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I. A HELIUM LIQUEFIER-CALORIMETER FOR HEAT CAPACITIES FROM 1-60 DEGREES K. II. THE ENTROPY OF ETHYL ALCOHOL FROM MOLECULAR DATA AND THE EQUILIBRIUM IN THE HYDRATION OF ETHYLENE. III. THE HEAT CAPACITY AND ENTROPY, HEATS OF FUSION AND VAPORIZATION, AND THE VAPOR PRESSURE OF ISOPENTANE.

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THE PENNSYLVANIA STATE COLLEGE
The Graduate School
Department of Chemistry
I.
A HELIUM LIQUEFIER-CALORIMETER FOR HEAT
CAPACITIES FROM 1°K. - 60°K.
II.
THE ENTROPY OF ETHYL ALCOHOL FROM MOLECULAR
DATA AND THE EQUILIBRIUM IN THE HYDRATION
OF ETHYLENE.
III.
THE HEAT CAPACITY AND ENTROPY, HEATS OF
FUSION AND VAPORIZATION,: AND THE VAPOR
PRESSURE OF ISOPENTANE.
A Thesis
SEYMOUR CYRUS SCHUMAN
Submitted in partial fulfillment
of the requirements
for the degree of
DOCTOR OF PHILOSOPHY'
August, 1940
Approved
Director of the Cryogenic Laboratory
Head of the Department of Chemistry
ACKNOWLEDGMENTS
The author wishes to express his appreciation and
thanks to Professor John G. A.ston for his direction
of these problems. The design and the majority of the
experimental work on the apparatus herein described in
Part I are due to him.
Thanks are due to Dr. G. H. Messerly and Mr. R. M.
Kennedy for the manometry readings described in Part
III, and especially to Mr. M. L. Sagenkahn for opera­
tion of the adiabatic shields essential to the obtain­
ing of the measurements in this part.
Finally, thanks are due Professor M. R. Fenske and
co-workers for the purification of the isopentane on
which the measurements of Part III were taken.
TABLE OF CONTENTS
Page
Summary ...........................
1
Introduction ..........................
3
A Helium Liquefier - Calorimeter for Heat
Capacities from 1 - 60°K................
7
Introduction........................
7
General Description.........
8
The Helium Bomb Liquefier...........
10
The Calorimeter............. *......
11
The, Double ResistanceThermometer
12
The Spiral System...................
13
The Shield..........................
15
Miscellaneous.......................
15
The Entropy of Ethyl Alcohol from Molecul­
ar Data and The Equilibrium in the Hydra­
tion of Ethylene......... .. ............
17
Introduction........................
17
The Entropy of Ethyl Alcohol Gas From
Thermal Data........................
18
The Entropy of Ethyl Alcohol Gas From
Molecular Data....... .. ..... .
Total Energy and FreeEnergy Tables...
18
26
Comparison with the Equilibrium Data..
26
Accuracy............................
30
Discussion..........................
31
Page
The Heat Capacity and Entropy, Heats of
Fusion and Vaporization and the Vapor
Pressure of Isopentane ...............
Purification of the Isopentane ........
33
35
The Apparatus and Heat Capacity Meas urements ...».........................
35
The Heat Capacity Measurements on
Liquid Isopentane
...........
40
The Heat Capacity Measurements on Solid
Isopentane ...........................
45
The Vapor Pressure Measurements .......
50
The Melting Point . .....
54
Heat of Fusion.......................
56
Heat of Vaporization.............. ...
56
The Entropy from Thermal D a t a ........
60
'The Entropy from Molecular Data.......
60
Accuracy .............................
64
Bibliography..............................
66
Appendix.................................
71
SUMMARY
Part I
A Helium Liquef lerrCalorlmeter for Heat Capacities From
1-60°K.-
Helium gas, expanded from 1500 IPs. /in.2 to
atmospheric pressure at 10°K. is partially condensed in
a-thick walled copper liquefier. It is likewise lique­
fied in a small chamber on the calorimeter by contact of
the entry tube of this chamber to the walls of the lique­
fier. The liquefier, calorimeter, resistance thermometers,,
spiral systems and other apparatus are described. It is
believed that this apparatus, now but partially’construct­
ed will be accurate to within an average of 0.5% in the
range 1-60°K.
Part II
The Entropy of Ethyl Alcohol From Molecular Data and The
Equilibrium in the Hydration of Ethylene.-
The entropy
and free energy of ethyl alcohol gas have been calculated
from the molecular data at several temperatures on the
basis of (a) free internal rotation, (b) restricted rota­
tion (with potentials; about C-C bond, 3000, C-0 bond,
10,000 calories). The latter values are in perfect agree­
ment with those from the third law and from the equilibr­
ium data on the hydration of ethylene.
Part III
The Heat Capacity and Entropy, Heats of Fusion and Vapor­
ization, and The Vapor Pressure of Isopentane.-
The heat
2.
capacity of isopentane has been determined from 20°K.to
the boiling point. The melting point of isopentane is
113.39°K.(-159.77°C) and the boiling point is 300.90°K.
(27.74°C). Heats of fusion and vaporization have been
determined. The molal values for isopentane are 1226.3
+ 0.5 and 5873 + 10 cal./mole, the latter value being
calculated at 25°C. The vapor pressure of liquid iso­
pentane over the range 217°K. to the boiling point is
given by the equation: logiopmm. = -9170.850/T 194.4680 log10T + 0.3108920 T - 1.936031 x 10"^ T-2 +
439.3143.
From the experimental data at the boiling point,
the molal entropy of the ideal gas at 298.16 °K. is
calculated to be 81.69 ± 0.3 e.u. To bring the value
calculated from molecular data into agreement with the
experimental value requires a potential of 38OO calor­
ies hindering the three methyl groups and the frequency
of 188 cm“- hindering ethyl group rotation in isopent­
ane.
Hysteresis in solid and liquid isopentane is describ­
ed. It is believed that these effects are manifestations
of a slow thermal equilibrium between two forms of iso­
pentane.
4
3.
HISTORICAL
INTRODUCTION
This:: thesis describes experimental and theoretical
work which began at the time when the mechanics of
complicated organic molecules was less understood than
we think it is now#
The uncertainty concerned the
extent to which there was free rotation about single
bonds in organic compounds. (1,2)
Attention was called
to this when it was discovered that the entropy of
tetramethylmethane at its normal boiling point as
calculated from spectroscopic and .molecular data
assuming free internal rotation, did not agree with
that obtained using the Third Law of Thermodynamics
in conjunction with complete thermal data extending
to 13°K. (3 ),
There was no proof that the crystal of tetramethyl­
methane was in a state which would allow safe extrapolation
to 0°K. on the basis of a perfect crystal (i.e. , one
with zero entropy at the absolute zero ).
Such crystals
had already been found in the case of H2 (4) , CO (5),
NgO (6 ), NO (7), and H2O (8); The first of these had
randomness due to molecular rotation. The remainder
possessed randomness frozen in at higher temperatures.
When disorder is frozen in, in this'way, it is probably
never removed# However, when disorder is produced by
i
4
rotation it can be removed and appears as unsuspected
anomolies in the heat capacity of the crystal below
o
10 Xi For example, part of the entropy due the
molecular rotation in solid hydrogen is removed at
1.4°K. and appears as an anomolous maximum (lambda
point ) of over one calorie per degree.
It seemed desirable to look for a similar behavior
in the heat capacity of tetramethylmethane below 10 °K .
The heat capacity apparatus and liquefier described in
Part I was designed for this purpose and partially
built. Fortunately, there are interesting problems for
which it is needed, because it has now developed
that the discrepancy in the entropy of tetramethylmethane
as calculated by the two methods is probably due to
hindered rotation about single bonds, and not to un­
certainty in the entropy of the crystal at low
temperatures. This was first indicated by a similar study
of ethane (9) where its entropy could unequivocally
be calculated from the equilibrium data in the reaction
CH3-CH3
=
0H2=GH2 + H2
(10, 11, 12, 5-3) and the heat of the reaction (14)
as determined directly. The entropy from the thermal data
and the Third Law agreed with the entropy obtained from
the equilibrium data.
To calculate an entropy from the
molecular and spectroscopic data which wa,s in agreement
with both values required the assumption of a potential
of 3200 calories restricting the Internal rotation
about the single bond.
This value of the hindering potential was also
found to give calculated heat capacities in
complete agreement with the measured ones (15) and
also was necessary to explain the rotational
structure of the perpendicular absorption bands in
the infra-red (16) •
The investigation on ethyl alcohol and on the
equilibrium in the reaction,
GgH4+ H20
=
C2H5OH
described in Part II, demonstrated that potentials
likewise hindered rotation about the single bonds
in ethyl alcohol.
Thus, it was no longer necessary to doubt the
practical applicability of the Third Law of Thermodynamics
to organic compounds. The work on. the heat capacity
of tetramethylmethane below 10°K. was therefore
postponed in favor of a complete study of the
thermal data on 2-ts is'omer,~ isopentane, from 10°K to room
temperature, in order to allow a value of the entropy
of the gas at the normal boiling point to be obtained
and compared with that calculated from molecular and
spectroscopic data. Thus, a value of the potential
hindering the internal rotation about the bond
Joining the ethyl and isopropyl groups could be
found. Simlar studies had already been made in this
laboratory on methylamine (17), methyl chloride (18),
n-pentane (19), isobutane (20), n-butane (21), dimethylamine (22), acetone (23), and isopropyl alcohol(23). The experimental
data on the last two was
already available.
In view of what has been said previously, it is
somewhat ironical that isopentane turned out to be the
first compound in which a lack of equilibrium existed
in both the liquid and the solid. This may give rise
to a zero point entropy due to frozen - in randomness.
Such a randomness, of course, is one which would not be
detected by measurements below 10°K.
7.
PART I
A HELIUM LIQUEFIER - CALORIMETER FOR HEAT CAPACITIES
FROM 1 - 60cK
INTRODUCTION
The attainment of temperatures down to 1°K has in
the past "been desirable for the study of
1. the thermal behaviour of the crystalline state
2.
the phenomena of superoermctivity
3.
the anomolous behaviour of liquid helium.
Various external liquefiers of helium have been designed
to meet the needs of cpyostats permitting leisurely ob­
servations in the range 1 - 10°K (24,25,26). Among these
F. Simon (27) in 1932, demonstrated that, given any
thermally Isolated pressure chamber at from 10 - 20°K,
this chamber could be cooled to "helium temperatures"
by
the-' adiabatic expansion of cold helium gas from with­
in it.
It is curious to note that, by a similar process,
Cailletet (28) first
liquefied air in 1877. The work of
Simon immediately suggested the combination of such a
pressure chamber with the familiar type of low temperature
vacuum calorimeter to obtain heat capacities at very low
temperatures with the use of only a moderate quantity of
liquid hydrogen. Accordingly to permit such observations
on organic compounds,with the objectives as previously
ndted, an apparatus was designed, and is described here
APPARATUS
General Description
The apparatus, although primarily designed for heat
capacity measurements from 2-20°K, allowed measurements
up to 60°K. if desirable. Apart from the internal hel­
ium liquefier, its design and operation were in princ­
iple similar to a calorimeter successfully used in this
laboratory before (29). The significant change in the
vacuum compartment was the use of the bomb liquefier
as the heavy radiation block, preventing heat leakage
down the filling tube to the calorimeter.
To attain the lowest possible temperatures about
100 atmos. of helium gas are introduced into the bomb
with the cryostat cooled to 10°K by pumping on liquid
hydrogen. The bomb-liquefier-calorimeter system is now
thermally isolated and the high pressure gas expanded,
part of the helium remaining - as liquid in the bomb.
Helium liquefied by contact with the bomb is introd­
uced into the calorimeter, which is subsequently pump­
ed out. At the immediate disappearance of liquid, the
heat capacity measurements are begun.
Between 2° and 20°K absolute temperatures are de.te.r-
9.
mined by the use of a small constant volume gas thermo­
meter, the bulb of which is dmbedded in the calorimeter.
Constantan and phosphor-bronze (30) resistance thermo­
meter heaters are employed in establishing heat interv­
als between 2 - 9°K. The constantan element serves both
as the heater and thermometer between 10 -25°K, above
which interval temperatures could be determined by means
of a copper - constantan thermocouple soldered onto the
calorimeter.
Figure I shows the vacuum compartment of the appara­
tus together with the deep glass Dewar vessel N
which
contains the liquid hydrogen. This Dewar is enclosed in
a tight monel can permitting evaporation of the hydrogen
under reduced pressure. Referring again to the vacuum com­
partment, the calorimeter
meter
DO
is shown with its gas thermo­
and helium chamber
. The leads from the
strain free resistance thermometer
are passed first
through a small tube adjacent to the calorimeter in which
thermal contact is established between the wires and the
calorimeter. The 3 tube German silver spiral
es up through the bomb
ca
above which another spiral
is formed. The radiation shield
which is screw­
ed up onto the bomb and the vacuum tight monel can
C u l complete this
pass­
assembly. Original diffi-
vs
HELIUM
LIQUEFIED
AMt>
CALOtUMETEK
INCHE.^
10.
culties due to plugging of the small German silver
tubes :(i20 mm. I.D.) were eliminated by blowing them out
before use with high pressure gas. No trouble was encount­
ered in leakage through these tubes? as has been stated by
others in a similar apparatus recently reported (31)•
THE HELIUM LIQUEFIER
The bomb liquefier is of copper,;0.54 inches thick
with a straight length of 5*10 inches• It is rounded at
both ends into the shape of-a hollow hemisphere of 1*515
inch exterior diameter, so as to have a total volume of
approximately 200 cc. and weight of 2030 grams. A 1 cm.
I.D. tube passes through the bomb? coaxial with the long
axis of this liquefier» Figure II represents the liquefier
at an early stage of construction. Silver-soldered to the
top of the liquefier is a hollow ring of 4.6 cc. capacity,
which serves as the bulb of a helium gas thermometer* The
bomb is wound with a thermometer heater of #30 constantan
wire, baked on with Bakelite laquer and surrounded with
a thin #36 B & S'? copper sheath which is soft-soldered to
the bomb at various places. This heater has a resistance
of 328 ohms at room temperature.
The pressure and vacuum tests on the liquefier are
described in the Appendix (I). It £s interesting to note
that expanding a pressure of 1600 lbs of hydrogen to at­
mospheric pressure at a starting temperature of 84°K
coooled the bomb 3.94° as read upon a copper constantan
Figure II
Helium Bomb-Li quefier
Preliminary
Construction
thermocouple attached to the bomb. It is conceivable
however that a mist of liquid hydrogen was produced
within.
The Calorimeter
The calorimeter i s m cylindrical copper container,
gold-plated inside and out of .02 inch wall thickness,
7 cm. long and 4.1 cm.I.D.
A reentrant tube is integral
with the bottbm of the calorimeter with an I.D. of 6.85 mm.
at its upper end and 6.95 mm. at its lower end. The plat­
inum case of the thermometer heater was inserted into the
tube and rose-metalled in. Radial vanes;(.003") inside the
calorimeter served to increase heat conduction within. Tie
calorimeter has a volume of 80.7 cc. and with its spiral
a weight of 99ol8 grams.
Fastened to the side of the calorimeter, a flattened
chamber of 5*31 cc. volume serves as the calorimeter helium
chambers Built into the calorimeter is a cylindrical tube
63 mm. long and 10 mm. I.D.
This bulb is that of the 4.79
cc. gas thermometer which serves as the primary temperature
standards A tube of 2.5 mm, I.D. is soft-soldered to the
outside of the calorimeter for purposes noted previously.
Figure III is a scale drawing of the calorimeter Indicating
the gas thermometer, helium chamber, and radial vanes.
11a
CM.
* Figure III
Calorimeter
Scale Drawing
The Double Resistance Thermometer
The double resistance thermometer is of the strain
free type described previously by the Bureau of Stand­
ards (32) and this -laboratory
■ (29). Constantan and
phosphor bronze thermometer heater filaments occupy
part of the mica cross on which they are wrapped. Both
of these are wrapped bifilarly on this cross which has
a length of 6.5 cm. and a cross section of 6 mm. The
mica has a thickness of 0*2 mm. and has 13 notches per
cm., each notch having a depth of 0.5 nun. This cross
was annealed in an inert atmosphere at 500 - 700°C
and then inserted into the 6 mm. I. D. platinum case.
A constricted soft glass tube was sealed to the plat­
inum case by means of a cobalt seal, and the thermo­
meter then filled with helium
at 2/3 of an atmos­
phere .
The constantan element of this thermometer had a
room temperature resistance of 118 ohms, the phosphor
bronze of 12.8 ohms. A photograph of this thermometer
is indicated as Figure IV. A #36 copper - #30 B & S
constantan thermocouple, soft soldered onto the calor­
imeter can be used in conjunction with the gas thermo­
meter for temperature measurements above 20°K.
12a
Pigar©
iv
Resistance Thermometer
4
The Spiral System
Except for the calorimeter filling tube, the small
german silver tubes supplying the vacuum compartment
enter thfough small holes drilled in the can top. These
tubes are conveniently coiled into a 70 cm. spiral above the bomb. This spiral, which consists of 6 tubes
held together with bismuth solder and small #40 B & S
collars takes 4 turns above the bomb liquefier. The
individual tubes are:
1. the inlet to the liquefier
2 . the outlet to the liquefier
3. the liquefier gaB thermometer inlet
4. the calorimeter filling tube
5. the calorimeter gas thermometer inlet
6. the calorimeter helium chamber inlet.
The three tubes which proceed to the liquefier diverge
from the spiral about 1 cm. from the bomb. The calori­
meter tubes then pass through the long axis of the
bomb, bismuth soldered to the well tinned walls of this
space. Emerging they are formed into a second spiral,
likewise of 70 cm. length and coiled into 4 turns, be­
fore reaching their respective destinations on the cal­
orimeter.
m
14
Except for the calorimeter gas thermometer tube,
these German silver tubes are *60 mm. I.D.#J6.i035M O.D.
The calorimeter gas thermometer tube is .20 mm. I.D. of
•040" O.D. so as to reduce the dead space volume in
regions of the temperature gradient to a minimum.
The outlet and inlet to the bomb and calorimeter
helium chamber tube are silver-soldered to l/8” O.D.
German silver tubes directly outside the vacuum com­
partment. The latter two tubes are then coiled about
and soldered to a cup which is directly connected to
the can top. In this fashion 100 cm. of tubing for each
tube is employed. The helium inlet and outlet tubes are
silver- soldered to the bomb. The tube to the gas therm­
ometer in the bomb is soft soldered to the ” bulb ".
In the formation of the bomb spiral, the helium outlet
tube and the calorimeter helium chamber tube make good
thermal contact throughout the spiral length.
The three tubes comprising the lower spiral are soft
soldered into the calorimeter. The calorimeter filling
tube is wrapped witha #30 constantan heater along the upp­
er as well as the lower spiral. The latter tube alone
passes through the tube from the cryostat chamber and
thence to the exterior through a glass nipple in which
it is sealed with Dekhotinski cement.
The Shield
Threaded to the bottom of the bomb, the cylindrical
radiation shield completely encloses the calorimeter
and lower spiral. This shield is 17 cm. long of 1.5U
outer diameter and 5 mm. wall thickness. It has a
weight of 990 grams-i It is wound with a #30 constantan
heater which is baked on with Bakelite lacquer and
shielded with #40 copper sheet. This heater has a room
temperature resistance of 153 ohms. A copper constantan
thermocouple is soft soldered onto the outside of this
shield.
Miscellaneous.
The cryostat is; generally similar in design to ones
previously used in the laboratory. The hydrogen trans­
fer tube has been described, (see M. L. Sagenkahn M. S.
dissertation The Pennsylvania State College 1940)
The
manometer used to measure the pressure in the calorimet­
er gas thermometer chamber is read with a cathetometer
capable of a precision of .002 mm. An accurate vacuum
gauge is employed for the helium gas thermometer.
Appendix I summarizes the vacuum and pressure tests,
the calibrations and other miscellaneous material essent­
ial to the design of the apparatus.
It is believed that the apparatus described should
provide measurements of heat capacities accurate to
0.5$ in the region 1° - 60°K.
17
PART II
THE ENTROPY OF ETHYL ALCOHOL FROM MOLECULAR DATA AND
THE EQUILIBRIUM IN THE HYDRATION OF ETHYLENE
I INTRODUCTION
Recently discrepancies have been found between
entropies of nonrigid polyatomic molecules, calculated
from the molecular data assuming free internal rota­
tions, and those.from thermal data down to liquid hyd­
rogen temperatures and the third law of thermodynamics.
(33r3>7)-The discrepancy of about 2 e.u., per group cap­
able of internal rotation, might be due to random
orientation in the crystal at low temperatures, corr­
esponding to a zero point entropy of 2 e.u., or to a
force associated with potential barriers of about 3000
calories restricting the internal rotations (33, 35)*
Kemp and Pltzer (35) have shown that restricting pot­
entials are the cause of a discrepancy of 1*51 e.u. in
the entropy of ethane at 298°K by considering the equil­
ibrium in the hydrogenation of ethylene, a conclusion in
agreement with the infra-red absorption spectrum (38)
and the low temperature specific heats of the gas (39).
Taken together these jfacts are convincing; but ob­
viously, it Is desirable to obtain similar evidence in
other cases. The requirements are:
18
a?. Equilibrium constants for a reaction
wherein the number of internally rot­
ating groups is changed.
b. Complete thermal data down to liquid
hydrogen temperatures.
c. Molecular data for each substance.
d. An accurate value of
close to the
temperature of equilibrium.
Such a reaction is that involved in the vapor phase
of hydration of ethylene.
C2H4(g) + H20(g) = C2H50H(g).
II THE ENTROPY OF ETHYL ALCOHOL GAS FROM THERMAL DATA
Table II summarizes the calculation of the entropy
of the hypothetically perfect gas at the normal boiling
point and at 403.2°K from the best available calorimetric data. The entropy increase from 298.l6°K was ob­
tained by integration of the equation expressing the
heat capacity data of Fiock, Ginnings, and Holton (41).
III THE ENTROPY OF ETHYL ALCOHOL FROM MOLECULAR DATA
a. The vibrational entropy
Table II
THE CALORIMETRIC ENTROPY OP ETHYL ALCOHOL AT 351.5°K
AND 403.2°K.
E.U./Mole
0°K (cryst.)-298.16°K (liq.) (40)
Liquid 298.16-351.5°K (41)
Vaporization 9255/351*5 (41)
38.4 1.3
4.90+.005
26.331.03
Entropy of actual gas at boiling
point (351.5°K) (43)
Correction for gas imperfection (42)
69.631.3
.14
Entropy of ideal gas at boiling point
69 78“1.3 "
0°K (cryst.)-298.16°K (liq.) (40)
Liquid 298.16-403.2°K (41)
Vaporization 8034/403.2 (41)
38.4 1.3
9.99
19.93
Entropy of act. gas at 403.2 and
5.682 atmos.
Correction for gas imperfection (42)
68.321.3
.32
Entropy of ideal gas at 403.2°K and
5.682 atmos. (43)
R In 5.682
68.641.3
3.45
Entropy of ideal gas at 403.2°K and
1 atmos.
72.11.3
The Raman Spectrum (44a,b) seems to contain lines
corresponding to all but one of the nineteen modes of
vibration. As only a partial normal coordinate treatment
has been made, (44a) , comparison of spectra with other
molecules was resorted to. On this basis the following
frequency assignment has been made
0 - C - 0 skeleton:
883;*0(S‘), 1096; ^ ( tt) 433:
CH3 (internal) :-£>(it), 2930; 20ft-), 2930; T f a ) ,1274;
2?(<S-), 1455:
OH (internal): \3, 3359
CH2 (internal):-v) (it) =Si>(c)> 2930;"^ (n), 1274.
G - 0 - H (hydrogen angle variation):^!, (700).
CH3 - CH2 - 0 (hydrogen angle variation)
2'*^ 3» 814;
. 5, 1051 ;T 6 , 1^55.
The nomenclature is as usual (45, 34, 36) for the inner
frequencies of the groups. The frequencles^'i,'^ 2>*^3>
5, a n d ^ 5 , correspond to modes of vibration in
which the angle of bonds holding hydrogen is changed rel­
ative to the whole molecule. At the same time the intern­
al angles of the groups CH3, CH2, and OH are unchanged
(34, 35b).
The frequenoy*^ 1 for OH bending is apparently ab­
sent from the Raman spectrum and for this its corres­
ponding value in methyl alcohol has been used (34). The
assignment of the remaining five frequencies is largely
21.
a guess., As the result due to all elx<3 1 frequencies is
about what would result if all were at 950 onT1 (the
corresponding average for ©thane and ethylene) (46), no
large error would be expected. The errors due to an ex­
treme misinterpretation will be discussed presently.
Taking
hc/k as 1.452 and R as 1.9569, the vibration­
al entropy and -<(P0 - E^)/T)vib ar© then calculated
from fternst'o tables.
b» The translational and rotational entropy
The distances and angles used were: CH=l.llAj OK0.95A; CC«3.54A; 00*1.42As <HC0» <,000= <HCH=10S° 2 3 ’;
< G0H=110l> . For the model in which the methyl and hyd­
roxyl groups are rotating freely, th© translational and
rotational entropy was calculated by conventional meth­
ods (47,48).
Kassel has greatly simplifled the method of Tl&inoff and Aston, particularly in the case where symmet­
rical tops are attached to a rigid frame (se© his B>.
(43)). However his fq* (11) is obviously valid
for
any molecule with simple tops attached to & rigid frame,
whether those be symmetrical or not. The only limita­
tion is that these tops themselvea must be rigid. If
the attached rigid tops are not symmetrical the deter­
minant in Fq. (11) of Kassel is a function of the vari­
ables
which represent the angular position of these
22.
tops. The rotational entropy is then given by
Q= (2TtkT/h2 )3//2(8^2/(S') ^...
f e ] id^idc^
^O
OQ
(yy) + (zz)-(XX)
A=
= k lk 2 • • • k s+3* A
-(xy)-(X^
-(xz)-(XO)
-(xy)-(Xyw)
(xx)+(zz)-(^yu)
— (yz)— (j**"t)
“ (xz)— (\p)
-(yz)-^)
(xx)+(yy)-( JJ}
Our choice of axes was dictated by other related
problems so as to simplify the total labor. Initially,
the y axis was taken to bisect the angle between the
C - C bond and one of the CH bonds of the CH2 group.
The x-y plane Included both of these bonds.
The terms of ^1^ about parallel axes through the
center of gravity x 1040 are:
(xx)=32.54-1.18 sin^+1.29 sin2 *.,
(yy)=43«67+1.97 cos *+0.86 cos2
(zz)=29.17-1.31 cosoC+0.42 cos2 «c,
(xz)=12.63-1.12 sin <<-0.35 cos <<+0.72 sinoccos <,
(yz)=25.76-0.20 cos <<+0.59 cos2 «*,
(xy)=-28.l4-0.49 cos**+1.22 sln*<+1.03 sin«<coso£
(where «<is the angle orienting the OH group),
(XX)=3.65X10-40,
(^=2,26X10-40,
(t)0 )=0.89X10- 40,
(Xyu)=- 2.58X10- 40 f
(X]pO=0
(^ 0 ) = -0 .6 3 X 1 0 -4 0 f
KoH = 1 .3 2 X 1 0 -4 0 f
Kch3 - 5 .4 6 x 10“ 4 0 .
The symmetry number is three.
It is necessary to Integrate Eq.l
graphically to
obtain the partition function.
The rotational and translational entropy is
St+r = 10/2 R In T + 11.194
CO
and the "free energy"
- ( (F°-E®)/T)t+r = 10/2 R In T + 1.260
Table III (columns 1 and 2) summarizes the.calcula­
tions of the total entropy (St+r+v) at the boiling
Point and at 403.2°K (130°C) on the basis of free rota­
tion.
The discrepancy of 3*2 e.u. at 351*5°K and of 3*0 e.
at 403.2°K will later be shown not to be due to random
orientation in the crystal.
TABLE III
THE ENTROPY OF ETHYL ALCOHOL FROM MOLECULAR DATA
T°K
St+r
Discrepancy
Restricted
Rotation
Rotation
3 5 1 .5
6 9 .4 4
3 .5 3
4 0 3 .2
7 0 .8 0
4 .2 9
7 3 .0
7 5 .1
3 5 1 .5
6 1 .1 3
3 .5 3
2 .5
2 .6
6 9 .8
6 9 .8
7 2 .1
6 9 .8
3.2
3.0
0.0
Sy
Sr r (CH3 ) (3000 cal.)
Srr(OH) (1 0 ,0 0 0 cal. )
Total (less nuclear
spin)
Calorimetric correct
to ideal gas state
Free
4 0 3 . 2°K
6 2 .3 0
4 .2 9
2 .8
2 .7
7 2 .1
On the basis that the discrepancy is due to the
incorrect assumption of free internal rotation, the
the potential hindering the rotation of the hydroxyl
group was chosen to fit the data at 403.2°K. The
method of Pitzer (49) was used, and from this work,
the potential hindering the methyl group was taken as
3000 cal. For this calculation Hs" in the first fact­
or of Eq. Q Q was taken as 3» The terms XX, \yu, etc.
and the factors
integral of
and Kg were omitted from ^r] . The
(new a
was evaluated as before but
divided by (2u)2 to obtain an average. As the entropy
of the rigid molecule changes by only 0.02 e.u. over
the range of c/- this method is obviously sufficiently
accurate. The symmetry number for the rigid case is
unity but there is a symmetry number of three in the
contribution of the methyl group. The expressions for
the rotational and translational entropy and free
energy were then
Sw .= 10/2 R In T + 11.209 - £ s f - S,
= 10/2 R In T + 1.275
t+r
00
F - F f __
•L5J
T
The last terms in t o and t o are the sums of the
effects of the potentials restricting the rotation
of the OH and CH3 groups (three minima in each case),
which are to reduce the S and F as calculated on the bas­
is of free rotation. They are obtained directly from
Pitzer's tables (49)•
The potential hindering the rotation of the hydroxyl
group to give the best fit was 10,000 cal. The results
of columns three and four (Table III) were obtained us­
ing these potentials.
IV. TOTAL ENTROPY AND FREE ENERGY TABLES
The values of the total entropy and free energy are
given in Table IV at several temperatures on the basis
of free and hindered rotation with the above potentials.
V.
COMPARISON WITH THE EQUILIBRIUM DATA
The remarkably accurate equilibrium data (40-44)
for the reaction
C2H4 (g) + H20 (g) = c2h5oh (g)
are plotted in Fig. V (on the basis of fugaclties). To
calculate the entropy of ethyl alcohol from these data it
is necessary to know the heat of reaction and the entrop­
ies of the reactants. The entropy of water vapor was ob­
tained from the results of Gordon (53) > that of ethylene
27.
table : iv
Restricted Rotation
S from Equilibrium
Data
(P° - E°)
°
T°K
Free
Rotation
S
S
T
400
74.93
71.92
58.97
71.15
71.87
450 . 77.33
74.53
60.58
73.88
74.54
500
79.67
77.02
62.10
76.48
77.08
550
81.93
79.43
63* 58
78.97
. 79.62
600
84.13
81.76
65.04
81.32
82.07
Cp^1S F •R .
Cp's R
was calculated using the data and method given by Egan
and Kemp (54). In both cases the values used were from
the molecular data. These are in complete agreement
with experiment (54,55).
The heat of reaction at 25° in the standard state
can be calculated to well within 400 calories from the
heats of formation of
the components with a correction
to the ideal gas state. Table V summarizes the calcula­
tion.
The correction to the ideal gas state was made on the
basis of the modified Berthelot equation and the thermo­
dynamic equation of state. It is
- (9TcRP/ 128Pc - 81RTC^P/ 64 PCT2 )
The "I.C.T.” critical constants were used in all cases.
The entropies in columns five and six of Table IV
were calculated from the best curve through the equil­
ibrium data (Fig.V ). The^H® value, used to get the re­
sults in column five,
was calculated from that at 25®C.
using heat capacities obtained from the molecular data
on the assumption of free rotation. For column six, heat
capacities, obtained on the basis of restricted rotat­
ion with the potentials already given, were used to ex­
trapolate & H 298.2 •
LOG..K
li 1000/T
Figure V
Equilibrium Constants for the Reaction
CsH4(g) + H20(g) = C2H50H(g)
TABLE V
HEATS OF F ORMATION OF IDEAL GASES IN CALORIES FOR ALL P
AND 298.2°K
Ethylene
Water
Ethyl
Alcohol
Liquid at 298.2
-
-68,313(56)-66,750(57)
Vaporization at 298.2
-
10,499(58) 10,120(41)
Saturated vapor at 298.2 Real gas at 1 atmos.
Berthelot correction
-56,630
12,140(59)
+12
Ideal gas at 1 atmos. 12,152
Limit of error +
-57,814
210
+ 1
+5
-57,813
-56,625
13
220
VI. ACCURACY
If the frequencies T i . T 2. and ^ 5 are all taken
at 1050, the entropy from molecular data is decreased
0.7 e.u. at 351.5°K, 0.8 e.u. at 403.2°K, and 1.3 e.u.
at 600°K. The -(F - E°)/T
value at 400 is decreased by
O
v
0.3 e.u. that at 600 by 0.5 e.u. The error in the third
law entropies might be 0.3 e.u. This seems an upper
limit to the error. The maximum error in A.H298.2 would
introduce 1 e.u. at 400°K and 0.7 e.u. at 600°K. The
maximum error in A S from the equilibrium measurements
would be the error in A H at 298.2 plus that extrapola­
tion to the temperature T. The error in the equilibrium
constants themselves produces a negligible error as is
evident from Fig. V- At 400 and 600°K, respectively the
limits of error due. to extrapolation are 0.2 e.u. and
0.4 e.u. (i.e. if IT 1
2
3 = 1050).
The comparison of the calorlmetric entropies with
those from the molecular dLata on the basis of free
rotation could thus be in error by 1.0 e.u. (0 .7+0.3)
at 351.5°K and 1.1 e.u. (0.8+0.3) at 403.2. The empiri­
cal potentials partly absorb the error in the calcula~
tion using restricting potentials.
The error in the comparison of the entropies from
the equilibrium data with those from free rotation
could be that in A H°298 2 plus that in the'entropy
from molecular data minus that in the extrapolation of
AH as both use the same frequencies. The maximum err­
ors at 400°K and 600°K are thus 1.6 e.u.
The arbitrary choice of potentials for the same
comparison on the basis of restricted rotation partly
absorbs this error.
VII. DISCUSSION
From the previous discussion it is at once evident
that no reasonable assumption as to error can reconcile
the discrepancy (about 3.0 e.u.) between the entropies
calculated on the basis of free rotation and the exp­
erimental ones either from the third law or the equili­
brium data. An assumption of random orientation in the
crystal would reconcile the third law values, but not
those from the equilibrium measurements. On the other
hand, the remarkable check of the entropy values cal-.
culated with the above restricting potentials, both with
the experimental results from the third law and from
the equilibrium data at all temperatures, practically
amounts to proof, not only of the existence of such pot­
entials, but that the values are essentially correct
(i.e., that the vibrational frequency assignment has
been properly made).
The practical significance of the results is shown
graphically in Fig. V. Curve A is the best curve through
the equilibrium data. Curve B represents equilibrium con­
stants obtained from the third law data.using heat cap­
acities calculated assuming free rotation, to extrapol­
ate above 403-2°K. The equilibrium constants plotted
on Curve C were evaluated using heat capacities, calcul­
ated on the basis of restricted rotation, to extrapol­
ate the third law entropies
and A^°2'98."2 * Tlie
extrapolation is noteworthy (60). Curve D was obtained
using entropies from the molecular data assuming free
rotation. The curve using entropies from
molecular
data with restricting potentials coincides with Curve C
because the potentials were solved for from the third
law data at 403.2°. It is thus evident that the thermo­
dynamic values in Table IV calculated on the basis of
restricted rotation (columns
and 4) can be looked
upon as values in best accord with all experimental
facts.
PART III
THE HEAT CAPACITY AND ENTROPY, HEATS OF FUSION AND
VAPORIZATION AND THE VAPOR PRESSURE OF ISOPENTANE
Recently the entropies of n-butane (61) and n-pentane (62) in the ideal gas state at their normal boil­
ing point have been determined in this laboratory from
calorimetrlc data down to 11°K. For each molecule it was
also possible to evaluate the entropy from molecular
data, except for that part due to the hindered
rotation
of the ethyl groups. This part of the entropy then, was
taken to be the difference between the two results. From
its value the potentials hindering the internal rotation
calculated by conventional methods (63)were found to be
30,000 cal. for n-butane and 16,000 cal. for n-pentane.
In the case of the Internal rotation of the methyl
groups in ethane a potential of 3000 calories restrict­
ing rotation was Interpreted as due to hydrogen interact­
ions within the two methyl groups (64, 65, 66). However
in the case of molecules with larger groups as n-butane
and n-pentane, the steric hindrance may give rise to
large repulsive forces
and accompanying potentials of
much greater magnitudes. In such a case it is convenient
to consider the internal rotation as a vibration; the
potentials restricting rotation of the ethyl groups in
n-butane and n-pentane then corresponded
to frequencies
of 272 and 185 cm”-*- respectively.
An exactly similar procedure was followed for isopentane as was followed for n-butane and n-pentane. Here
the entropy due to rotation of an ethyl with respect to
an isopropyl group was the quantity ascertained by comp­
aring the measured entropy with the calculated. Prom this
part of the entropy the potential hindering the rotation
of the ethyl group was found to correspond to a frequency
of 188 cm™'*".
For so large a barrier there seems a possibility of
actually detecting and differentiating between the two-geo­
metrical isomers made possible by the hindered rotation
of the ethyl group with respect to the isopropyl. If the
rate of attainment of equilibrium with respect to the
isomers in the sample were slow, the thermal measurements
would naturally be irreproducible. Anomolies in the heat
capacity curves of ethylene dichloride and ethylene di­
bromide have been interpreted along somewhat similar lines
(67). In the present investigation certain hysteresis effects
have been observed for isopentane in both the solid and the
liquid. The accumulated evidence presented in this research
supports the hypothesis that these effects are manifestations
of a slow thermal equilibrium between the two forms of iso­
pentane. A future investigation is intended to throw addition­
al light on this phenomenon.
35.
Purification of the Isopentane
The sample was kindly prepared for us by Professor
M. R. Fenske. and coworkers (68). It was obtained by
fractionating a cut from a straight run petroleum solvent
through a column of approximately 100/ theoretical
plates with subsequent refractionation through a very
efficient low temperature column to eliminate possible
traces of n-butane. Two hundred cc. of the final dist­
illate boiled within .02°.
About 45 cc. of the middle
cut of this distillate was dried over P2O5, deaerated,
weighed and introduced into the calorimeter by the pro­
cedure which is now standard in this laboratory. The iso­
pentane thus obtained was later found to contain less
than 0 .005^ liquid - soluble^solid - insoluble impurity,
as estimated from the melting point range.
The Apparatus and Heat Capacity Measurements
The apparatus, method, temperature scale and accur­
acy were as already described (69).
One calorie (15°)
was taken equal to 4.1833 international Joules. In
correcting for material vaporized into the filling line
the available data for the density of the liquid (70)
and the vapor pressure results described later were used.
In all cases the molecular weight of Isopentane was tak­
en to be 72.15.
Due to the importance of the thermal history of the
sample in evaluating the possible causese and effects of
the hysteresis in the heat capacity values to be describ­
ed, it will be discussed in detail.
The sample was introduced into the calorimeter at 240260°K, cooled to liquid air temperatures (90°) over eight
hours and after remaining at these temperatures for 24
hours,the melting point measurements were made*
The isopentane was refrozen over a period of two days
and the heat capacities of Series I taken continuously.
The sample remained in the liquid for 4 days between 115°200°K before the points of Series II were taken. For 3
days the apparatus stood at 133° - 150° K, following which
the vapor pressure measurements were made, the sample
ending at room temperature. The sample was now rapidly
cooled to the melting point (12 hours) and allowed to
freeze completely over 2 days. The solid was then melted
and heated rapidly up to the initial temperature of Series
where measurements were taken immediately. Following this
the sample was frozen over 24 hours, melted, and then
allowed to warm up over night before taking the remaining
heat capacities on the liquid. These measurements form a
continuous run of 18 hours and are listed in TaoleVl as
Series IV.
37.
Cooling the apparatus to solid temperatures, this
time, took 48 hours, after which the sample stood be­
tween 90° - 110°K for 5 days, A heat of fusion A (4 )
was taken. The sample was refrozen. It stood as solid
at 100°k for 23 hojirs, then a second heat of fusion
B (4) was measured. The sample remained around the melt­
ing point (113°K) for 3 weeks. Before the points of
Series V were taken, the sample was pumped down to 60°K
over one hour, and stood at approximately this temperature
for 4 hours. After 5 days, the sample was then again
cooled to 60°K, heated up to 200°K and removed from the
calorimeter.(A leak had developed in the outer monel can
which made the evaporation of hydrogen under reduced
pressure impossible and prevented furthur work.)
Out of the calorimeter the temperature and thermal
history of the sample could not be accurately ascertain­
ed. For one week it was kept in a glass bulb probably
oscillating between .90° - 200°K day by day except for
one space of about 4 hours when the weight was checked
and the bulb raised to room temperature. Two heat cap­
acities at 150°K and 190°K taken on the empty calorimet­
er at this time checked the previous results to +0.07
and -0.11^. At this time, too, calculations of the heat
capacities taken previously revealed a region of trans­
ition between 63 - 78°K and an uncertain behaviour of
the liquid at about 200°K.
The sample was replaced in the calorimeter at 200°210°K, cooled to the melting point over 36 hours, then
two solid points taken (Series VI). The sample was
melted once, partially refrozen and allowed to stand
at the melting point for about a week. Then the one
measurement of Series VII was made. The apparatus now
stood between 90°K - 110°K for almost a week before the
run down to 11°K was made. In this run the calorimeter
o
was first cooled to 60 K over 2 hours, and stood at this
temperature for 12 hours before cooling to hydrogen
temperatures over an interval of three hours. TableVI
lists this run as Series VIII. Keeping the isopentane
solid, 2 days later Series IX was taken, the sample being
cooled to 55°K by/the routine procedure. (Two hours cool­
ing to about 60°K, 4-6 hours standing at this temperature)
Two weeks later, keeping the sample at about 90-100°K at
all times, the same procedure was followed. These measure­
ments extended up to the melting point and are listed as
Series X. The apparatus now remained from 100-110°K for
3 weeks. Again cooling down to 60°K, consecutive measure­
ments were now taken to 80°K in 2° rises. These measure­
ments over the transition hump are listed as Series XI.
Series XII (2 points) were taken by rapidly cooling the
apparatus down to 60°K, rapidly heating up to 105°K. One
measurement was then made, the apparatus recooled a few
degrees, and the second point taken at the same temperat­
ure 3 hours later. At the completion of the latter point
the heat of fusion was measured A (12). The sample now
stood between 115° - 200°K for a week following which
the heat capacities of Series XIII on the liquid wdre
continuously taken. The apparatus was next cooled back
to 113°K over 8 hours, allowed to freeze over 3 days
whereupon one heat capacity measurement (Series XIV)
at 109°K and a heat of fusion A (14) were taken. The foll­
owing three hydrogen runs were taken as follows, each
with heat capacity measurements from 20°K to the melting
point and a heat of fusion accompanying:
Series XV taken after standing 24 days at 100°120°K, cooled to 60°K, warmed to 82°K over 12
hours, then immediately cooled to 20°K in 25
minutes. The heat capacities were taken contin­
uously to 60°K and then the apparatus stood 7
hourB before the remaining heat capacities and
the heat of fusion were taken.
Series XVI taken after standing 23 days at 100°120°K, cooled to 90°K standing at this temperat­
ure over 20 hours, then immediately cooled to
20°K in 35 minutes. The heat capacities were
taken continuously to 60°K and then the apparaus stood 7 hours before the remaining heat cap-
acltles and the heat of fusion were taken.
Series' XVII taken after standing 16 days
at 100° - 120°K, cooled to 60°K over 4
hours, standing at this
temperature for
12 hours and then cooled to 20°K in 3
hours. The run to 60°K was taken contin­
uously as in Series XV and XVI but the
apparatus was kept at this temperature
84 hours before the measurements to 113°K,
the heat of fusion was completed.
The corresponding determinations of the heats of
fusion for Series XV, XVI, and JCVII will be denoted
A (15), A (16), and A (17) respectively in a later table.
TableVI lists completely all the heat’ capacity measure
ments described in this section.
The Heat Gapacity Measurements on the Liquid
FigureVI is a graph of the liquid heat capacities
listed in Series II, III, IV* and XIII. The results of
Parks are plotted in the same graph. The preliminary
measurements between 200° - 230°K (Series III) differ
from those of Series XIII and the smooth curve formed
by the measurements of Series II and IV by an average
of 2%. Unfortunately uniquely large drifts in the heat
40 A
Vi
m
m
325
IV&
MS
205
Flgare
255
255
295
VI
®i® Heat Oapaeity of M | u i 4 Xsope&te&e I'kjs li5»295%«
’Q
Q
f ^ l e s IXX
Series*
XX, X?,
XIII
0
« &
41.
TABLE .VI
THE MOLAL HEAT CAPACITY OF ISOPENTANE
Mol. Wt . = 72.15;
0.33532 mole in calorimeter
0°C = 273»l6°K
Temp.
°K
Cn
cal./deg.
Series
Temp.
°K
Cp
cal./deg.
Series III (cont.)
102.78
19.279
199.68
34.933
110.07
20.728
205.65
35.339
112.45
22.441
212.64
33.584
Series:: IV
Series II
122.78
29.760
217.61
33.827
128.69
29.956
223.42
34.191
134.76
30.158
229.12
34.532
140.42
30.366
235.03
34.952
146.38
30.595
241.34
35.332
156.52
30.969
247.32
35.709
162.96
31.224
253.79
36.149
168.96
31.464
259.09
36.531
175.18
31.725
265.20
37.002
271.46
37.504
277.23
38.083
283.23
38.773
Series III
I8I.36
33.413
187.14
32,968
193.50
33.290
42.
TABLE VI (cont.)
Temp.
°K
cal./deg.
Series V
Temp.
°K
Op
cal./deg.
Series VIII (cont.)
60.34
13.052
34.41
6.616
66.71
14.521
38.18
7.556
71.64
15.631
42.67
8.591
76.62
14.818
47.23
9.522
81.63
15.244
51.87
10.270
86.28
16.385
56.36
11.258
Series VI
Series IX
92.65
15.768
60.04
11.998
97.50
16.674
64.54
12.877
69.16
14.092
74.19
14.184
78.84
14.479
Series VII
90.32
15.963
Series VIII
Series X
13.43
1.089
15.80
1.658
17.78
2.231
19.78
2.771
21.75
3.422
24.28
4.123
27.42
30.80
55.11
11.121
59.67
12.013
65.25
13.940
70.67
14.635
76.21
14.286
82.08
15.183
87.45
16.016
92.68
16.955
5.158
5.847
4
45.
TABLE VI (cont.)
Temp.
°K
Cp
cal./deg.
Series X (cont.)
Temp.
°K
Cp
cal./deg.
Series XIII (cont.)
98.37
18.247
193.69
32.595
CL04.64
19.121
198.69
32.847
110.04
20.815
203.66
33.122
208.52
33.338
Series XI
59.77
12.027
Series XIV
61.90
12.436
108.78
63.91
12.755
20.487
Series XV
66.01
13.227
67.85
13.707
69.59
14.301
71.35
14.554
73.06
14.465
75.22
21.90
3.603
24.36
4.382
27.50
5.438
31.06
6.106
35.00
7.046
38.72
7.951
42.79
8.984
14.190
Series XII
109.93
20.076
47.34
9.839
110.18
20.073
52.38
10.800
57.53
11.841
63.32
13.016
69.17
14.771
75.18
14.636
Series XIII
178.42
I83.68 .
188.82
31.891
32.100
32.336
44.
TABLE VI (cont.)
Temp•
°K
Cp
cal./deg.
Temp.
°K
cal./dei
Series XV (cont.)
Series XVI (cont.)
79.91
15.175
91.88
17.310
85.72
16.258
98.66
18.552
92.15
17.332
105.79
19.985
99.34
18.668
L06.85
20.181
Series XVII
Series XVI
22.26
3.724
24.78
4.576
22.50
3.744
28.36
5.727
24.76
4.591
32.37
6.467
28.35
5.661
36.65
7.648
32.24
6.391
41.03
8.663
36.53
7.479
45.86
9.590
40.83
8.567
51.28
10.613
45.50
9.457
57.59
11.878
50.70
10.422
70.34
15.067
56.46
11.634
75.64
14.699
62.07
12.758
81.74
15.553
67.75
14.149
88.36
16.724
73.79
14.858
94.67
17.835
79.91
15.133
101.27
19.096
85.38
16.158
107.22
20.266
er potential readings on the measurements in Series III
necessitated unusually large corrections to the energy
input of 0.2 - 0,5%,
Thus errors of 0.1 to 0,5% may be
introduced.The differences of Series III from the smooth
curve are ten times this uncertainty and must therefore
be credited as real.
The Heat Capacity Measurements on the Solid Isopentane
The accuracy of heat capacity measurements in the
calorimeter used for this research has been previously
described.(71). This accuracy has been verified during
this research in the following ways:
1. Before commencing measurements two heat capacities
on the calorimeter checked previous data within
the claimed accuracy at 200° - 220°K. (0.1$ or
better).
2. Two measurements on the empty calorimeter at 150°
and 190°K between Series V and VI likewise verified
the claimed accuracy (0 .1$ or better).
3. Calibrations of the resistance thermometer with
respect to the thermocouple agreed with an average
deviation of .005° and a maximum deviation of .02 .
Forty-one such calibrations were taken over the
complete temperature range.
46.
4. The accuracy of energy Inputs could be checked by
evaluations of the function
(Re - Rt) t
J
f ohm x minutes
\
calories
where
Re is the mean resistance obtained from the energy
readings during heating.
Rt is the mean resistance obtained from the thermo­
meter readings during drifts,
t
is the heating time in minutes.
J
is the energy input in calories.
This function is plotted against the absolute temp­
erature and gave smooth reproducible curves con­
sistent to an amount corresponding to .05$ in the
energy input.
5. At various times, four points were takenon the liqu­
id isopentane at 120°K. These agreed with
a maximum
spread of .12$.
It will be assumed then with certainty that the hyster­
esis in the solid (and for the same reason in the liquid)
is a real phenomenon. From the thermal history and the heat
capacity results, the following fact clearly emerges. From
47.
Series VI to Series XVI the heat capacities of isopentane
are slowly increasing, till they have reached a seeming­
ly constant value with Series XV and XVI. This increase
of heat capacity takes place over a total time of four
months and is most marked from Series VI to Series VIII
and from Series XII to Series XIV. It is most important
to note that the sample was replaced in the calorimeter
hefore Series:VI, and in so doing was subjected to a drop
of 100° in an interval of time of the order of seconds,
to bring it from room temperature to about 210°K.
In contrast, the preliminary results of Series I and
V are differentiated by the fact that distillation into
the apparatus was accomplished with the calorimeter at
about 250°K. These results check those of the later
Series of the second sample. It is necessary to conclude
then, that the rapid cooling, in insertion of the sample
into the calorimeter the second time, preserved either
the constitution or structure of the liquid at room temp­
erature and that maintenance of the sample at low tempera­
tures greatly reduced but did not prevent the rate of
change to the equilibrium configuration.
In further sup­
port of this hypothesis the following facts are noted:
1. The large changes in the height of the heat capa­
city curves in the second group of measurements
were directly after the sample was introduced
48.
(Series VI - VIII) when the thermodynamic instab­
ility of the system might be very large and a
source of energy of activation exists to speed up
attainment of equilibrium . Other such changes
were noted from Series XII to Series XIV in be­
tween which heating of the sample to 230°K in Ser­
ies XIII conceivably should have speeded up the
attainment of equilibrium.
2. That the liquid region from 200° - 230°K may be a
critical region of change from glassy to fluid
material is suggested by the hysteresis noted in
that region.
3* The work of Smyth (72) on the dielectric properties
of isobutyl bromide suggests that similar phenomena
might be expected for structurally similar isopentane. Smyth notes a tendency for isobutyl bromide to
form a vitreous condition which is in a very slow
equilibrium with the solid and the liquid. This in­
troduced hysteresis in liquid as well as solid di­
electric constants.
4. Similar properties in ethylene dichloride and di­
bromide have been claimed, (73) •
5* That the differences in the runs from 10° - 60°K
are due to rate of cooling is eliminated by Ser­
ies XIV, XV and XVI. That the differences from
60° - 113°K are due to rate of cooling is elimin­
ated by contrast of Series V with any of the lat­
er series. That the differences from 60° - 113°
are caused by inequalities in the time standing
at 60°K is overruled by the check of Series XV
with Series XVI. That they are a result of lavk
of equilibrium caused by a too rapid energy input,
is invalidated by Series XI and Series XII. (That
the low results of Series VI to XIV are due to
material condensed in a tube is overruled by the
large change in Cp from Series VT. - VII, the very
low vapor pressure of the material ( about 10“^
mm.) at its melting point, and overwhelmingly by
the actual volume of the tube which could not con­
ceivably contain 5% of material.)
These considerations lead one to believe Series I, XVI,
and XVII on the solid, and Series II, IV, and XIII on the
liquid were taken on material in which equilibrium was
approximated between the forms. Entirely apaft from these
considerations the check between Series I, XVI, and XVII,
on the solid is a positive indication of the correctness
of this supposition.
Figure VII is a graph of the heat capacities on solid
isopentane. Table VII compares values of the equilibrium
heat capacities, at rounded temperatures, obtained by
this research, with values obtained by Parks (74). The
results of Parks, although of lesser precision and gener­
al accuracy where no hysteresis is involved, were taken
on a sample which was weighed in the calorimeter as liqu­
id and had therefore stood at room temperatures presum­
ably long enough to attain equilibrium between the forms.
These results are in agreement with our equilibrium val­
ues. The increasingly higher values in Parks' data from
80°K to the melting point may be due to impurity.
The Vapor Pressure Measurements
The measurements were made as already described (75).
In view of the high purity of the sample, except for the
lowest pressures, the accuracy is determined solely by the
temperature. The results are given in Table VIII. Column
I gives the absolute temperature as read by the resistance
thermometer. Column 2 lists the observed pressure in inter
national millimeters while Column 3 gives the differences
between these pressures and those calculated from the equa
tion
loS10p mm = - 9170.850 / T - 194.4680
logioT
+ 0.3108920 T - 1.936031 X 10-* T2
+ 439.3143
24
Crl6
0
Q;
/O
J- 8
d
u
0
30
0
60
120
90
Temp. ° K*
Figure
VII
The Heat Capacity of Solid Isopentane 12-113 °K.
0 Series I
e
Series V
Series VI
$
©
Series XV
Series X
Series XVI
Series XI
Series
Series VII
Series VIII
Series IX
e
XII
Series XIV
O
Series XVII
Parks
51.
TABLE VII
THE MOLAL HEAT CAPACITY OF ISOPENTANE AT ROUNDED TEMPER­
ATURE VALUES
Mol. Wt. = 72.15
Temperature
°K
0°C = 275.16°K
CB
cal./deg.
This Research
Cp
cal./deg
Parks
20
3.25
25
4.82
30
6.00
35
7.24
40
8.41
45
9.46
50
10.41
55
11.37
60
12.38
70
15.00-
80
15.19
15.60
90
16.96
17.13
100
18.81
19.53
110
20.75
120
29.68
29.50
52.
TABLE VII (cont)
Temperature
K
Cp
cal/deg
Thia Research
Cp
cal/deg.
Parka
130
29.99
29.95
140
30.38
30.42
150
30.72
30.77
160
31.06
31.12
170
31.48
31.56
180
31.95
32.00
190
32.40
32.46
200
32.91
33.06
210
33.42
33.48
220
33.98
34.02
230
34.57
34.61
240
35.20
35.20
250
35.89
35.90
260
36.59
37.63
270
37.37
37.36
280
38.31
37.95
290
40.49
53.'
TABLE .VIII
THE VAPOR PRESSURE OF ISOPENTANE
0°C = 273«l6°K;
b.p. = 300.90°K; (g for State College=
980.124 I.C.T.)
T obsd
°K
P obad
Int. mm. Hg
Pobsd - P calc.
Int. mm. Hg.
T calc - T obsd
°K
217.206
10.95
-.001
-.001
231.421
29.08
+.017
+.009
238.811
45.67
+.007
+.002
245.332
66.28
+.038
+.010
250.394
87.14
-.030
-.006
255.761
114.89
-.012
-.002
263.604
168.56
-.018
-.002
270.597
231.49
-.027
-.002
276.940
304.43
-.104
-.008.
281.631
369.37
-.130
-*009
286.987
456.51
+.053
+.003
292.208
556.43
+.318
+.016
295.196
620.98
-.072
-.003
Column 4 lists the temperature difference corresponding
to this pressure difference.
The Melting Point
The equilibrium temperature of the pure sample was
observed over a period of eleven hours, with several
fractions of the material melted as estimated from the
heat input and the measured heat of fusion. The results
are given in Table IX. From these results and the heat
of fusion, the impurity present was found to be 0.005
mole per cent, assuming no solid solution. After correct­
ing for this impurity the melting point of pure isopentane is II3.39 ± .05°K.
Timmermans (76) has encountered difficulties in get­
ting reproducible values of the melting point of isopentane. It is believed that the uncertainties in his results
are manifestations of the phenomena in the solid described
above. However the result for the melting point given
above is judged correct since
1. The heat capacity results on solid isopentane
immediately following are on the "equilibrium
curve", thus the melting point is judged to be
an equilibrium value.
2. An estimate of the melting point can be obtained
from the heats of fusion to be described, giving
113.6°K as an average value. These values havd a
TABLE IX
MELTING POINT OF ISOPENTANE
melted.
T°K
Thermocouple
2
113.362
113.367
14
113.365
113.377
26
113.367
113.378
45
113.386
113.392
75
113.386
113.383
97
113.383
113.385
113.39
113.39
Melting
Point
T°K
Res. Thermometer
spread of 0#4°K and would toe slightly high due
to superheating tout otherwise correct as the heat
capacities preceeding these also lay on the equil­
ibrium curve.
Previous data on the tooiling point and melting point of
isopentane are listed in Table X.
Heat of Fusion
The method has been described before (77,78). The re­
sults are summarized in Table XI. Deviations may toe expect­
ed in cases where the sample did not represent the equili­
brium configuration. Unfortunately only one heat of fusion
was taken on solid which deviated from the equilibrium
heat capacity curves. The agreement in the other five meas­
urements is very satisfactory and substantiates the choice
of the equilibrium curve.
Heat of Vaporization
The results of the measurements of the heat of vapor­
ization are summarized in Table XII. The method has been
reported previously (79,80,81). The pressure was held
constant by having the condensation bulb immersed in a
thermostat which was constant to .01°. Thus the material
was vaporized at about 20°C. A value of the heat of vapor­
ization at the above temperature can also be calculated
57.
TABLE X
MELTING AND BOILING POINT TEMPERATURES OF ISOPENTANE
M.P.,°C
B.p,,°C
Observer
-160,0
Timmermans (1929)
-159*6
Timmermans and Martin (1926)
-159.65
Timmermans, Horst and Onnes
(1923)
-160,5
27*95
Young and Thomas (1897)
30.55
Brown and Carr (1926)
28,05
Anderson and Erskine (1924)
28.0
29.7
-159.6
Parks, Huffmann and Thomas
(1930)
Fischer and Klemm (1930)
Hoog and Smittenberg
(1937)
-160.6
27.8
Hoog and Smittenberg (1938)
-159.77
(113.39°K)
27.74
(300.90°K)
This research
TABLE XI
HEAT OF FUSION OF ISOPENTANE
No.
Corr'd
Heat input
Cal/mole
^)cpdT
cal/mole
Premelting
cal/mole
A H fusion
cal/mole
A (4)
1460.6
235.1
0.3
1225.8
B(4)
1430.2
204.7
0.6
1226.1
A(12)
1324.5
138.3
7.5
1193.6
A (15)
1444.1
218.3
0.0
1225.8
A(16)
1444.3
217.3
0.0
1227.0
A (17)
1438.3
211.6
0.0
1226.7
Average eliminating A (12) =
1226.3+O.5
TABLE XII
MOLAL HEAT OF VAPORIZATION OF ISOPENTANE
T K.
vap.
Corr'd.
-Heat Input
cal./mole
(
A H vap.
) CpdT
. Moles AH vap. cal/mole
cal./mole
vap. cal/mole 298.16°K
293.92
7746.6
1809.7
0.04970
5937
5875
293.98
6249.9
317.8
0.04434
5932
5870
5935*4
5873-4
293.95
Average
A H yap. ( vapor pressure ) at 298.16
5850
from the vapor pressure data represented by equation (1)
using a modified Berthelot equation with Tc = 461.0°K
and Pc = 32.9 atm. for obtaining the volume of the real
gas.
The Entropy from the Thermal Data
The calculation is summarized in Table XIII. The
correction for gas imperfection is based on the modified
Berthelot equation of state and is probably in error
accordingly. To obtain the entropy of compression the
vapor pressure results described above have been used. To
extrapolate the values for the gas to 298.16°K and the
boiling point, the molecular data to be described were
employed.
The Entropy from Molecular Data
The calculation is in most respects similar to that
for n-butane (82, 85). The two forms obtained by rota­
tion of the ethyl group will be denoted as symmetrical
and unsymmetrical, with symmetry numbers of 2 and 1 resp0
ectively. Assuming the C - G distance to be 1.54/\, the
C - H distance to be 1.11A and the H - C - H angle to be
109°28' the translational entropies of the rigid forms are
calculated to be (84, 85, 86)
St + r (sym.) = 4R In T + 19.313
St + r (unsym.) = 4R In T + 19.490
TABLE XIII
THE ENTROPY OF ISOPENTANE FROM THERMAL DATA
0°C = 273.16°K
E.u./mole
0 - 20.00°K
Debye extrapolation
20.00 - 113.39°K
Fusion
Graphical
Vaporization
Graphical
5893/298.16
Entropy of actual gas 298.16°K
Correction for gas imperfection
Entropy of ideal gas
18.331
10.814
1226.3/113.39
113.39 - 298.16°K
0.884
298.16°K
31.803
19.764
81.596 + 0 . 3
.093
81.689 ± 0.3
exclusive of terms for the symmetry and probability fact­
ors. Assuming equal heat contents, the mole fraction in
the gaseous state is found to be 0.685 for the unsymmetrical and 0.315 for the symmetrical. The total trans­
lational and rotational entropy of the mixture is then:
St + r = 4R In T + 21.61 + Srr (3CH3) + Srr (C2H5)
The last term
of this equation
is the one to be solved
for using theresults from the thermal data. Table
XIV
summarizes this calculation. The following frequency
assignment was made:
Carbon Skeleton Vibrations
cZ) 1 = 250; c O g
6
= 366; 2
= 948;
= 469; < ^ 4 = 796
= 906;
^ 7 = 979 cm”1.
Hydrogen Vibrations
I2O C H 3 = 2900;
4X C H 3 = 1327;
6^TcH3 = 1448;
lljrr = 950
cm"-1
The skeletal stretching vibrations ,0^)4, w^ 5»'^5
and C-O7 have been identified in the Raman spectrum by the
theoretical treatment of Mecke (87). The bending modes
cannot be so surely assigned. The strong Raman lines ob­
tained by Kohlrausch (88) at 366 and 469 cm"1 are assumed
to be the skeletal bending modes *-^2 anc^ ^
ly
and
resPec"klve“
by analogy with the known assignments on n - butane
isobutane
respectively.
The
remaining
bending
TABLE XIV
THE ENTROPY OF ISOPENTANE FROM MOLECULAR DATA AT 298.16°K
E.u./mole
S
t + r (mixture)
S
vib =
v\
S rr (3CH3) V = 38OOcal.
S rr (C 2 H5 )
£>= 188cm-1
66,89
6,35
6.09
2.35
S total
81.69
S experimental
81.69
64.
mode Is missing from all spectral and the value 250
cm"-*" was arbitrarily chosen, again by analogy with nbutane (87). For the hydrogen vibrations, the values
chosen can bring little error except for the 11 vib­
rations representative of the angular oscillation of
the methyl group. Here, the value used is consistent
with results obtained for many other molecules, (90,
91, 92). The appreciable errors in this assignment will
result from the selection of this vibration and that of
tZ>r
Comparison of the thermal data with the molecular
and spectroscopic, assuming a potential of Vqh3 = 3800
cal. (93) leads to the value VC2H5 = 16,000 cal. corres­
ponding to a frequency of 188 cm”-*-.
Accuracy
The thermal data can conceivably be in error by 0.5
e.u. if the results on the solid do not represent the
HtrueM curve within 2%» In face of the evidence presented,
however, it is believed that equilibrium has been attained
in Series XVI and XVII. The estimate of an error of 0.3
e.u. therefore is a liberal one, since reproducible
results have been obtained in the solid to an average
accuracy of less than 0.1% three separate times. The error
brought in by the other thermal measurements cannot con-
ceivably be greater than 0.15 e.u.
If the frequencies c O a n d
are each in error
by 50 cm"^ a more serious inaccuracy results. The c o r r ­
esponding errors in Svit> at 298.16 are then 0.4 and 0.25
e.u. respectively. The total error in the value of the
entropy difference used to solve for the potential barr­
ier restricting rotation of the ethyl group in isopentane may thus be 0.95 e.u. out of a total of 2.26 e.u.
That thB results obtained are in agreement with those
of n-butane and n-pentane and with structural and steric factors is then perhaps fortuitous. Nevertheless,
these results should provide accurate data for obtain­
ing thermodynamic tables up to 1000°K.
66
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(1)
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(2)
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(3)
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(b) J, Am. Ohem. Soc. 58, 2354(1936)
(4)
Giauque, ibid. 52, 4816(1930)
(5)
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(6)
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(7)
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(8)
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(12)
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(15)
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(16)
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(17)
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(18)
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67.
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(22)
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(32)
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(33)
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(34)
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(35)
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(37)
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(39)
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Fiock, G-innings, and Holton, Nat. Bur. Stand. J.
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(42)
Calculated from thermodynamics and the modified
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("i.C.T")
*
68.
(43)
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(44)
(a) Bo 11a, Zeits. f. Physik. 89, 513 (1934):
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(46)
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Kassel, J.
Chem. Phys.
4, 276 (1936)
(49)
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Chem. Phys.
5, 469 (1937)
(50)
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(53)
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(54)
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(55)
Giauque and Archibald, J. Am. Chem. Soc. 59, 561
(1937)
(56)
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(59)
Rossini and Knowlton, Nat. Bur. Stand. J. Research
19, 339 (1937)
(60)
Parks, Ind. Eng. Chem. 29, 845 (1937), has also used
this reaction for a third law check with a long
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(61)
Messerly and Aston, J. Am. Chem. Soc. 0,000 (1940)
(62)
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(63)
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(64)
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2, 65 (1934)
Chem. Phys.
At
5, 469 (1937)
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69.
(65)
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(66)
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(67)
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(68)
Thanks are due Professor Fenske and Messrs Lawroski,
McCormick, Benoliel and Schubert for this prep­
aration.
(69)
Aston and Eldinoff, J. Am. Chem. Soc. 61,
(70)
International Critical Tables. Me Graw Hill Book
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(71)
Aston, Eidinoff and Forster, J. Am. Chem.
1539 (1939)
(72)
Baker and Smyth, Ibid. 61. 2063, 2798 (1939)
(73)
Railing, Ibid. 61, 3349 (1939)
(74)
Parks, Huffmann and Thomas, Ibid. 52, 1032 (1930)
(73)
Aston, Eidinoff and Forster, Ibid. 61, 1539 (1939)
(76)
Timmermans, Comm. Phys. Lab. Leiden Supp. 64, 3 (1929)
(77)
Aston, Eidinoff and Forster, J. Am. Chem Soc. 61,
1539 (1939)
(78)
Aston and
Messerly, Ibid. 58,2354
(1938)
(79)
Aston and
Eidinoff, Ibid. 61, 1531
(1939)
(80)
Messerly and Kennedy, Ibid. 0,000 (1940)
(81)
Aston and
(82)
Pitzer, J. Chem. Phys. 5,
(83)
Aston and Messerly, J. Am. Chem. Soc. 0,000 (1940)
(84)
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(85)
Eidinoff and Aston, Ibid. 3, 379 (1935)
(86)
Pitzer, Ibid. 5, 469 (1937)
(87)
Mecke, Z. Physik. Chem. B 36, 347 (1937)
Messerly, Ibid. 58,2354
13 (1938)
1531 (1939)
Soc. 61,
(1936)
473 (1937)
70
(88)
Kohlrausch and Koppl, Ibid. B 26, 209 (1934)
(89)
Messerly and Aston, J. Am. Chem. Soc. 0,000
(1940)
(90)
Aston, Siller and Messerly, Ibid. 59, 1743 £-1937)
(91)
Pitzer, J. Chem. Phys. 5, 473 (1937)
(92)
Schumann and Aston, Ibid. 6, 480 (1938)
(93)
Pitzer, Ibid. 5, 473 (1937)
71.
APPENDIX I
Tests on Bomb - Llquefler
1. Under oil pressure at 5000 lbs./ln.2 No drop in
pressure (+ 200 lbs) after one half hour,
2. Under 1800 lbs./in.2 hydrogen pressure. No drop
in pressure (+ 100 lbs.) after 65 minutes.
3. The Bomb liquefier was set up as in apparatus
with accompanying spiral. The outlet was solder­
ed shut, the inlet connected to a pressure source 1
of 1600 lbs./in.2. The can was soldered tight about this system and the following observations
recorded:
A. Can vacuum ...... 10-6
—6
B. Can vacuum in liquid a i r ..... 10 mm. Hg.
(Preliminary cooling gave 3 X 10”^ mm. Pass­
ing to room temperature and recooling seemed
to eliminate this degassing effect).
:<3. Tests with 1500 - 1600 lbs/in.2 in the bomb..
Pressure in
Bomb
Can
Vacuum
o
T K
0
I X 10-5
298
0
I X lO-o
93
1600
I X 10“°
88
72
The leak rate into the can was 1-2 X lCT^
mm./hour at all times except when the can
was completely covered with liquid air.
The leak rate then varied from 1.2 X 10“^
mm./hour to 3 X 10”5 mm./hour. It was con­
cluded that the top of the can leaked to
the atmosphere since there was no evidence
of increased leak rate immediately after
pressure was introduced into the "bomb.
Tests on the Calorimeter
Completely surrounded with liquid air, the calori­
meter gave a leak rate of 3-5 X lCr^mm./hour.
Tests on the German Silver Tubing
The .035”, .040" and .125" O.D. German silver tubing
were all tested under 5000 - 7000 lbs/in^ pressure of oil.
Samples of the former two sizes were tested under vacuum.
The leak rates per hour were less than 5 X 10**^mm.
Calibrations on the German Silver Tubing
1. All samples of the .035” O.D. tubing were .20 + .01 mm
I.D.
2. All samples of the .040" O.D. tubing were .600 + .005
mm. I.D.
3. The calorimeter gas thermometer tube is exactly
0.200 + .005 mm. I. D.
Further Calibrations
All volume calibrations were made by evacuating the
system to 2-3 mm and then filling with ethyl alcohol.
From the Increase of weight and the density the volume
was ctebermined.
Calorimeter
80.7 + -8 cc
Calorimeter Helium Chamber
5.31 ± *05cc
Calorimeter Gas Thermometer
4.809 cc
4.800 cc
4.774 cc
Average
Liquefler Helium Chamber
4.794 ± .02 cc
4.6 ± .2 cc
Composition of Bismuth Solder Used on Spirals
Bismuth
53$
Tin
24.5$
Lead
22.5$
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