CHEM. LIB.
QD
463
.M113
ulbe
B 397748
The Drop Weight of the Associated
Liquids-Water, Ethyl Alcohol,
Methyl Alcohol and Acetic Acid
DISSERTATION
SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRE-
MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
IN THE FACULTY OF PURE SCIENCE IN COLUMBIA
UNIVERSITY IN THE CITY OF NEW YORK.
BY
A. MCD, MCAFEE, B.A.
NEW YORK CITY
1911
EASTON, PA.:
ESCHENBACH PRINTING COMPANY.
1911.
・
The Drop Weight of the Associated
Liquids---Water, Ethyl Alcohol,
Methyl Alcohol and Acetic Acid
DISSERTATION
SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIRE-
MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
IN THE FACULTY OF PURE SCIENCE IN COLUMBIA
UNIVERSITY IN THE CITY OF NEW YORK.
BY
A. McD. MCAFEE, B.A.
NEW YORK CITY
1911
EASTON, PA.:
ESCHENBACH PRINTING COMPANY.
1911.
CHEM. LIB.
QD
4 63
M113
0 17 My 13 TG
ACKNOWLEDGMENT.
The author begs to thank Professor J. Livingston R.
Morgan for his advice, assistance and encouragement, with-
out which this work would have been impossible.
CONTENTS
Introduction and Object of the Investigation.
Experimental Results.
Discussion of the Results.
Summary.
• •
•
...J.
1
5
9
18
22
OBJECT OF THE INVESTIGATION.
According tc Ramsay and Shields' liquids may be divided
into two great classes-the so-called non-associated and
associated liquids, the former following the law,
7₁(M/d₁)³ = K(tc — t₁ —6)
where by definition
K
˜₁(M/d₁)³ —ɣ₂(M/d₂)³ 2
t₁ — t₂
The associated liquids do not follow this law, but show
different values for K, as defined. A new way of calculating
K is soon to be given by Morgan³ which avoids the multiplica-
tion of error inherent in this equation. In brief, this method
consists in finding once for all a value of K from
r(M/d)3 KB (288.5-t—6),
where 288.5 is the observed critical temperature of ben-
zene. Using this K then for other liquids in
r(M/d)? KB (t-t-6)
C
he shows that normal molecular weight is characterized by
the giving of a calculated value of t which is independent
of the temperature of observation. An associated liquid
then is one which does not give the same calculated t at all
temperatures of observation.
C
Naturally, this is just what is contained in the Ramsay
and Shields relation, only removing the multiplication of
error in the form for calculation,
K = A[r(M/d)³].
At
1 Z. physik. Chem., 12, 433-475 (1893).
2
7, here, is the surface tension in dynes per centimeter, M the molec-
ular weight, d₁ and d₂ the densities at the temperature t, and t₂, to the
critical temperature of the liquid and K a constant with a mean value
2.12 ergs.
3
³ May Journal, Jour. Am. Chem. Soc., 1911.
6
It has been shown in former researches¹ that the weight of a
drop of liquid, falling from a properly constructed tip, is
proportional to the surface tension of the liquid. It has
further been shown that for all non-associated liquids thus
far investigated, falling drop weights may be substituted
for surface tensions in the above formula. By this simple
method, surface tensions, molecular weights and critical
temperatures of the non-associated liquids may be more
easily and accurately calculated than that attained by
capillary rise.
The
The object of the present investigation was to apply this
method of falling drop weights to certain typical associated
liquids to determine whether the same relations obtain with
this class of liquids as with the non-associated ones.
liquids so investigated were water, ethyl alcohol, methyl
alcohol and acetic acid. The water used was distilled from
potassium dichromate and sulphuric acid and then redistilled
with a little barium hydroxide. The alcohols and acetic
acid used were Kahlbaum's "Special K." The acid was
further purified by freezing. While in the apparatus they
were protected from any moisture by suitable drying agents.
2
The apparatus employed together with the thermostat is
the same as that recently described by Morgan. It was
necessary not only to have as constant temperature as possi-
ble, but to have also a wide range of temperature; the thermo-
stat described by him fulfilled both these requirements
admirably, and also permitted a quick change from one
temperature to another.
Standardization of the Tip.
The tip used in this work was approximately 5.530 mm.
in diameter. The first requisite was the standardization
of the tip, or, in other words, to find K in the formula
B
Morgan and Stevenson, Jour. Am. Chem. Soc., 30, No. 3, March,
1908; Morgan and Higgins, Jour. Am. Chem. Soc., 30, No. 7, July, 1908.
2 Jour. Am. Chem. Soc., 33, No. 3, March, 1911.
7
W₁(M/d,)³
KB
288.5
(t+6)
where W is the falling drop weight, expressed in milligrams,
of the liquid at the temperature. t, and is substituted for
surface tension in the formula of Eötvös as modified by
Ramsay and Shields, i. e.,
K
=
7.(M/d)i
tc (t+6)
Benzene was used as the standardizing liquid with the
following results:
W.
Vessel+5 drops.
Vessel+30 drops.
8.7888
60.4°
9.4232
8.7888 25.37
9.42305
8.7888
60.4
9.4229
d.
W.
M.
(M/d)?
tc.
KB..
2.3502
60.4 0.83583 25.37 78 20.574 288.5
B
As a preliminary check on this KR value, quinoline was
observed with the following result.
t, Vessel+30 drops.
Vessel (empty).
W.
60.3° 9.9562
9.9561
8.6487
43.58
60.3 9.9560
d.
W.
M. (M/d)3.
KB.
tc (calc.).
60.3 1.06149 43.58
129 24.536 2.3502
521.25
As Morgan found here from results of Morgan and Higgins¹
a value of 521.3 for t this value of K may be regarded as
satisfactory and will be used throughout this work.
B
As already alluded to, drop weight is proportional to
surface tension, and since
and
W¸(M/d₁)³ = 2.3502 (tc
2.3502 (t—t—6)
7₁(M/d₁)² = K(t—t—6)
1 Loc. cit.
1
or
W
8
t
2.3502
rt
K
K
W
2.3502
}
The second important constant to be determined was
therefore the one necessary for the correct fulfilment of the
Ramsay and Shields formula. Knowing the value of this
'constant, surface tension from drop weight can be immediately
calculated as shown above.
As has already been indicated the value of this constant
is approximately 2.12 ergs. In this work, the average K¹
from the benzene values of Ramsay and Shields, Ramsay
and Aston, Renard and Guye and P. Walden has been taken
as being nearest the truth.
Ramsay and Shields K (from benzene) values 2.1012
Ramsay and Aston K (from benzene) values
Renard and Guye K (from benzene) values
P. Walden K (from benzene) values
2.1211
2.1108
2.1260
The average of these K values is 2.1148 which is used
throughout this work.
In the capillary rise method rh = a² (the height of the
liquid in a capillary of 1 mm. radius). For purpose of com-
parison it was thought well to transform drop weight into
a² values also.
Since W
and a²
constant r
Y
constant
d
W
a²
= constant
Knowing the density and drop weight of a liquid at any
one temperature a² is thus readily calculated by the em-
ployment of the proper constant.
To calculate this constant, the a² values for benzene ac-
cording to the four workers above referred to were taken.
Knowing the value of a² and the value of W at the corre-
1
¹ May Journal, Jour. Am. Chem. Soc., 1911.
9
sponding temperature, which can be readily calculated from
the formula,
W₁
t
2.3502 [288.5-(t+6)]
7813
di
the desired constant is obtained.
RAMSAY AND SHIELDS.¹
1.
n.
Y.
W.
a².
K.
80°
3.945
0.012935
22.75
5.104
0.18287
90
3.772
0.012935
21.43 4.879
0.18308
100
3.603
0.012935 20.14 4.662
0.18371
RAMSAY AND ASTON.2
II.2 3.642
0.01843 32.27 6.7122
0.18473
46
3.213
0.01843
27.35
5.9216
0.18432
78
2.810
0.01843 23.01 5.1789
0.18475
RENARD AND GUYE.3
II.4 4.346
0.01522
32.25 6.6146
0.18217
55.1 3.744
0.01522
26.10
5.6984
0.18376
78.3 3.385
0.01522
22.97
5.1520
0.18319
P. WALDEN.4
0.0193
0.0193
31.28
6.550
0.18446
18.1 3.392
38.3 3.157
28.42 6.090 0.18417
The average of these constants (0.1838) is used throughout
this work for transforming drop weight into a² values,
a₁ = 0.1838
W
di
EXPERIMENTAL PART.
Water.
With water the checks at times were very much poorer
than with the other liquids. This may be due to impurity
on the tip, or to the fact that the drop is so large that slight
variations may occur in releasing it. In every case every
precaution was taken to remove any impurity by aid of
sulphuric acid and bichromate.
1 Loc. cit.
2 Z. physik. Chem., 15, 1, 91.
3
Jour. d. Chimie Physique, 5, 92 (1907).
4
• Z. Physik. Chem., 75, 568 (1910).
Vesse!,
1.
30 drops.
Average.
ΙΟ
TABLE I.
Vessel,
Io drops.
r
Average.
W.
11.1770
9.4905
11.1770 1.1770
9.4905 84.325
II. 1770
9.4905
1.8 11.1697
9.4886
II. 1695
9.4886 84.045
11.1693
9.4886
4
11.1572
9.4844
11.1572
9.48445 83.638
11.1572
9.4845
6
II. 1459
9.4804*
II. 14625
9.4804 83.293
II. 1466
9.4807
9.4801
7.5 11.1387
9.4781
11.1382
9.4780
11.1389 11.1385
11.1385
9.4778 9.4780 83.027
11.1385
9.4780
11.1383
11.1385
12.95
II. 1088
9.4678
11.10845
9.4678
82.033
11.1081
9.4678
15
11.0973
9.4640
11.0964 11.09686
9.4640
81.643
9.4640
II.0969
17
11.0858
9.4605
II.0862 II.08626
9.46045 81.291
II.0868
9.4604
19.25 II.0740
9.4556
II.0740
9.4556 80.92
11.0740
9.4556
ΙΙ
TABLE I.-(Continued).
t.
Vessel,
30 drops.
Average.
Vessel,
10 drops.
Average.
W.
22.5 11.0555
9.4495
+
11.05565
9.4495
80.308
II.0558
9.4495
25.3 11.0422
9.4464
11.04255
9.4465 79.803
II.0429
9.4466
27.81 11.0275
9.4409
1
11.0278
9.44105 79.338.
II.0281
9.4412
30.
11.0174
9.4383
11.0176 11.0172
9.4385 9.43847 78.937
II.0166
9.4384
36.46 10.9797
9.4252
10.98005
9.42505 77.750
10.9804
9.4249
}
40
10.9608
9.4195
10.9608
9.41936 77.972
10.9608
9.4193
45
10.9323
9.4105
10.9319
9.4105 76.070
10.9315
9.4105
55
10.8735
9.3921
10.8737 10.87346
9.3920 74.073
9.3919
10.8732
60
10.8456
9.3825
10.8456
10.8456
9.3828
9. 38265
9.38265 73.148
70
10.7821
9.3604
10.7820
9.36065 71.068
10.7819
9.3609
12
TABLE I.-(Continued).
t.
Vessel,
30 drops.
Average.
Vessel,
10 drops.
Average.
W.
77
10.7410
9.3487
10.7410 10.7413
9.3487
69.630
10.7419
9.3487
ETHYL ALCOHOL.
9.3168
8.7988
9.3168
9.3168
8.7988
25.90
9.3168
8.7988
ΙΟ
9.3969
8.8964
9.39675
8.8966
25.01
9.3966
8.8968
20
9.3702
8.8878
9.3702
8.8878
24.12
9.3702
8.8878
40
9.3197
8.8735
9.3201 9.31993
8.8734 22.33
9.3200
8.8733
50
9.2955
8.8660
9.2955
8.86605 21.47
9.2955
8.8661
60
9.ì663
8.7537
9.1656
9. 16596
8.7538 20.61
9.1660
8.7539
65
9.2613
8.8575
9.26145
8.85745 20.20
9.2616
8.8574
1
70
9.2506
8.8539
9.25065
8.8541 19.83
9.2507
8.8543
METHYL ALCOHOL.
9.4379
8.9104
9.4383 9.4379
9.4375
8.9100 8.91026 26.38
8.9104
13
TABLE I.—(Continued).
t.
Vessel,
Average.
30 drops.
Vessel,
10 drops
Average.
w.
20
9.3819
8.8918
9.3822 9.38225
8.8917
24.53
9.3826
8.8916
30
9.3565
8.8846
9.35665
8.8846
23.60
9.3568
8.8846
40
9.3300
8.8764
9.32975
8.8765
22.66
9.3295
8.8766
50
9.3042
8.8694
9.3045 9.3045
9.3048
8.8694 8.8694 21.76
8.8694
ACETIC ACID.
20
9.5445
8.9464
9.5438
8.9464
9.54417
8.9464
29.89
9.5439
8.9464
9.5445
40
9.4820
8.9268
9.4824 9.48246 8.9270 8.9270 27.77
9.4830
8.9272
60
9.4239
8.9100
9.4243 9.4242
8.9100
25.71
9.4244
8.9100
70
9.3960
8.9023
9.39625
8.90225 24.70
9.3965
8.9022
In the following table is given the surface tension of water
at intervals from o°-80° as calculated from drop weight
14
which is multiplied by
2.1148
2.3502*
Columns 4 and 5 contain the
values for surface tension of water at intervals from o°-80°
by the method of capillary rise. Volkmann's values¹ from
0°-40° and Brunner's values from 40°-80° as given by
Landolt, Börnstein and Meyerhoffer, Physikalisch Chemische
Tabellen, p. 102, are contained in column 4. Ramsay and
Shields' values³ are given in column 5.
TABLE 2.
t.
W.
7.
r (V. & B.).
°°
84.325
75.88
75.49
T (R. & S.).
73.21
1.8
84.045
75.63
75.23
4
83.638
75.26
74.90
6
83.293
74.95
74.60
7.5
83.027
74.71
74.38
ΙΟ
82.597*
74.32
74.01
71.94
12.95
82.033
73.82
73.55
15
81.643
73.46
73.26
17
81.291
73.15
72.96
19.25
80.920
72.81
72.63
20
80.760*
72.67
72.53
70.60
22.5
80.308
72.26
72.15
25.30
79.803
71.81
71.73
27.81
79.338
71.39
71.36
30
78.937
71.03
71.03
69.10
36.46
77.750
69.96
70.02
40
77.072
69.35
69.54
67.50
45
76.070
68.45
68.60
50
75.152*
67.63
67.60
65.98
55
74.073
66.65
66.90
60
73.148
65.82
66.00
64.27
70
71.068
63.95
64.20
62.55
77
69.630
62.66
62.90
80
69.000*
62.09
62.30
60.84
In Table 3 is given the t¸ of water as calculated from drop
weight according to the formula
1 Ann. d. Physik. u. Chemie, 56, 457 (1895).
2 Pogg. Ann., 70, 481 (1847).
3 Z. physik. Chem., 12, 433 (1893).
*Read from curve.
15
W₁(M/d,)³
2.3502(t − t — 6)
2.3502(to-t
and from capillary rise according to the formula
T₁(M/d₁) i
2.1148(t¸ — t — 6)
TABLE 3.
t.
W.
d.1
W(M/d)}.
tc.
84.325
0.999868
579.22
252.45
1.8
84.045
0.999961
577.16
253.42
4
83.638
I.000000
574.45 254.42
6
83.293
0.999968 572.09
255.42
7.5
83.027
0.999902
570.29
256.16
IO
82.597*
0.999727 567.40
257.43
12.95
82.033
0.999404
563.65
258.75
15
81.643
0.999126
561.07
259.73
17
81.291
0.998970 558.71
260.73
19.25
80.920
0.998382
556.39
262.00
20
80.760*
0.998230 555.34
262.30
22.5
80.308
0.997682 552.43
263.56
25.30 79.803
0.996994 549.21
264.98
27.81 79.338
0.996316
546.26
266.24
30
78.937
0.995673
543.73
267.36
36.46
77.750
0.993355
536.38
270.69
94558
40
77.072
0.992240
532.II
272.41
76.070
0.990250
525.90
274.76
50
75.152
0.988070
520.31
277.39
74.073
0.985730
513.65
279.56
60
73.148
0.983240
508.10
282.19
70
71.068
0.977810 495.47
286.82
77
69.630
0.973680
486.82
290.14
80
69.000
0.971830
483.03
291.52
r(M/d)}.
r(M/d)s.
t.
(V. & B.).
(R. & S.).
tc.
(V. & B.).
tc.
(R. & S.).
O
518.53
502.90
251.19
243.80
ΙΟ
508.41
494.20
256.41
249.69
20
498.74
485.30
261.84
255.48
30
489.27
476.10
267.36
261.13
40
480. II
466.30
273.02
266.50
50
469.41
456.40
277.97
271.81
бо
458.44
446.20
282.78
276.99
70
447.59
436.00
287.65
282.01
80
436.12
425.30
292.22
287.10
¹ Landolt, Börnstein and Meyerhoffer, Tabellen, p. 37.
*Read from curve.
16
In Table 4 a further comparison is made by means of a²
as calculated from drop weight (a² = 0.1838 W/d) and
rh observed from capillary rise by Volkmann, Brunner
and Ramsay and Shields.
a²
=
1!
TABLE 4.
t.
a2
from W.
a²
(V. & B.).
a2
(R. & S.).
15.501
15.405
14.921
10
15.185
15.103
14.664
20
14.870
14.823
14.412
30
14.572
14.566
14.138
40
14.277
14.295
13.860
50
13.980
13.990
13.605
60
13.674
13.700
13.314
70
13.358
13.390
13.032
80
13.080
13.080
12.750
TABLE 5.
W(M/d).
W(M/d)}.
W(M/d).
t.
Obs.
Calc.
Theoretical.
O
579.22
578.96
579.22
IO
567.40
567.36
568.25
20
555.34
555.65
556.98
30
543.73
543.84
545.41
40
532.II
531.93
533.53
50
520.31
519.91
521.35
60
508.10
507.79
508.86
70
495.47
495.57
496.08
80
483.03
483.24
482.99
In the following tables the Ramsay and Shields values
have been calculated from the equations for their function
values as derived by Morgan'. With acetic acid only one
determination was made at low temperature by these ob-
servers, and, as was pointed out in the article just referred
to, the equation for acetic acid functions does not give good
results at low temperatures; hence the values given here for
acetic acid from capillary rise must be regarded as only
approximate. With ethyl alcohol Timberg2 agrees very
closely with Ramsay and Shields.
Jour. Am. Chem. Soc., 31, 309.
2 Wied. Ann., 30, 545 (1887).
17
TABLE 6.-ETHYL ALCOHOL, M
=
46, tc
244.
r.
Timberg.
t.
W.
7.
(R. & S.).
25.90
23.31
23.80
ΙΟ
25.01
22.51
22.90
23.35
20
24.12
21.70
22.03
22.61
30
23.27*
20.94
21.II
21.63
40
22.33
20.09
20.20
20.70
50
21.47
19.32
19.31
19.82
60
20.61
18.55
18.43
18.93
65
20.20
18.18
17.97
18.05
70
19.83
17.84
17.52
TABLE 7.
r (M/d)}.
t.
d.
W(M/d)3.
(R. & S.).
tc.
from W.
tc.
(R. & S.).
0.8095
382.88
350.2
168.9
171.6
10
0.8014
372.12
340.5
174.4
177.0
20
0.7926
361.56 330.4
179.8
182.2
30
0.7840 349.95 319.9
185.5
187.3
40
0.7754 339.61
308.9
190.5
192. I
50
0.7663 329.20 297.6
196.1
196.7
60
0.7572
318.47 285.9
201.5
201.2
65
0.7523
313.52
279.9
204.4
203.3
70
0.7474
309. 12
273.8
207.4
205.5
TABLE 8.
t.
a² from W.
a² (R, & S.).
a² (Timberg).
5.879
6.180
6.019
ΙΟ
5.740
6.035
5.896
20
5.593
5.890
5.773
Lagu Aw
30
5.434
5.601
5.583
40
5.293
5.313
5.402
50
5.150
5.140
5.252
60
5.003
4.967
5.070
65
4.933
4.875
4.978
70
4.871
4.783
4.886
TABLE 9.-METHYL ALCOHOL.
W.
T.
† (R. & S.).
a² from W.
a² (R. & S.).
26.38
23.74
24.36
5.986
6.129
ΙΟ
25.45*
22.90
23.50
5.846
5.986
20
24.53
22.07
23.02
5.704
5.937
30
23.60
21.24
21.74
5.540
5.660
40
22.66
20.39 20.84
5.378
5.486
50
21.76
19.58
19.55
5.228
5.213
*Read from curve.
18
TABLE IO.
r (M/d)}.
t.
d.
W(M/d)?.
(R. & S.).
tc.
tc.
(R. & S.).
0.8100
306.00
282.66
136.2
139.7
IO
0.8002*
297.62
274.77
142.6
145.9
20
0.7905
289.20 271.40
149.0
154.3.
30
0.7830
280.01 257.97
155.00
158.0
40
0.7745
270.81 249.06 161.2
163.8
50
0.7650
262.22 235.60 167.6
TABLE II.-ACETIC ACID.
167.4
1.
W.
T.
•
T (R. & S.).¹
a² from W.
a² (R. & S).¹
20° 29.89
26.90
25.01
5.237
4.859
30 28.83*
25.94
23.87
5.099
4.682
40
27.77
24.99
23.49
4.963
4.656
50
26.74
*
24.01
23.19
4.830
4.646
60
25.71
23.14
21.75
4.697
4.408
70
24.70
22.23
21.01
4.563
4:307
TABLE 12.
r(M/d)}.
tc.
tc.
t.
d.
W(M/d)}. (R. & S.).¹
from W.
(R. & S.).¹
1
20°
1.0491
443.70
371.2
214.8
201.5
30
1.0392
430.67 356.6 | 219.3
204.6
40
1.0284
417.74
348.8
223.7
210.9
50
1.0175
405.10
340.6
228.4
217.0
60
I.0060
392.47*
332. I
233.0
223.0
70
0.9948
379.88
323.2
237.6
228.8
B
Discussion of Results.
As has already been shown, surface tension as calculated
from the drop weight of a liquid is influenced by only the
drop weight of the liquid and the density of benzene from
which the KR values are calculated; and from the foregoing
results it is seen with what extreme accuracy drop weight
may be determined. On the other hand, by the method of
capillary rise, errors may occur from incorrect readings of
the volume of the liquid, the non-uniformity in diameter of
the tube, and incorrect values for the density of the liquid.
As an example of the magnitude of the first error a few
*Read from curve.
¹ Approximation.
19
determinations on water by Ramsay and Shields¹ may be
cited.
1.
h₁ obs.
h₂ (corrected).
hz from curve.
7.4
7.86
8.00
8.00
19.3
7.69
7.83
7.85
40.0
7.395
7.525
7.525
50.0
7.24
7.37
7.385
60.0
7.105
7.23
7.23
70.0
6.96
7.08
7.075
В
Here is a correction of the observed reading of over 11/2
per cent.
A glance through the literature on capillary rise
method shows widely varying results among the most accurate
workers. By the drop weight method, knowing the value of
KB for the tip, surface tensions may be readily duplicated,
as has been repeatedly done with water during the course of
this investigation. Hence it would seem that the surface
tensions given in this paper for water, ethyl alcohol, methyl
alcohol and acetic acid are the most correct values thus far
determined under saturated air conditions.
The splendid results on water obtained by Volkmann and
by Brunner by capillary rise agree very closely indeed with
surface tension results obtained by drop weight method.
As regards the surface tension values obtained by Ramsay
and Shields, it is significant that the higher the temperature
at which the drop weight is determined the more closely do
the latter results agree with the former. Volkmann as well
as Brunner worked under the same conditions under which
this investigation was carried out, namely, saturated air
conditions; Ramsay and Shields, however, excluded air, the
pressure being that of the vapor pressure of the liquid itself.
As will be seen, the greatest difference is with water at the
lower temperatures; this is to be expected since the greater
the surface tension, the greater the solubility of air in the
liquid. Naturally enough then, the higher the temperature
at which the drop weight is determined the more nearly
should the Ramsay and Shields' values be approached, since
the conditions under which they worked is also approached.
1 Z. physik. Chem., 12, 471 (1895).
1
1
20
As will be seen, the results by the two methods on the alcohols
agree satisfactorily at the higher temperature.
C
C
What has been said in regard to surface tension applies
equally as well, of course, to t calculations, since drop weight
is substituted for surface tension in the formula of Ramsay
and Shields. Referring to the tables containing to calcula-
tions it is seen here again that the higher the temperature at
which drop weight is determined the nearer is the true critical
temperature of the liquid approached. In a paper by
Morgan,¹ it was shown that by applying the method of least
squares to the function values 7(M/d) obtained by Ramsay
and Shields for water, ethyl alcohol, methyl alcohol and
acetic acid, the critical temperature of these associated
liquids could be calculated, the resulting calculation agreeing
very closely with the observed critical temperature values.
The functions so treated had a range of temperature of not
less than 140°.
In this work it was hoped that by applying this method of
least squares to the function values W(M/d)³ the critical
temperatures of these liquids could be calculated. In every
case, however, the method has failed. The function values
for water so treated give the equation,
W(M/d)?
578.96–1.155-0.0005212.
In Table 5 column marked "W(M/d)³ calc." is shown how
closely this equation agrees with the observed values. How-
ever, as Morgan' has shown, the coefficient of t divided by
twice the coefficient of t gives critical temperature less 6.
As is seen, the coefficients here so treated give an absurd
number.
It was suspected that since the highest temperature at
which a determination by this method can be made is several
degrees below that of the boiling point of the liquid, the
extrapolation necessary for calculating critical temperature
would be too great. This is clearly shown in figuring out the
function values necessary for correct to. Assuming 579.22
¹ Jour. Am. Chem. Soc., 31, March, 1909.
2 Loc. cit.
21
(the observed function value at zero) as correct, and 357 as
the critical temperature of water less 6, the theoretical
equation for function values becomes,
W(M/d)3
579.22-1.0817t-0.001512.
In Table 5 column marked "W(M/d) theoretical" is given
the calculated function values from this equation, and it is
seen that the observed values agree very closely at high
temperature.
The method of least squares was next applied to the
function values for water from o°-80° as used by Morgan.
The resulting equation gave just as absurd value for critical
temperature; indeed, it showed practically a linear rela-
tionship through this temperature range. The drop weight
and also the function value show practically a linear rela-
tionship in all four cases, especially at the lower temperatures;
there is a slight curve in each case as the boiling point of the
liquid is approached.
C
An equation for the different te values for water was worked
out according to the method of least squares with the follow-
ing result:
tc
=
252.41 0.508t-0.000225ť.
When 357 is substituted for t here t¸ becomes 405.
C
The values for t from 50-80 were treated in the same
manner with the resulting equation,
to
284.28 0.4895t-0.00736t.
C
When 357 is substituted for t here t becomes 365 thus
showing clearly that the higher values are necessary for
calculating critical temperature of associated liquids.
Many other possibilities for calculating critical tempera-
ture were tried out with the same negative results. They
all showed, however, that the observed function values agree
with the theoretical, and hence it must be concluded that the
extrapolation is too great even when treated by the method
of least squares.
SUMMARY.
The results of this investigation may be summarized as
follows:
1. The drop weights of the associated liquids-water,
ethyl alcohol, methyl alcohol and acetic acid have been
accurately determined at small temperature intervals from
zero to a few degrees below the boiling point.
2. It has been shown that the resulting drop. weights.
transformed into surface tensions give the most accurate
values for same, under saturated air conditions, thus far
determined.
3. Unlike the non-associated liquids, critical temperature
could not be calculated even with a wide range of temperature,
still higher temperatures are necessary.
BIOGRAPHY.
A. McD. McAfee was born in Corsicana, Texas, September
24, 1886.
He entered the University of Texas in 1904,
taking the B.A. degree there in 1908. He was Fellow in
Chemistry in 1907-'08 and the following two years he was a
graduate student and Tutor in Chemistry in the University
of Texas. In the fall of 1910 he entered Columbia Uni-
versity as Goldschmidt Fellow in Chemistry. His major
work has been in Physical Chemistry.
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