
26.45 26.34 26.24 26.18 26.00 25.82 25.68 2546 25.13 2 4 ,84 24.68 24.45
....
549.5 548.6 547.8 547.6 547.3
304.7 306 o 106 6 307.9 307,4 3Ob.3 308.0 308. I 307.8 307.1 306.3 306.0 305.4 304.5 304.1 301.3
551.0
....
570.7
I 554.5
1
232,8 235.4 237.4 239.9 241.7
....
203.1
.... .... ...
242.4
243.6 244. I 244 9 244.6 244,8
SI.3
.... .... .... ....
83.8 86 I 87.S 90 4 92.2
'99.9 199.2 197.6
94.7
96 h 98 5
106.2
242.7
100.7
242.1 241.0 241.0 241.1
24.20
23.96 23 63
1
-1-1Critic'] ~ 8 6 . 5 5 360 ~ temp. -~ -
26.20
45.16 2335 44,99 22.96 44 47 22.47 43.90 I 22.15
44.38 44.68 45,IO
...
199.2
__
.... .... .... .... ....
44.94
! ":9, .... .... 1 . . . . . . . . . .... ~
240.1
....
43.52 43.58 43.58 43.64 43.67 43.79 43 79 43.83 43.86 43.92 44.00 44,16 44.34 44.55
.... ....
54.09
81.3 81.3 81.6 81.8 82.3 83.1 83.6 84.3
....
5448 54,98 55.21 41.87 42.66 55.45 55.9' 43.06 5537 43.64 56 25 , 43,73 56.19. 44.03
81.2
'
.... .... .... .... .... .... .... ...
....
'
84.7 84.7 84.7 84.8 84.7 85.1 8s 5 85.8 86.2
26.0 ~
~
80.8 81.3
__
44,3
_84.6 81.6 .... . . . . ..... .. .... . . . . . . . . .... .... 5874 ... .... .... ... , . *... .... .... 1 :... .... . . . . . . . . ........ 86.8 87.2 .... I .... 86.9 .... I 56.93 86.7 . . . . ! .... .... .... 86 3 .... 85.7 79,5 sj.0 .... 80.3 84.6 .... 81.1
__ __
__
I I
....
209.z
544.9 535 5
.... ....
.... .... .... ....
.... .... ...
_ I-
~
264.7
,
124 I
126.4 128.4 130.0 131 5
....
..... .... 131.2 --I
~ 4 3 . 61 ~~ 6 3 . 71321.65~ ~
I
and cover a range of 290' in temperature. T h e foregoing discussion has shown that errors of observation may often be multiplied and are always coinpounded in their effect upon this constant. T o cover this range of temperature, the number of substances, and the variously compounded errors of observation in vapor pressure, vapor density, and density of the liquid, errors which may be multiplied in the calculation, it has seemed to me reasonable to pass without discussion all variations in the constant less than two percent from the mean values chosen and given at the top of each column. An agreement within two percent of this mean value we therefore consider satisfactory. All values not showing this agreement are in italics.
MoZecu la Y A t tra ction
'
399
Excepting values within ten degrees of the critical temperature the eleven substances, ethyl oxide, di-isopropyl, isopentane, normal pentane, normal hexane, normal heptane, normal octane, benzene, hexameth ylene, fluo-benzene, and carbon tetrachloride, show out of two hundred and seventeen observations only two that are not within two .percent of the mean value adopted for that particular substance. T h e two exceptions are normal octane at 0' C and ethyl oxide at 180' C, and both of these divergences, as well as those occurring within ten degrees of the critical temperature, are, as shown below, easily explained. In six of the eleven substances above mentioned, the observations allowed the tests of the formula to be carried to within one degree of the critical temperature, and in the case of normal pentane to within 0.05' of that point, yet in no case is the divergence greater than ten percent from the mean value adopted for that substance. Nearing the critical temperature an inspection will show that an error in the vapor pressure will be multiplied proportionately some seventy times in the constant if the error ap
likewise affects the e a n d , as already explained, (p. 395), at the end points of the Biot formula curve these errors do affect, to a considerable degree, the
ap -
ar
*
T h e same explanation will hold for normal octane at 0" C. For ether at 180' C reference to the original data shows that the Biot formula adopted differs from the observations sufficiently to account for the divergence, and it is but proper here to add that Prof. Young writes, "Above 180' thesubstance (ether) was heated with methyl salicylate which was not quite satisfactory. In later work quinoline was used." I think it may be safely said that every error occurring in these eleven substances could be entirely eliminated by changes in Biot's formula, in no case affecting any vapor pressure so much as five-tenths of one percent, and I therefore emphasize the fact that the on& divergences shown f y o m the theory by these eleven substances are not errors of observation, primarily, but of c a hlation.
400
'
J. E. Mills
It may be well to mention that of the 217 observations for these eleven substances, 152 are within I percent of the average value, and the 63 that are within 2 percent of that value group themselves more largely at those points where errors of calculation and of observation would be the greatest. These eleven substances, therefore, from o' C to their critical temperature, show, it seems to the author, as perfect accord with the theory as the method and observations will permit. Of the other substances, the following observations are not within two percent of the mean values given. Di-isobutyl, 120' to 190' C, inclusive, shows a divergence amounting at the greatest to five percent from the mean value. This may be caused by an error in the vapor density, because PAV does not show a maximum value at 2 0 0 0 mms pressure, and tlie same value at 5000 to 6000 mms as at 500 to 600 mms, as is the case with similar substances. Prof. Young has very kindly examined for me his original notes and calculations upon di-isobutyl. T h e measurements and calculations were abundantly checked, and there would seem to be no chance for unusually large errors. H e suggests that if a lower mean value were adopted the errors would be shifted toward the end points of the curve. T h e author would here remark that a theory by Crompton to which attention will be called in a following paper, seems to bear out this suggestion, but also points more strongly to the fact that di-isobutyl does not give the results that similar substances would lead one to expect. Chlor-benzene, 240' to 270' inclusive, may easily be due to the wrong trend
(g)
of the Biot formula at this, its end
point. Brom-benzene at 30' C. T h e error here is due to the Biot formula, as shown by the fact that at 100' C the constant, from a theoretically calculated density, is correct. At 160' and 170' C the error may be due to the measurement of the vapor density. Prof. Young writes, ' ( T h e observed volumes of saturated vapor are generally much less accurate at
MoZecu la Y A iira ciion
401
low temperatures than at high, because, by the method employed, a given error in reading would have much greater influence at the lower temperature.'' Also regarding brom-benzene Prof. Young says, "After heating in ordinary daylight at 180°, 190', 200") brom-benzene slightly acted on by mercury, small quantity of solid being formed, chiefly in form of minute needle-shaped crystals.' I n a second series' the brom-benzene was ' carefully shielded from the light, no crystals formed.' T h e volumes were read in the first series only-the quantity of liquid in the second being small-and the results do not seem to me so satisfactory as with the other substances examined." Iodo-benzene at 190" to 210' C, inclusive, may be due to measurement of vapor density. Dr. Young writes, In the case of iodo-benzene similar crystals (to those with brom-benzene) were found, although the substance was shielded from daylight. All readings had to be taken by gas light and are therefore less accurate than usual." T h e tendency towards continually increasing values of the constant with rise in temperature in the case of chlor-benzene, brom-benzene and iodo-benzene, may easily be without significance, for in the first mentioned the tendency is not marked, and in the last two the final values are not far from the probable true values as shown by the results at 30" and 100' C. On the other hand they may indicate progressive changes commenting within the molecule, and the remarks of Dr. Young above given are significant. Stannic chloride may be said to be in agreement with the theory from 0" C to 170' C, but the values from 100" to 280" continually decrease, and there is little doubt that the cause of the variation is operative froin the first. I would call attention to the high specific heat per atom that we find in stannic chloride and the conclusion, based on grounds having nothing to do with the present theory, drawn therefrom by the author,I viz : " A high scientific heat per atom indicates that the poten. tial energy of the atoms is being rapidly increased and that the Jour. Elisha Mitchell Scientific Soc. Vol. 18.
402
J . E. Mill.
molecule is approaching the point of dissociation." Prof. Young writes, "Stannic chloride spoils the surface of mercury even at low temperatures and special methods had t o be used throughout. T h e accuracy is certainly not so great as with most of the other substances, but this will not, I think, explain the regular fall in the value of the constant." Water shows divergence oo to 30' C and at 270' C. Both may be explained by the multiplication of error through the at the elid points of the Biot formula curve. Ramsay and aT Young's observations of the vapor pressures at 230' to 270' are in themselves rather conclusive that the troublc at 270' Crests with the Regnault-Biot formu1a.I See also remarks on page 399. T h e measurements of Griffiths would indicate that the divergence at the lower temperatures is but partly due to the vapor pressure formula used. T h e divergence in ethyl alcohol at oo C is probably caused by the end point of Biot formula used. Methyl alcohol, 210' to 238.5" C, ethyl alcohol, 190' to ~ 4 2 . 5C,~and propyl alcohol, 120' to 260'~ evidently should be grouped together. They are associated substances, as was water, and the theory was not expected to hold for associated substances, because the molecules may not be evenly distributed, the molecules are of different kinds, and the number of molecules changes with changing temperature. The f a c t that the theory does hold, to a very considerable degree, f o r these substances also, is szgnzjt;cant, and points strongly to the conclusion that the cause o f the molecular association in ihese substances must he the attraction which we are discussing and not some other attraction such as we mighi denote by the lerm chemical a@nity. And the fact that these associated substances do not agree even more closely with the theory may be entirely due to the supposition embraced by the formula that the molecules are uniformly distributed throughout the space occupied by them - a supposition probably untrue for associated substances. See Phil. Trans. 1892A,p.
112.
Maleczrlav Attvaction
403
Bearing in mind the comments above, we conclude that the divergences shown by di-isobutyl, chlor-benzene, brom-benzene, iodo-benzene, and water, all occur at such points and are of such magnitude (none greater than 5.4 percent) that they may easily be due to errors of observation, or the multiplication of such errors by the calculations. Stannic chloride fails to agree with the theory. Water, methyl, ethyl, and propyl alcohols and acetic acid are associated substances to which the theory is not applicable a p v i o ~ iand , yet these substances, acetic acid excepted, appear within limits to agree with the theory. I n conclusion, to prevent further misapprehension, I would notice a review by Mr. G. N. Lewis1 of the former paper on this subject. This paper presents additional evidence in favor of the theory, and i t is the intention of the author to extend the work to the ten esters for which measurements have been made by Prof. Young. T h e other assumptions of doubtful validity ” upon which the present theory is based, referred to in that review, were mentioned in the original paper as they are in this (here they are numbered, however, so that he who runs may read), without attempt a t proof. True equations are seldom deduced from wrong assumptions, and if we can establish the truth of the equation the assumptions will probably be admitted by those who now doubt their truth. A11 of theassumptions made, except possibly the law of attraction assumed, are, we are inclined to believe, regarded favorably by scientists on other grounds. Coiicerning the statement made in that review that “ t h e author does not point out the simple relations between the densities of vapor and liquid, and the difference in their specific heats, which would be the direct consequence of his equations,” we would say that we are of course aware that the equations that we have deduced can be combined with certain other thermodynamical, empirical and rational equations, so as to produce certain relations. (See for instance, equation 13 of this paper, which equation is similar to the relation, p = 6t - a , of Professors Ranisay and Young.) T h e theory itself here given ((
Jour. Ani. Chem. SOC.3, 107 (1903).
404
J . E. MiZZS
is capable of further direct and very promising application. T h e author hopes shortly to complete and publish a paper calling attention to some of these extensions of the theory. For the measurements used we are indebted almost entirely to the labors of Profs. Ramsay and Young, and of Prof. Young. After months of laborious acquaintance with these measurenients we cannot conclude this paper without giving expression to the sincere admiration excited by the accuracy and completeness of the data they have furnished. And we would express a thanks, heartfelt, and echoed doubtless by hundreds of workers elsewhere, for their labors. We wish further to express our thanks to Prof. Young for some unpublished details of the measurements and for comment upon the work, and we have taken the liberty of making in this paper some extracts from his letters. Summary I.
T h e equation,
- constant was deduced for the I/d-- $1/D -
purpose of testing the assumption that the attraction between the molecules of any particular substance obeyed the law of gravitation, i. e., varied directly as the product of the masses, inversely as the square of their distance apart, and does not vary with the temperature. 2. Twenty-one substances were examined. Of these, eleven : ethyl oxide, di-isopropyl, isopentane, normal pentane, normal hexane, normal heptane, normal octane, benzene, hexamethylene, fluo-benzene, and carbon tetrachloride were, from oo C to their critical temperature, making allowance for errors of observation and the multiplication of such errors in the calculation, in reasonably perfect agreement with the deduced equation. T h e divergences in di-isobutyl, chlor-benzene, brom-benzene, iodobenzene, and water, all occur at such points and are of such magnitude that they may easily be due to the errors of observation (or the multiplication of such errors in the calculation). Stannic chloride failed to agree with the equation. 3. T o the associated substances water, methyl, ethyl, and
405
MoZecuZaar Attraction
"
propyl alcohols, and acetic acid, the equation was not supposed applicable ; but within wide limits the agreement of these substances, acetic acid excepted, is such as to suggest the conclusion that the molecular association with which we are there dealing is caused by the niolecular attraction whose law we are considering.
TABLE2 Ethyl Oxide
$I
%
0.7362 0.7248 0.7135 0.7019 0.6894 0.6764
00
IO 20
30 40 50
0.6658
60 70
0.6532 0.6402 0.6250 0.6105
80
so IO0 110 I20
0.i942
130
140 '50
I60
170 I80
185 190 192 '93
0.0~8270 0.001264 0.001870 0.002677 0.003731 0 005079 0.006771 0.008920 0 01155 0.01477 0.01867 0.02349 0.02934 0.03638 0.04488 0.05551 0.06911 0.08731 0.1135
0.4947 0.4658 ?1804.3 0.4268 E3532.4 0.4018 0.1320 0.1620 25355.1 261I 1.2 0.1826 26495.0
0,2012
93.27 90.77 87.90 85 60 83.18 80.95 78.a4 76.42 75.95 71.39 68.35
: :E:
7.11 7.33 7,50 7.68 7.82 7.94 8.05
86.16 83.44
8.08 8.02 7.01
6;:;;
59.11 55 52 51.18
0.50
45.99 39.69 31.58 26.78
6.2i 5.5: 4.49 3.82 2.79 2.14 1.64
20.90
17.10
13.67
80.40
77.92 75.36 73.01
0.8091 0,7901 0 7704 0,7499
106.5 105.6 104.4 103.9 103.5
0.7059 0.6840 0.6603 0.6359 0.6096
IO2.A
0.7283
60.33
0.5830
58.07
0.5543
54 91 51.62 48.3: 44.38 39 74 34.18 27.09 22.96 r x I1 14.96 12.03
0.5238
0.4919 0 4582
0.4216 0.3805 0.3315 0.2687 100.4j 0,1704 106.3 0.1339 111.6) 0.1051 "4.5) 0.2287
J. E. MiZZs
406
TABLE3 Di-isopropyl
:
i
d
5 I
~
OC 50
60 70 80 90
'I 1
cl 76.05 584.1 006.8 ' 1090.3 14448 1880.9 2409.7
0.6039 0.5931
1
ooo6ooC o 00775:
5821 0.5708
I 0.009901 1 o.01~50
0.5584
O . O I . ~
140
11.5334
150
0.5197 0.5049 0.4885 0 4705 0.4508 0,4274 0.3088 0.3758 0.3565 0.3198
0.02358 0.02825 0.03521 0.04292
IO0 I10
I20
1
0
1041.0
130 160
170 I80 190 200 210
216 220 225
1 22585.0
0.05216
0.06161 0.07831 0.09862 0.1163 0.1321 0.1649
1.57468 1.06573 o.wz78 0.g654 84.05 0.86685 86 90 0.81327 89.26 0.76498 91.15 0.72144 91.18 0.68219 94.54 0.64677 95.28 0.61479 97.46 0.58592 94.13 0.55982 92.05 0.53623 X9.06 0.51488 84.50 0.49555 77.71 0.47807 67.28 57 80 49 45 33.04
1
85.11 78.47 76.90 75 i o 72 86 70167 68.28 65.76 63.57 61.15 58.58 57.10 52.70 49.36 45.86 4I,87
6.30 7.26 7.41 7.54 7.58 7.62 7.61 7.58 7 54 7.47 7.34 7,33 6.92 6.61 6.26
17.14
5.23 4.43 3.76 3.19
78.81 ;I.?I 69.49 67.76
0.8065 97.81 0.7224 1 98.57 0.7036 98.7.5 0.6842 I oo.oz 0.66i5 98.3; 0.6423 98.16 0.6203 i 97.81
1
65.28
63 05 60 67 58.18 56.03 53.68 51.24 49 77 45.78 42.75 39.60
" ,
5242 0.4994 0.4685 0.4375 0.4042 0
1
1
1 ,
931.7; 99.67 97.72 97.71 97.98
5.81
2.11
I2
46
0.1355
91.96)
0.7106 0.6916 o 6720 0.6517 0.6316 0.6102 o5r89
88.73 86.98 85.76: 84.97) 84.94) 84.j g ) 8j.09)
0.5197 0.4935 0.4655
86.78) 86.96 87 34
TABLE4 Di-isobutyl
5 -I-
O0
12:
I IO 120
130 140 150
I60
170 I80 190 200 210
220
1'
I-7.11
425.6 581.1 777.9 1322.5 1684,g 2118.2 2630.6 3231.3 3930,2 4738.0 5666.5 67W5 7941.0 9319.0 10883.0 12654.0 14660.0 16929 o 1boo6.o
I
d
J
1.98712 1.01836 0.95256 0.89276 0.83846 0.78921 0.74460 o.jo425 0.66783 0.63500 0.60549
76.24 65.91 63.05 60.16 57.63 55.38 53.65 51.62 50.11 48 60 46.90 45.10 4 2 91 40.66 38.32 35.70 32.59 28 96 ?4.31 7 01 ,2.39
~
0.7102 0.6328 0.6236 0.6143
0,044762 0.002I74 0.002967 0 003984 o 005236
40.76
70.82
72 70 74.30 76.08 77.98 80,37 82.06 84.30 86.30 87 61 88 39 87,93 86 80 84,94 81 89 77.10 70.40 50.55
:.:::::;
0.01072 o.or'~19 O.Ol610
01957 0.02370 0.02874 0 03484 0.04202 0 0,5094 0.06223 0.07680 3.09699 1.1321 1.1572 0
13.21
11.72
YJ
,y
61 54 59.84 57.79 56 30 54.80 53.05
,
".A"
6.16 6.19
6.17 6.19 6.20
6.15
:,;::::a:;:{
3:;: E:0.3663 : 88.97
Molecular Attraction TABLE5 Isopen tane
_-__
_-s 257 74 390.52 572.59 815.34 1131.1
1533.2 2035.6 2653.0 ?A00 8 4195.6 5354.5 6596.1 8039.9 9766. j 11620.0
13804.0 16285 o '9094.0
20950.0
22262.0 23286.0 23992.0 24350.0 24713.0 24880.0
3.6392 0.629j 0.6196 3.6092 3 . 5988 0. 5881
0.5769 0.5656 0.5540 0,5413 0.j z j a
0.5140 0,4991 0.4826 0.4642 0 4445 0.4206 0,3914 0.3694 0.3498 0.3311 0.3142 0.3028 0.2857 0.2761
0.001090 0.001646 0.002358 0.003300 0.0&80
o.ooj967 0.007819 0.OIOII
0.01284 0.01617 0.02022
0.02513 0.03106 0.03831 0.04728 0 05834 0.07289 0 09337 0.IIOI
0.1258 0,1418 0,1574 0.1676 0.1833 0.1951
88.86 84.93 82.91
54.43 1,37910 56.06 I 26846 70.68 1.16990 74.45 1.08206 78.41 11.00375 82.14 0.93390
107.2
7.51 7.53
77,40
7.70 7.82
80,jj
78.69 76.71
;!I . ;
8.18 8.20 8.24 8.20
88.36 0.81591 72.09 91.36 0.76618 70.00 93 54 0 . 7 2 1 7 1 67.51 95.00 0.68194 64.78 95.64 0.64631 61.81 95.42 0.61439 58.62 94.02 0,58574 55.07 91.19 0.56002 51.07 86.92 10.53689 46.67 79.98 0.51605 41.27 68.93 0.49728 34.28 j9,go 0 48690 ;9.17 51.33 10.48031 24.65 42.80 0,47555 20.35 34.86 0.47245 16.47 29.76 0.47093 14.01 22.22 0.46942 10.43 17.21 10.46882 8.07
8.11
~
~
o.58ji 0.5621
1 ,;,,o; 35 39 0.3316 29 33 j 0.2778 24.92 1 0.2382 21.04 0.2635 0.1703 17.36 1405 0.1399 11.95 0 , 1 2 0 1 8.89 o.ogos 0.0712 6.88 40.1j
3.61
1
67.76 59.31 56.67 53.86
0,5357 o 5081 ~ 0 . 8 9 0.4788
7.95 7.73 7.43 7.03 6.54 5.58 4.95 4,25
~
72.73 70.72 68.62 66.38
0.7389 0,7194 0.6988 0.6781 0.6564 0.6340
75.21
2.99 2 42 2.06 1.54 r.19
'
104.8 104.5 104.1 104.3 104.5 104.7 104.6 105.2 1oj.j
IOj.8 106.0 106.3 106.5 106.7 106.9 106.7 105.5 104.6 103 4 101.9 100.4 99.5 98.2 96.6
__
I
+ h
w"
Q .?
&%
rs
El '2
1190.2 1601.8 2114.0
jo
60 70
,
Ro ..
90 100 I10 120
1
130
:'!:
..
160 1;o
180 I 86
1
1
..
2742.1
3501 5 4409.1 5482.5 6740.5 8203.0 9890 0 11826.0 14C32 0 16535.0 19362 o 21225 o 22540.0 23566.0 24271.0 24629 0 24810 o 24991.0 25027.0 25045.0
0.6454 0.6165 o.606a 0,5957 0.j8jO
04739 0 5624 0,5503 0,5378 0.5248 0 5107 0.4956 0.4787 0.~604 0.4394 0.4161 0 3867 0 3643 0,3445 0.3253 0.3065 0.2915 0.2809 0.2640
0.2560 0 2172
I In
0 087756 0.0024 7j 0.003390 0.004545 o.ooto24 0.007868 0.01013 0.01289 o 01627 0.02026
0.02503
0.03 106 0.03861 0.04762 0,05910 0 07347 0,09354 0.1109 0.I 269 0.1441 0.1609 0 I745 0.1842 o 2004 0.2090 0.2167
64.48 74.84 79.47 83.91 87.65 90,yj 01.86 Gg.30 97.99 9962 100.65 99.78
I
d
7.44799, 93,36 7.51 11.13456 84.91 7.86 ' I.Oj22I 83.63 8.08 0.97878 82.13 8.27 0 . q 1 ~ 4' 80.04 8.38 0.8j466 77.71 ' 8.44 I 0.80221 , 74.10 , E.46 0.75519 $;.?3 8.45 0 71297 69.87 8.36 0.67497 1 67.24 8.28 0.64073 64.48 8,Ij I0.6097~1 60.85 7 88
85.85 77.05 75.55 73.86 71.66 69.27 66.84
7.09 6.53 5.90 4.99 4.24 3.57 2.90
45 30 4O.89 36.16 30.02 25.23
2.28 I $0
13.38 I O 55
1
1
1
111.1
107.6 108.5 109.3 06544 109.5 0.63% 109.6 0.60~1 109.7 109.9 109.9 110.4
1
~
'9,9R 15.& 12.35 10.12
1.48
6.55 4.79 3.11
0 96
0.70 0.45
111 I 111.0
1 0.3707 4+7 0
i
0.2337
21.11
17.08
h.66
5 59
4.09 2.66
0,3278 0.2746
I
0.1985 o 7634 0,1303 0.1042 0.0850 O.O$j
0415 0.0269
0
110.5 110.5
110.3 110.3 109.3 108.0
106 3) 104,5)
102.7) 101.2)
100.6) 99.3) 98.5) 98 4
J. E. Malls
408
TABLE 7 Normal Hexane
_-
__ ~
c
0
'5;
fir
0 0
;g
__ 00
60 70 80 90 IO0 I10 I20
130 140
150 160 170 I80
190 200 210 220
226
230 233 234
44.92 567.62 784.80 1062.0 1409.0 1838.0 2358.0 2982.0 3723.0 4593,O 5606.0 6778.0 8123.0 9659.0 :1407.0 :3385.0 ~5619.0 ,8133 0 19788.0 ?0957.0 21870.0 12181.0
m
b.
.5; 2
0.6770 0.6221 0.6122 0.6022
0.5918 0.5814 0,5703 0.5588 0.5467 0.5343 0.5207 0.5063 0.4913 0.475' 0,4570 0.4365 0 4124 0.3809 0.3557 0.3329 0,3040 0.2883
P
I
4 2 -
J
~
0.0~2268 0.00249 0.00337 0.00446 0.00585 0.00752 0.00952 0.01200
0.01502 0.01862
0.02299 0.02833 0,03472 0.04228 0 05155 0.06329 0.07900 0,1011
0.1203 0 I404 0.1658 0.1807
54.05 75.68 79.51
2% 90.00 93.18 95.54 97.24 98.25 98.64 97.73 96.44 94.31 90 89 85.52 77.23 64.93 53.97 43.43 30.32 23.24
1.68307 1.06787 0.99598 0 93083 0.87180 0.81835 0.76998 0.72623 0.68669 0.65098 0.61874 0.58968 0 56352 0.53998 0.51883 0,49986 0.48289 0.46773 0.45943 0,4542 I 0,45045 0,44923
g3ff 79.19 77.55 75.51 73.65 71.75
2:;: 2::; 57.63 54.34 50.93 47.16 41.75 37.29 30.37 24.79 19.73 13.66 10.44
6.30 7.23 7.38 7.51 7.60 7.68 7.74 7.74 7.68 7.57 7.42 7.18 6.93 6.63 6.25 5.75 5.09 4.19 3.46 2.75 1.90 1.46
84.68 73.59 71.81 70.04 67.91 65 97 64.01 61.64 59 10 56.39 53.61 50.45 47.41 44.30 40.91 37.00 32.20 26.18 21.33 16.98 11.76 8.98
$
E
E
103.6 102.4 102.7 103 o 101 0
105.3 103.7 103.6 103.5 103.2 I0j.I
102.5 102 4 102.6
8 102.7
:.0.3152 :E:;
102
102.1 101.~
0.2590 0.2148 0. I732 0.1230 0.0953
99.3) 98.0 954 94.2)
~ ~
, Fi
I
c
a QJ
o 8171 0.7182 0.6992 0.6799 0.6594 0.6387 0.6174 0.5947 0.5710 0.5464 0.5201 0.4921 0.4629 0.4319
TABLE8 Normal Heptane
g k"
.ii
j
;?
~
d
2*
!-
_4 2
__ ~
4
b. I
P a,&
'G;
I
!-
j-
R2
~
00
70 80 90 100 I10 I20
130 140 150
11.45 302.77 427,IO 588.74 794.93 IO53,3 1372,I '759.9 2226.1
200 210
2780.4 3433.3 4196.0 5080.9 6101.3 7271.8 8608.6
220
101~0.0
160
170 I80 190
230 240
250 260
264 266 266.5
11857.0 13811.0 16020.0 18511.0 19595.0 20150 o 20300.0
0.7005 0.6402 0 6311 0.6218 0.6124 o 6027 0.5926 0.5821 0.5711 0.5598 0.5481 0.5359 0.5232 0.5096 0,4952 Q.4793 0.4616 0.4414 0.4177 0.3877 0.3457 0.3166 0.2907 0.2819
3.0~6725 46.46 1.93123 3.001435 72.17 '1.13368 3.001996 75.22 1.05722 3.002703 78.66 0.98784 3.003584 82.13 0.92493 3.004692 85.33 0 86789 0.006068 87.95 10:81624 0.007752 90.27 0,76948 92.39 , 0.72719 3 009775 0,01222 94.08 10.68898 0.01508 95.87 ,3.65447 0.01848 97.02 '0.62337 0.02242 98.30 0.59536 0.02717 98.30 0.57017 0.03304 0.04005 0.04892 0.06002 85.81 0,49305 78.24 '0.47869 0.07446 0.0946 I 67.05 10,46598 0.1287 48.15 0,45475 0.1538 35.15 0.45066 0.1778 23.73 0.44869 0.1895 ~
89.86 81.84 79.52 77.70 75.96 74 06 71.79 69.46 67.19 64.81 62.74 60.48 58.52 56.05
42.31 37.45 3r.25 21.90 15.84 10.65
5.42 6.70 6.78 6.90 7.01 7.09 7.12
?.I3 7.12
7.08 7.05 6.97 6.90 6.76 6.54 6.27 5.89 5.43 4 85 4.08 2.88 2.08
1.40 1.12
84 44 75.14 72.74 70.80 68.95 66.97 64.67 62.33 60.07 57.73 55.69 53.51 51.62 49.29 46.63 43.90 40.57 36.88 12.60
27.17 19.02 13.76 9.25 7.38
0.8474
99.6
3.749i 0.7319
100.1
0.6576 0.6371 0.6159 0.5939 0.5713 0,5479 0.5238 0.4982 0.4703 0,4405 0.4071
98.3 97.8 97.5 97.2 97.5 97.7 98.5 98.9 99.2 99.2 99.#
99.4
1
Mobcular Aiiraciion
409
TABLE9 Normal Octane
__
c
x *
'G
a
3 ;; 8%
F 7 WG,
0.7185 0.6168 0.6071 0.59?3 0.5875 0.5772 0.5667 0.5556
5441 0.5317 0.5189 0.5053
0
E
x
ns __ 2.90 649.3 859.4 1114.5 1426.9 1802.4 2249 0 2775.4 3390,7 4105.0 4928.9 974.6 6955.0 8184.5 957'1.8 111560 12937 0 I4942 0 17198.0
8
w
LI
nc
0 041942 0.003300 0.00429, 0.00 5464 0.006897 0.008584 0.01065 0.01314 0.01608 0 01957 o 02364 o 02874
o.oB223
o 07716 0.04b33
0.1346
40.77 76.91 80.16 83.47 86.50 89.59 91.74 93.41 9432 95.54 96.17 95.00 93.41 90.29 86.87 81.87 73.96 62 38 43.18
2.1942 3.91369 3.85906 o 80944 o 76440 0.72354 o 68649
89.46
4.75 6.24 6 33 6 43 6.51 6.jS 6,59 6.56 6.?2 6.i3 6.34 6 13 5.91 5.60
70.27
68.86 67.56 66.12 64 82 62.98
0.59j;I' 26.87 0.57015 54 83 0.54769 52.03 0,52743 49 27 0.50018 45.97
84.71 64.03 62.53 61.13 59.61 58.24 56 39 54.43
I
1
I
~
TABLEIO Beiizene I
_ _ _ _ -I 00
So 90 IO0 I10 I20
130 140 150
I 60
170 180 190 200 210 220
230 240 2 50 260
270 280
26.54 753.62 1016.1
'344,3 1748.2 2238.1 2824.9 3520.9 4334.8 I 5281.9 6374.I 7625.2 9049,4 10563.0 12482 o
14526.0 16815.0 19369.0 22214.0 25376.0 28585 o 32772.0
0.pOI
0.031215 ,
107.05 94.40 92 76 91.05 89.26 87.36 85.43 83.48 81.35 79.20 76.90 74.53 71.93 69.01 65 80 62.32 58.49
1
8145 0.002722 0 003570 0.7927 0 004690 0.7809 0.006035 0.7692 0.007634 0.7568 0.009515 0,7440 0,01174 0.01436 0.7.710 0.01734 0.02087 0.02487 0.6758 0.02977 0.6605 0.03546 0.6432 0.04207 0.6255 0 05015 o 6065 0.06024 0 5x5; 0 07138 54.21 0.5609 0 08554 49.40 0.5328 0.1038 43.76 0.4984 0.1287 36.97 0.4514 0.1660 27.43 1 0
0.8041
~
1
97.50) 3.7023 91.17 3.6842 I 91.39 0.6661 91.77 0.6471 92.12 0 6278 92.77 o 6075 I 92 8 2 0.5861 92.87 j2.jI 0.5640 01.10 50.44 0.2406 Gi.30 48.49 o 5166 93.86 45.90 0.4902 93.63 43.36 0 4618 93 90 40.37 0.4307 93,73 17.41 0.3981 94.22 ". 34.25 0.3622 94,56 30.05 0.3186 94.32 24.67 0.26391 93,40 16.66 0.1831I 91.00 3.8685
1
-I
6.95
i
0.9160 0.7943 83.74 0,7771 9.07 1 81.08 0.75EI 80.05 0.7388 9.15 7R.12 9.24 0.7794 $6.10 0.6994 9.33 9.39 74 09 0.6789 9 42 71.93 0,6577 9.46 69 74 0.6368 67.47 0.6144 9.43 65.12 0.5920 9.4' 62.68 0.5676 9.25 9.06 59.95 0.5424 8.83 56.97 0.5154 8.48 53.84 0 4864 8.00 50.49 0.4545 7.58 46.63 0.4216 7.01 42.39 0.3841 6.27 37.49 0,3407 5.30 J 31.67 0.2880 3.98 23.45 0.2175 8.78
9.02
100.10
85.62
:;.a
107.8 108.1
108.3 1086 108.8 109.I 109.4 109.5 109.8 110.0
110.4 II0,j 110.5
I10 7 111.1
110.6 110.3 110.0 110.0
107.8
J E. LWiZZs
410
TABLE11 Hexaniethylene
__ ~
'IG
$;as I
/
4 % 1%
__ 90 IO0 110
I20
130
140 150 160 170
I80
190 200 210
220
230 240 250
260
1
270
277 279
96.22 0.031374 86.17 0,003759 0.7003 0 004902 83.7' 0.6898 0.006289 102.03 0.79610 81.23 o 6191 0.00796S 105.01 0.74938 78.69 0.0I000 107.52 0.70695 76.01 0.01238 IIO.II 0.668~~ 73.60 0.01508 1 1 2 90 0 63349 71.52 0.6325 0.01818 115.78 060183 69.68 0.6200 0 02183 117.93 0,57314 67.59 0.6067 o 02625 119.0.i10.54721 65.15 118.62 0.52377 62.13 O.OZIA0 118.11 I0.50267 59.37 116.84 0.4835a 56.50 114.82 0.46645 53.56 I 1 0 8 1 0,45107 49.98 I5622 .o 0,5271 17961.0 0 5063 0,07496 10465 0.43732 45.76 20565.0 0.4820 0.09058 96.52 0.42504 41.02 23461.0 35 16 26680 o
[email protected] 29878.0 2735 992.34 1306.8 1691.0 2155.4 2709.1 3362.0 4124.5 5007.3 6021.9 7'99.9 8494.5 9980.2 11651.0 13526o
OC
1
6.45 8.36 8.43 8.48 8 51
8.49 8.49 8.49 8.51
8.47 8.36 8'5 7.95 7.70
7.41 7.01
6.49 5.87 5.07
89.77 0.8754 102.6 77.81 0.7369 105.6 0.7181 1048 75. 0.6990 104.1 72.75 70.18 0.6793 103.3 0.6588 102.5 67 52 6j.11 0.6378 102.1 102.2 0.6168 63.03 61.17 0.5955 102.7 59.12 0.5732 103.1 56.79 0,5494 103 4 53,98 0.5245 102.9 51.42 0.4986 103.1 48.80 0.4715 103.5 46.15 0,4427 104.2 42.97 0,4109 104.6 39,27 0.3754 104.6 35.15 0.3350 104.9 30.09 0.2874 104.7 22.85 0,2210 103.4 14.40 0.1438 100 I) 10.07 0.1026 98.1)
TABLE1 2 Fluo-benzene -
I C " -1 0.031 179
00 80
90 IO0 110
I20 130
140 150
160 170
I80
190 200 210
220 230
240 250
260
270 280
2529.5 3173.0 3931.4 4816.7 5841.6 7018.9 8963.5 9890.5 11617.0 13561.0 i 15745.0 181go.o 20924.0 23977.0 27384 0 31182.0
1
,
0.002885 0,003831 0.005040 0.006515 0.8955 0.008333 0.8811 o 01055 o 8665 0.01321 0.8519 0.01634 0.8363 0.01992 I3 0.8201 0.024 0.8037 0.02g11 0.7857 0.03496 I84 0.7671 0,04 0.04968 0 7480 0.7265 0.05907 0,7036 0,07037 o 6789 o 08403 0.6504 0.I008 0.6163 0.1226 0.5739 0.1535 0.5133 0.2034
5.65 7.10
97.67 0.70128 68 50 99.78 0.66379 66.26 0.62970 64.37 104.081 o 59878 62.32 10528 0.57076 60.09 105.84 0,54542 57.83 105.71 0.52257 55.24 10.5 43 0. j o z o z 52.93 103.97 0.48356 :0.28 101.300.46708 47.32 97.32 0.45241 44.03 91.7C 0.43941 40.29 83.50 0.42796 35,74 .0.96 0.41796 29.66 51.20 0.40928 20.95 102.23
1
7.28 7.38 7.48 7.53 7.54 7.53 7.51 7.51
7.48 7.40 7 28 7.11 6.95 6.71 6.41 6 04 5.58 4.99 4.16 2 95
81.74 0.9662 84.60 72.96 0.8405 86.80 71.69 0 8219 87.22 0.8023 86.86 0.7821 86.75 o 7611 86.29 85.69 85.03 84.63 84.73 84.74 84.70 0.5958 84.85 84.66 85.09 0.5095 85.51 0.4766
:.;$?
O.AAO0 ,, ,
o 4010 0 3541 0.2956 0.2f26
:86.58 56.; 8635
86.26 84.69
.
Molecu day
A t tract ioiz
TABLE
13
Chtor-benzene
-
1E
E
i
0'
i
'
2,56
IZO
1
1x0
190 220
230 240
1.1278 0.9836 0.9723 0.9599 0.9480 0.9354 0.9224 0.9091
720.01
938 8; 1206.0 1528.3 19128 2367.2 2899.4
I ~ O
150 160 170
I
0.0~1689 0.003409 0.004316 0~00.5394 0.006761 0.008312 0.01020
0.01240 0.01500 0.01798 5 0 ~ ~ . 80.8672 0.02145 0.8518 0.02544 5991.8 0.8356 0.03000 7059.6 0.8196 0.0354 82705 0.8016 0.0417 9639.8 I;I@,.o 0,7834 0.0492
~
i
250
101.00
0.69585 0.66150 0.63023 0.60183 0.57607 0,55273 0.53164 0.51263 0,49553
103.97 106.80 109 08 111.36 113.27 114.92 116.36 116 9 2
'
260 270
TABLE
4.82 6.70 6.89 7.08 7.14 7.26 7.31 7.34 7.34 7 34 7.31 7 27 7.22
87.72 73.77 73 37 72.89 71.26 70.28 68.77 67 31 65.65
2.2 61,10 59.65 57.93 56.06 53,95
7.12
82.90 1.0152 67.07 0.8440 66.48 0.8279 6.5 81 ' 0.8111 64.12 0.7933 63.02 0.7754 61.46 0.7566 59.97 0.73'3 58.31 0,7173 56.81 0.6964 55.29 0.6757 53.83 0.6538 52.43 0.6312 50.81 0.6075 0.5821 0.5554
81.65 79.46 80 30 81.13 80.83 61.27 81.24 81.34 81.29 81.58 81.82 82.33 83.06) 83.64) 84.33) 84.93)
14
Brom-benzene ~
i
I
I L
h
c
w'
;:
I
'-
2%
5.67 1,4815 141.23 1.3864 840.81 1.2994 1.2847 1071.6 I. 2697 '349.3 I 2534 1679.9 I. 2385 2070. I 1.2210 2527.0 1.2037 3057.8 1.1876 3670 2 1.1689 4372.5 1.1510 5173.0 1.1310 6080.8 1.1099 7104 8
30° IO0
160 170
IS0 190 200 210 220
230 210 250
260 270
'1
--__
230
1.48 50.23 787.88 990.60 1232.0 1517.1 1851.5
240
2241 2
300 IO0
190 200 210 220
250 260 270
1
,
1 1.8149 1.7079 ~
1
1
1.5627 1,5470 1.5316 1.5115 1.4941 1.4764
0.044702 0,089519 0.005255 0 006553 0.008071 0.00991I 0.0I 205
01450 0.01750 o 02080 o 02482 0
0,02927
0.03427 o 04016
cl
0.01070
0.01296 0 01552 0 , OI849 0.02 199 0.02605
$
__ __ 68.99 10.79276 72.06 j 0.75220 75.24 0 71501 77.88 I0.68085 80.49 0.64942 83.18 0.62046 84.90 0 59370 87.21 0.56895, 88 45 0.54600 9 . 0 6 0.52467 91.72 0 . ~ 0 4 8 3 ~
1
I
54.69 54.21 53.80 53.02 52.27 51.61 50.41
49.62 48.29 47.25 46.30
~
1 ~
' ,
5.07 5.18 5.29
5.35 5,42 5.48 5,48 j 52
5.49 j.48
5.48
64.84 57.86 49.62 49.03 48.51 47.67 46 85 46.13 44.93 44.10 42.80 41.77 40.82 39.60
-- I__-'O.OaI.595 0.034400 0.006020 0 007215 o.oo8R89
1
6037 63.77 66.51 6937 71.25 73.32 75.20 76.71 78.06
58,74) 56.93 54.09) 54.48) 54.98 55.21 55.45 55.91
0.8041
55.87
1
074721
45.11
0.71100
45 34 45.10 44.94 44.22 43.70 43.15 42.50 41.85
0.67797 0.64792 '0.62066 10 59602 0.57374 0.55395 10.53614
1.1039 I 0166 0,Y174 0.9000 0.8822 0.8634 0.5447 0.8250
1.1946 44.99 1.1193 44 65 09785 4r.87) 0.9624 I 6 2 661 .I 38
4.47 4.50 4.54
40.72 40.47 39.72 39.16 0.8268 1 45,Io
J. E. Mills TABLE16 Carbon Tetrachloride
1
71.08
00
I
6127
90 IO0 I10 I20
3009. I 3725.1 4559.6 5524.6 6631.9 7894.8 9326.7 10943,O 12759.0 14793.0 17066.0 19596 0 28992.0 32825.0
I .36So
I
1
1,3450 1.3215 1.2982 I 2734 1.2470 1.2192 1.1888 1.1566 1.1227 I.08c17 1.04144
1
0.8666 0.7634
0.0@984 0,007974 0.01026 0 , OI304 0.01634 o.ozo24 0.02481 0.03021 0.03650 0.04386 0.05249 0.06250 0.07418 0.08787
30.27 50.56 52.89 54.99 57 08 59,05 60.92 62.37 63.70 64.66 65.27 65.55 65.42 64.83
-
1.7135 0.89103 0.83580
51.87 45.C5 44.20
2::: 59.01
0.1040
0.1232 0.1464 0.1754 0.2146 0.2710 0,3597
~
w'
/-I-
__
-
~
d.10
3.91 3.65 3.34 2 92 2.34 1,53
55.08
48 99 39.92 26.68
~
1.1107 0,9334 0.9105 o H866 0.8623 0 8376
3.52 4,43 4.52 4.57 4.61 4,67 4.70 4.67 4.67 4.64 4.57 4.52 4.39 4.26
0.8121
25.35 23.73 21.91 19.85
'7.15 13.62 8.90
0.7860 0.7592 0.7312 0.7020 0.6714 0 6391 0.6051 0.5690 0 530' 0.4875 0,4395 0.3812 0.3063 0.2027
43.53 43.52 43.58 43.58 43.64 43.67 43.79 43.79 43.b3 43.86 43.92 44.00 44.16 44 34 44.55 44.76 44 94 45.16 44 99 44.47 43.90
TABLEI 7 Stannic Chloride Y
n8
2
c)
3
w'
35.38 31.40 30.72 30.02 29.32
2.08 2.72 2.76
~
oo ' IO0 110
I20
1
130
1
I40
150 1 160 I70 180 190
zoo 210
220
230 240
zjo 260
270
280
1
,
I,
1 1
,
5.88 498.5 672.7 891.4 1162.0 1491.0 1888.0 2359.0 2914.0 3561.0 4309.0 5168.0 6147.0 7257.0 8509 0 9915 0 11488.0 13242.0 15190.0 17351.0 ,
2.2789 2.0186 1.9916 1.9639 1.9357 1,9073 1,8772 1.6481 1.8182 1.7873 I 7556 1.7224 I , 6866 1.6488 I 6090 1.5667 1.5221
1.4747 1.4219 1.3628
I
8996 0.005764 0.007634 o 009~40 0.01276 0.01616 0.02024 0.02506 0.03077
17.84 31.89 33.24 14 54 35,82 36,95. 37.93 38.92 39.63
1.98373 0.98455 0.92427 I o 86900 0 81835 10,77193 ' 0,72941 ,0.69047 0.65482
0.077~
60.00
l0.62210
0.05450 0.06502 0.07728 o.o~r49 o 1083
40.65 40.64 40.39 39.89 38.96 37.79
i!::;
0,56504 0.54009 0,51730 0.49648 o 47748 0.46016 (0.44438 0.43001
31.38
041694
0.0
0.1280 0.1520 0.1812 0.2160
i
28.52
27.67 26.86
2:g 23.87 22.97 21.95 20.89 19.80 18.60 17.39 16.03 14 54 13.08
2.80
2.83 2 85 2.85 2.86 2.85 2.81 2 77 2.74 2.68
2.61 2.52
2.42 2.30 2.15 I .y8
1.81
33.30 28.68
;;::: 26.49 2567 24.82 24.00 23.10
22.08 21.10
20.23 19.27 18.28 17.28 16.18 15.09 13.88 12.56 11.27
1.2711 1.0845 I 0612 1.0373
26.20 26.45 26.34 26.24 26 16
0.9873 0.9611 0,9345 0.9071 0.8786 0.8494 0.8195 0.7882 0,7554 0.7212 0.6847 0.6463 0.6045 0.5586 0,5087
26.00
1.0126
25.82
25.68 25.46 25.13 24.84) 24.68 24.453
;::;:]
;::2j 22.96) 22.47) 22 15)
MoZecu Zar Attraction
413
TABLE18 Water
___
E
P t 00 IO 20
30 40 50 60
70
80 90 IO0 I10 120
'30 140 '50 160 170 I80
190 200 210 220
230 240 250
4.569 9.140 17.363 31.510 54.865 91.978 148.88 233.302 354.873 525.468 760.000 '075.37 1484.0 2019.0 2694.0 3568.0 4652.0 5937.0 7487.0 9403.0 1625.0 j365.0 0936.0 50'9.0 9734.0
260 270
Pi 0.9997 0.9982 0,9957 0.9923 0.g881 0.9833 0,9779 0.9719 0.9655 0.9586 0.9512 0.9441 0.9365 0.9283 0.9193
::%;$ 0.8881 0.8766 0.8646 a=-"
0.0e9200 0.0~1699 0.042995 0.045071 0.0~8278 O.OSI303 0.031g8g 0 082952 0.0~4273 0.0,6031 0.038389 0.001138 0.001522 0.002000
0.002592 0.003313 0.004181 0.005216 0.006439 0.00785: 0.00950f 0011 0
0.8256 0.8117 0.7980 0.7840
0:013%9 0.01632 0.01944 0.02315 0.02766
506.5 599.5 jg2.6 585.7 j78.6 j71.6 564.7 557.6 550.6 543.5 536.5 529.4 522.3 515.1
30.7 31.6 32.5 33.5 34.4 35.4 36.3 37 3 38.2 39.1 40.1 40.8 41.4 42.1 42.8 43.7 44.5 45.0 45.4 46. I 46.7 47. I 47.8 48.4 47.8 47.5 46.8 45.6
508.0
500.7 493.6 486.2 479.0 471.6 464.3 456.8 449.4 441.9 423.8 410.4 394.0 374.5
575.8 567.9 560. I 552.2 544.2 536.2 528.4 520.3 512.4 504.4 4964 488.6 480.9 473.0 465.2 457.0 449.1 441,2 433.6 425.5 417.6 409.7 401 6 393.5 376.0 362.9 347.2 328.9
0.9831 0.9790 0,9737
585.7) 580.1) 575.2) 0 9675 570.7) ~ 9 6 0 4 566.6 3.9524 563.0 J.9437 559.9 3.9342 556.9 J.9240 554.5 0.9131 552.4 o.go15 550.6 0.8892 549.5 0.8766 548.6 0.8634 547.8 0.8495 547.6 0.8349 547 3 0.8198 547.8 0.8040 548.7, 0.7878 550.4 0.7711 551.8 0.7539 153.9 0.7363 556.4 0.7182 559,1 0.6989 ,563.0 0.6791 553.6 0.6586 551.0. 0.6371 544.9 0.6162 535.5)
TABLE19 Methyl Alcohol __ I
PI 2
,x
.$ u
e" 00
IO 20
30 60
'n
Y yl
Y
e$ n+
I
a
E CI
$
u
Y
- 3 ; s 29.6 54.7 96.0 160.0 260.5 406.0
0.8101 0 8000
625,o
0.7555 0.7460 0.7355 0.7250 0.7140
926.6 1341 0 1897.0 2621.0 3561.0 4751.0 6242.0 8071.0 10336.0 13027 0 16292.0 20089.0 24615.0 29787.0 35770.0 42573.0 46297.0 50414.0 52202.0
53939.0 55624.0 57576.0 58329.0
0.7905 0.7830
E:;:$
0.7020
0.6goo 0.6770 0.6640
3;:;
0.6160 0.5980 0.5770 0.5530 0,5255 0.4900 0.4675
0.4410
0,4295 0,4145 0.3955 0.3705 0.3635
0.0~5620 o.oagg60 0.0~1695 O.Oy2772 0.0~4394 0.0~6739 0.001006 0.001465 0.002084 0 .oozgoj 0.003984 0.005376 0.007142 0,009379 0.01216 0.01562 0.01994 0.02526 0.03186 0.040 IO 0.05075 0.06521 o 08635 0.1003 0.1187 0.1277 0.1381 0.1505
0.1681 0.1789
289.17 287.36 284.54
1 $ 8
16.77 17.48 18.03 282.07 18.37 277.78 18.87 2 j 4 . i4 '19.16 269.41 19.15 266.~1 20.I O 258.96 20.43
263.70 258.91 254.98
232.00
211.0s
304.7 306.0 306.6
2ao.66
0.8565 0,8423 0.8269 0.8106
1
224.07 216.12 206 13 I 834 188.25 177.16 165.64
20.95
20.88 20.74 20.55
20.15 19.70 19.01 18 18
203.1g 195.38 185 58 178.19 168.55 156.15 147.46 134.87 119 49 99.61 87.96 74 60 68.59 61.86 54.39 44.26 38.96
0.6672 0.6424 0.6160 0,5879
0 557s 0 5255
0 4902
0.4506 0,4045 0.3464 0.3114 0.2697 0.2509 0.2287 0.2020
0.1663 0.1502
j07.9 307.4 308.3 308.0 308. I 307.8 307.1 306.3 306.0 305.4 304 5 304 1 301.3 303.1 302.3 300.9 300.8 299.3 295.4) 287.6) 282.4) 276.5)
I;:;:
269.2) 266.1) 259.4)
,
\
J. E. Mill's
414
TABLE20 Ethyl Alcohol
~
IC
+I IW
k __ 00
IO 20
30 40 50
60 70
80 90
IO0
I10 I20
130
140 150 I 60
170 I80
I90
12.24 23.73 43.97 78.11 I33,42 219.82 350.21 540.9' 811.81 1186.5 1692.3 2359.8 3223.0 4318.7 5686.6 7368.7 9409.9 II858.0 14764.0 18185.0
200
22182.0
210
26825.0 32196.0 I 38389.0 1 45519.0 46288.0
220
230 240
241 242
0.7722
~
0.7633 o.ji46 0.7348
0.3825
0.3705 0.1546 0.&9
I
12.6
220.I
13.0
7
,
14.5
'97.' 190.3 184.2
~
184.7 156.9 148.4 139.2 128.4 116.6 103.2 88.2 70.6 403 35.0 28.4
1 1 1
1
209.2 209.0 208.0
207.1 205.3 202.2 199.2
195.4
14.8 15.0 15.3
1
191.6 186.6
15.4 15 4
I
174.9 168.8 162.1
15.5
2;:
1
13.4 13.8 IA.2
201.6
0.014&
II
12.2
220.6 218
0.01152
0.01916 0.02446 0.03115 0.03970 o.o$080 0.06550 0.08540 0.1135 0.1715 0.1835 0.1990 0.2164
11.7
221.2
216.0 213.4 209.9 206.4
o.o%i90 0.001740 0.002500 0.003510 0.004860 0.006580 0.008770
0.7251 0.7157
0.7057 0.6925 0.6789 0.6621 o 6489 0.6329 0.6165 0.5984 0.5782 0.5568 O.Zi9I 0,4958 0.4550
O.OS3i50 0.0~5060 O.On7400
0.7561
220.9
181.8
0.8986 0.8879 0.8761 0.8633 0.8494 0.8342 o 8178 0.8004 0.7821 0.7627 0.7425 0.7209 0.6973 0.6727 0.6461 0.6198 0.5910
14.8 14 3
;;,;
133.6 124.9 114.8 104.0
0.560X 0.5281 0.4919 0.4523 0,4057 0.3511 0.2849 0.1703
0.1499 0. 1239 0.0989
22.1
232.8)
235 4 2.17.4 239.9 241.7 242.4 243,6 244.1
244.9 244.6 244.8 242.7 242.1
241.0 2AI.O
241.1 239,8 238 2 236.5 233 3 ) 230.0)
226.3) 223.0)
219.7) 209 2)
206.81
202.6) '97.2)
TABLE2 1 Propyl Alcohol __ ~
C
c
c"c E *
00
80 90
IO0 I10 I20 130 140
150 160
3: I90 200 210 220
2.10
240 250 260
?.Ad
379.0'
574.0
841.5 1206 o 1683.0 2293.0 3074.0 4052.0 5264.0 6695 0 8383.0 10466.0 12801.0 15575.0 18679.0 22154 0 26194.0 30785 0 36103.0
0.8193 0.7520 0,7425 0,7325 0.7220 0.7110
I
5
__ o.op1212
Iq4.4-
0.00104
I g.0
0.00320
142.4 135.3 129.0
12.0
122.8
11.9 11.9 11.7
116.3 1m.6
11.4 11.4
0.1610
185.4 161.5
1
33.5
152.2 147.1 141.0 '35.0 130.4 123.4 117.1
111.1
0.9127 0.8081 0.7895 0 7702 0.7497 0.7284 0.7055 0.6822
0.6571 0.6308 0.6014
203.1
199.9 199.2
; f?: 193.6) 191.3) 191.1) 187.8) 185.6)
184.1)
10.8
;E$ 178.6)
10.4 9.6 8.7 7.5
176.6) 173.2) 168.8) 164 1)
4.2
157.0)
6.2
0.3905
~
157.3
0.6995 0.6875 0.6740 0.6600 0.6450 0.01770 ,.
{
cl
0.00156 0.00226 0.00443 0.00605 0.00805 0.01060 0.01380
$ I ! . .e
160.2)
TABLE22 Acetic Acid ~
I' I 41%
w' 1.0491 I,0392 1.0284 1.0175 1.0060 0.9948 202.3 0.9835 293.7 0.9718 4'7.1 0.9599 580.8 0.9483 804.0 0.9362 IO8Z.O 0.9225 1431.0 0.9091 1863.0 0.8961 2392.0 0.8818 3034.0 0.8688 3809.0 0.8554 4735.0 0.8417 5836.0 0.8264 7134.0 0.8117 8655.0 0,7943 10426.0 0,7758 12475.0 0.7576 14832.0 0.7358 17527.0 0.7138 20590.0 0.6896 24055.0 0.6596 27951.0 0.6337 32312.0 0.5956 37168.0 0.5423 42550.0 0.4615 11.73 20.61 34.77 56.56 88.94 136.0
4.88 5.19 5.17 5.81 6.12
0.047645 0.0~1264 0,032012
0.033100 0.0~4621 0.0~6729 0.039588 0.001338 0.001833 0.002468 0.003271 0 004275 0.005516 0.007032 3.008873 s.01084 3.01370 3.01681
.. . .... ....
.... .... ....
90.43 91.59 91.88
8.21
134.23 0.62709 84.17 ~
3.03021
3.03626 1.04327 3.05163 1.06165 7.07364 3.08834 1.1073 3.1331 1.1718 ).2591
2:;
6.98 7.23 7.47 7.79 8.02
3.02052
9.024b8
Ib
~
-1-1-1 200
137.82 139.43 139.69 138.42
0.58171 0.56084 0.54097 0,52199
80.16 78.18 75.55 72.26
8.37 8.49 8.80 8.70 8.78 8.83 8.85 8.77 8.72 8.64 8.50
8.26 7.95 7.50 6.89 6.00 4.71 2.29
79.17 80.69 81.85 82.33 83.57 84.00 84.88 84.90 85.09 85.32 86.59 85.09 83 62 82.37 81.14 81.85 79.01 77.97 76.72 75.32 73.25 71.44 69.54 67.05 64.00 60.37 55.89 50.32 42.95 33.06 15.75
0.9737 0 9627 0,9507 0.9381 0.9247 0.9107 0 8959 0.8803 0.8641 0 8474 0.8298 0.8112 0.7920 0,7725 0.7519 0,7329 0.7100 0.6880 0.6646 0.6409 0 6147 0 5879 0,5605 0 5304 0.4986 0.4643 0.4251 0 3837 0.3308 0 2595 0.'353
81.3 83.8 86 I 87.8
90.4 92.2 94 7 96.4 98,5 100.7
104.3 104.9 105.5
1066 107.9 111.7 111.3
113.3 115.4 117.5 119.1 121.5 12a.1
126.4 128.4 130.0 '31.5 131.2 129.8 127.4 116.4
8
