WEIGHT OP A FALLING DROP AND THE LAWS OF TA‘I‘E.
X.
I713
staiit, the remainder of the curve (I1 or 111) clearly will not justify the statement that the mass-action law is obeyed by this salt when r is obtaiped from freezing-point data. With cesium nitrate, therefore, as with the other strong electrolytes, the freezing point method cannot be relied upon to give correct values for 7, for t h e validity of the mass-action law is implicitly assumed whenever r is calculated by this method. 11.
Summary.
I . Tbe freezing point lowerings, densities, relative viscosities, and equivalent conductances of solutions of cesium nitrate, potassium chloride, and lithium chloride a t o o have been investigated and a complete set of these data are given in Tables V, VI, and VII. The data extend to normal solutions in the case of potassiun and lithium chlorides and to o 5 normal in the case of cesium nitrate. 2 . The cryohydric point for cesium nitrate is -I ,254’. 3. When the freezing-point curvc s (Fig. 2 , mole fraction of solute plotted against freezing-point lowering) for the three salts are compared with the curve of the “normal solute,” potassium chloride is found to agiee exactly up to about o 5 normal, lithium chloride deviates decidedly in the direction of hydration while cesium nitrate deviates decidedly in the opposit direction. The conclusion is drawn that deviation from the behavior of a “ normal solute” (an unhydrated non-electrolyte) cannot serve as a basis for the calculation of the degree of hydration of an electrolyte. Another method for making this calculation is outlined and, as a provisional result, about 9 molecdes of water are f o m d to be in combinatior! with one of KC1 and about ;S with one of LiCl in a half normal solution of the electrolyte. 4. The freezing-point data for cesium nitrate are compared with the data of Biltz and his conclusion, that this salt obeys the Mass Action Law, is only partially substantiated. URBANA.ILL
[CONTRIBUTIONSFROX
THE
HAVEMEYER LABORATORIES OF COLUMBIA UNIVERSITY, NO. 199.1
THE WEIGHT OF A FALLING DROP AND THE LAWS OF TATE. X. THE DROP WEIGHTS OF SOME FURTHER ASSOCIATED AND NON-ASSOCIATED LIQUIDS, AND THE SURFACE TENSJONS AND CAPILLARY CONSTANTS CALCULATED FROM THEM. Y Y J. LIVINGSTON,R. M O R G A N A N D F. T.
Owsa.
Received September 19, 1911.
The associated and non-associated liquids used in this research were selected for the following purposes: ( I ) The further testing of the new
1714
GENERAL, PHYSICAL AND INORGANIC.
definition of normal molecular weight in the liquid state;’ (2) the further comparison of the surface tension and capillary-constant values calculated from the results of the Morgan drop weight apparatus2 with those found by other observers from measurements of capillary rise; and (3) to supply additional data for a later quantitative study of the relationship existing between the drop weight, or the values derived from it, and the other physical and chemical properties of the liquid. For convenience, and to avoid unnecessary loss of time in case of accident, two pieces of. apparatus, with tips of different diameters, were employed, but i t was not necessary in any case to complete the study of any liquid on one tip after having started i t with the other. If an accident had happened, however, this would have been possible, as has already been brought out in a previous paper,3 and just as it is possible to calculate values of t,, or of the surface tension, or the capillary constant, from the results on one tip, which would be identical (within the limits of error) with those obtained by a similar calculation from the results with the same liquid a t the same temperature on another tip. Thus for the same liquid, a t the same temperature (to) we would have for the two tips the relationships w’(M/d)* = k~(t,-to-6) and w”(M/d)%= kk(tc-to-6), from which i t is evident, since a t the same temperature for the same liquid, M, d , t,, and to are identical in the two equations, that w’ : w” . : k k : k k , the weight of a drop of liquid from one tip i s related to that of tke same liquid, at the same temperature, from another tip,as are the k , values of the two tips. By similar reasoning i t can be shown that the k , values themselves of the two tips are related as the respective drop weights of benzene falling from them a t the same temperature of observation (to), for then we would have w; (78 / d ) 8 = kk (288 .5-to-6) and wk(78 / d )3 = k; (288 .5-to-6) which would reduce to , ” w, : wB : : k; : h i .
’ Morgan, THISJOURNAL, 33, 643-657 ( 1 9 1 1 ) . The mokcular weight of a liquid is to be regarded a s normal (i. e., i s identical with that as a gas) when t , in the equation i s found to be constant at all temperatures 01 observation ( t o ) , w(M/d)g = kB(tc-to-6) k , being the value found for benzene on t L same tip, when t, is taken as equal to t L observed critical temperature, viz., z88’.5. a THISJOURNAL, 33, 349-362 (1911). Morgan and Cann, THISJOURNAL, 33, 1069-1071 ( 1 9 1 ~ ) ~
WEIGHT O F A FALLING DROP AND THE LAWS O F TATE.
X.
1715
And in the same way the surface tension values can be calculated from the drop weight, for then we would have, for the same liqwid at the same temperature, y ( M / d ) ' = K,(tc-t0-6) and w(Mjd)g = kB(tc-t0-6) , where M, d , t, and to are the same and consequently y : w ::K, :kB 5. e . , T = w X KBlkB, y in dynes and w in milligrams, being values a t identical temperatures. Here again K, : k , : : rB: wB, where yB and w, are the respective values for benzene a t the same temperature of observation (to), for y, (78/ d )3 = K , ( 288.5-to-6) and wB(78/d)3= k,(288.5--t0-6), the values of to and d being identical, so that yB : wB : : K, : k,. Since no general relationship like the above holds for the capillary constavt, a3, the relationship between the drop volume (i. e., drop weight a t t,/density a t to) and the capillary constant can be found only by a direct comparison of individual results a t various temperatmes, and then finding the mean of the constant by which the drop volume must be multiplied to give the observed capillary constant. I n a previous paper' i t was shown that for a tip giving a value of k, = 2.3502, a2 ( = height of ascension; times radius of bore) for benzene as found a t a number of temperatures by four of the best modern workers with the capillary rise method can be obtained from the drop weight from that tip by aid of the equation ai = 0.1837 w;ld,, so that for any new tip, since the drop weight is proportional to the normal (benzene) constant uf the tip, for , n wt : wt: : kk : k k , i. e . , W; = k k / k ; w ; , we have for a n y liquid from any tip a: = 0.1837 X 2.35oz/kk X wild, where kk and wz are the values for the new tip. The benzene values for the two tips employed in this research are given in the table below, the mean value of w from several determinations '.Morgan and McAfee, THISJOURNAL, 33, 1275-1290 (1911).
1716
GENERAL, PHYSICAL AND INORGANIC.
(which varied among themselves as slightly as those given in the previous papers) being the one used.' CALIBRATION WITH
BENZENE. Tip No. I.
t.
d.
W.
30.3
0.86792
30.088 Tip No. 29.058
30. I
0.86792
=
78; t,
=
288.5.
603.68
2.3936
582.87
2.3098
2.
To obtain the surface tension in dynes per centimeter from the drop meights then, we have the equations 2.1148 I. Tifi No. I. r = w l x ____ = 0.88352 x w,; 2.3936 2.1148 11. Tip NO. I I . r = w, X = 0.91558 x w 2 ; 2.30 98 where 2.1148 is the average value of K, for the surface tension of benzene from capillary rise, using t, = 288.5' and calculated from the work of the four best modern investigators.2 And to calculate the values of the capillary constant, as mentioned above, we have then only to make use of the equations: 2.3502 111. a2 = 0.1837 _ _ X w J d = 0.18037 x w,ld. Tip No. I . 2.3936
11'.
'
2..j'502
X w,ld = 0.18691 x ",Id. TiF N o I I . 2.3098 From the k, values of the two tips given above we can also, of course, calculate the mean diameters of the tips, for in a previous paper3 it was shown that diameter = (kB/o.4z24)mm. According to this relationship the diameter of tip No. I was 5.643 mm., while that of tip No. I1 was 5.445 mm. In the following tables are given the results obtained with the 1 2 ( 7 non-associated, 5 associated) liquids studied, together with the calculated values of t,, surface tension, and capillary constant, and, wherever it is possible, the similar values observed by other investigators. Methyl Hex91 Ketone, CH,COC,.H,,; M = 128.13. Kahlbaum's preparation, redistilled, density a t ' 0 extrapolated, and that a t 30.1 ' interpolated, from the results by Falk4 on the same sample. Tip No. I . a' = 0.1837
~
In order to save space the mean only of the drop weight a t the various temperatures is also given for the other liquids studied. cit., 1280. Morgan and McAfee, LOC. Morgan and Cann, LOC.cit. THISTOURNAL, 31, 86 and 806.
WEIGHT O F A FALLING DROP AND THE LAWS OF TATE. d.
t. 0
30. I
0.8362 0.8106
.
w(M/d)8.
31.324 28.202
896.96 824.47
ZL’
X.
1717
tc from kg = 2.3936.
380.7 380.5
It is evident that this liquid is perfectly normal and qon-associated, the values of t, agreeing (0.05 per cent.) within the experimental error. Assuming a linear relationship between the drop weight and the temperature, and also between the drop volume and temperature, we find W , = 31.324 - O.I0372t, and vi = w J d , = 37.460 - o.o8864t, from which i t follows, by aid of equations I and 111 respectively, that rr = 27.675 - 0.09164t and ai = 6.757 - 0.016t. Benzyl Cyanide, C,H,CH,CN ; M = I I 7. I . Kahlbaum’s preparation, redistilled. Densities interpolated from Falk’sl observations on this sample. Ti$ No. I . d.
t.
45 60
0.9981 0.9850
-a.
w(M/d)t.
42 ‘ 654 40.772
1022.20
985.77
IC from k B = 2.3936.
478.1 477.8
This compound, according to the new definition of normal molecular weight, is non-associated, the deviation in the value of t, being less that 0.1per cent. Assuming linear relationships, we have .Zet, = 48.302 - 0.12551 and vi = 46.763 - 0.0895t, from which by aid of I and I11 we find rt = 42.676 - o.IIogt and ai = 8.435 - 0.01614t. Benzaldehyde, C,H,CHO; 1cI: = 1oG.05. Preparation of Kahlbaum’s, redistilled. Densities from K ~ p p . Tip ~ No. I. 30.2
1 .0349
50.0
I
,0169
42.358 39.9’4
927.56 884.33
423.7 425.5
At 20’ Lanqolt finds a density of 1.0473 (his only value) as compared to 1.0442 of Kopp, which would leave some doubt as to the accuracy of Kopp’s figures. The value of w a t 50’ here was determined immediately after the distillation, while that a t 30.2’ was not found until the following day. Considering these two facts, especially in view of the a
L O G . cit. Liebig’s Ann., 94, 316 (1855).
1718
GENERAL, PHYSICAL AND INORGANIC.
known instability of this substance, i t is more than probable that the liquid is normal and non-associated, for the above discrepancy in the values of t, of 1.8', i. e., of 0.42 per cent. can readily be ascribed to them. From capillary rise Ramsay and Shields find for this liquid: t.
d.
r.
T(M/d)$.
15.4 78.3
.0480 0.95915
39.19 31.72
850.6 714.4
I
tz from
k B = 2.1012,
426.3 424.3
Regarding the temperature change of drop weight, as well as drop volume, as linear we find wt = 46.084 - 0.1234t and 21, = 43.491 - 0.08481, the application of I and I11 giving rt = 40.716 - o.Iogt and ai = 7.844 - 0.0153t. Interpolating between the values of Ramsay and Shields, we find for r and a2the following values compared with those from the above equation : t.
rM&o.
rR&S.
a2M & 0.
0 2 R & S.
30.2 50.0
37.424 35.266
37.43 35.09
7.382 7.079
7.360 7.014
Piperidine, CH,(CH,CH,)NH; M = 85.08. Kahlbaum preparation, redistilled. T i p No. I . Above 30' the liquid in the apparatus turned yellow, so that no determinations above that point were attempted. The densities here were taken from the formula dt = 0.88125 - o.ooog91t obtained as a mean of the equations found from the densities employed by Ramsay and Shields and by Ramsay and Aston, viz.: 0.88025 - o.ooogg5tI and 0.8822 - o.ooog87t, for i t seems to agree better in general with the results obtained by others than do theirs; thus a t o o Ladenburg and Roth' find 0.8810. The values calculated for t, here are t.
0
30
d.
0.88125 0.85 152
W.
w(M/d)$.
35.720 31.648
751.73 681.45
tc from
kg =
2 3936.
320.1 320.7
from which i t is evident that the liquid is perfectly normal m its behavior, and non-associated. The values of t,, as well as those quantities from which that is derived, as found by Ramsay and Shields and by Ramsay and Aston, are given in the following tables : Ber., 17,513.
WEIGHT OF A FALLING DROP AND THE LAWS OF TATE.
Ramsay and Shields, k,
16.5 46.4 78.4
0.8640 0.8337 0.8024 Ramsay and
15.2
0.8670 0.8363 0.8048 0.7256
46.2 78.4 132.5
1719
= 2.1012.
29.89 26.43
637. I 576.8 509.3
22.75
Aston, kB
X.
325.7 326.9 326.8
= 2 . I 2 I2 .
635.6 570.7 501.8 390.6
29.67 26.21 22.46 16.72
320.9 321.7 321 .o 322.6
Assuming the relationships to be linear we find for drop weight and for drop volume from this tip the equations Wt = 35.720 - 0.1357t and vt = 40.534 - 0 . 1 1 2 2 4 from which i t follows from I and I11 that rt = 31.559 - o.IIggt and a: = 7.311 - 0.02024t; while from 16.5' to 46.4' Ramsay and Shields find r, = 31.79 0.1155t and Ramsay and Aston rr = 31.35 - o . r r t ; and a: = 7.392 - 0.0205t and a: = 7.260 - o.o187t, respectively. From these relationships we find a t o o and 30' the various values of r and a2 to be:
-
0
30
rM & 0.
rR & S.
TR & A.
31.559 27.962
31.79 28.32
31.36 28.03
a%
&
0.
a2R & S:
aaR & A .
7.392 6.777
7.260 6.700
7.311 6.704
Diisoamyl, ((CH,),CHCH,CH,),; hi = 142.18;t, obs. = 402'. Kahlbaum preparation, redistilled. Density a t ' 0 from Wurtz ;' that a t the others interpolated from the results of Falk on this same sample. With TiP No. I the following results were obtained: 1.
0
30
d.
0.74'3 0.7161
W.
26.114
23 344 9
w(M/d)#.
tc from k p = 2.3936.
868.50 794.48
368.3 368.0
It is evident that this liquid, also, is non-associated. The variation with temperature of the drop weight, assuming it to be linear, is W t = 26. I 14 - 0.09203t and that of the drop volume is Vt = 35.227 - 0.0873f which by aid of I and 111 lead to yt = 23.072 - 0.08131t and
Jahresber. Fortschritte d . Chem., 8, 573.
1720
GENERAL, PHYSICAL AND INORGANIC.
a2 = 6.354 - 0.01575t. The only measurements of the capillary rise of this liquid are those by Schiff which lead to the quite different values a:,B = 6.603 and a:so,l 3.579 as compared to 6.313 and 3.848 (the latter extrapolated through 129') from the above formula. Isoamyl Acetate, C,H,O,C,H,,; M = 130.1I. Kahlbaum preparation, redistilled. Densities from Bolle and Guye.' Tifi No. ZZ.
-
1.
0
49.7
d.
w(M/d)t.
W.
0.8941 0.8444
28.076 23.032
776.80 662 .or
fC
from
-
kg
2.3098.
342.4 342.4
This liquid; according to the definition, is perfectly normal and nonassociated. From the above values, assuming linear relationships, we find w8 = 28.076 -o.IoI5t,
and
31.401 - O.O83Ot, from which i t follows, employing I1 and IV, that rt 25.706 - o.ogzg3t and a: = 5.869 -0.oI55It. No results of capillary rise are to be found in the literature. Nitrobenzene, C,H,NO,; M = 123.05. Kahlbaum preparation, redistilled. Densities from Guye and d, = 1.3057 - 0.000845(~-11)- o.ooooo125(t-11)~.Tip No. IZ. Vt =
-
2.
30.2 49.7
d.
I . 1908 I , 1729
W.
w(M/d)%.
44.950 42.592
989.82 947.42
tC from
k,
-
2.3098.
464.8 466.0
From capillary rise the following results have been obtained : t.
9.4 55.5 98.8 I53 .o 13.6 78.4 156.2
Guye and Baud, k , d. r.
-
2.1012. 8, 954.5 856.5 760.9 650.8
7( M/d)
I .2ogo I. 1680
43.80 38.41 I . 1240 33.26 27.40 I .0625 Ramsay and Shields, k , = I. 188 42.75 I . 124 34.89 1.047 26.94
tc
.
465.4 469.2 467.0 469.0
2.1012.
942.8 798.2 646.0
468.3 464.3 469.7
Owing to the varying values found by various observers for the density of this liquid, the results from drop weight may be taken as showing that J . chim. phys., 3, 39 (1905). Arch. sci. ph.y.v.T. et nat. Geneuo, [4]11, 466
(1901).
WEIGHT OF A FALLING DROP AND THE LAWS OF TATE.
x. 1721
it is non-associated not-ithstanding the discrepancy of 1.2' in t,. The values of w, and vt found above, assuming linear relationships, lead to the equations wt = 48.601 - 0.1209t and v; = 39.970 - 0.07359t from which by I1 and IV we obtain r, = 44.498 - o.1107t and a: = 7.471 - 0.01376t. Waldenl expresses the results of Guye and Baud by means of the equations rt = 44.945 - 0.1178t and a: = 7.533 o.orqg2t. A comparison of the values from these equations a t the temperatures 30.2' .and 49,7' with the values from the equations from drop weight as well as those interpolated from Ramsay and Shields is made in the following table : Values of a' and of I. 1. a%&o. aaW. dR&S. rM80. 7W. TR & s.
-
7.055 6.787
30.2
49.7
7.072 6.791
7.080 6.776
41.155 38.996
41.387 39.090
40.74 37.38
The striking thing about these results is that while the Ramsay and Shields values differ widely for 7, they are in good agreement with the others as far as concerns a2. This, of course, is due to the fact that Ramsay and Shields used the quite different densities of Kopp, nhich affect the results r = x h x d x Y , while the a2 values are simply the product of the height and the radius. The values of r calculated from the drop weight are of course independent of the density, while those for a2 are calculated with a knowledge of that factor. Methyl Ethyl Ketone, CH,COGH,; M = 72.06. Sample from Eimer and Amend, prepared by Emerson. Densities from the volumes of Thorpe and Jones.a The drop weights from Ti# No. ZZ, together with those calculated from the eqdation found from them by the method of least squares, are given below: W; 1.
-
28.358
- 0.I279t + O.CJOOr99f'.
w (obs.).
28.353 26.514 30 24.664 45 23.020 2. physilt. Chem., 65, 142 (1908). a J . Chem. SOC., 63, 283 (1893). 0 1.5
w (from
A.
equation).
28.358 26.484 24.700 23.005
+0.005
.030 +0.036
-o
4.015
GENERAL, PHYSICAL AND INORGANIC.
1722
while the drop volumes are Z't
1. 0
'5 30 45
= 34.IpO
- O.II434t + 0.000170gt2.
w/d.
v (from equation).
A.
34.176 32.553 30.874 29 ' 404
34.190 32.513 30.914 29.391
+0.014 --o .040
$0.040 -0.013
The application of the new definition of normal molecular weight leads to the following values of t,: 1. 0
15
30 45
d.
W.
0.82961 0 . 8 I449 0.79886
28.353 26.514 24.664
w(M/d)%.
0,78288
2,7.020
556.09 526.47 496. I3 469.28
tc from kB
-
2.3098.
246.8 249.0 250.8 254.2
from which it is evident that the liquid is abnormal, i. e., associated. No values from capillary rise are to be found in the literature but the application of I1 and IV to the drop weight and drop volume equations lead to rt = 25.964 - 0.1171t o.ooo1822t2 and a: = 6.391 - 0.02137t o.oooo31g4t~.
+ +
Diethyl Ketone, C,H,COC,H,; M = 86.08. Sample obtained through Eimer and Amend from Emerson, redistilled within 0.1'. Densities calculated from the volumes given by Thorpe and Jones1 The observed drop weights from Tip No. I, as well as those calculated from the equation derived from them, are as follows: 29.394 - 0.2233t. (obs.). w (from equation).
Wt =
t. 0
'5 30. I 45
w
29.394 27.694 25.984 24.295
29.404 27.696 25.958 24.310
A. ---o.OIO *.Go2
S0.626 +o.o15
while for drop volumes we have = 25.253 I,
0
I5 30. I 45
- 0.10634 - o.0001787t~.
w / d (obs.).
v (from equation).
35.278 33.618 32.300
35.253 33.698 32.214 28.830
28.800
A.
4.025 +0.080 4 .086
+0.030
The application of the definition of normal molecular weight leads to the following values of t,: LOC. C i t .
WEIGHT OF A FALLING DROP AND THE LAWS OF TATE. d.
1.
'5 30.I 45
29.404
647.25 618.11 585.46
27.696 25.958 24.310
-
1723
2.3936. 276.4 278.7 280.7 282.8
w(M/d)*. tc from kB
W.
0.83350 0.82384 0.80365 0.78929
0
X.
554'92
from which i t is clear that the liquid is abnoimal, i. e., associated. The use of I and I11 leads here with the equations for wtand vt to Tt = 25.970 - 0 . I O O I t a', = 6.363 - o.oIgIgt 0.0000322~t2 but no values from capillary rise are to be found in the literature.
+
Profiyl Alcohol, C,H,OH; M = 60.06. Kahlbadm preparation, redistilled. Densities are from Young.' The drop weights found and calculated from an equation are as follows: Tifi No. I. 27.817 - 0.08857t. w (from equation). 28.362 28.322 27.740 27.799 27.188 27.188 25.872 25.833 24.761 24.744 22.662 22.636 21.620 21 499 ~1
=
A.
w (obs.).
-5.7 f0.2 7.1 22.4
34.5 58.2 70.2
4. 040
$0.059 0.000
-.039 $0.017 +0.026 --0.021
The drop volumes (w,/d,) given below are a t temperatures a t which Young gives values for the density, the values of w being those from the above equation. vt =
d.
1.
20
40
60
- o.oooogo2t,.
w/d,
W.
0.8193 0.8035 0.7875 0.7700
0
33.950 - 0.07586t
27.817
33.952 32.416 30.824 29.225
26.046
24.274 22.503
u (from equation).
'33.950 32.413 30.836 29.217
A. 4 . 0 0 2
-0.003 +0.012 -0.008
That propyl alcohol is abnormal in molecular weight, i. e., is associated, is shown by the following values of tc (a fact which is also confirmed by results from capillaq rise): 1. 0
20
40 60
d.
0.8193 0.8035 0.7875 0.7700
W.
27.817 26.046 24.274 22.503
w(M/d)f.
487.21 462.18 436.55 410.81
tc
from kg =. 2.3936.
a09.6 219.1
228.4 237.6
From the above equations for w and v, we find, by aid of I and 111, the following values for and a2: Proc. Roy. SOC.Dub., Ia (N.S.),442 (19x0).
I724
GENERAL, PHYSICAL, AND INORGANIC.
rt and
-
24.577 - 0.07825t
a: = 6.124 - 0.o1368t - o.ooooog06t2. A comparison of the values of r and a2 found from these equations with those found by other observers (Renard and Guye, Ramsay and Shields) by the method of capillary rise is made in the two tables below, at the temperatures a t which they worked. All numbers which are in parentheses are foilnd by interpolating or extrapolating, using the ternperature coefficient found from the two nearest figures; this is also true with all the other tables given later. Values of 1.
M 8 0 (trom equation).
10.2 16.4 36.0 44.5 46.3 57.8 65.9 75.8 78.3 90.6
r. R & 0.
23.69 (23.19) 21.61
23.778 23.294 21.760 21 .egg 20.954 20.054 19.420 18.646' 18.450' 17.488'
21.05
(20.90) I9,97 I9 .a7 18.33 (18.19) I7.48
Values of ax. 1.
5.8 10.2
16.4 36.0 44.5 46.3 57.8 65.9 75.8 78.3 90.6
97.1
M
a 0.
6.044 5.984 5.897 5.620 5 a497 5.465 5 303 5.183 5.035l 4.997l 4.810' 4.710' 9
R & s.
(6.181)Schiff 6.223 (6.112) 6.014 (5.7041 (5.570) 5 * 543 (5 364) (5.237) (5.083) 5.045 (4.853) (4.752)Schiff 4.718
As will be observed from the above the values from drop weight always lie between those found by Renard and Guye and those of Ramsay and Shields, more closely approaching, however, those of the former. Profiwnitrile, C,H,CN; M = 55.04. Kahlbaum preparation, redistilled. Densities from Thorpe.2 d, 0.80101- o.ooog815t- 0.000000125t2. Tifi No. I . Extrapolated. Trans. Chem. SOC.,37, 141 and 327.
WEIGHT OF A FALLING DROP AND THE LAWS OF "ATE. Wt
6.5 17.7 37.7 60.3 71.2 qt
w (from equation).
31.I90 29.859 27.560 24.950 23.608 = 39.840 - o.09066t
0.80101 0.78117 0.76093 0.74027
20
40 60
31 e942 29.611 27.279 24.948
A.
-0.005
31.185 29.879 27.547 24.913 23.642 - 0.0002045t2.
+0.020
-0.013 ---o.037 $0.034
w/d.
v (from equation).
A.
39.877 37.906 35.850 33.70'
39.840 37.945 35.886 32.664
-.037 +0.039 $0.036 --a. 037
d (Thorpe). w (from equation). 0
I725
- 0.11657t.
31.942
w (obs.).
t.
X.
That this liquid, also, is abnormal, i. e . , associated according to the new definition, is shown by the following t, values a t the above even temperatures. t.
w(M/d)l.
0
535.87 515.14 473.57
20
40 60
kg = 2.4936. 229.9 At 16.8' R. and S. find 238.7'
tc from
337.0 243.9
61.8OR.and G. find 249.7'
2 5 0 . 3 At
441.13
From the equations for drop weight and drop volume, we find, using I and 111, Tt = 28.221 - 0,1032 a; = 7.186 - 0.01639 - o.oooo368gt2. I n the table below the values of and a z as found by aid of these equations are compared with those found a t other temperatures by the capillary rise method.
--
Values of a*.
Values of 7.
.
c
1.
M&0.
11.8 27.006
16.8 31.3 46.4 48.I 61.8 78.1 78.3 89.9
26.491 24.997 23.442 23.267 21.856 20.177' 20.156~ 18.961~
R&S.
c
R&G
I
11.8 (26.74) 16.8 25.13 31.3 (23.39) 46.4 61.8 23.19 127.29
21.69
78.1
M&0.
6.988 6..901 6.638 6.348 6.035 5.685l
78.3 5.681' (19.90) 89.9 5.4'7' 18.67 97.o 5.253l 19.92
R&S.
RLG
(7.030) 7.038 6.933 (6.913) (6.652) 6.652 6 . 3 5 8 (6.329) (6.018) 6.000 (5.657) 5.631 5 ' 6.53 (5.627) (5.397) 5.382 (5.240) ( 5 . 2 3 2 ) Schiff 5.453
Acetone, CH,COCH,; M = 58.05. Kahlbaum preparation, redistilled. Densities from Thorpe's volumes. Tip No. ZZ. t.
15 30.I 60
w
Wt = 27.666 - 0.1.739t. (obs.). II) (from equation).
25.674 23.610 19.642
25.657 23.636 19.632
A.
-0.017 S0.026
--o. 0 1 0
1726
GENERAL, PHYSICAL A N D INORGANIC. 2’ t =
d.
t.
15 30. I 60
0.80177
0,78348 0.74962
33.993 - 0.1296t. (w obs./d.
32.022 30. I35 26.203
v (from equation).
32 ,049 30.092 26.217
A fo.027 -0.043 S0.014
The values of t, calculated for this liquid show it, also, to be abnormal,
i. e., associated. w(M/d)#.
445.99 416.50 356.86
lc from kg = 2.3098. 214.1 216.5 220.5
From the above weight and volume relations, by aid of I1 and I V , we obtain rt = 25.330 - 0.1226t and a:= 6,354 - 0.02422t. The values of r and a2 observed by the various investigators (Ramsay and Shields, Dutoit and Friederich, and Renard and Guye), or interpolated or extrapolated from their work, are compared with those calculated from the above equations in the following tables : t.
M & 0.
-1.2
25.477l 23 ‘ 748l 23.271 22.755 22.657 21.652 21.186 19.923 19.641 18.575 18.513 15.73O1
12.9 16.8 2 1 .o
21.8
30.0
33.8 44.1 46.4 55.1 56.6 78.3 I .2
12.9 16.8 2 1 .o 21.8
30.0 33,8 44. 1 46.4 55.1 55.6 78.3
6.383l 6.042~ 5.974 5.845 5.826 5.627 5.535 5.286
5.230 5 .OI9 5.007 4. 458l
WEIGHT OF A FALLING DROP A N D THE LAWS OF TATE.
X.
I727
Just as with nitrobenzene, the agreement in the a2 values here is better than that of the y values. It must be remembered again in this connection that the surface tensions from capillary rise are dependent upon the density, and the various observers have not all used the same values while the y value from drop weight is independent of density, except that of benzene, for i t is from the y values of that only that the constant for the transformation of w into. y is found. The a 2 values, on the other hand, are dependent, when found from drop weight, upon the density, while those from capillary rise are directly observed. The better agreement of the u 2 values, then, is a proof that the densities we have employed (Thorpe’s) are the correct ones, for they transform directly observed drop n eight results into indirect values agreeing with the directly observed capillary rise, or would transform directly observed capillary rise values into calculated surface tensions agreeing with those found directly from directly observed drop weights.
Summary. I. On the basis of the new definition of normal molecular weight in the liquid state, the finding of a calculated value of t, independent of the temperature of observation (to) in the equation w(M/d)s = k,(t,to- 6), where k , is found from the same equation for benzene a t all temperatures when its observed critical point, 288.5 O , is used as t,, it is shown that methyl hexyl ketone, benzyl cyanide, benzaldehyde, piperidine, diisoamyl, isoamyl acetate, and nitrobenzene are perfectly normal, i. e . , nonassociated, the calculated 1, remaining constant within the limits of error. Methyl ethyl ketone, diethyl ketone, propyl alcohol, propionitrile, and acetone on the other hand are abnormal, 2. e., associated, for the values of t, calculated for them increase with increased temperature of observation. 11. The values of surface tension in dynes, y, and of the capillary constant az,calculated respectively from the drop weights and the drop volumes, are found to agree with the values observed from capillary rise even better than these do when found by different observers, for in most cases where comparison is possible, the values from the drop weight method lie between those found by the investigators on capillary rise. 111. Equations giving the variation of the surface tension y and the capillary const. u2, as found from the drop weight, are given for all the above liquids, that for r being especially important for i t is independent of any knowledge of the density of the liquid, a cause of variation, all too often encountered in the results by the capillary rise method. The values of a2, on the other hand, are here dependent upon the density, but as great care has been taken in the selection of the observed values, those of Thorpe or Young being used when possible, i t is thought that great stress may also be laid upon them. LABORATORY OF PHYSICAL CHEMISTRY.
