Almer McDuffee McAfee.

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LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.

RECEIVED BY EXCHANGE

Class



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, McAFKE, B.A.

NEW YORK CITY
1911



EASTON, PA.:

ESCHSNBACH 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



EASTON, PA.:

ESCHENBACH PRINTING COMPANY.
1911.



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.



226929






CONTENTS

Introduction and Object of the Investigation 5

Experimental Results 9

Discussion of the Results l %

Summary. 22



OBJECT OF THE INVESTIGATION.

According to Ramsay and Shields 1 liquids may be divided
into two great classes the so-called non-associated and
associated liquids, the former following the law,



where by definition



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 Morgan 3 which avoids the multiplica-
tion of error inherent in this equation. In brief, this method
consists in rinding once for all a value of K from

r(M/d) == K B (288.5 < 6),

where 288.5 * s the observed critical temperature of ben-
zene. Using this K then for other liquids in

r(M/d) = K B (* C * 6)

he shows that normal molecular weight is characterized by
the giving of a calculated value of t c which is independent
of the temperature of observation. An associated liquid
then is one which does not give the same calculated t c at all
temperatures of observation.

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*

1 Z. physik. Chem,, 12, 433~475 (1893).

2 f, here, is the surface tension in dynes per centimeter, M the molec-
ular weight, d t and d 2 the densities at the temperature t v and t v t c the
critical temperature of the liquid and K a constant with a mean value
2.12 ergs.

3 May Journal, Jour. Am. Chem. Soc., 1911.



It has been shown in former researches 1 that the weight of a
drop cf 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 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. The
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.

The apparatus employed together with the thermostat is
the same as that recently described by Morgan. 2 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 B in the formula

1 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.



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 Eotvos as modified by
Ramsay and Shields, i. e.,

-TJT __



Benzene was used as the standardizing liquid with the
following results:

t. Vessel +30 drops. Vessel +5 drops. W.

60.4 9.4232 8.7888

9.42305 8.7888 25.37

60.4 9.4229 8.7888

d. W. M. (M/J) tc. KB-

60.4 0.83583 25.37 78 20.574 288.5 2.3502

As a preliminary check on this K B value, quinoline was
observed with the following result.

/, Vesself 30 drops. Vessel (empty). W.

9.9561 8.6487 43.58

60 . 3 9 . 9560

d. W. M. (MA*)3. KB- fc(calc.).
60.3 I.06I49 43-58 129 24.536 2.3502 521.25

As Morgan found here from results of Morgan and Higgins 1
a value of 521.3 for t c this value of K B may be regarded as
satisfactory and will be used throughout this work.

As already alluded to, drop weight is proportional to
surface tension, and since



= 2.3502 (t c t 6)
and



1 Loc. tit.




or



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 K 1
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 2.1211
Renard and Guye K (from benzene) values 2 . 1 108
P. Walden K (from benzene) values 2 . 1260

The average of these K values is 2.1148 which is used
throughout this work.

In the capillary rise method rh = a 2 (the height of the
liquid in a capillary of i mm. radius). For purpose of com-
parison it was thought well to transform drop weight into
a 2 values also.

Since W = constant -y
**

and a 2 = constant ~
a

W

a 2 = constant r.
a

Knowing the density and drop weight of a liquid at any
one temperature a 2 is thus readily calculated by the em-
ployment of the proper constant.

To calculate this constant, the a 2 values for benzene ac-
cording to the four workers above referred to were taken.
Knowing the value of a 2 and the value of W at the corre-
1 May Journal, Jour. Am. Chem. Soc., 1911.



spending temperature, which can be readily calculated from
the formula,

w 2-35Q2 [288.5 (* + 6)]

(7*\*
UJ

the desired constant is obtained.

RAMSAY AND SHIELDS. *

t. h. r. W. a 3 . K.

80 3.945 0.012935 22.75 5.104 0.18287
90 3.772 0.012935 21.43 4.879 0.18308

ioo 3-603 0.012935 20.14 4.662 0.18371

RAMSAY AND ASTON. 2

11. 2 3-642 0.01843 3 2 - 2 7 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

RKNARD AND GUYK. S

11.4 4.346 0.01522 32.25 6.6146 0.18217

55.1 3-744 0.01522 26.10 5-6984 0.18376

78.3 3-3 8 5 0.01522 22.97 5- I 52o 0.18319

P. WALDKN.*

18.1 3.392 0.0193 31.28 6.550 0.18446
38-3 3-!57 0.0193 28.42 6.090 0.18417

The average of these constants (0.1838) is used throughout
this work for transforming drop weight into a 2 values,

W,

a] = 0.1 838.
a t

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.

8 Z. physik. Chem., 15, I, 91.

3 Jour. d. Chimie Physique, 5, 92 (1907).

4 Z. Physik. Chem., 75, 568 (1910).



10

TABLE i.

Vessel, Vessel,

I. 30 drops. Average. 10 drops. Average. W.

o 11.1770 94905

11.1770 11.1770 94905 84.325

11.1770 9-4905

1.8 11.1697 9.4886

11.1695 9.4886 84.045

11.1693 9.4886

4 11-1572 9-4844

11.1572 9-48445 83.638

11.1572 9-4845

6 11.1459 9.4804

11.14625 9.4804 83.293

11.1466 9-4807
9.4801

7.5 11.1387 9-478i

11.1382 9-478o

11.1389 11.1385 9-4778 9-478o 83.027

11-1385 9-478o
11-1383
11-1385

12.95 i i. 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

11.0862 11.08626 9-46045 81.291
i i . 0868 9 . 4604

19.25 11.0740 9 4556

11.0740 9-4556 80.92
11.0740



II

TABLE; I. (Continued}.

Vessel, Vessel,

t. 30 drops. Average. 10 drops. Average. W.

22.5 11.0555 9-4495

11.05565 9-4495 80.308

11.0558 9-4495

25.3 11.0422 9-44 6 4

11.04255 9-44 6 5 79-803

11.0429 9.4466

27.81 11.0275 9 .4409

11.0278 9.44105 79 .338

11.0281 9-44 12

30 11.0174 9-4383

11.0176 11.0172 9.4385 9-43847 78.937

11.0166 9-4384

36.46 10.9797 9-4 2 52

10.98005 9-42505 77-750

10.9804 9 .4249

40 10.9608 9 .4195

10.9608 9.41936 77.072

10.9608 9-4I93

45 10.9323 9-4105

10.9319 9-4 J o5 76.070

10.9315 9 4 I0 5

55 10.8735

9.3921
10.8737 10.87346 9-3920 74-073

9 3919
10.8732

60 10.8456 9-3825

10.8456 9-38265 73-I48

10.8456 9-3828

70 10.7821 9-3604

10.7820 9.36065 71.068

.10.7819 9.3609



t.

77



10



20



60



70



12

I. (Continued^).



Vessel,
50 drops.


Average.


Vessel, Average.
10 drops.


w.


0.7410




9.3487




0.7410


10.7413


9-3487


69-63<


o-74 J 9




9-3487




ETHYL ALCOHOL.


9.3168
9.3168
9.3168


9.3168


8 . 7988
8 . 7988
8 . 7988


25.90


9.3969
9.3966


9-39675


8 . 8964
8 . 8966
8.8968


25.01


9.3702
9.3702


9.3702


8.8878
8.8878
8.8878


24. 12


9-3I97
9.3201
9.3200


9-3I993


8.8735
8-8734
8.8733


22.33


9-2955
9-2955


9-2955


8 . 8660
8 . 86605
8.8661


21.47


9.1663
9.1656
9.1660


9.16596


8-7537
8.7538
8-7539


20. 6 1


9.2613
9.2616


9 26145


8-8575
8.85745
8-8574


20.20


9.2506
9.2507


9.25065


8.8539
8.8541

8-8543


19.83



METHYL ALCOHOL.
9.4379 8.9104

9.4383 9-4379 8.9100 8.91026 26.38
9-4375 8.9104



13
TABLE I. (Continued').

t. Vessel. Average. Vessel, Average. w

30 drops. 10 drops

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 8.8694 8.8694 21.76

9 . 3048 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 9-396o 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-8o as calculated from drop weight



which is multiplied by - . Columns 4 and 5 contain the
2.3502

values for surface tension of water at intervals from o-8o
by the method of capillary rise. Volkmann's values 1 from
o-40 and B runner's values 2 from 4O-8o as given by
Landolt, Bornstein and Meyerhoffer, Physikalisch Chemische
Tabellen, p. 102, are contained in column 4. Ramsay and
Shields' values 3 are given in column 5.

TABLE 2.

(R. &S.).
73.21



71-94



70.60
69. 10

67.50
65.98

64.27
62.55

60.84

In Table 3 is given the t c 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.



/.


w.


r-


r (v. &B.)





84-325


75 88


75 49


' 1.8


84.045


75.63


75-23


4


83.638


75.26


74.90


6


83 2.93


74-95


74.60


7-5


83.027


74-71


74-38


10


82.597*


74 32


74 oi


12-95


82.033


73-8.2


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


22.5


80 . 308


72.26


72-15


25-30


79.803


71.81


7i-73


27. 8i


79-338


71-39


71.36


30


78.937


71.03


71.03


36.46


77-750


69.96


70.02


40


77.072


69 35


69 54


45


76.070


68.45


68.60


50


75-152*


67 63


67.60


55


74-073


66.65


66.90


60


73 148


65-82


66.00


70


71.068


63 95


64.20


77


69.630


62.66


62 .90


80


69 . ooo*


62.09


62.30



W,(M/<y = 2.3502(^ ^ 6)
and from capillary rise according to the formula

* c * 6)



TABLE; 3.



t.


w.


d. 1


W(M/<*)i.


tc.





84-325


0.999868


579-22


252.45


1.8


84.045


0.999961


577-i6




4


83.638


I . OOOOOO


574-45


2 54.42


6


83.293


o . 999968


572.09


255.42


7-5


83.027


o . 999902


570.29


256.16


10


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


o . 996994


549-21


264.98


27.8l


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


40


77.072


0.992240


532.li


272.41


45


76.070


0.990250


525-90


274.76


50


75-I52


0.988070


520.31


277 39


55


74-073


0.985730


513-65


279.56


60


73 H8


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 . ooo


0.971830


483-03


291 52




r(M/d)f.


r(M/<*)i.


tc.


tc.


/.


(V. &B.).


(R. &S.).


(V.&B.).


(R. &S.).





518.53


502 . 90


251.19


243 . 80


10


508.41


494-20


256.41


249.69


20


498 - 74


485-30


261.84


255.48


30


489.27


476. 10


267.36


26I.I3


40


480 . i i


466 . 30


273.02


266.50


50


469.41


456.40


277.97


27I.8I


60


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, Bornstein and Meyerhoffer, Tabellen, p. 37.
*Read from curve.



i6

In Table 4 a further comparison is made by means of a 8
as calculated from drop weight (a 2 = 0.1838 W/d) and
a 2 = r h observed from capillary rise by Volkmann, Brunner
and Ramsay and Shields.

TABLE 4.

02 a a cfl

t. fromW. (V. &B.). (R. &S.).

o 15-501 I5-405 14.921
10 15 -^S I 5- I 03 14.664

20 14.870 I4-823 14.412

30 I4-572 I4-566 I4-I38

40 I4-277 I4-295 13.860

50 I3-980 I3-990 I3-605

60 I3-674 I3-700 I3-3I4

70 ' I3-358 I3-390 I3-032

80 13.080 13.080 12.750

TABLE 5.

W(M/d)l. W(M/d)f. W(M/d)i.

t. Obs. Calc. Theoretical.

o 579-22 578.96 579-22

10 567-40 567-36 568.25

20 555-34 555-65 556.98

30 543-73 543-84 545-41

40 532-11 531-93 533-53

50 520.31 5I9-9I 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 1 . 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 Timberg 2 agrees very
closely with Ramsay and Shields.

1 Jour. Am. Chem. Soc. t 31, 309.
* Wied. Ann., 30, 545 (1887).



TABLE 6. ETHYL ALCOHOL, M = 46, t c = 244.



/.


w.


r-


(R.&S.).


Timberg.





25-90


23-3I


23.80




10


25.01


22.51


22.90


23-35


20


24. 12


21 .70


22.03


22. 6l


30


23.27*


20.94


21 . II


21.63


40


22.33


20.09


20.20


20.70


50


21.47


19.32


I9.3I


19.82


6o


20. 61


18.55


18.43


18-93


65


20.20


18.18


17.97


18.05


70


I9-83


17.84


17.52





TABLE 7.



t.


d.


r (M/d)a.
W(M/<i). (R. & S-).


tc-
from W.


t c .

(R. & S.).


O





o


8095




382


.88


350.2


168


9


171.


6


10







.8014




372


. 12


340.5


J74


4


177.


o


20







.7926




36i


-56


330.4


179


.8


182.


2


30




o


.7840




349


95


319-9


185


-5


I8 7 .


3


40







7754




339


.61


308.9


190


5


192.


i


50







.7663




329


.20


297.6


196


. i


I 9 6.


7


60







7572




3i8


47


285.9


201


5


201 .


2


65







7523




313


52


279.9


204


4


203.


3


70




o


7474




309


. 12


273.8


207


4


205.


5














TABLE


8.










/. a 2 from W. o


: 2 (R. &S.).


a* (Timberg).











5


.879




6.180




6


.019






10






5


740




6-035




5


.896






20






5


593




5.890




5


773






30






5


434




5.601




5


-583






40






5


293




5.3I3




5


.402






50






5


.150




5 - HO




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.



r (R. &S.). a 2 from W. a* (R. & S.).






26.38


23-74


24.36


5.986


6. 129


10


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


I9-58


19 55


5.228


5.213



*Read from curve.



i8
TABLE 10.









f (M/d)5.




tc.


*.


d.


w(M/<2).


(R. &S.).


tc.


(R. &S.).





O.SlOO


306 . oo


282.66


136.2


139-7


10


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


i55-oo


158.0


40


0-7745


270.81


249 . 06


161 .2


163.8


50


0.7650


262.22


235.60


167.6


167.4



TABLE n. ACETIC ACID.

r. r (R. &S.). 1 a 2 from W. a*(R. &S).



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


25-7I


23-I4


21-75


4.697


4.408


70


24.70


22.23


21 .OI


4-563


4-307



TABLE 12.

r(M/d). * c . t c .

(R. & S.)- 1 from W. (R. & S.). 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 392-47 332.1 233.0 223.0

70 0.9948 379-88 323.2 237.6 228.8



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 K B 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.






hi obs.


h z (corrected).


A 3 from curve.


7.86


8.00


8.00


7.69


7-83


7-85


7-395


7.525


7-525


7.24


7-37


7.385


7-105


7-23


7-23


6.96


7.08


7-075



19

determinations on water by Ramsay and Shields 1 may be
cited.

t.

7-4
19-3
40.0
50.0
60.0
70.0

Here is a correction of the obseived reading of over i l / 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
K B 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 B runner 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 B runner 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).



20

As will be seen, the results by the two methods on the alcohols
agree satisfactorily at the higher temperature.

What has been said in regard to surface tension applies
equally as well, of course, to t c calculations, since drop weight
is substituted for surface tension in the formula of Ramsay
and Shields. Referring to the tables containing t c 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 ^-(M/J)^ obtained by Ramsay
and Shields for water, ethyl alcohol, methyl alcohol and
acetic acid, the ciitical 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)^ 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' 0-00052*2.

In Table 5 column marked "W(M/rf) J calc. " is shown how
closely this equation agrees with the observed values. How-
ever, as Morgan 2 has shown, the coefficient of / divided by
twice the coefficient of / 2 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 t c . Assuming 579.22

1 Jour. Am. Chem. Soc., 31, March, 1909.
* 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) ? = 579.22 1.08172 O.OOI52 2 .

In Table 5 column marked " W(M/cf) theoretical" is given
the calculated function values from this equation, and it is


1

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