ON A THERMODYNAMIC MEASURE OF THE DEGREE O F POLYMERIZATION O F LIQUID SUB-
STANCES BY M. M . CARVER
Introductory A t the present time physical chemists are dependent almost entirely upon two general sources for, their knowledge of the molecular constitution of liquid substances; (a) the remarkable generalizations of van der Waals and the experimental results due to many investigators embodied in the numerous tests of the van der Waals equation, and ( b ) the monumental experimental work of Sir W. Ramsay and J. Shields' in connection with their modification of the equation of Eotvijs. These two sources of information, each interpreted in connection with the corresponding experimental data do not always lead to consistent results, although both agree in attributing to special classes of liquids a considerable degree of polymerization. I n the interest of pure science it is very desirable that a reliable criterion of the molecular changes accompanying the process of condensation from the vapor to the liquid phase should be established. The theoretical foundation of the method of Ramsay and Shields is not fundamental and when accepted a t all, is accepted as open to doubt. In the first place the latter method, based as it is on the surface tension of the liquid, is capable of giving only relative values as compared with certain substances taken as standards because they agree with each other in possessing the same surface-tension-temperature characteristics. But what proof is there that the half-dozen standard liquids are not polymerized? The van der Waals equation was originally based on the principle of continuity between the vapor and liquid states on the assumption that there is no material molecular change Zeit. phys. Chem.,
12,
433 (1893).
Polymerization of Liquid Substances
45 5
accompanying the transition from vapor t o liquid and vice versa. Latterly, van der Waals has concluded’ that all substances in the liquid phase must consist, more or less of polymerized molecules. This latter conclusion is a t variance with the Ramsay and Shields’ criterion. The subject is then in a somewhat unsettled state so that a reliable criterion containing only assumptions that may be regarded as experimentally established and in accordance with the principles of thermodynamics and the accepted laws of energy, cannot fail to afford interesting results. The present paper is an attempt to establish such a thermodynamic criterion. The degree of success of the attempt must be determined solely by its consistency with, and ability to explain, experimental facts and obvious deductions from those facts. Whether tenable or untenable as a theory, the facts and deductions upon which the theory is based seem to justify at least a careful consideration before a final judgment is passed.
The Theoretical Exposition In a recent paper on the “Range of Molecular Action and the Thickness of Liquid Films,”2 it was shown that for a number of substances representing different classes of chemical compounds and for a considerable range of temperatures the surface tension of the liquid phase per unit area of crosssection is practically equal numerically to the pressure the substance would exert if it were a perfect gas. In the same connection it was shown that both the thickness of the liquid film and the molecular attraction in the film vary with the temperature. Hence the surface-tension is a function, not of the temperature alone, but of the thickness of the film as well, or, mathematically expressed, (A)
where
’
r
is the experimentally observed surface-tension, T the
Die Zuskmdsgleichung. See remark by Prof. Bancroft: Jour. Phys. Chem., 15,882 (1911). Jour. Phys. Chem., 16,234 (1912).
M . M . Garver
456
computed thickness of the liquid film, p the density of the liquid, m the molecular weight of the substance as a vapor, R the gas constant and T the absolute temperature. If this equation be analyzed and studied in connection with the established numerical relations of the experimental facts it shows that the value of the ratio p/m i s independent of polymerization. For i t holds true for widely different sorts of substances and, so far as tested, for considerable differences in temperatures. Since m is the molecular weight of the substance in the form of vapor and p/mRT gives the surfacetension per unit area of cross-section we have the striking R fact that p - T, the pressure per unit area the substance would exert as a perfect gas, is numerically equal to the tension per unit area exerted by the liquid film. If the number of molecules per unit mass is different in the two phases, liquid and vapor, and p
5 T r m RT, m
then it must be true that any
variation in the numerical value of m, the molecular weight, merely changes the density p in the same proportion. This peculiarity in turn becomes explicable and consistent with the experimental facts if we assume the applicability to both liquids and gases of Maxwell’s law of distribution of molecular energies. This is that m 1u1 --
mZu: =
m3u;
=. . . . . .
or, that the translational energy of the molecule is independent of the mass of the molecule and of the phase of the substance, but is proportional to the absolute temperature. An interesting experimental verification of Maxwell’s law is given by Philip Blackman,’ who uses it t o determine the relative molecular weights of dissolved substances. If Maxwell’s law holds, and it seems necessary to assume its truth in order t o understand the above-mentioned characteristics, then when two or more molecules coalesce to form one there is a change in the total volume with a correspondJour. Phys. Chem.,
15, 866 (1911).
Polymerization of Liquid 'Substances
457
ing change in the density but no change (if the temperature be kept constant) in the average energy of translation per molecule, while there is a change in the aggregate molecular kinetic energy, E1/,muz because the total number of molecules has changed. The effect of the change in the number of molecules by polymerization during an isothermal process involving an increase in the density woiild, with a given volume of a gaseous substance, be to diminish the outwardly directed pressure per unit area to something less than would have been found with the original number of molecules. Or, we should infer that the external pressure necessary to compress a gas or vapor would increase more slowly when there is polymerization than when there is no polymerization, but molecular attractions only. For suppose polymerization in a vapor to take place a t a certain definite minimum molecular volume which we will assume is a function of the temperature; then any decrease in the aggregate volume a t that temperature must necessarily bring about a decrease in the number of molecules instead of an increase in pressure, for the pressure could not be increased without diminishing the average molecular volume of the vapor which we have supposed t o have reached a definite minimum. This is exactly what we observe in the so-called saturated vapors,there is a definite maximum pressure and minimum volume corresponding t o each temperature. Hence at this particular temperature the pressure per unit area will remain constant although the aggregate volume may be steadily diminished because there is a corresponding decrease in the average molecular volume, either by supersaturation (i.e . , polymerization) or liquefaction. This view of the function performed by polymerization as a preliminary to change of phase from the vapor to the liquid furnishes a rational explanation of the experimentally observed rectilinear portion of an isothermal curve and eliminates two of the three values for the volume in the reflexed theoretical portion of a van der Waals isothermal. This
458
M . M . Garver
cubic curve arises from the theoretical assumption that the liquefaction takes place in consequence of the action of molecular forces which are proportional t o the square of the density. But from equation (A) for the surface-tension, if T is the thickness of the superficial layer, it is evident that the attraction in the film is proportional to the density and not to the square of the density, so that van der Waals’ assumption that the molecular attraction may be represented by a/v2 cannot be maintained as in accordance with the laws of molecular attraction. If the force action be directly proportional to the density, and a polymerized molecule occupies the same vplume as a simple molecule, then both density and surface-tension are linear functions of the polymerization. If molecular volumes are limited to a minimum value then the only remaining way the density can be increased is by the union of molecules. But from Maxwell’s law a union of molecules implies that, when the temperature is constant, internal molecular energy must leave the system; and from Clausius’ virial, an equal amount of molecular potential energy must escape from the system with the molecular kinetic energy. If, then, it be found that the heat given out during the change of phase from vapor to liquid is in excess of the equivalent of the work done by all the forces, external or internal or both combined, we must conclude, if the process be isothermal, that a portion of the internal molecular energy has left the system as heat because the actual number of molecules has decreased. I t is evident, then, that if we can determine experimentally the total heat given out during an isothermal process and can otherwise estimate how much of that heat is equivalent to the action of any forces concerned, then the excess of the heat over that which can be attributed to work done by forces, external, internal, or both combined, must be due to a decrease and consequent union of the molecules concerned, i. e., to polymerization.
Polymerization of Liquid Substances
459
Theoretical Summary If the molecular forces are directly proportional to the densi ty-and the evidence seems incontrovertibly to prove that such is the case-then we have in liquids exactly the same law of force-except as to sign-that holds for a perfect gas. Then in order to determine the proportion of the heat of vaporization that is due to the action of forces and that due to polymerization, it will merely be necessary to compare the experimentally found heat of vaporization with the heat equivalent of the work required to produce the same change in density in the given substance on the assumption that the force varies directly as the density. Hence if the preceding statements can be established as legitimately deducible from undoubted experimental facts, then it follows as a consequence that during a n isothermal change in the density of a n y fluid substance accompanying a change in the volume, the heat given out or absorbed during such process will exceed the heat given out or absorbed by a perfect gas of the same molecular weight by a n amount exactly equivalent to the polymerization or change in the number of molecules. This statement may be expressed mathematically by the equation 1
H=I,-JP~~ I
where H represents the heat of polymerization, I, the experimentally determined heat of vaporization, and the integral 2
P d v represents the work in calories required to produce I
isothermally the same change in density in a perfect gas of the same molecular weight and temperature. For from Maxwell’s law the internal kinetic energy of a fluid is proportional t o the absolute temperature and is independent of the volume provided the number of molecules remains constant. Hence, also, the amount of heat given out or absorbed in an isothermal change in volume, or change in density, must be independent of whether the force be an external pressure or an internal attraction or both combined so long as there is
M . M . Garver
460
no change in the number of molecules,-the only effect of internal attractions being t o reduce the amount of external pressure required. Otherwise expressed, the work 2
W=
2
( p + y)dv =
I
P dv I
+
if ( p y) = P, where P is a force equivalent to the externally applied pressure p , and the internal attraction r. I t has been shown that we may substitute an ideal gas pressure for the actual, combined, pressure and attraction because the pressure exerted by a molecule-as a vapor is numerically equal to the attraction of a molecule of the liquid quite independently of whether the vapor molecule constitutes the whole, or only a part, of the liquid molecule. It is then immaterial whether we ass’ume all the forces to be external pressures or internal attractions, since the heat equivalent of the work due to the forces i s independent of whether the force is a n externally applied pyessure or a n internal molecular attraction, irrespective of all polymerization in the molecules that cause the attraction. This being established, it follows that the ratio L r = ____ 2
Pdv I
will be unity for an isothermal change in volume from a vapor t o a liquid in which there is no change in the number of the bi molecules concerned in the process. Unfortunately the value of H as thus determined, being a pure energy relation, does not lend itself directly and readily to the determination of the molecular weights of liquids as compared with the molecular weights of the corresponding vapors, but the relative values themselves are interesting and instructive. Also when applying the theory it is necessary to take in to consideration the principle disclosed in Clausius’ theorem of the virial, that in the case of a liquid one-half the excess heat given out represents potential energy and onehalf kinetic. That is, with the disappearance of the molecular
Polymerization of Liquid Substances
46 1
kinetic energy from the substance, molecular forces to the same extent also disappear, for when the molecules coalesce the potential energy due to molecular attractive forces also disappears to, the same extent. Since the whole theory turns on this point and is likely to be misapprehended, some additional discussion is necessary before proceeding to illustrative applications of the theory.
Some Points of Conflict with the Current Theory The view of polymerization and of the relation the energy changes bear to polymerization presented above is of course incompatible with that conception of the kinetic theory which regards molecules as spherical masses necessarily separated from each other by a distance equal to the two radii and that they collide and rebound from each other like billiard balls. On the contrary, it seems to me that the experimental facts indicate that the union of two molecules to form one molecule requires us to conclude that the two molecules after union have the same center of mass, so that the two molecules after union occupy only the amount of space, or volume, previously occupied by each constituent separately. The more recently developed corpuscular, or electronic, theory of the atom necessitates this view of a molecular union, and consequently leads to a different interpretation of the b in the factor (v-b) of van der Waals’ equation. Coalescence, or polymerization, of molecules affords us a perfectly rational explanation of the difference in behavior between gases and vapors and accounts for the fact that less external work is required to produce a given increase in density in a vapor than in a gas, and that a larger quantity of heat is given off by the former than can be accounted for by the work done on the assumption that the number of mokcules remains unchanged. Again, consideration based on the relation of potential to kinetic energy in such a molecular system must lead to a revision of the conception of intrinsic or molecular pressure. When two pr more molecules unite to form a single molecule
462
M . 111. Garver
there is no physical thing remaining that can be made to represent, or be interpreted as, a pressure. The pressure per unit area exerted by, and the attraction per unit area between, polymerized molecules seem t o be unaffected by the polymerization even though the polymerization increases the density. So long as forces exist between molecules pressure may be used to represent the force relation; but when two molecules unite to form one single molecule one-half the sum of the two energies in a n isothermal change must leave the system as the molecular energy of heat. There remain, then, no forces to represent a pressure,-the molecular kinetic energy of the vanished molecule with its complement of potential energy having left the system as heat nothing remains but an increased density t o represent the decrease in the number of molecules. In a fluid system of discrete flying corpuscles there is nothing corresponding to a static pressure. If the molecules are close enough together to be held partially by the molecular forces the external pressure required is merely diminished ; but when two molecules unite, the internal tension or force acting between them disappears simultaneously with the distance as the molecular energy of heat. The hypothetical distance between molecules involving, mathematically, an infinite force when the distance becomes vanishingly small, simply does not exist when molecules unite because they then both possess the same center of mass without leaving anything to be represented by the force function except the change in density and the heat that is dissipated when they unite. A careful consideration of the experimental evidence will show that the use of the pv function to represent the energy changes caused by the changes in the number of molecules due to polymerization is as impossible to interpret in terms of pv as the union of hydrogenand chlorine in terms of pv where there is no change in the volume of th'e constituents, since in the case of polymerization we do not know what aggregate amount of volume change is introduced by the polymerization. In each case the energy takes the form of heat and leaves the system; hence all expressions of such energy
Polynzerizatiolz of Liquid Substances
463
changes in terms of changes in p and v must be more or less illusory. However, since energy in whatever way expressed must have the same dimensions in the fundamental units, pv may be used and may be made to yield consistent numerical results even in cases where the symbols separately have no physical meaning as in the osmatic theory of electromotive force. The frequent references in the current literature to the molecular pressures in liquids and solids involving pressures running up to hundreds of thousands of atmospheres, and even in one case, to millions,’ cannot represent any real physical quantity because the assumed force function is erroneous.
The Present Theory Supported by Recent Osmotic Theory If there still remains any doubt as to the validity of applying the equation of a perfect gas to the work done by the forces concerned during an isothermal change in volume from a vapor to a liquid, the attention should be directed to what is known as the van’t Hoff equation for osmotic pressure and to the equation for the work done by osmotic pressure. Here the work is due to the molecular pressure of a liquid and is given by an equation identical in form with that required to express the work done by a perfect gas. The present writer has given a rigid thermodynamic proof2 (the only one, so far as his knowledge goes) of that which the labors of Professor Morse and Dr. Frazer3 had already conclusively established experimentally, that the volwnie in the equation UT = pv log, 3-,2 Vl
where p is the osmotic pressure, really refers to the volume of the liquid solvent and not to the volume of the solute; and as thus interpreted is not confined to dilute solutions. In a later paper (1. c., p. 651) it was shown that “the volume con-
-_
~I
For a resum4 see W. C. Lewis: Trans. Faraday S O ~ .7,, 94 Jour. Phys. Chem., 14,260 (1910). -4m. Chem. Jour., 36, 39 (1906).
(1911).
M . M . Garver
464
cerned in osmotic pressure is the volume of the solvent inN creased in the ratio - while the pressure is diminished in the 12
n ratio N’
This is equivalent to ascribing to the one-rtth part
of the solvent a volume n times as large as it actually occupies with a corresponding diminution in pressure.” The present proposal is then merely extending to the whole liquid what has been experimentally and theoretically established for years and has given satisfactory and consistent results when applied to the one-nth part of the liquid solvent. This evidence taken in connection with the additional evidence that the attractive forces in a liquid film may be expressed in terms of the pressure which the substance would exert as a perfect gas seems to establish conclusively the validity of the proposed application.
Illustrative Applications In accordance with the theory above presented as to the relation of the heat liberated to the molecular change which takes place when a substance passes from the vapor to the liquid phase, a few examples representing different sorts of chemical compounds will be calculated so as to indicate the method and determine the numerical results. Since, as stated above, the value of H being a pure energy relation, it remains to express it as a function of the change in the number of molecules. In order to do this satisfactorily, data are necessary which are available in only a comparatively few cases. As a first illustration we shall take the case of water a t o o C. Since in all the cases to be considered the mass will be unity, we may substitute the reciprocal of the volume for the density, ,and vice zleysa, depending upon which value is most readily available. Also in order to avoid the use of double, negative signs, the order of integration limits will be reversed, when necessary. The volume of I gram of saturated vapor of water a t ob C is 204,000 cc. The liquid density will be taken as I . The intrinsic pressure of liquid water a t oo C or 273’ A is 1 2 3 5
Polymerization of Liquid Substances
465
atm., as calculated from ET. L the heat of vaporization exm
pressed in ergs will be 606.5 X 4 . 2 X IO'O ergs. The value of
10' ergs =
2.543 X
204,000
I" P
- T .v_ = 1 . 5 2 4 x 1 o l O e r g s
?n
=
W (say)
1
Hence r
=
L
w
=
2.543 1.524
= I
.67, and H
='
(2543-1524)
IO'
ergs. The ratio r will be found the more convenient value to use as a check. In order to simplify the discussion H may be expressed in calories. Hence since H = I, - W = 1019 X IO' ergs, 243 may be taken as the number of calories representing the excess heat given out over and above all the work due to forces, external and internal, done upon the substance. From the preceding theory, this excess must be attributed to a decrease in the number of molecules. To determine approximately the molecular change we may apply Maxwell's law, writing E, and E, for the molecular kinetic energies and n, and nzfor the relative number of molecules. That is, we must have, if x = nJn,
The value of H = 243 calories may be taken as representing 2 (E, - EJ. Hence an assumption as to the relative number of molecules enables us a t once to calculate E, ip calories, and such calculated value must, a t least, not be inconsistent'kith experimental facts. If we assume that the molecule of water has the formula 4(H,O) as indicated by Ramsay and Shields in their determination, then n2 = l / * n 1 ,so that
or the total molecular energy remaining is 81 calories. Now
M . M . Garver
466
we know that water in freezing gives out about 80 calories per gram while the specific heat drops to about one-half its former value. Therefore no assumption making the residual molecular energy of the water a t oo C less than 160 calories could be entertained as agreeing with the experimental facts. The total energy may be more but probably not less than 160 calories. If we suppose the specific heat of ice to be the same a t low temperatures as a t oo C the total residual molecular energy might reach 216 calories. The value of
x(
=
"),
when we write
2E2 =
160, is 2 . 5 and for
2E2 =
n2
216, x
= 2.1.
In case no other limit as to the residual molecular energy is available an upper limit may be obtained by assuming that the total residual molecular energy of a liquid cannot exceed the product of the specific heat and the absolute temperature. In this case the value of x may possibly be too small but is probably not too large. If we apply this criterion to water a t o o c we get 243
=
x -
1
... x
= I. 9
273 (nearly). Of the three values for x the second seems the
most probable and is also almost exactly the mean between the other two. It should not be overlooked in this connection that the value of x as above determined shows only the change in the number of molecules. In the case of acetic acid, for instance, L = Y is only I . 3 a t the normal boiling we shall find that W point. From Ramsay and Young's value' for the vapor density' it may be seen that the molecular weight is. already 1.7 x 60. Hence the molecular weight of the liquid way be considerably over twice the molecular weight of the normal vapor. We may next consider water a t its boiling point. The data required are I, = 537 X 4 . 2 X 107 ergs = 2255 x 1 0 7 and Winkelmann's Handbuch: Il.'iivme, p. 1050.
Polymerization of Liquid Substances 2
I
H
467
1650
I .093
I,- W = 537 - 300 = 237 calories. To find x or the ratio nJn, we may take the residual
=
energy zE, as roo cal. greater than a t 0'. The most probable value a t oo was 216 cal. Therefore we may assume 316 from 1 . 7 5 , a value which should be compared with the mean or most prsbable value a t oo, 2 . I , showing, as should be expected, a consideFable decrease. It is evident that to interpret the value of the excess heat, H in terms of molecular change, some clue as to the value of the residual energy 2E, is necessary, or a t least some experimental grounds for an assumption. In the case of water the evidence seems to be convincingly strong against the possibility that the molecular weight of liquid water can reach a value as great as 3 X 18.' If the present molecular theory is confirmed by further investigation and expeL as indirience,' then a t least we may rely on the value r = W
cating a degree of polymerization if r > I , for if there were no polymerization the ratio should be unity. To emphasize this point, this ratio for as many of the Ramsay and Shields standard liquids as data can be found for, will be computed Unless a very curious and interesting hypothesis is tenable, if the molecular weight of liquid water a t o o C is taken to be H,O, as found by R. and S. it makes the residual molecular energy just 8 0 calories. If we assume that the kinetic energy of solids is entirely atomic as compared with the molecular energy o f fluids, we are led to a confirmation of the result found by Ramsay and Shields. Other indications based on kinetic considerations seem to confirm this low value for the residual molecular kinetic energy of liquid water a t o o C. Since the foregoing was placed in the printer's hands the supplementary paper by Dr. Ramsay in Zeit. phys. Chem., 15, 106 (1894) has come under the writer's notice. The previous results are considerably lowered and the value of .x for water a t o o C is given as 1.707 and compared with Dr. van der Waals' value of 1.9 for the same quantity. The latter value 1.9 agrees with the minimum value found by the present writer.
M . M . Garvey
468
and exhibited separately. In addition data can be found for a few acids, alcohols and esters for which the value of I, will be appended in a table. W
Y = -
The formula Log W
=
+ log (273 + t ) + log log a - log m,
0.6570
giving W directly in calories and requiring only an ordinary 4-place table of logarithms, is convenient for use in the actual computing. The first five of the following six substances are all included in those assumed to be non-associated and which were used as standards or ?zorms in their extensive and valuable work above referred to. No data are available for their sixth substance, chlorbenzene. Carbon bisulphide, which they also find to be normal, or non-associated, is substituted in its place: ___ , I Calories Substance
I
p
Ethyl ether m = 73.6 Methyl formate m = 59.6 Benzene m = 77.4 Ethyl acetate m = 87.4 Carbon tetrachloride m = 153,~ do
10.695 1 10,955 lo. 0024 lo. _ _ _813 10.0027
10.830
lo,
r=
'4.594
/o-ooos ~1.48
-l(k-o.*) 4 W
___
2.03
1.97
110.0
1.82
1.84
80.0
93.5
1.82
1.90
77.0
92 7
2.11
2.03
20.0
51.1
28.6
77.0
44.3
25.1
35.0
90.0
31.8
44.3
0032
Carbon bisul- I - '1 I .26 phide 75.5
,Temp.
u
/ O . 0055
=
I
Heat t L I I _____ __
m =mol. wt. 1
45.7
'
I
22.5
, 1.79
19.2 1 1 . 7 6
I
.g1
1.91
I
88.0
20.0
IO. 0012 r
7
The present criterion,
y
=
5,indicates that all these w
substances contain a large proportion of complex mole-
Polymerization of Liquid Substances
469
cules. Ramsay and Shields’ criterion, k was assumed to be normal when it had the value 2 . 1 2 . Their value of k for the five substances, each diminished by 0 . 2 , is shown in the last column. The two sets of criteria, after deducting the constant difference, do not differ from each other as much as they differ among themselves. It is hardly possible that this peculiar agreement can be purely fortuitous. It seems much more probable that the observed agreements and differences arise from the accidental variations in the different estimates of the same quantities. For such they are. k is the ratio of two energies and r is the ratio of two energies; and both were deduced, although from different viewpoints, with the same value as the ultimate expectation. Both ratios, however, remain to be interpreted. Neither gives the polymerization directly. The surface-tension is a function of the density; and the density in a given substance is, in part, proportional to the polymerization. Hence it seems possible. to express the polymerization as a function of the critical temperature; and that is what the Ramsay and Shields formula actually does. The two theories, then, instead of being in opposition, as a t first appeared, really afford each other mutual support. To be accurately compared the values of Y and k should represent the same temperatures. The value of b is determined from
where y is the surface-tension, (p)the volume of a gram mol, T a temperature difference measured from the critical point, and d a constant to be determined for each substance. It is not intended at present to discuss the relation of the two theories further than to call attention to the fact that they are not necessarily antagonistic. In conclusion, attention may be directed to the three necessary, experimentally determined values required by the present theory-the ratio of the two densities, p/o, the heat of vaporization, and the corresponding temperature, The separate densities need not be known, hence the method of
M . M.Gaiver
470
Sidney Young1 which gives this ratio directly and accurately without necessarily determining the separate values is particularly applicable. Different observers frequently give quite different values for the heat of vaporization, L. The temperature may easily be observed with sufficient accuracy, since a whole degree variation would be unimportant as compared with the accuracy attainable in the other quantities. The heat of vaporization L has been found for a large number of substances; also the densities for most liquids and for many vapors. But I can find the necessary complete data mentioned above for comparatively few substances. The value of
Y =
4
-
W
for such substances whose data are
accessible to me will be computed and appended. I f
DATA A N D ADDITIONALVALUESOF W ________-___-
Substances
I
r = -L
wt.
L ~
66
.
0.75
~-
0.00128
Ethyl alcohol
46
7 8 . 4 0.74
Propyl alcohol
60
97.4
0.737 0.00202
118.0 0.938 0.0031 2 982 101.3 140 Propyl acetate 1.27 Methyl propionate 8 7 . 4 7 9 - 7 I . 3142 189 Water
18
1 18
Water
_
I34
2O~OOO? 0
IO0
I
_ I
.96
5.37
0.0017 I
60
Acetic acid
262
W
W
166.8 1 7 1 . 8
2.32
97.0 176.3
1.27 2.11
89
44.3
606.5
363
1650~ ____ 1.043
State College, Pa.,
Afiril 6, 1912 Phil. Trans., 178,go8 (1891). Winkelmann, p. 934. Ratio of specific volumes.
2.10 I
.67
1.79
