SOME NETT RELATIONS BETWEEN THE PHYSICAL P R O P E R T I E S OF LIQUIDS BY DANIEL, TYRER
I t is a remarkable fact that when an empirical relationship between certain of the physical properties of a liquid is found to be true for a given liquid over a certain range of temperature, it is always found t o be true for all other liquids over a similar temperature range. For instance, the wellknown Ramsay-Eotvijs equation for the surface tension of a liquid is true not only for one liquid or for a certain class of liquids but for all liquids.’ And if we discover a new relationship and find it applicable to one liquid we may be sure t h a t it is also applicable t o others. These remarks d o not, however, apply to all physical properties but only t o that class which are not what is called “constitutive,” that is, do not depend upon the inner nature or structure of the molecule. A constitutive property, for example, is viscosity and, as is well known, this does not lend itself to the construction of relationships with other physical properties. We may find a relationship between viscosity and other properties which is true for one liquid but which does not hold or only roughly holds for other liquids which are chemically dissimilar. Specific heat is another case of a constitutive property. N o general relationship which expresses the variation of the specific heats of liquids with temperature has yet been discovered, for such a relationship is not possible. On the other hand, other physical properties such as density, surface tension, latent heat, etc., are not constitutive or only slightly so and a relationship between such physical properties is always found applicable t o all liquids. Associated liquids are included in this statement as well, for presumalily if we knew t h e correct molecular weights a n d t h e correct values of the other terms in the equation, they would give a n equally good agreement as d o nonassociated liquids.
But probably every physical property is to some extent, however slightly, of a constitutix7-e character and if we take two liquids of extremely dissimilar character ( I c , chemicallv dissimilar) we find that many relationships are only approuimately applicable t o both or else fail altogether to agree n i t h the experimental data For instance. the constant in the Ramsay-Eotx-os surface-tension equation is usually equal to about 2 1 2 but it has been found hy V'alden,' t o take a single case that for tristearin the constant is about 6 2 Thi5 is not due to any possible association, for in thii case the constant is decreased. I n looking for tien relationships hetneen the physical properties of liquids it is ad1 isahle, therefore, to study properties which are not constitutise or only slightl? so, as for esample latent heat and surface tension The former property in particular lends itself to the disco1 ery of empirical relations with other properties and it is this property which has formed the basis of the present study Already there exist three accurate empirical? latent heat relations 111115'~Equation
/ill = pld,
-In Equation'
1111 =
C ( d , -- d )
Ihctcrici's Equation
1111 =
C,'l' log
--
li
'i
ti, d
nhere 1 is internal latent heat. z L , latent heat minus the external work done in vaporization, 111 is molecular weight, d , and il' the densities of liquid and saturated vapor respectively and p, C and C1 are constants, the first two being dependent on the nature of the liquid though independent of the If alden Zeit p h \ i Cheni 75, - - - 1 \ Bat\chinAi 14, 2 b 8 11904)1 and m a i later di>co\crcd indeptndentl\ anti tcited I Drude s r l n r i by Kleeman [Phil Mag 20, 678 1 9 r o ) ' Ilrude's Ann , 2 5 , j 6 9 iI 908 ) I
temperature, and C1 i j approximately the same for all normal 1iq u id s These three rela tionships, together with various surfacetension relation\, can be combined with any new latent heat relation that may bt discox-ered and, as will be seen later, the!- supply a means of producing a number of interesting nenrelationships To avoid the repeated explaining of the terms used continuall!- throughout this paper they are all collected and given below with their meariingi L = ordinary lalent heat of vaporization 1 = internal latent heat, I t' , I,minus external nork of vaporization. T = temperature \ absolute 1 . T, = critical temperature [absolute) T, = boiling point iabsolute I d, = density of liquid. d~ = density of saturated vapor. ti, = critical density t i , = density a t the boiling point. Y = surface tencion 1 2 1 = molecular iveight. C is a constant independent of temperature hut dependent on the nature of the liquid E; is a constant the same for all liquids a t all temperatures In regard t o the experimental data used in the calculations the internal latent heats are taken from tables calculated 1)y T. E. AIillsl by aid of the Clapeyron-Clausius formula, uiing the experimental data of S . Toung. The surface-tension data are those of Ramsay arid Shields. The densities of liquids and saturated vapors are according to Young." ! Jour. I'hys. C h m . . 5, ,3S,3 i i g o 4 ) ; IO, I (19061; Jour. Chem. Soc., 31, 1099 (19091: 13, ~ 5 1 2(19091. Phil. Tram., 184.1,04j 11893): &it. p h p . Chem., 12, 433 ( 1 8 9 3 Proc. Roy. Dull. Sot,.. 12,3j4 (19101. I'
Daniel Tj'rer
720
The following latent heat relation has been discovered empirically : C,(T, -T)"? 1172
=
d,
+ dL
CI is a constant dependent on nature of the liquid. To prove the validity of the equation the latent heats of four dissimilar liquids have been calculated by aid of the equation and the results are compared in the following tables with the thermodynamic values of Mills (see above). Lnder 1 are the thermodynamic values and under l1 the values calculated according t o equation ( I ) :
ETHER _
_
t3
T,
-~ ~
=
466 S o
7~
=
~~
(1L
60 80
d;
I70
190
0.9001
0 000121
0.811j
0 00272
o 00469 0 00763
240 2 60
0,7927 0.7692 0.7185 0.6906 0.6610 0.62j6 0 . 5852 0 . 532 7
280
0.4514
I 80
2 00 220
I1
99.16 86.70
102. I
0.0187 0.0293 0,0449 0.0691 0.0873 0.1620
140 I 60
I 60
1
0.0lIjj
IO0 I20
IO0 I20
~ ~
0.00083 0.0018j 0.0037 3 0.00677
40
0
~ ~~
0 20
so
74 08
o 0173 0 0249 0 0355 o 0503 0 0715 0 I040 o 2209
82.37
86.63 82.30
77.39 69.48 6 5 ,2 1 59.75 53.76 46.53 37.55 23.45
68.60 63.65 j8.25 52.42 45.72 37.40 22.29
77.Sj
1
Relil t i o m betweeit P y o p e h e s o j Liquids IL-HEPTASE ? ' = 339.9; ?I? = 100.1; _
t"
dL
_
dz -
~_
0
0 7OOj
0 OO3j8
I20
o 6311 o 6124 o 5920
0 04672 0 0020
82.6s
80 140
0 ,5711
0
68.52 64.66 60.35
I 60
0
5481 j232 0 4951 o 4610 0 4'77
0
I 80
0
0
I00
2 00 22 0
240 250 2 60
0
0
38;; 3457
o 00607 00977
01508 02242 0 03304 0 04892 0 07446 o 09461 o 1289
10
72.82
55.52 j I .01
4j.7 6 39.67 32.14 27.14 19.75
il
I00
2
.0ISA
0 , 0 0 5 76
2s. g s
I20
I I
.SASI
I
so
I
I , is73
0,00994 0.01616 0 . 0 2 j06 0.037i9
27,62
140 I 60
,96319 . 907.3
2 00 220
1.7224
0
I . 64S3
0.07725 0.108; 0 . I520 0.2160
2 40 260 250
I . j667 1 ,4747
I
,3623
05450
2 6 . 19 24. 7 3
'3.20
21.62 19,9; IS. Iti
16.14 13.73
There is a good agreement between the observed latent heats and the calculated. The greatest divergence is a t the initial temperature o 3 b u t this is probably due t o the somewhat uncertain value of the observed latent heat a t this temperature. Otherwise the disagreement is on the average less than one percent and this is probably no greater than the experimental error in the data. The value of the constant C1in equation ( I ) differs for different liquids but we may generalize it in the following way. This, it may be added, is a general method of generalizing a constant.
At the boiling point of a liquid the equation may be written
E being external work of vaporization and, therefore, L - E
=
1. T o w a t this point according to the law- of corresponding states we have T, (Y T, and d, CY dLs,so that we may write
K being a constant the same for all liquids. Now according to Trouton’s well-known equation we have Liiz =
K, ’l‘>
and =
PI-= R’l‘%
Theref ore, (L
E))??=
~
T,(K
-
R)
Therefore.
or C1
=
K1’1‘1 d :
K1 being constant for all liquids. Equation [ I ) may, therefore, be written
The values of Kl have been determined for a number of liquids and are given in the following table: ~~
Liquid
Ether Benzene n-Heptane Diisopropyl Diisobutyl Carbon tetrachloride
K1
26 86
Liquid
Isopentane n-Pentane 60 n-Hexane 26 46 Bromobenzene 2 7 90 Chlorobenzene 2 5 74 Iodobenzene Mean 1-alue of K, = 26.74 25 2Q
70
Ki 2 j
87
26 29 27
30
26 j 6
27.07 26 53
Rclaiioizs betweeit Properties o j L i q u i d s
723
For the boiling-point constants T, and d, we may, of course, substitute their proportional values T, and d, but the agreement between the values of K1 for different liquids is not then so good. The constancy of K2 depends, of course, upon the validity of the law of corresponding states and upon Trouton’s equation. A further new relationship may be obtained by combining equation ( I ) with Mills’ equation (see page 718) so t h a t the latent heat is eliminated. This relation may be written
(TC - T,”
=
C2idll - d:’)
(2)
If we generalize the constant Czby taking the equation a t the boiling point and applying the law of corresponding states as before, we find
E=? being an independent constant. The equation may then be written (20)
The validity of this equation depends, of course, upon the validity of the equations from which it has been deduced. Since these appear to hold true within limits of experimental error it follows theoretically t h a t equation ( 2 ) should hold equally good. But i t is not always practically true t h a t a relation deduced in this way from other relationships agrees with facts. For an empirical relationship never holds absolutelj- true and when two such relationships are equated together thus producing a third relationship, certain of the variables may be thrown into such conspicuity in the resultant equation that it may only agree roughly with the facts. It is, therefore, always necessary to test the relationships though they may be founded on others which give a very good agreement with experimental data.
724
The approximate validity of equation the four following cases :
(2a)
is shown in
CARBON TETRACHLORIDE CHLOROBENZENE T,=632 I O , T , = q o j 0 T , = j j 6 I O , T = 349 7 s d, =
I
A
to
o 100 I20
140 160 I80 200
240 260 280
1
1.6327 I ,4343 1.3902 1 3450 I ,2982 I 2470 I 1888 1 0444 0 9409 0 7634
d, = 0 9842
4s3 K?
11 0 000;
0
0 01026 0 01634
0
0 0
0 0 0 0 0
02481 036j 0525 0742
1464 2146 3597
0 0 0 0
876 0 8j%j 130 85-1 140 8 j 1 160 8jI 180 8j0 2 0 0
o 8jZ 0
to
862
o 874 o 822
220
260 300 333
I
0 0 0
0 0 0
1278 9836 9723 9480 9224 89jj 8672 8016
0~169 00341 00432 o 00676 0
0 0
0 01020 0 OI
