MOLECULAR ASSOCIATIOX O F LIQUIDS BY DANIEL, TYRER
In a previous paper' a study was made of the various methods of determining the association factors of liquids which have a t various times been proposed, and it was shown that there does not exist a reliable method by which the molecular weight of an associated liquid may be determined. Each method was shown t o be founded on untenable assumptions. Also several conditions were established which any equation employed to determine the molecular weight of an associated liquid must follow. In the present paper it is proposed to extend this study to several other methods that have recently been proposed, to investigate some new equations containing the molecular weight as one term, and to study generally the properties of associated liquids. To the conditions laid down in the previous paper, that any exact equation employed to calculate the association factors of liquids must follow, must be added the condition that the equatio7z m i s t co?ijornz to tlac la&# oj mixtifics. For it must be remembered that in the case of an associated liquid we are really dealing with a mixture and not with a pure liquid in the chemical sense. I mean, for example, that in the case of ethyl alcohol we are dealing very probably with a mixture of C?HjOH2,(C?H,OH)?,JC2HjOH),,etc., and not with a liquid consisting of only one kind of molecule. This must follow from the progressive dissociation which an associated liquid appears to undergo as the temperature rises. If A I , be the molecular weight of a molecule ROH, AI2 the molecular weight of (ROH)? and AT3 the molecular weight of (ROH),, etc., the mean molecular weight of the associated liquid (ROH), is XMl =
+ + n&13 + etc. + + n3+ etc.
nlhl, n& nl n2
'
where nl, ?z2, etc., are the numbers of the respective kinds of Zeit. phys. Chem., 80, 50 ( 1 9 1 2 ) .
Daniel Tyrer
82
molecules present in the mixture. Suppose now we have an equation connecting the molecular weight M of a liquid with the various physical properties a , 0,y,etc. M = F ( a , 0,y)... . . . . . . . . . . . . . . . . ( 2 ) which we have found to be true for normal liquids. If, then, we have a mixture of liquids A, B, C, etc., whether they be associated molecules or not, we should have for the mean molecular weight A I m of the mixture if Equation z is valid for mixtures h1, = F(a,, P,, y m ) .. . . . . . . . . . . . . . . .( 3 ) where a,, P, and y m represent the observed physical properties of the mixture. Therefore, we should have from Equations I and 3
F(a,, P?n, y m )
nll.11
+
X&
XI
+
n3M3
+ etc. . . . . .(4)
+ n? + + etc.
= L-~
~-
~3
This equation should be valid for all mixtures whether an associated liquid or a mixture of normal liquids and every true equation for the determination of the association factor of a polymerized liquid should satisfy this condition. n’ow, any particular equation may be tested in this respect by applying it to a mixture of two normal liquids of known composition and seeing whether Equation 1 above holds. It is useless to apply this condition to any of the methods proposed for they have all been shown to fail to satisfy other less exacting conditions. A new method for the determination of the association factors of liquids has been proposed by Bingham and Harrison,l based upon viscosity measurements or rather upon the reciprocal of viscosity, tliz., the fluidity. Briefly, the method is as follows: For a large number of liquids that temperature is experimentally determined a t which the fluidity is equal to 2 0 0 units, and it is shown that this temperature is a constitutive property of the substance, that is, i t depends upon the number, kind, and arrangement of the atoms in the molecule. They calculate the fluidity value of each atom, of Zeit. phys. Chem., 66,
I
(1909).
Molecular Association o j Liquids
83
each double bond and triple bond, of each benzene ring formation, etc., and the sum of these values for the atoms of a given molecule is the temperature a t which the liquid has a fluidity of 2 0 0 units. If z(t) represents this sum for a simple molecule of an associated liquid, xS(1) is its true x-alue, ?c being the association factor. Hence, knowing the experimental value of the fluidity and the constitutional formula of the simple molecule, the value of ?c for an associated liquid can be determined. The method, however, contains this very grave error, that it is assumed that in an associated molecule there are no constitutional effects, i. c., nothing must be added or subtracted from the value of x Z ( i ) which takes into account the manner in which the simple molecules are combined in the associated molecule. The inadmissibility of this assumption will be appreciated when it is mentioned that the constitutional influences are relatively enormous. For instance, whereas the value for a hydrogen atom is 59.2 and for an ether oxygen atom 2 4 . 2 , the value for a ring formation is 141.8 and for a double bond 114.4.How do the authors of the method know that in an associated molecule of, say, water, there is not a double bond which would possess a value almost as much as that of two hydrogen atoms together' The molecule (HLO)? might, for instance, have the constitutional formula H
H>o = 0/H \H
Exactly the same objections apply to the method of Bingham and Harrison as applied to Traube's co-volume method (see previous paper). Furthermore, the results obtained by this method do not agree qualitatively with results obtained by other methods. For instance, Bingham and Harrison found that benzene and ethylene chloride are appreciably associated (for benzene x = 1.17 a t 39" and for ethylene chloride x = 1.21 a t 63.5") while these liquids always show in their accordance with various equations that they are strictly normal. Another method of determining the association factors of
84
Daniel T y e r
liquids has recently been proposed by Garver. This method depends upon the following considerations concerning the latent heat of vaporization of a liquid. If L is the latent heat, then L=I+E+H where 1 is work done against molecular attraction, E is external work done and H is the heat of dissociation of any associated molecules which split up as the liquid vaporizes. For normal liquids H is, of course, zero. E can be easily calculated by the equation E = -P - ~ - - L!=)
J
(L,
where p is 1-apor pressure and i, and ;,, are 1-olumes of vapor and liquid, respectively. If, then, we know 1 for an associated liquid we can calculate H and knowing H Gar\-er has shown how, by aid of certain assumptions, the degree of association may be calculated. The trouble lies in determining I and in this Garver makes a fundamental error. The quantity 1 as already mentioned represents the 11-ork done against molecular attraction as the liquid expands to the vapor state and this force of attraction is equal to a balancing force tending to expand the liquid, set up by the motion and energy of the molecules. This is, of course, the usually accepted idea of liquid equilibrium. Xow Garver assumes that this expanding force is equal to the Boyle pressure that a perfect gas would exert a t the same molecular concentration. That is, if p be the expanding force or intrinsic pressure then
and
1 J Z'W
R r ds = 1,
-I
t'ilL
i'L
This assumption is perfectly unjustifiable for several reasons. First, because the Boyle pressure of a perfect gas is caused by Jour. Phys. Chem., 16,454, 669 (1912).
Molecular Association o j Liquids
85
the impact of particles of negligible size against the walls of the containing vessel while the intrinsic pressure in a liquid is caused by the impact of particles of comparatively appreciable size against each other. The two phenomena are radically different. The intrinsic pressure must be much greater and
RT
can, in fact, be shown to be much greater than -?y.Secondly, ‘I,
assuming for a moment that the intrinsic pressure is really
RT
equal to 7 the ,expression L L
“L
is not equal to the internal latent heat as Gamer supposes, for in no case does this agree with facts1 but gives latent heats much too small. To take a case in point, the internal latent heat of pentane at 30’ is approximately 77 calories, whereas the s-alue calculated according to the above expression is only 2 0 . 2 calories. A11 liquids show a similar discrepancy. To explain this, Gamer must assume that all liquids are strongly associated, an assumption which is quite untenable as it destroys the distinctiveness shown by hj-droxyl compounds in their differences of behavior from other liquids. If all liquids mere associated and to different degrees as they would naturally be, then none would follow such equations as the Ramsay, Shields-Eotvos equation or Trouton’s equation. Again, supposing that we could discover the correct expression for the intrinsic pressure of a liquid, let us call it Ra(c,T), then we could not, even then, employ Garver’s method, for the integral E’s
-I
J
1
Rp(v,l’)dv
VI.
I n the equation of Dieterici (Drude’s Ann., the integrated product of the expression (CT log greater than
R
-. J
25,
’>, d
du
569 (1908)) which is
the value of C is much
Daniel Tyrer
86
is not equal to the internal latent heat for the simple reason that the force Rq(2,T) is not equal to the attraction force when the volume lies in between 7% and vL, for if it were so i t would be possible for liquid to exist in this intermediate state at the same temperature. There are many other objections to Garver's method, but those already mentioned are so fundamental that the method need not be further considered. In the previous paper by the author a modification of the Ramsay-Shields method proposed by Batschinski was adversely criticized. In a reply' to my criticisms fresh evidence was brought forward by Batschinski which led me to make a further study of the method. And though the method obviates some of the objections to the Ramsay and Shields method I still consider that at the best it can only be considered as giving a rough idea of the degree of association. The principle of Batschinski's method is simply to substitute in the wellknown Ramsay-Shields equation ~ ( W Z X Z ) '3 =
K(T,-'I-d)
for the undeterminable critical temperature of an associated liquid (called by Batschinski the ' ' metacritical" temperature) the value given by the following expression
'rc= 16.31(7T3)' '
7
i
where 7 is the viscosity a t the absolute temperature T and p c is the critical density. In the previous paper I pointed out that for an associated liquid pc is not determinable and hence the equation is not really applicable. However, Batschinski pointed out that for pc one can substitute the density a t o o C, and the resulting equation, with a fresh value for the constant, is approximately correct. However, attempting to calculate critical temperatures by aid of this equation I found, for normal substances, results which were in great disagreement with the observed values. This led me to examine the equation more carefully with the result that I found that the product 77T3 1
Zeit. phys. Chem., 82, 86 (1913).
hfolecular Association o j Liquids
87
cannot by any means be regarded as constant as it ought to be according to Batschinski’s equation. This is shown in the following three cases, using viscosity measurements by Thorpe and Rodgers : ~
~
____
~
Liquid
to
~
__
_
Carbon tetrachloride
-
qT3 X IO-*
_ _ _ ~ _ _ _ _ _ ~~ ~ ~ ~ ~ _ _ Liquid to qT3 x 10-2
~ ~~
%-Hexane
o
o
27jO
20
2453
20
40 60 70
2287
40
2189 2156
60
Methyl butyrate
0 20
40 60 80 100
816.3 819.6 830.3 844, j Ijj2
1458 1406 1381 1371 1373
For carbon tetrachloride over a range of 70’ the “constant” varies by about 25 percent. However, I found that a t a certain range of temperature for each normal substance the value of 7T3is really constant and it is this constant value that Batschinski has taken in his equation. But there is no use in determining the metacritical temperature of an associated liquid a t o o , for a t this temperature ( 0 ’ ) it will have a very much different metacritical temperature from what i t has a t the temperature a t which the function 7T3 is constant. However, in calculating the metacritical temperature of associated substances Batschinski did not make this error but used the values of the viscosity at each point corresponding to which he wished to know the metacritical temperature. Since, however, i t has just been demonstrated that the function 7T3is not constant under such circumstances it becomes necessary to test how far wrong the calculated critical temperatures will come. In the following equation are given the values of the constant C of Batschinski’s equation for some liquids a t 0’.
* Phil. Trans., 185A, 397
(1894);18gA, 71 (1897).
Da&l
88
Tyrer
The values of q are mostly from Thorpe and Rodgers' measurements, and the other data are mostly according to Young. __
-
~~
I
Liquid
Ether Carbon disulphide Pentane Octane Carbon tetrachloride Ethyl acetate Propyl acetate Benzene
Ethylene bromide Methyl alcohol Ethyl alcohol Water
17 Tc
x
Io,-"
at o
dc
0.2622 466,8 29j 437.7 0.377 289.4 0.2323 j69.2 706.0 0.2327 jj6.I 13.51 0 . 5 5 7 6 523, I 9 4 3 . 5 0 . 3 0 7 7 549.2 773.4 0.2957 561.j 9 0 6 . 0 0.304j j82.8 2435 j 1 3. 0 816.6 0 . 2 7 2 2 j16 I 1 7 7 1 . 6 0.27jj 643 1785
536.0 470.2
C
do
C1
16.63 0,7362 1 9 . 2 7 18.26 1.293 21.82 16.jj0.6454 19.15 15.53 0 , 7 1 8 5 18.26 14.29 1.632j 16.j9 13.67 0.9244 16.00 1 5 . 1 1 0.9102 17.71 14.83 0.9001 17.32 2.213 Ij.40 13.73 0.8101 16.05 1 1 . 1 00.8062 1 2 . 9 2 1.000 16.60
The last three liquids of the table are associated. The rest are usually considered t o be normal. It will be seen that the values of C in Column 5 vary considerably, and what is more important is that the constant for methyl alcohol, a strongly associated liquid, lies within limits of variation of the constant for the normal liquids. And if for the critical density d, we substitute the density at o o (da), the results are worse, as the figures under C1 in the last column of the above table indicate. Here the constant for water comes within the limits of variation of the constant for the normal liquids. It cannot, therefore, be considered that Batschinski's equation is sufficiently accurate to be applied to the calculation of critical temperatures. The equation only appears to be true when for the function 7T3 the constant value is taken which occurs for each liquid at a different and arbitrary temperature. Even if the correct metacritical temperatures could be determined the method of determining the association factor would, as pointed out in the previous paper, only give results which referred to the condition of a liquid at its surface, and it is highly probable that the density of the surface layer is much different from that of the interior of the liquid.
Molecular Associatiox o j Liquids
89
Investigation of Some New Equations Containing t h e Molecular Weight Below are given and studied some new relationships between the molecular weight and other properties which, though they do not allow of the exact determination of association factors, yet will furnish valuable evidence of the degree of association in fixing for this minimum value. Also some of the equations relate to other physical properties than surface tension and hence do not give results which merely refer to the surface condition. The following equation has been shown by the author' to be approximately true for any given class of normal liquids T, = K 3 \ V s where T, is the temperature of the boiling point, V, the molecular volume a t this temperature and K is a general constant. The value of K varies somewhat for different classes of liquids. If, however, we modify the equation and write it T, = K1 3t I T. log. A I where h l is the molecular weight, the variation of the constant for the different classes of liquids is considerably diminished and the value of K1may be regarded as approximately constant for all normal liquids, as the following table will show. The constitutional effects on the value of the constant K1 for normal liquids are quite marked but small enough to be neglected in comparison with the effects of association. Taking the mean value of K1 to be 37, the deviation from this value for any normal substance seldom amounts to more than 6 or 7 percent. As will be seen from the liquids given in the latter part of the table the effect of association is considerably greater than this deviation. For an associated liquid the equation should be written T, = K1 3 Y ~ ? L l ~log s . XM where x is the association factor, M the molecular weight of the simple molecule and os the specific volume at the boiling point. -I
Phil. Mag., [ 6 ] 20,
522
(1910).
Daniel Tyrer
90
vs
Liquid
Benzene Toluene Carbon tetrachloride Ether Hexane Butyl ether Ethyl benzoate Phenyl propyl ether Amyl chloride Propyl bromide Bromobenzene Fluobenzene Chloroform Diallyl Ethyl butyl ether p-Xylene Aiesitylene Methylene chloride Allyl chloride Amyl butyrate Propyl acrylate
95.9 117.9 103.7 106. I 139.8 197.3 174.2 I72
136.3 972 119.8 101.9 84.5 125 ' 7 150.1 140.2 102.4 65. I 84.5 222.3 143.9
I
353.2 382.2 349.7 307.6 341.9 413.9 482 463.5 374.5 344 429 358.2 334.1 332.2 364.4 411 437.5 3'4.6 318. j
457.8 395.9
40.9 39.7 34 34.7 34.1 33.9 39.7 39.1 35.9 35.8 39.4 38.7 36.6 34.7 34.1 39.1 38.6
40.5 38.5 34 4 36.6
Associated Liquids Water Methyl alcohol Ethyl alcohol Propyl alcohol Formic acid Acetic acid Acetone Phenol Methyl cyanide
18.78 42.6 62.2 81.2 41. I 63.6 77.3 103.6 57.2
3 73 337.9 35' . 3 370.4 373 391.5 329.2 467 354.2
111.8 64.3 53.3
48.I 65
j j . 2
43.8
50.4 57
Putting K1 = 37, we may write the equation x1/3
log xhI
TS
= ____
37
>1'1311~'/3'
If we knew Tsand vs for an associated liquid we could, therefore, calculate the association factor x. But unfortunately we do not know these terms and have no means of determining them, For an associated liquid the observed boiling point is lower than the true boiling point T, that should be taken in
Xolecular Association of Liquids the equation and it is found that the value of
91
T
v;, increases
with rise of temperature; hence, if in the above equation we calculate x, using the observed values of T, and L',, we shall obtain results that are too small. However, these results will be interesting as fixing approximate minimum values to the association factors a t the observed boiling points. In the following table are given these minimum values for a few cases of associated liquids : ___~ ~
_
~
_
_ ~_ _
Liquid
11
1Yater Methyl alcohol Ethyl alcohol -Icetic acid Formic acid Allyl alcohol Phenol
I8
46 60 46
58 94
~
~
~
x a t TS (minimum)
Ts
VS
-
32
~
--
18 78 42 6 62 2 63 6 41 1
74 1 103 6
~-
-
373 337 9 351 3 391 5 373 369 467
6 3 2 . jj 1
1.89 2.05 2 ;I I 70 1
77
The remarkable feature about the above results is the very high value for water in comparison with results obtained by methods based on the surface tension. This may possibly be explained by the fact that results obtained by surface-tension measurements can only refer to the surface condition and in the case of water the associated molecules in the surface layer may, owing to a smaller concentration, be much more dissociated than the molecules in the interior of the liquid. I n the other cases there is no considerable difference from the values obtained by other methods. But it must be remembered that the true values are all bigger than those given in the above table. In the case of acetic acid, however, since the vapor is already considerably associated, the A-alue of x given in above table will only be comparatively slightly less than the true value. I n contrast to the above method a new equation by which approximate values for the association factor may be
Daniel Tyrer
92
determined, but which depends upon the surface tension, is given below. I have shown1 that the following equation is true:
where y is the surface tension, T, the critical temperature, m the molecular weight, d, the density a t the boiling point and d, and d, the densities of liquid and saturated vapor, respectively. If this equation be equated with Walden's2equation
so as to eliminate T, we obtain the equation
This equation gives the molecular weight in terms of temperature, surface tension and density. Now for an associated liquid we cannot take for d, the observed value, since the liquid and vapor phases are not chemically the same. If, however, we restrict the application of the equation t o temperatures well below the boiling point we can neglect d,. Putting in observed constants the equation may now be written
where d, is the density of thie lquid at temperature T. The validity of the equation is tested in the following table for some normal liquids a t a temperature of 0 ' . The values of the surface tension y, a t o o have been calculated for the most part from the results of Ramsay and Shields. The value of the small quantity b has been taken equal to 6. 1 2
Jour, Phys. Chem., 17, 7 1 7 (1913). &it. phys. Chem., 65, 129 (1909).
Molecular Association o j Liquids l
Liquid
Carbon tetrachloride Carbon disulphide Phosphorus trichloride Phosphorus oxychloride n-Octane %-Hexane Toluene
so2c12
Ethyl iodide
Aniline
Benzene
28 36.61 30.80 34.18 22.69 19.11 30.44 31.19 32.j8 45 30.3
I .6325 I 483 I ,2921 I 2 2 2 4
93 m (calc.)
m (obs.)
6 78 4 I ,612: 1 4684 136 3 1,7116 I jog7 148 j 0.718j o 6119 1 1 1 0,6769 o 6160 92 2 0.8850 o 7809 86 4 I . 7081 I j602 140 6 Ijj 1.975 I 806 86 I 1.0379 0 8 7 2 7 0.9001 0 8135 79 5 1j2
There is quite a good agreement between the calculated and observed molecular weights as given in the last two columns of the above table. l l o s t of the values of y were obtained by extrapolation of results obtained by Ramsay and Shields a t higher temperatures and are not, therefore, as accurate as otherwise might be. Also some accuracy is sacrificed in neglecting the term d , in the original equation, particularly for the liquids with high vapor pressures. I n applying the equation to associated liquids we find that we cannot strictly take for d, the observed value a t the observed boiling point, since, if the liquid did not dissociate on vaporization the vapor pressure would be less and the boiling point consequently higher. Hence, the observed values of d, are too high. Therefore, if we calculate the molecular weights of associated liquids using observed values for d, we shall obtain results too small. However, since the density changes only comparatively slightly with the temperature, the results would not be 7-ery far from the true values. I n any case they can only be regarded as minimum values. Also it must be remembered that as the equation contains the surface tension the results will refer only to the surface condition. In the following table are given a few of these minimum values for some associated liquids for a temperature of o o:
Da?ziel Tyrer
94
Minimum values Liquid
Yo
do
ds
m (calc.)
Water Methyl alcohol Ethyl alcohol n-Propyl alcohol =Icetone
Acetic acid
x
28.9 1.61 1.000 0.9j96 2j.17 0.8101 0.7j18 7 7 . 5 2.42 23.86 0.8062 0.7405 84.7 1.84 2 5 . 2 1 o.S193 0.7396 87.7 1.63 1.38 25.43 0.8186.0.7537 80 24.78 1.0697 0,9435 128.6 2 . 1 5 73,21
It will be seen from the above table that the values of the association factor x are, on the whole, much smaller than the results given by the previous method at the boiling point. This is particularly the case with water. At the boiling points the above results (except acetic acid) would, of course, be still smaller. It would appear then, as highly probable, that in the surface layer of an associated liquid the molecules are much less associated than in the interior of the liquid. I n the case of acetic acid, since the vapor is already practically double molecules (and it will be shown later that acetic acid undergoes but little dissociation on vaporization), the degree of association at the surface will be but slightly different than in the interior of the liquid and hence the above result will not be far from the truth. I t may be remarked, too, that the above association factor for acetic acid is in very good agreement with the result found by the previous method a t the boiling point.
The Qualitative Detection of Association The various equations which ha\-e already been studied in regard to the quantitative determination of the degree of association, although they have been found unsatisfactory for this purpose, may nevertheless be advantageously used for the detection of molecular association. Several of the methods, however, have so far disagreed with each other that in some cases it has become doubtful whether a liquid is associated or not. For instance, as already mentioned, Bingham and Harrison found some liquids to be associated which,
alIolecular Associatiow of’Liquids
95
according to the Ramsay-Shields method, appear to be quite normal, and according to Garver most of the so-called normal liquids are associated. Also, it is quite possible that, since methods which depend upon surface tension only really refer to the surface condition of a liquid, there are liquids which are really associated but which, according to such methods, appear to be quite normal. For example, the lower esters are, as will be shown in what follows, in all probability associated, though, according to Ramsay and Shields they are normal. It becomes, therefore, a matter of importance to study the effect of association on the various equations and to determine the best means by which one can find whether a given liquid is associated or not. Tvoz4toiz’s Eqziation.--This well known equation is often used as a test for association. That i t is not a reliable test, however, is proved by the fact that acetone, an associated liquid, gives a constant ( 2 2 . 0 ) which lies within limits of variation of the constant for normal liquids. S o r do all associated liquids affect the constant in the same way; for example, for water the value of the constant is 2 5 . 9 , while for formic acid it is 14.9, the normal value being about 20. This varied influence is easily explained. The equation may be written LAI. = K T, where L is the latent heat at the boiling point T,, hI the molecular weight and K is a constant. Sow, for an associated liquid which dissociates on vaporization, the observed value of L is too great, since it includes the heat of dissociation. Also the observed boiling point is too low.
L is too great while Hence, the observed value of T,
that of 11 is too small. Obviously, therefore, the effect of association on the constant K will depend upon the relative effects on
$s
and on 11. In the case of water and the alcohols,
whose associated molecules dissociate completely on vaporiza-
Daniel Tyrer
96
tion, the effect on
L will r,
preponderate and the value of the
constant will appear larger than the normal. On the other hand, in the case of, say, formic acid, in which the amount of dissociation which occurs on vaporization is relatively small, the factor RI will have the greater effect with the result that the constant falls below the normal value. If the two effects balance each other then we should have a case like acetone giving approximately a normal constant. It is clear, therefore, that Trouton's equation is not an infallible test for association. Kisdiakowlski'sRelation.--A similar relationship to Trouton's is that of Kistiakowskil
where CY? is the capillary rise in a tube of I mm radius at the boiling point T,, and K1 is a general constant equal to about 1.14. For an associated liquid the value of a 2 will sometimes be too large and sometimes too small according to the relative effects of too low a value for T, and a partial dissociation of molecules in the surface layer. However, probably the observed value of
for an associated liquid is but little different
from the true value, and hence the chief influence lies in the value of MI which being too small (i, e . , normal value of simple molecule), the constant for associated liquids will be always smaller than normal value. For methyl alcohol the value is 0.482,and for acetic acid 0.576. Kistiakowski's relation may therefore be considered a good test for association. If Trouton's equation and Kistiakowski's equation be equated together so as to eliminate T, we obtain a relationship independent of the molecular weight ff2
= 0.0556
L which is true a t the boiling point only. This equation could be used to detect association, but the following equation dis1
Zeit. Elektrochemie,
12, 5 1 3 (1906).
LIlolecular Associatiou oj' Liquids
97
covered by the author' expresses the same relationship and is independent of the boiling point, and, therefore, is better to studv.
I n this equation y is the surface tension, (17, the density at the boiling point, I the internal latent heat and d, and d, the densities of liquid and saturated vapor. respectively. Restricting the application of the equation to temperatures below the boiling point we may neglect d, and the equation becomes
By the aid of this equation,which is independent of the molecular weight, we can calculate the approximate latent heat of vaporization of an associated liquid minus the heat of dissociation of the associated molecules. The observed value of d, will, however, be slightly too great for liquids which dissociate on vaporization. Also probably the x-alue of y for such liquids will be too small on account of the partial dissociation in the surface layer. The two factors counteract so that the observed value of ~ d , will ' ~ not be far from the true value. In any case the variation can only be small compared with effect of association on the value of 1. In the'following table are given for a few liquids, both normal and associated, the values of the internal latent heat 1 calculated according to the above equation. In the last column of the table under H are given the heats of dissociation of the associated molecules (i. e . , difference of c;tlculated and observed latent heats). The surface-tension data are for most part calculated from Ramsay and Shields' results, while the observed values of 1 are mostly according to Mills.? It will be seen from the table that for the normal liquids the calculated values of the internal latent heat agree well 2
Jour. Phys. Chem., 17,717 (1913). Jour, Am. Chem. SOC.,31,1099 (1909);Jour. Phys. Chem., 13,512(1909).
Daniel Tyrer
98
Liquid
to
Benzene I oo Octane O0 Hexane O0 Chloroform 20 Chlorobenzene O0 Ether I oo Carbon disulphide o Carbon tetrachloride o Water
O0
Methyl alcohol Ethyl alcohol Acetone Methyl formate Ethyl acetate Acetic acid
O0
O0 O0 O0
O0 O0
Yt
dt
30.30 0.9001 0.8135 99.9 22.69 0.7185 0.6119 84.9 19.11 0.6769 0.6160 8 4 7 2 j.88 I .48 I 1.409 j6.4 34.16 1.128 0.984 84.7 18.69 0.7362 0.6956 81.1 32.2 1.292 1 . 2 2 2 79.7 1.632 I .483 j I .4 28 73.2' I .ooo 0.9596 2 3 2 j . 1 7 0.8101 0.7518 96.3 23.86 0.8062 0.740j 90.2 2 3 4 3 0.8186 0.7j37 87.6 27.68 1.0032 0.957 89.5 26.03 0.9244 0.8282 82.3 24.78 1.0697 0.9435 65.9
99.1 84.7 84.7 j8.I 8j 85.4 82.8 48.4 565 272.4 209.2 131.8 113.2 94.4 76.4
- 0.9 - 0.2 -
+
1.7 0.3 4.3 3.1 - 3 +325 +176 +119 44.2 23.7
-k
++ + + ++
12.1
10.5
with the observed results, and the heats of dissociation H are practically zero. For the associated liquids, on the other hand, the values of H are very large. It is interesting to note that in the case of acetic acid the value of H is comparatively small, indicating that on vaporization of liquid acetic acid very few molecules dissociate. lye may, therefore, in the case of acetic acid, employ several of the methods of determination of association factors which in other cases are rendered invalid on account of the dissociation of associated molecules which occurs on vaporization. I t is also interesting to note, in the above table, that the two esters given are markedly associated. The above equation may be considered a good test of association. A second, but less satisfactory, method of calculating the latent heat of vaporization of associated liquids minus the heat of dissociation of associated liquids is by aid of an equation by Lewis1
L=-
(3 JP
Phil. Mag., [6]22, 268 (1911); Zeit. phys. Chem., 81,626 (1913).
Moleczdai Association o j Liquids
99
where L is the latent heat a t the temperature T, D is the specific volume, p the compressibility and J the mechanical equivalent of heat. I n the following table are given a few cases of the application of this equation. The data for ,8 and dtl,dt are by the author, and most of the observed values of L are according to hlills. _-~ ____ ___ _
~~
-_
~_
Liquid
~~
to
O0 Ether oo Benzene Toluene 0' Carbon tetrachloride O C oo Chlorobenzene 0' Bromobenzene O0 Chloroform 30' Hexane Ethyl iodide 72.52' Ethyl bromide 38;40° Carbon disulphide o 0' Ethyl acetate 0 ' -icetic acid Methyl alcohol 0 ' Ethyl alcohol 0 ' jOc IYater
dr
'
~
~
~~
~~~
'
IO6
~
L L ( c a l c ) (obs.)
0.002oj1 152.97 88.6 0.001316 81.95 106.1 0.001163 79.34 96.8 0.000720 91.03 j 2 . 2 67.02 82.9 0.000841 O.OOOjjj8 56.32 67.7 0.000794 85.90 61 0.002120 178.3 87.1 0.0007242 149.6 40.4 46.1 0.001052 I j j . 4 0.0008818 81.44 71.5 0.001370 96.29 93.9 O.OOIOI~ 88.71 j j . 9 o.001409 107.j9 S6.j 99.95 85.1 0.001288 0.0004jj 44.4 SO
92.5 106.I IO1
j1.9
89.9 67.4 64.8 86 46 59.9 90 100.6 84 289.2
H
+ + -
+
-
+ + ++ + +
-
3.9
4.2
0.3 7 0.3 3.8 1.1
5.4 13.8 I8.j 6.7
8.1
+202.j
220.9 + 1 3 j . 8 j 6 . j +18j
It will be seen from the table that for most of the normal liquids the value of H is very small, but, on the other hand, very large for the strongly associated liquids except in the case of acetic acid, for which, as was found also in the previous method, the heat of dissociation is comparatively small, indicating that very few molecules dissociate on vaporization. There are, however, some differences from the results found by the previous method. For instance, carbon disulphide would appear to be associated, and also slightly, ethyl bromide and iodide. Carbon disulphide shows in other respects some peculiarities which will be discussed later. In the cases of water and the two alcohols the values of H found are considerably greater than in the previous method, but it is prob1
LOC.cit.
Dawiel Tjlrer
IO0
able that in the previous method the values obtained were minimum values on account of the surface tension being included in the equation. The effect of molecular association on the RamsayShields equation is not necessarily always the same. Writing the equation y (?WzV)?/'3
(T,-T- b )
= K
we see that while the observed value of (T, - T - b ) for an associated liquid is too small, the values of nz and probably also of y are also too small. The two effects react upon the value of the constant K in opposite ways, with the result that it is quite possible to have an associated liquid which gives a normal value for the constant or even a value greater than the normal. The lower esters, for example, are in all probability associated, yet they give normal values for the constant K . Carbon disulphide is possibly another case. On the other hand, if a liquid gives a value of the constant less than the normal value, it is undoubtedly an associated liquid. For substances of very- high molecular weight it has been shown' that the equation is no longer valid, values of K being obtained much higher than the normal value even for liquids which are probably normal. In such cases it is probable that owing to the very great size of the molecules, comparatively speaking, the value of the molecular volume is no longer proportional to the other terms in the equation but is much too high. As further tests of association the two equations
T,
=
K '\
vs log A 1
and
which have already been applied to the determination of 1 IValden: Zeit. phys. Chem., 75, 5 3 5 (1910); Dutoit and Friderich: Comptes rendus, 130, 3 2 7 (1900).
-Molecular Association o j Liquids
IO1
minimum values of the association factor, may be used but they are only applicable with certainty when the degree of association is comparatively large. Some Special Cases ( I ) The Asssociatio.tz of the Lowei Esters.--As already mentioned the lower esters behax-e in general towards the RamsayShields equation like normal liquids. There is, however, considerable evidence that they are appreciably associated. In the following table are given a list of the constants for a number of esters of the various equations which have already been discussed. The normal values are given at the bottom of the columns. ~
~-
- -~
~~~~
Dc -
Liquid
- ~~~
~
as
K
dc
~
=
Ts
.
~
~~~~
-
Equa-
Equa-
tion XI tion
-
~~
x from H from ~2
cr2hI ~
-
Ts
Methyl formate 0 255 2 74 -13 7 I 38 23 7 0 957 - 11 0 2 O 257 Ethyl formate 2 j I I 39 9 I 02 Methyl acetate 0 254 2 7 2 I 40 1 Ethyl acetate o 254 2 69 3 8 . 1 I 11 12 I 1.07 S o r m a l values of constants o 267 2 61 37 I 00 0 I 1.1D, = theoretical critical density; d, = observed critical density. A11 other terms and equations have already been given.
The above table affords ample evidence of the association of the esters. The lowest ester methyl formate appears to be quite strongly associated. According to Equation A the value of its association factor x must be greater than 1.38. It may be mentioned also that Bingham and Harrison3 also concluded that the lower esters are appreciably associated. Traube4 also found them to be associated. 1
Equation A - xRI = y
Equation B - H
= lobs
)I;([
- 0.42641
- --y d s S ’ ,
0.295 dLT3’
3
LOC.cit.
4
Ber. deutsch. chem. Ges., 3 0 , 2 7 3 (1897)
.
Daniel Tyrer
I02
( 2 ) T h e AssGciation Factor oJ Acetic Acid.-It has been shown by two different methods that when liquid acetic acid vaporizes comparatively little of it dissociates. We may, therefore, with a fair approximation determine its association factor by means of any of the foregoing equations which contain the molecular weight and for which the other terms are known. In the following table are collected the results obtained by various methods :
VALUESOF
--
x
BY
DIFFEREXTMETHODS
~
~
~
Ramsay and Shields' equation with observed Tc
~
~
fb'
-
- ~ ~ ~ _ _ _ _ ~
z o j at 118'
-
'jdLtT
l
~
'
Equation Equation m= Ts = 37VL3log AI
~
1
Equation' Kistiakowski's I ~ ~ ~ ( c ~ - ( c ~ ) equation = 2 I2 ~~
V' 3
2
- .___
~-
~
I j
at
0'
I
92 a t 118'
1
~
2 02
ato'
It will be seen from the table that in each case the value of the association factor x approximates closely to 2 . 0 . That is to say, the molecules appear to be simply double molecules. It is interesting to compare these results with the values found by methods at present in use Ramsay and Shields found for x between 16" and 46" the value 3.62 and Batschinski the value 3.47 a t 20". These results are widely different from the values found in the above table and the divergence serves to illustrate the inapplicability of the methods of Ramsay and Shields and of Batschinski. Traube, on the other hand, obtained the concordant result 2 . I . It would appear from these results that acetic acid does not undergo a gradual association of simple gas molecules depending upon the concentration, but that two simple gas -
~
This equation is discussed later
,Volecular Association o j Liquids
I03
molecules unite to form a stable compound and a normal liquid which will undergo no further association.
(3) T h e Case of Carbon Disul9hide and S o m e R e m a r k s the Theory os Molecular Association .-Carbon disulphide is usually considered to be a normal liquid and in its behavior in many respects it appears to be quite normal, but I have discovered that it shows certain peculiarities from which it would appear that it is really an associated liquid. In the Ramsay and Shields equation it gives an approximately normal constant ; it follows Trouton's equation and Kistiakowski's equation ; its heat of dissociation H as calculated according t o the equation 0%
'
(see page 97) is practically zero and it gives a normal molecular weight as calculated according to Equation A given on page 101. On the other hand, for the ratio of the theoretical critical density to the observed critical density it has a value 0.328, whereas the normal value is 0.267; the ratio of the critical temperature to the boiling-point temperature for normal liquids varies from about 1.45 to 1.58, but for carbon disulphide the value is I .7 I ; the value of the ratio of the density a t the boiling point to the critical density is, for normal liquids, about 2.65, but for carbon disulphide the value is 3.24; the value of the function T,,3t'V log PIT (page 90) for normal liquids is about 37, but for carbon disulphide the value is 42.8; and according to Lewis' equation (see page 98) i t appears to be an associated liquid. Is, then, carbon disulphide a normal or an associated liquid? But these are not all the peculiarities shown by this substance. I have found that for a number of normal liquids the function N ( C 9 - Ct,j,W8 where 11 is the molecular weight, C, and C, the specific heats a t constant pressure and constant value, respectively, and V is the molecular volume, is approximately constant at constant temperature. In the following table are given some values of the function for the temperature of o o:
Daniel Tyrer ~~-
_ _ _ __~ ~ -~ ~~
Liquid ~
Benzene Ether wz-Xylene Ani 1in e Nitrobenzene Carbon tetrachloride Chloroform Ethylene chloride Toluene Xnisol Hexane Bromobenzene Mesityl oxide Ethyl iodide Ethyl bromide Carbon disulphide Acetic acid Methyl alcohol Ethyl alcohol Propyl alcohol Acetone Water
I
I
2.13 I .78 1.80 I 1
60 34
o 928 I
06
I 22
I 93
o.0oL)r.F
I
1.33 1.29 1.36 2 02
I
1
3 51 2.90 2 25 1 13 1170
It will be seen that for the majority of normal substances in the above table the value of M(C, - C,)/V'/3 approximates to a constant. The associated liquids and a few liquids of high density, chief among which is carbon disulphide, form exceptions to this generalization. The question arises, therefore: Do carbon disulphide and ethyl bromide and iodide disagree with the above relation because the relation is inexact or because they are associated liquids? The constancy of the function in other cases excludes the explanation of the anomaly by inexactitude of the relationship. If we make use of the constancy of the function M(C, - C,), V'I3 to calculate association factors (x),we get the results given in Column 3 of the above table. It will be noticed the value of x for acetic acid agrees very well with values previously found. For water, owing to the very small value of (C, - C,) the value of x appears to be extremely high. It is evident t h a t for some reason the equation is not applicable in this
Lllolecular Associatioqz o j Liquids
10.5
case. Carbon disulphide too, it will be noticed, would appear to be strongly associated. The anomaly shown by water is connected with the peculiarity shown by water between o o and 4' for the calculation of the function C , - C , involves the value of d v j d t . There are other equations in which carbon disulphide and also water show curious results. I have shown previously1 that the following equation is approximately true
where p is the isothermal compressibility, y the surface tension, T the absolute temperature and K is a constant independent of the nature of the liquid. In the following table are given in Column 4, values of K for a number of normal and associated liquids. The values of y have been obtained for the most part from Ramsay and Shields' determinations and the values of p are from my own determinations. All the values are for temperature of oo except otherwise stated. Liquid
$
x
106
K
"i
~-
Benzene
Ether
81 95 97
152
30.30 I8.gj 29.15
I .
28.17 32.34
1.20
29.75
I ,
41.95
1.11
30.I j 16.4 26 32.46 21.9 36.61
196
I . 19 I , 19
I
.06 13
1 .og 1.11 I.I j
I
.36
I
.40
1.53
2 j .j
I .23
23.46 23.86
0.93 I .06
2j.17
1.22
73.21
2.37
I 06
Daniel Tyrer
Now it will be noticed that the preceding equation does not contain the molecular weight and it should, therefore, be valid for both normal and associated liquids. As, however, for associated liquids the chemical composition of the surface layer is probably different from that of the interior of the liquid owing to dissociation of associated molecules, the surface tension will probably be too small and hence for associated liquids we should find the value of K somewhat smaller than the normal. This is, however, only the case for acetic acid, and in this case the effect of the surface layer should only be slight, because acetic acid only dissociates a little on vaporization. In the other cases we find curious results. Ethyl alcohol gives a normal constant, methyl alcohol a constant rather too high and water, carbon disulphide, ethyl iodide and ethyl bromide, values of the constant much too high. We find again the same substances as before in disaccord with the general behavior of normal liquids. Also the associated liquids themselves do not show any similarity of behavior among themselves. It is possible that the value of the compressibility p for the associated liquids may be too high on account of the possible increase of association with a resulting diminution of volume, which occurs on compression. But this would not explain completely the high value of K given by water, for it would mean that more than half the decrease of volume which occurs when water is compressed would be due to an increase of the molecular association. And in the case of carbon disulphide it does not seem a t all possible that it could be so much associated that the change of association on slight compression by one atmosphere pressure would be sufficiently great to account for the high value of K given by this substance. Nor can the anomalies be due to inexactitude of the relationship or to constitutional effects for, as seen from the preceding table, a large number of liquids of greatly differing constitutions give values of K, which, in the extreme case of carbon tetrachloride, only differ from the mean value ( I . 14) by about 5 percent, whereas the variation in the case of carbon disulphide is about 27 percent.
’
A2101ecular AssociatioTa o j Liquids
107
The existence of these anomalies renders necessary an examination of the theory of molecular association of liquids. Since the work of Ramsay and Shields in 1893 on the surface tension of liquids and the application of the equation of Eotvos to the determination of molecular weights, it has come to be regarded as chemical law that such liquids as the alcohols and water behave in their properties in general, and in particular in their disaccordance with various empirical relationships, such as the Ramsay, Shields-Eotvos equation, differently from the majority of other liquids because the simple gas molecules of these liquids are, in the liquid state, combined or associated together. This conception, however, rests upon no fundamental chemical principles, but is purely hypothetical. Only in the case of such liquids as acetic acid and nitrogen peroxide, which are associated in the gaseous state, can we be perfectly sure that there is molecular association in the liquid state. -Ind the fact, as was seen above, that water and the alcohols along with carbon disulphide and several other liquids show differences of behavior to acetic acid, calls into question the truth of this theory. It may be mentioned here also, that Ramsay and Young1 found that for the alcohols and the ordinary normal liquids the value of the function (dp d t ) , is independent of the temperature but that this is not the case for acetic acid and nitrogen peroxide, which seems to indicate some difference in the molecular condition between the alcohols and acetic acid. To explain these anomalies I put forward the following hypothesis: In the cases of such liquids as water and carbon disulphide and also probably, though to a lesser degree, the alcohols, the molecules in the liquid state have not a translational kinetic energy strictly proportional to the absolute temperature as is the case with gases; but that, through the crowding together of molecules under the influence of strong attractive forces, the motion of the molecules is hindered somewhat so that the mean kinetic energy is constantly less Phil hlag.. 151 24, 196 (1887).
I 08
Daniel Tyrer
than the mean kinetic energy of external free molecules with which the liquid is in thermal equilibrium. The number of stationary molecules or molecules possessing little energy becomes greater than can be compensated for by molecules possessing extremely great kinetic energies. It is not difficult to understand that in a compact group or system of molecules there is a limit to the velocity or energy that a molecule may have while any number of molecules may for an instant be stationary. Or it may be regarded that such liquids are approaching the condition of the solid state when the molecules possess comparatively little kinetic energy. It may be mentioned in support of this hypothesis that Amagat' has demonstrated from his experiments on compressibility under very high pressures that as the molecules come closer together a t constant temperature the internal pressure (pressure of molecular attraction) a t first increases, reaches a maximum and then begins to decrease rapidly with further diminution of the volume. If now, we imagine the same phenomena occurring when the volume is diminished by cooling a t constant pressure instead of by pressure, it would necessarily mean that the molecules began either to associate or to be losing kinetic energy a t a greater rate than gas molecules at the same temperature. But, as we have seen, association will not explain all the facts, and hence we are compelled to accept the alternative of an abnormally low kinetic energy. It may be mentioned also that van der Waals? has found it necessary to introduce a very similar hypothesis in order to explain the disagreement between the observed results and those determined from the equation of state for liquids at high density. He prefers to consider, however, that the molecules (of normal substances even) tend to form loosely combined groups which for an instant behave as single molecules. This process he calls quasi-association. Unless, however, it be considered that each molecular complex has not the normal Ann. chim. phys., [ 8 ' 28, I (1913). Proc. K Akad. IVetensch. A m s t , 13, Pt. I, 107 (1910).
Molecular Association o j Liquids
I09
molecular kinetic energy, then, so far as the effect on the physical properties of the substance is concerned, it will be just the same as ordinary association. If, however, it be granted that these molecular complexes possess less kinetic energy than the normal free molecule a t the same temperature, then the hypothesis of quasi-association reduces to the same conception as I have put forward here, and the reason for the abnormally large compressibilities of water, carbon disulphide, etc., becomes comprehensible. The molecules bombarding each other with less energy than external gas molecules at the same temperature will offer less resistance to an external pressure, and hence the compressibility coefficient p is abnormally large and the value of the function 3-y' T' in consequence greater than the normal value. X liquid composed of associated molecules possessing the normal kinetic energy would, of course, behave towards pressure like a normal liquid and give a normal value for the above function. I n most other respects the retardation of the motion of the molecules would have the same effect qualitatively, at least, as molecular association. For instance, the latent heat would be abnormally large (though the effect would not be so great as association), since it would include the extra energy required to raise the kinetic energy of the molecules to the normal value. The boiling point and vapor pressure would be similarly affected. On the other hand, for such a liquid the molecular weight as calculated by an equation such as the Ramsay-Shields equation mould be normal or approximately so. But this hypothesis is not sufficient in itself to account satisfactorily for the quantitative results. For instance, if we took an extreme case in supposing that for water all the molecules are at rest in the liquid state, then on vaporization a t the boiling point 373 X 3 = I I 19 calories would be absorbed per gram molecule to give the molecules their proper energy, and taking the value 325 calories per gram as calculated on page 98, as the latent heat absorbed other than work done against molecular attraction in vaporization, we find for I gram molecule 325 X 18 = 5850 calories. Hence, the theory
Daaiel Tyrer
I IO
of the retardation of the velocity of the molecules is not sufficient to account for the high value of the latent heat. We are, therefore, compelled to conclude that molecular association also exists in the case of water and probably also for hydroxyl compounds in general, and that the two factors, i. e., the retardation of the velocity of the molecules and molecular association both play a part in affecting the physical properties of the liquids. It must be concluded also that in the cases of carbon disulphide, ethyl iodide and bromide and perhaps also for many other liquids that there is no molecular association, but only the retardation of the molecular kinetic energy. So long as these two factors cannot be separated the determination of association factors is futile. It is hoped later, when more experimental data are available, to study this hypothesis and conclusions more closely.
Summary Any equation used for the exact determination of association factors of liquids must be valid for mixtures as well as for pure liquids. The method of Bingham and Harrison of determining association factors based upon measurements of fluidity is not reliable because it leaves out of account constitutional effects in the associated molecules. The Batschinski modification of the Ramsay and Shields method rests on an unsound basis. The method of Garver is based on untenable assumptions. By means of the following equation
T,
=
K 3Y'rTi log bl:
where T, is the boiling-point temperature, V, the molecular volume at the boiling point, M the molecular weight and K is a general constant equal to about 37, approximate minimum values of the association factors a t the boiling points are determined. The minimum value for water thus determined. is about 6.3.
hfolecular Association o j Liquids
I11
Approximate values of the molecular weights of liquids are calculated by aid of the following equation
where d is the density at absolute temperature T, d , the density a t the boiling point and y is the surface tension. Applied to the calculation of association factors this equation gives values which are minima. Several methods for the qualitative detection of association are examined. It is shown that an associated liquid does not necessarily disagree with Trouton’s equation. The relation of Kistiakowski Q2bI __
= K
T S
where a?is capillary rise in a tube of I mm radius, M the molecular weight, T, the boiling point and K a general constant may be considered a good test for association. By means of the following equation 7dS63 ~
Idsa3
= 0.29j
where I is the internal latent heat and the other terms are as before, the heats of dissociation of associated molecules on vapc rization are calculated. It is shown by this means that acetic acid dissociates comparatively slightly on vaporization. The following equation of Lewis
da T-
L=--dt JP
where I,is the latent heat and /3 the compressibility, is applied to the same object as previously. According to this equation carbon disulphide and a few other “normal” liquids appear to be associated. It is shown that an associated liquid does not necessarily give an abnormal constant in Ramsay-Shields’ equation. Evidence is adduced to show that the lower aliphatic esters are quite appreciably associated.
I
Daniel Tyrer
I I2
Taking advantage of the discovery that acetic acid dissociates only slightly on vaporization, fairly accurate values, of the association factor are calculated in various ways and a good agreement is obtained in the results by the different methods. In the liquid state acetic acid appears to exist simply as double molecules. The special case of carbon disulphide is discussed. This substance appears to behave sometimes as a normal liquid and sometimes as an associated liquid. By means of the equation
where C, and C, are the specific heats a t constant pressure and constant volume, respectively, molecular weights of liquids may be calculated and it is found that carbon disulphide and a few other liquids behave like associated liquids. The following equation
Pr':
=
K
T' not containing the molecular weight should be valid for associated liquids as well as for normal liquids, but it is found that water and alcohol and carbon disulphide give too high constants, while acetic acid gives a constant too low. To explain these and other anomalies the theory is put forward that in the cases of carbon disulphide and water and some other liquids the mean kinetic energy of the molecules is, owing to dense crowding together under influence of attractive forces, less than the kinetic energy of free gas molecules a t the same temperature. Eyidence is adduced in support of this theory. It is concluded that in the case of water and the alcohols both molecular association and the retardation of the kinetic energy of the molecules exist and affect the physical properties, while in case of carbon disulphide and a few other liquids only the retardation of the molecular kinetic energy comes into play, 3
Xanchester Cnzverszty August, 1914
