THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
259
stancy of calorimeter volume, the following equation may be obtained:
(R, - RW) = p + (h." - R.) nw' - p
Vd(1
- 2)
U
(1)
vw,
For the case of pure water and may be replaced by the molar quantities &, and ow,, since the solubility of air in water is slight. In order to evaluate R,, Rwt, and the molar volume of the vapor phase, v , the following equation of state for moist air as predicted by statistical methods (3) is used: PV
RT - [A.,,z*
=i
Noting that V = (n.
+
G)V,
["I
+ 2AaWz(l- Z) + A w ( 1
- z)']P
(2)
and from the relationships of thermodynamics
ani
=[*I
T , P . ~ ~
3P
T
,
~
~
(3)
and
the following expressions may be derived:
R. 8 =
S =
T IJ
u,,'
V
P
= =
= = =
z = A=N =
=
B ( l - z)'P,I
- Bda1
+ h:
molar entropy partial molar entropy absolute temperature molar volume of vapor phase molar volume of liquid water total volume of vapor phase partial molar volume mole fraction of air 2Aaw
Aa
+ A-
, interaction
coefficient for moist air in dimensionless form
chemical potential
Suban'pts: a = air air = air stream before calorimeter cal = calorimeter vapor space i = constituent i j = constituent j 8 = pure water, saturation w = water vapor IO' = liquid water
Supersmipb: a = vapor phaae 0 = standard state sat = saturated
(5)
260
ERNEST F. JOHNSON, JR., AND MELVIN C. MOLSTAD
and Rw
=
IWPP,,i - BwvPoni
+
xBP,.i
+
ht
(6)
But writing equation 5 for the case of pure air gives h, =
- BoaPo,, +
(7)
h:
and by elimination of hi between equations 5 and i:
+
= B(1 - T ) * P ~ ~&a(l’asr I - IJcd
+ ha
(8)
This expression differs from Hunter’s derivation by the B, term. ’ipplying equation 6 to the case of pure water at its saturation pressure gives h:t =
+ h:
- B,,p,
(9)
whence by elimination of h: betneen equations G and 9:
R,
=
h2t
- B,,(P
- p.)
+ x’BP
(10)
Inserting equations 8 and 10 in equation 1, noting
n. - X nw 1 - 2 and rearranging and collecting terms, there results the expression for latent heat of vaporization: namely,
(hF
- R d ) = p - BZPd + B d P d - p,)
This expression is exact within the limitations of the initial assumptions and the definition of q. Kinetic energy changes are negligible. The relationship between q and the latent heat of vaporization over the concentration and temperature ranges studied is shown in figure 5.
Vapor pressure For air-water systems the expression for the vapor pressure of pure water is given by the saturation equation of Goff and Bates (4):
where
Hunter used this expression to compute his results for pure water. I t is not suitable for calculating the vapor pressure of salt solutions. However, by equat-
TIIERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
261
ing the expressions for the chemical potential of water in the vapor phase and in the liquid phase there results
RT In
QW
- Awwp, =
RT In (1 - z ) P
+ (Aaa - 2A,, + Jww)z2- A,,P
(13) This relation and equation 12 are only valid if the vapor and liquid phases are in equilibrium. Hunter calculated p w , for his results on salt solutions by means of the equation : p,. = (1 - z ) P
(14)
Related properties
Iliflerential heats of dilution, chemical potentials, and entropies are calrulable from gas current results. The differential heat of dilution, which is identically equal to thc relative partial molar enthalpy of water, (Rwtis equal to ( h v t - a",) - (hvt R w j )Assuming . that for all practical purposes a",is equal to hw,,this is merely the difference between the latent heat of vaporization of pure water and the latent heat of vaporization of water from the salt solution. The expression for the chemical potential or partial molar Gibbs frcc cnergy of water in aqueous solution relative to the molar free energy of pure ater, both at the pressure of the experiment, is obtained directly from the exprcssion for the chemical potential of water in the vapor phase. The final equation is
n:,),
Hunter used the expression pwt
- gU,,= RT In
P" P.
(16)
t o calculate chemical potentials. This is based on the definition of activity, - gw, = RT In aw,, using the fairly accurate approximation that h, =
put
Pwp/Ps. The partial molar entropy of water in solution may be computed from the defining equation for Gihbs free energy in terms of enthalpy and entropy:
Corrections based on performance of apparatus Equation 11 may be used to calculate the latent heat of vilporiz:btion, provided the values of q and z obtained by gas current measurements arc accurate. The net heat input required to vaporize a unit weight of water, q, is thr elrctric
262
ERNEST F. JOHNSON, JR., AND MELVIN C. MOLSTAD
power input per unit weight, corrected for any heat transfer between the calorimeter and its surroundings, and for sensible heat changes in the gas stream and in the calorimeter and its contents during the period of measurement. The correction for heat exchange between calorimeter and surroundings is made by computation, using the difference between the average calorimeter and bath temperatures and an average overall heat-transfer coefficient which waa determined experimentally. Sensible heat changes in the gas stream as it passes through the calorimeter are assumed to be calculable directly from the difference between the mean calorimeter temperature and the mean bath temperature and the heat capacity of the gas stream. Sensible heat changes in the calorimeter are computed from the change in the calorimeter temperature between the beginning and end of a run and the heat capacity of the calorimeter and its charge. Theoretically, the attainment of equilibrium between gas and liquid phases in the calorimeter requires either an infinite contact surface or an infinite contact time. Neither requirement is consistent with the need for a compact adiabatic apparatus for measuring thermal quantities. I n view of the high precision of the apparent vapor pressure data obtained with the present gas current method, it was proposed to use the concept of a “saturation efficiency” rather than attempt to improve the interphase contact by elaborate equipment revision. At each temperature the saturation efficiency for dilute solutions can be determined by comparing the gas current results for pure water with accurate steam tables ( 5 ) values. For concentrated solutions the saturation efficiencies should be lower than for dilute solutions because of the increased viscosity. EXPERIMENTAL
Apparatus The apparatus used was that of Hunter, modified to increase the precision of measurement and to permit operation a t temperatures above normal room temperature. The latter modification required the design and construction of a new calorimeter and heater. Figure 1 shows the air system of the final gas current apparatus, figure 2 the electrical system, figure 3 the new calorimeter, and figure 4 a view of the assembled apparatus. The apparatus and its operation have been described in detail (11). Only the new calorimeter will be described here. For temperatures above 30°C. Hunter’s calorimeter design proved unsatisfactory because of excessive heat losses from the calorimeter heater power leads and faulty mixing of air and liquid a t the low gas rates used at high temperatures. A new calorimeter was made up to overcome these defects. The details of the mixing system were altered and an entirely new heater was used. Like that of Hunter, the new calorimeter consists of a glass jar, 7.6 cm. inside diameter by 24.2 cm. deep, stoppered with a tapered hard-resin plug, ground to fit the mouth of the jar. Fitted to the plug are the gas inlet downcomer, gas
THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
263
outlet entrainment separator, calorimeter heater power lead sheaths, and calorimeter thermometer sleeve. Dry gas enters the calorimeter L ~ U the downcomer and passes through a small jet pump at the bottom of the jar. Slugs of mater or solution are carried up by the gas inside a riser, around which the calorimeter heater is coiled loosely.
B
r -
FIG.1. Air system of the final gas current apparatus I. .. 2. ... 3, .. 4. . .. 5 . ... 6, ,,. 7, , 8. 9. , . 10. . . . 11. . . . 12. . . . , 13. . . . 14. . . . 15. . . . 16. . . . ~
.
.. . .. .
1 7 . .. . . 150 p.s.i. air supply 18. . . . Reducing valve 1 9 . .. . . Pressure gauge 20 . . . Capacity bottles 21 . , Regulator vent Water column air-pressure regulator 22 , . . 23 . . . . Primary air dryer, silica gel 24. .. Ascarite tower, COS removal 25 Secondary air dryer, silica gel 26. .. Keedle valve 27 . . Pilot dehydrite tower 28 . , Bath Air preheater 29.. . Air-inlet thermometer 30.. . 31. .. Submarine Glass calorimeter
Four-way valve Calorimeter thermometer Bath thermometer Stirrer Three-way valves Calorimeter pressure manometer Dummy dehydrite towers Weighed dehydrite towers Guard tower, indicating alumina Trap Saturator Entrainment separator Air-flow manometer Trap Wet test meter
After leaving the heated riser the gas and entrained water or solution flow down through a spiral glass coil. From the bottom of the coil the gas bubbles up through the liquid in the calorimeter, then out through the entrainment separator. The separator is a single baffle made from concentric glass tubing. As a precaution against misting, a small wad of glass wool is kept in the gas outlet just above the separator baffle. In the Hunter calorimeter the riser is a jacketed section with the heater immersed in Aroclor in the jacket. The new calorimeter employs a riser of the same internal dimensions, but the spiral glass coil is much longer (approximately
.
264
ERNEST F. JOHNSON, JR., AND MELVIN C. MOLSTAD
100 cm. of 8-mm. O.D. tubing) to increase the contact time of gas and liquid. This coil is connected by a short rubber sleeve to the elbow on the riser from the jet pump. Rubber tubing is also used to connect the gas downcomer in.the calorimeter stopper to the jet pump downcomer. Thus all the glass within the calorimeter is secured flexibly. The new calorimeter heater eliminates the two causes of excessive heat leak along the power leads of Hunter's calorimeter: namely, the mercury contacting pools and the Aroclor jacket. I t consists of over 50 cm. of 16-gauge Nichrome wire wound into a helical coil 2.8 cm. in diameter and 4.5 cm. high. The ends of the coil are silver soldered to 12-cm. lengths of 12-gauge copper wire which
" FIQ.&-
2. Calorimeter heater circuit-wiring
diagram
are soft-soldered into %-in. copper rods sealed into the calorimet,er stopper. Since the heater coil and copper leads are entirely immersed and the rods dip into the calorimeter liquid, the heat losses from the heater along the leads are negligible. To prevent stray electrolytic effects the exposed part of the heater circuit below the stopper is double-coated with a baked alkyd resin enamel. The upper ends of the copper rods are drilled out to take jacks in which the power leads and the potential measuring leads are soldered together. Since the electrical resistance of the copper rods is very small, the measured potential drop is that occurring in the heater alone.
Procedure The experimental procedure used was essentially that of Hunter, although a number of refinements in technique were devised. It is outlined below.
.
Fie. 3. Calorimeter (approxirnnto scale. i in.
FIG.4. Assembled apparatus 285
= 1
in.)
200
ERSEST F. J O H S S O S , JR., A S D MELVIS C. MOLSTAD
First, the calorimeter operating temperature is determined by allowing the calorimeter and its charge to soak in the bath for 24 hr. at the set temperature for the experiment. S e a r the end of this soaking period and before starting the 26 24
22 20
18 J
IS
= I4 >I2
-
J IO
2 6 4 2 0 -20
20
40 so GLICLIIOOGH20
IO
100
FIG.5. Correction for gas current theory
TABLE 1 Resulls of slndies of pure water at W C . EXPF.RINE\T
30-W-1 30-W-2 30-W-3 30-W-4 30-W-5. 30-W-6 30-W-7 30-W-8 30-W-9. 30-W-10 30-W-11 30-W-12 30-W- 13 30-W-14
hO
P.
L,
mm. Hg
k r o l . / p -mole
31.91 31.79
10.455 10.483 10.432 10,465 10 468
31.93 31.96 31.79 31.82 31.65
31.73 31.74
Mean Probable error of mean
10.457 10.436 10.464 10.472 10,441 10.451 10.464 10.476
EXPERIMEYT NO.
PI
L,
m m . Hg
kcol./g.-mole
30-W-15 30-W-16 30-W-li 30-W-18
31.89 31.85 31.91 31 .ci7
30-W-20 30-W-21 30-W-22 30-W-23 30-W-24 30-W-25 30-W-26 30-W-27 30-W-28
31.65 31.73 31.77 31.78 31.92 31.85 31.83 31.84 31.87
10.456* 10,456* 10.471 10.486 10.462 10.444
31 823 f0.016
fO ,0025
10,460
* Xot included in mean. Vapor pressure value adjusted for water in gas stream
pre-run, dry air is blown through the apparatus, by-passing the calorimeter, for 1 hr. to dry out the gas lines. The pre-run is started by switching the air flow to the calorimeter via the four-way valve. At the same time the switches in the battery charging rircuit and the calorimeter heater circuit are closed. Constant calorimeter tempera-
Fie. 3. Calorimeter (approximate SCBIP: 2 in.
Fm. 4. Assembled apparstus 265
= 1
in.)
206
ERKEST F. J O H K S O S , J R . , AXD MELVIP; C . MOLST.\D
First, the calorimeter operating temperature is determined by allowing the calorimeter and its charge to soak in the bath for 24 hr. at the set temperature for the experiment. ?;ear the end of this soaking period and before starting the 26
24 22 20 I8 IS
= I4 >I2
-3
10
1 8 $ 6
4
2 0
20
20
40
60
10
100
G L I CL/IOO G.Ht0
FIG.5 Correction for gas current 1 iory 8.
TABLE 1 Reszilla of s l i i d i e s of pure water at 80°C.
kcol./g.-mole
30-W-3 30-W-4 30-W-5 30-W-6 30-W-7 30-W-8 30-W-9. 30-W-10 30-W-11 30-W-12 30-W-13 30-W-14
I
' ~
I
31 93 31 96 31 79 31 82 31 65
31 73 31 74
10.432 10.465 10.468 10.457 10.436 10.464 10.472 10.441 10.451 10.464 10,476
1
30-W-li 30-W-18
31.91 31 ,'I7
30-W-20
31.65 31.73 31.77 31.78 31.92 31 85 31.83 31.84 31.87
30-W-22 30-W-23 30-W-24 30-W-25 30-W-26 30-W-27 30-W-28
Mean Probable error of mean
* N o t included in mean. Vapor pressure value adjusted
I-
____
I
31 823 fO 016
1
10.456* 10.456* 10.471 10.486 10.462 10,444 10.460 0025
1 =to
for water in gas stream.
pre-run, dry air is blown through the apparatus, by-passing the calorimeter, for 1 hr. to dry out the gas lines. The pre-run is started by switching the air flow to the calorimeter via the four-way valve. At the same time the switches in the battery charging circuit and the calorimeter heater circuit are closed. Constant calorimeter tempera-
THERMODYS,AMIC PROPERTIES OF LITHIL'M CHLORIDE SOLUTIONS
267
tures at a fixed convenient electrical potential drop across the heater are maintained by adjusting the air flow rate with the needle valve in the foretrain. The resistors in the battery charging circuit are adjusted to maintain a constant potential drop across the heater. TABLE 2 Resvlfs of studies of lithium chloride solutions af SOOC 1EAS COHCEXTPA.
EXPEPIYPNT NO.
TION
,. LiCI/lM) G.
-__
30-5-1 30-5-2 30-5-3 30-S-4 30-5-5 30-5-6
30-S-7 30-5-8 30-5-9 30-S-10 30 5 11 30-s-12 303-13 303-14 30 5-15 30-5-16 30-5-17 30-5-18 30-5-30 303-31 30-S-32 30-S-33 30-5-34 30-5-35 303-36 303 3 i 30-S-38 30-5-39 30-5-40 30-5-41 30-S-45 30 5-46
i9.16 i9.28 79.42 79.50 66.51 66.66 57.41 57,5i 45. 79 45.98 33.40 33.58 33.84 34.01 24.19 24.32 15.38 15.52 14.28 14.37 7.09 7.13 4.73 4.74 4.78 4.80 4.82 4.85 85.20 85.20 85.20 85.20
H10
P1'
L
mm. Hg
kcol./g.-mole
4.39 4.36 4.35 4.33 6 21 6.16 8.21 8.15 12.05 11.97 17.74 17.60 17.55 17.40 22.42 24.26 26.35 26.43 27.53 27.35 30.10 30.05 31.18 31.15 31.06 30.95 30.90 30.88 3.61 3.58 3.58 3.57
kcd./g.-molc
11.76 11.67 11.76 11.76 11.50 11.51 11.36 11.38 11.08 11.05 10.610 10.614 10.639 10.659
1.30 1.21 1.30 1.30 1.04 1.05 0.90 0.92 0.62 0.59
10.504 10,520
0 044 0.060
10.458 10.421 10.497 10.439 10.482 10.475 11.91 11.82 11 90 11.90
-0.002 -0.039 0.037 -0.021
0.150 0.154 0.179 0.199
0.022 0.015 1.45 1 36 1.44 1.44
After operating conditions have held constant for 30 min. or more the gas flow is switched from the dummy set to the weighed set of Midvale towers by means of the three-way cocks before and after the towers. The switch is made at a convenient reading on the wet test meter, and at the instant of switching the electric timer is started. During the course of the run the air rate and battery charging rate are ad-
268
.
ERNEST F JOHNSON. JR., AXD MELVIN C
. MOLSTAD
TABLE 3 Results of sfudiea of pure water at 50°C . (old calorimeter)
.
mm Hg
50.W.1 . . . . . . . . . . . . 50-W-2. . . . . . . . . . . 50-W.3 . . . . . . . . . . . 50-w-4 . . . . . . . . . . .
1,
92.55' 92.54 92.55; 92.47
1 I
I 10.246 10.237 10.252 10.243
50.W.8 . . 50.w.9 50.w.10 . . 50-W-ll . . 50.w.12 . . 50.W.13. . .I
92 55 92 47
~
' 10 10 10 10 10 10
~
1
I
02 55 92 59 92 62
1
'1
245 223 211 248 208 224
92.55 1 10.238 f0.04 f0.003 . _ Not included in mean L value adjusted for water in gas stream
Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Probable error of mean . . . . . . . . . ..e. . . . . . . . . . . . . . . . . . . . .
__ *
mm Hg
~
~
.
.
.
TABLE 4 Eesult8 of studies of lithium chlo7ide solutions at 50°C. (old calorimeter) EXPEPIYPNI NO
.
I.
YEAN CONCENIPAT10N
(G
50-s.2. . . . . . . . . . . . . . . . . . .
50-s.3 . . . . . . . . . . . . . . . . . . . 50-5-4 . . . . . . . . . . . . . . . . . . . 50-s-5 . . . . . . . . . . . . . . . . . . . 50.5-6 . . . . . . . . . . . . . . . . . . . . 50.5.7 . . . . . . . . . . . . . . . . . .I. 50-5-8. . . . . . . . . . . . . . . . . . . 50-s.9 . . . . . . . . . . . . . . . . . . 50-s-10 . . . . . . . . . . . . . . . . . . 50-5-11. . . . . . . . . . . . . . . . . .
LiCI/lM) G.HIO)
90.17 90.41 77.24 77.51 65.96 66.16 58.33 58.60 43.44 43.72 28.42 28.67 15.12 15.25 15.41 9.04 9.11 5.21 5.25 3.19 3.26 3.28 3.31 3.33 3.37 93.10 93.10
.(Em. .E.
PI'
h
mm . Hg
kcal./z.-molo
kcol./g.-molc
11.42 11.36 15.19 15.06 20. 47 20.36 25.35 25.18 39.60 39.29 60.28 59.95 58.56 78.38 78.03 85.14 85.13 88.76 88.74 90.38 90.33 90.32 90.29 90.27 90.22 10.37 10.37
11.76 11.82 11.66 11.70 11.493 11.518 11.202 11.237 10.733 10.702 10.373 10.395 10.291 10.308 10.328 10.248 10.239 10.240 10.225
1.52 1.58 1.42 1.46 1.255
0.001 0.002 -0.013
10.244 10.223 10.220 10.234
0.006 -0.015 -0.012 -0.004
1.280
1.964 0.999 0.495 0.464 0.135 0.157 0.053 0.070 0.090 0.010
)
269
THERMODYXAMIC PROPERTIES O F L I T H I U M CHLORIDE SOLUTIONS
justed as necessary to maintain constant calorimeter temperature and constant power input to the heater. At the end of the run the gas flow is switched back TABLE 5 Results of studies of pure water at 50°C. (new calorimeter)
50-W-sc-1. . . . , , , . 50-w-sc-2 , . . , , , . 50-W-NC-3 . ,, .) 50-w-Pic-4.. . . . . . , , . 5 0 - w - s c - 5 .. . . . . . . . .
,
.
~
I/
PI
h
mm. Hg
k d . fg.-mole
92.20 92.50 92.47 92.78 92.53
10.231 10.222 10.266 10.223 10.244
EXPEPIYEhT KO.
________ ____
Mean . . . . , . . . . . . . . . . . . . . . . Probable error of mean. , . . . ,
, ,
I
P.
EXPEPIXENT NO.
50-W-KC-6. , . . . . . . 50-W-NC-7. . , , , , 50-W-NC-8. . . . . . . . 50-W-ixc-9. , , . . . . , 50-W-NC-10, , , . . . . ,
..... . . . . . ... .... . . .. ... . , . . . .. , , ...,.. .. .... . .. ..., ,., ,
.L kd./i.-mok
a m . Hg
92.72 92.44
10.224 10.256
92.55 10.04
1
10.245 10.004
TABLE 6 Results of studies of lithium chloride solutions at 50°C. (new calorimeter) YEAN CONCENIRAEXPERIXEST NO.
TlON
1
'9.
(C.L~CI/IWG.HIO)
,
I
I
5 0 - 9 - s c - 1 ,. . . . . . . . . . . . . I 50-s-sc-2. . . , .. , . . . . . . 50-9-sc-3,. . , . . . . . . . . . .I 50-Y-sc-4. . . . . . . . . , . . . . 50-s-xc-5. . . .. . , . . . . . , , 50-S-SC-6, , . . ,. .. . . . 50-s-sc-7, . , , . . . . . . . . . 50-S-NC-8. , , , . . . . . . . . . . #
79 79 79 79 80 80 80 80
.I
I
, , ,
83 99 59 75 01 16 35 51
kcd./;.-molc
mn. H g
I
14.30 14.29 14.31 14.27 14.18 14.11 14.05 13.99
1 1
1
1
, ~
I
,
11.62 11.65 11.55 11.61 11.76 11 59 11.72 11.68
1.38 1.41 1.31 1.37 1.51 1.35 1.47 1.43
TABLE 7 Results o j studies of pure water at 7OoC EXPERIYEYT h O
- -
I
70-IT-1 70-W-2 70-W-3 70-w-4
Mean 1'rob.ible error of m e a l - _
I I I
_-
I
Lo
m m Hq
I
id./$-mole
233 234 233 233
89 15 30 76
1
233 77 *o 10
I
Pa
--___
I
-~
10 10 10 10
029
037 049 041
10 039
*o 005
to the dummy towers, agmn at a convenient wet test meter reading, and at the same time the timer is stopped. The towers are removed from the train, capped off, and allowed to cool overnight in a desiccator before weighing
270
E R N E S T F. JOHNSON, JR., AND MELVIN C. MOLSTAD
TABLE 8 Results of studies of lithium chloride solution at 70'C. MEAN CONCENTRATION
LXPLPIYENT KO.
( 0 . LiC1/100 0.
1
8p.
Ha)
kcal./i.Nls
mm. Hg
70-5-1 . . . . . . . . . . . . . . . . . . 7023-2. . . . . . . . . . . . . . . . . 70-5-3, . . . . . . . . . . . . . . . . 703-4. . . . . . . . . . . . . . . . . . 703-5,. . . . . . . . . . . . . . . . . 70-S-6. . . . . . . . . . . . . . . . . . 7043.7. . . . . . . . . . . . . . . . . 70-5-8 . . . . . . . . . . . . . . . . . 703-9 . . . . . . . . . . . . . . 70-S-10. . . . . . . . . . . . . . . .
83.87 84.20 58.63 59.12 39.55 39.83 21.96 22.14 22 40 56
1
37.44 37.04 68.03 67.39 115.62 114.58 176.33 175.62 175 16 174 61
11.505 11.540 10.966 10.983 10.515 10.583 10.045 10.069 10 091 10 123
kcaI./g.mk
1.466 1.501 0.927 0,944 0.476 0.544
I
0.006 0.030 0 052 0 084
TABLE 9 Vapor pressure& of lithium chloride solutions CONCENTRATION G.
LiC1/100Q. HtO
3O'C.
SOT.
70'C.
mn. Hg
mn. Hg
mm. Hg
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
31.82 30.57 28.96 26.98 24.61 22.03 19.39 16.88 14.50 12.44 10.57 8.95 7.64 6.58 5.66
80
4.30 3.61 3.58
92.55 88.91 84.24 78.57 72.02 64.85 57.45 50.39 43.70 37.90 32.66 28.09 24.23 21.07 18,35 16.16 14.31 12.95
233.77 224.57 212.82 199.74 183.04 165.80 147,76 130.52 114.23 100.11 87,32 76.16 66.30 58.08 51.25 45.45 40.70 36.88
11.45 10.36
33.09
85 85.20 90
93.10 95 100 1'04.5
4.90
30.11 27.94 26.17
The water vaporized from the calorimeter during a run was assumed to be absorbed completely by the anhydrous magnesium perchlorate in the weighed Midvale towers. By following a fixed procedure for cleaning the outside surface
THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIOSS
271
of the towers and by maintaining a constant humidity of approximately 55 per cent within the balance case and the desiccator (ZO), a reproducibility of better than 1 part in 100,000 was attained in weighing the towers. The constant humidity was maintained by means of a saturated solution of calcium nitrate. Single-distilled mater was used for the pure water runs and for making up all solutions. Baker C.P. analyzed lithium chloride mas used for all the work with salt solutions. At 30°C. it was used without further purification except for filTABLE 10 Differential heat of dilution of lithium chloride solutions -
-
__
EKAT 01 DILUTION IN K l M C A I O P f E S PIP GRAY-MOLE OP WATLP
CONCENTPATION G. LiCI/lW G. HzO
-
0 5 10 15 20 25 30 35 40 45 50 55 60
65 70 75 80 85 85.20 90
93.10 95 100 104.5
WC.
0 0.004 0.008 0,021 0.047 0.086 0.144 0.249 0.388 0.543 0.693 0.840 0.976 1.097 1.197 1.292 1.365 1.435 1.438
SOT.
IO*C
0
0
0.004 0.008
0.004
0.022 0.049 0.090
0.150 0.258 0.400 0.559 0.712 0.862 1.002 1.127 1.230 1.328 1.405 1.478 1.533 1.564
0.008 0.023 0.051 0,094 0.156 0.267 0.412 0,575 0.731 0.884 1.028 1.157 1.263 1.364 1.445 1.521
1 ,580 1.622 1.660 1.682
tration of the solution after preparation. At the higher temperatures, 50" and 'iO"C., the salt was recrystallized twice from distilled water before use. The calorimeter charge was sampled after each pair of runs. Samples of the lithium chloride solutions used in the present work were analyzed with a precision of better than 1 part in 1000 by the volumetric method of Mohr (22). Titrations were carried out in yellow light for greater accuracy in detecting the endpoint. The error of analysis introduced negligible error in the results. Experimental work The selection of the system chosen for study, lithium chloridewater, was based on the availability of good data on differential heat of dilution and activ-
272
ERNEST F. JOHSSON, JR., AND MELVIN C. MOLSTAD
ity a t 25°C. and on the fact that aqueous solutions of lithium chloride are among the best of liquid absorbents used in the control of air humidity and in the drying of air. Studies were conducted over a range of temperatures to permit cross-checking the thermal data and the vapor pressure data for thermodynamic consistency. The latent heat of vaporization and vapor pressure were measured for pure water a t 30", SO", and 70°C. and for solutions of lithium chloride from moderate ThBLE 11 Latent heat of vaporization of water from lithium chloride solutions ~~
CONCENTPATION
G. LiCI/IW G. HIO
0 5 10 15 20 25
30 35 40 45 50
55 60 65 70 75 80
85 85.20 90 93.10 95
1
M I E N 1 EEAI OF VAPOUZATION IN YIUKALQRIES PEP GRAX-XOLE OF W A T E l
30.C.
10.460 10,464 10.468 10.481 10.507 10.546 10.604 10.709 10.848 11.003 11.153 11.300 11.436 11.557 11.657 11.752 11.825 11.895 11.898
SOT.
I
10.245 10.249 10.253 10.267 10.B4 10.335 i n 395 10.503 10.645 in,804 10.95i 11.107 11.247 11.3i2 11.475 11.573 11.650 11.723
ji
11.7iS
I
i
I
70'C.
10.039 10.043 10.047 10.062 10.090
i '
10.133 10.195 10.306 10.451 10.614 10,770 10.923 11.067 11.196 11.302 11.403 11.484 11.560 11.619
ll.m 11.661 11.699 11.721
100 104.5
dilution to high concentration at the same temperatures. Studies were also made with saturated solutions at 30' and 5OoC. Hunter's calorimeter was used for all the 3OOC. runs and forty of the 5OoC. runs. The new calorimeter was used for the other runs. RESULTS
The results for latent heat of vaporization were computed from equation 11 or from figure 5. Values of p obtained in runs using Hunter's calorimeter were corrected for heat loss along the power leads as well as for net heat exchange between calorimeter and bath and sensible heat changes in the gas stream and
THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE S O L ~ I O N S
273
in the calorimeter and its charge. The correction for heat loss along the power leads exceeded 2 per cent of q a t 50°C. The results for vapor pressure were computed from equation 14 with adjustment for the calorimeter saturation efficiency. A few of the results of runs made early in the present investigation were rejected for known experimental errors. Two rejections were based on failure
Fro. 6. Differential heat of dilution of lithium chloride solutions
to meet Chauvenet’s criterion of precision (23). In cases of error due to inaccurateaccountingfor water it was possible to correct one of the results, for example, vapor pressure, by using the deviation of the other result, for example, latent heat of vaporization. These corrected results are indicated in the tables of results. The results are listed in tables 1 through 11, which show results of studies of pure water at 30°C. (table l ) , lithium chloride solutions at 30°C. (table 2 ) , pure water at 50°C. (old calorimeter) (table 3), lithium chloride solutions at 50°C. (old calorimeter) (table 4), pure water at 50°C. (new calorimeter) (table 5 ) ,
274
ERNEST F. JOHNSON, JR., AND MELVIN C. MOLSTAD
9.Li CI / 1009.He0 FIG.7. Latent heat of vaporization of water from lithium chloride solutions
9.Li CI I Io0 9.He0
FIQ.8. Vapor pressure of lithium chloride solutiona
lithium chloride solutions at 50°C. (new calorimeter) (table 6), pure water at 70°C. (table 7), lithium chloride solutions a t 70°C. (table 8), smoothed values
THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
275
of vapor pressure (table 9)' differential heat of dilution (table IO), and latent heat of vaporization (table 11). The results are plotted in figures 6, 7, and 8. Figure 6 shows the differential heat of dilution a t 30", 50°, and 70°C.'figure 7 the latent heat of vaporization at 30°, 50", and 70°C.,and figure 8 the vapor pressure a t 30°, 50'' and 70°C. The experimental results for the solubility of lithium chloride in water are compared in table 12 with values from the literature. These solubilities were determined a t 30" and 50°C.when the saturated solutions used in the gas current studies were analyzed. In reporting the gas current results for saturated solutions the solubility data of Applebey (I) have been used. While Seidell's TABLE 12 Solubility of lithium chloride i n water SOURCE OF DATA
SOLWBILITY 0.
LiCI/lOO c. H B
Current experimental. . . . . . . . . . . . . . . . . . . . . Applebey et al. ( 1 ) . . . . . . . . . . . . . . . . . . . . . Seidell (19). . . . . . . . . . . . . . . . . . . . . . . . . . . International Critical Tables (10) . . . . . . . .
85.92 85.20 86.2 84.3
Current experimental . . . . . . . . . . . . . . . . . . . . . Applebey et a l . . . . . . . . . . . . . . . . . . . . . . . . . . Seidell , . ...................... Internatio l Tables. . . . . . . . . . . .
95.10 93.10 93.42 96.2
Current experimental Applebey et al.. . . . . . . . . . . . . . . . . . . . . . . . . . . Seidell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . International Critical Tables . . . . . . . . . . . . . .
104.50 104.5 108.9
(19) values are means which include the data of Applebey, data of other workers have been included which seem less reliable than those of Applebey. DISCUSSION
An indication of the reliability of the gas current method may be obtained by comparing the results of the present work on pure water with those of Hunter and with the best current values for water properties. The values for water properties adopted as standard in this work are those of the Kational Bureau of Standards (16) for latent heat of vaporization and those of Goff and Gratch ( 5 ) for vapor pressure. Hunter's work did not allow for a number of factors of appreciable importance, including (1) the pressure drop of the gas stream across the calorimeter, ( 2 ) the uncertainty of power measurement due to the manner of contacting the leads, (3) the heat leak along the power leads, (4) the failure to saturate the gas stream, and (5) the buoyancy correction for hydrate formation in the absorption
SOUPCZ OF DATA
TEKPERATUXX
'C.
LATENT HLAP 01 VAPOPIZATION
kcal./g.-mlc
~
30
Hunter, a8 reported. . . . . . , . . . . . . . . . . . , , . , . . . Hunt,er, as recalculated. . . . . . . . , . . . . . . . . . . , . . Current experimental. . , . . . . . . . . . . . . . . . . . . . . . . . National Bureau of Standards, . . . . . , . . . . . , . , .
10.452 f 0.003 10.440 += 0.003 10.460 f 0.003 10.4565 f 0.0003
50
Current experimental (new calorimeter). , . . . , . . [ National Bureau of Standards. . . , , . . . . , , . . . . . . I
10.245 f 0.004 10.2510 f 0.0003
70
Current experimental . . . . . . . . . . . . . . . . . . . . . . . Kational Bureau of Standards. . . . . . . , . . . . , , ,
..
.
.
10.039 z t 0.005 10.0402 f 0.0003
16 35
14
30 25
10
20
0 IN 8 J
15
0
. I
6
1
0
3
3
10
4
x
5
2
0
0
0 G LICL/IOO
G
nzo
0 L I C L / 100 G H20
FIG.10 FIG.9. Differential heat of dilution of lithium chloride solutions a t 30°C FIQ.9
FIG 10 Vapor preasure of lithium chloride solutions at 30°C.
virial coefficients for air, water, and their mixtures and correcting for buoyancy, the verification no longer holds; and the accuracy falls off further if the results are corrected for the pressure drop of the gas stream and for the power lead heat leak. Table 13 shows a comparison of Hunter's value for latent heat of vaporization
THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
277
&s reported by him, the bame as corrected by the authors, the present values, and the National Bureau of Standards' values. The precision index used in this table is the probable error of the mean based on the precision of the experimental data. The only experimental work affording a direct comparison of the thermal studies of lithium chloride solutions is that of Lange and Diirr (13). These workers, using a highly developed twin calorimeter, measured heats of dilution for solutions of lithium chloride over the full range of concentrations a t 25OC. Their vaIues for the differential heat of dilution after calculation to 30°C. have been plotted in figure 9, along with the results obtained a t 30°C. in the present work. Lange and Diirr estimate the reliability of their tabulation of values of the differential heat of dilution at f10 cal./g.-mole over the full rar.ge of con' centration. The precision of the present results for latent heat of vaporization is in agreement with the estimated reliability of the data based on the individual errors involved in each measurement. The estimated reliability of a single determination of the latent heat of vaporization by the gas current method was, for pure water, 9 parts in lO,OOO, and for saturated salt solutions, 50 parts in 10,OOO. Smoothed values for latent heat of vaporization, shown in table 1 1 , were obtained from smoothed plots of differential heat of dilution. The vapor pressure results for the salt solutions were smoothed by the method of Leopold and Johnston (15), using an enlarged plot of molar vapor pressure lowering as a function of salt concentration. The accuracy of the vapor pressure results obtained with the present method depends ultimately on the saturation efficiency of the calorimeter. Since it is impossibile to predict values of this saturation efficiency, the reliability of the vapor pressure results cannot be predicted from the accuracy of the individual measurements involved in the determination. If it is assumed that the saturation efficiency is constant for constant gas rate and the same system properties, it is possible to calculate the probable precision of determinations of the vapor pressure. With this assumption the estimated precision of a single vapor pressure determination is 1 part in 1OOO for pure water and for saturated solutions, 3 parts in 1OOO. The apparent vapor pressures for pure water as determined from the experimental results, using equation 14 without allowance for calorimeter saturation efficiency, are listed in table 14, together with the definitive (12) values of Goff and Gratch (5) and the result of Hunter. Saturation efficiencies calculated from the ratio of apparent vapor pressures to the actual vapor pressures are also shown. The precision index used for the current experimental values and the Hunter value is the probable error of a single determination based on the experimental precision. The probable errors for the Goff and Gratch values are based on their estimate of the reliability of their method of calculation. The improvement in saturation efficiency obtained with the new calorimeter may be attributed to the improved design. The decline in saturation efficiency
278
ERNEST F. JOHNSON, JR., AND MELVIN C. MOLSTAD
of both calorimeters with increasing temperatures is probably due to a decline in jet pump performance with the decreased gas rates used at the higher temperatures. A comparison of gas current results for vapor pressures a t 30°C. with the accurate data of Robinson (18) on the water activities of lithium chloride solutions over the full range of concentrations at 25OC. is shown in figure 10. Robinson's data mere calculated to 30°C. by means of equation 18, using the differenTABLE 14 Apparent vapor pressure of pure water and calorimeter saturation eflciency
OC
SATURATION LZ?ICIINCY
souam OF DATA
TIMPERATUPE
.
pncenl
mm. Hg
*
30
Hunter . . . . . . . . . . . . . . . . . . . . . . . . . . Current experimental (old calorimeter). . . . . . . Goff and Gratch . . . . . . . . . . . . . . . . . . . . . . . .
31.10 0 . 1 2 31.64 f 0.06 31.82 f 0.01
50
Current experimental (old calorimeter). . . . . . . Current experimental (new calorimeter). . . . . Goff and Gratch . . . . . . . . . . . . . . . . . . . . . . . . .
91.73 0.08 92.44 =k 0.12 92.55 & 0.03
99.11 99.88
70
Current experimental (new calorimeter). . . . . . 233.43 f 0.20 Goff and Gratch.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.77 f 0.07
99.85
TEMPERATOPE
I
97.74 99.43
*
TABLE 15 Vapor pressure of saturated solutions of lithium chloride VAPOR
SOURCE OX DATA
'C.
30
Current experimental . . . . . . . . . . . . . . . . . . . . . International Critical Tables (10). . . . . . . . . . . . .
85.92 84.3
50
Current experimental.. . . . . . . . . . . . . . . . . . . . .
,I
95.10
1
'
I
3.58 3.56 10.36
THERMODPN.4hlIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
279
latent heat of vaporization and vapor pressure has two convenient means of checking the reliability of its results. One means of checking stems from the fact that errors in measuring the quantity of water vaporized affect the latent heat of vaporization result and the vapor pressure result to the same extent but opposite in sign. The other means of checking lies in the use of thermodynamic relations. .\ sensitive relationship that may be used for testing the data for thermodynamic consistency is the expression for the change of activity with temperature (7).
Equation 18, with the smoothed data for the differential heat of dilution and water activities a t 50°C. computed from the vapor pressure data by the relation ai,, = p w f / p 8 ,was used to compute water activities at 30°C. and 70°C. These activities were compared with the activities obtained from the vapor pressure data a t 30°C. and 70°C. The maximum percentage discrepancy found between an observed and a calculated activity was less than the percentage uncertainty in the mean differential heat of dilution a t the same concentration. It is concluded from the foregoing that the ultimate reliability of the results of the gas current method as developed and employed in the present work is =k 0 r:tl. 'g.-mole for the latent heat of vaporization of pure water or of water from very dilute solutions at all three temperatures, $= 50 cal./g.-mole for the latent heat of vaporization of water from concentrated solutions at 30°C. and possibly somewhat better at the higher temperatures; f 0.1 mm. of mercury for thc vapor pressure over the full range of concentrations at 30" and W C . , and i.0.2 mm. of mercury over the full range of concentrations at 70°C. For engineering purposes thermal data on solutions are best represented by the entlialpy-concentration diagram (2). The use of the enthalpy-concentration diagram eliminates entirely the need for separate consideration of heats of solution, heats of mixing, heats of dilution, or heat capacities. Ordinarily two types of thermal data are necessary for the calculation and construction of the tliagr:im: ( 1 ) differential heats of dilution over the full range of concentration at one temperature, and (2) heat capacities over the full ranges of concentration and temperature. The gas current method provides data of the first kind-namely, differential heats of dilution-and in addition provides vapor pressure data. Unfortunately, for acculnt e calculation of enthalpy additional outside data on the differential heat of dilution are required for the concentration range from approximately 0.001 molar to 1 molar. B e h v this range the Dcbye-1Iuckel theory (7) applies, and ahove it the gas current data are sufficiently reliable. Within the range the percentage accuracy of the gas current data is too poor for carrying out the integration of the basic expression for solution enthalpy in terms of differential heats of dilution (11). The twin calorimeter technique (7, 14, 171 can be used to obtain accurately both differential heats of dilution and heat capacities over the full r:inges of
280
ERNEST F. JOHNSON, JR., AND MELVIN C. MOLSTAD
temperature and concentration. Hence, it is a more useful tool than the gas current method for determining thermal properties of solutions, since it can be used alone to evaluate solution enthalpies. Since the results obtained from the gas current method must be corrected by allowance for the interaction coefficient for moist air, it should be possible to calculate this coefficient from a comparison of gas current data with data obtained by methods not involving air-water interaction. Also, since the temperature coefficient of the interaction coefficient is used to correct gas current results, its evaluation should be possible. However, by an analysis of the probable errors of the determinations of these coefficients it was shown (11) that the present gas current method cannot be used with any useful accuracy for either determination, not only because of the inaccuracies of the gas current results but also because of the uncertainty of the published values (20) of the temperature coefficient of the second virial coefficient for pure water. SUMMARY
An evaluation of the gas current method as a useful tool for the determination of the thermodynamic properties of aqueous salt solutions has been made in the course of studies of pure water and solutions of lithium chloride. It was demonstrated that the gss current method could be used with highly concentrated and saturated solutions and over a range of temperatures. Studies of lithium chloride solutions were conducted over the full ranges of concentrations at 30°C. and 50°C. and over a wide range of concentration at 70°C. Pure water studies were made a t each temperature. For use at the higher temperatures a new calorimeter was designed and constructed to eliminate heat leak along the heater power leads and to improve the mixing of gas and liquid phases in the calorimeter. As a result of the present studies new data are reported for the latent heat of vaporization, differential heat of dilution, and vapor pressure of lithium chloride solutions over the full ranges of concentration at 30°, No, and 70°C. I n addition, new solubility data a t 30" and 50°C. are reported. The accuracy and reproducibility of the results were in agreement with the estimated accuracy based on the accuracies and reproducibilities of the individual readings. It was shown that certain data in addition t o gas current data are required for computing solution enthalpies. Hence the gas current method is less useful for this purpose than, for example, the twin calorimeter method, which with the proper care can supply all the necessary data. While the gas current method as used in the present work is less accurate than the best calorimetric methods or the best vapor pressure methods, it has a number of advantages. It requires no special apparatus, it is relatively simple to operate, and its results can be fairly accurate without extreme caution. I t measures two quite different properties, which can be related thermodynamically to check the reliability of the results.
THERMODYNAMIC PROPERTIES OF LITHIUM CHLORIDE SOLUTIONS
281
The accuracy of measuring these two properties-vapor pressure and latent heat of vaporization-is well within the limits required for many applications. On the other hand, the method is not suitable for as exacting a calculation as the determination of the interaction coefficient for moist air or its temperature coefficient. The work described in this paper was performed in the Thermodynamics Research Laboratory of the University of Pennsylvania under support by the Navy Department Bureau of Ships and the Office of Saval Research. REFERENCES (1) APPLEBEY, M . P., et al.: J. Chem. SOC. 1954, 1635. (2) BOSNJAKOVIC, F.: Technische Thermodynamik, Parts I and 11. Theodor Steinkopff, Leiprig (1935). (3) GOFF,J. A., ANDERSEN, J. R., A N D GRATCH,S.: Trans. Am. SOC.Heat. Vent. Engrs. 49, 269 (1943). (4) GOFF, J. A., AND BATES,A. C.: Heating, Piping Air Conditioning 13, 442 (1941). (5) GOFF,J. A., A N D GRAWH,S.: Trans. Am. SOC.Heat. Vent. Engrs. 61, 125 (1945). (6) GOFF, J. A., AND HUNTER,J. B.: J. Applied Mechanics 9, No. 1, 21 (1942). (7) HARNED, H. S., AND OWEN,B. B.: The Physical Chemistry of Electmlytic Solutions. Reinhold Publishing Corporation, Kew York (1943). (8) HUNTER,J. B. : Doctoral dissertation, University of Pennsylvania, 1942. (9) HUNTER, J. B., AND BLISS,H.: Ind. Eng. Chem. 56, 945 (1944). (10) International Cn'tical Tables, 1st edition, Vol. 111, p. 368.McGraw-Hill Book Company, Inc., New York (1928). (11) JOHNSON, E. F., AND MOLSTAD, M. C . : Final Report on Project H-1, University of of Pennsylvania Thermodynamics Research Laboratory (1949). (12) KEYES,F. G.: J. Chem. Phys. 16, 602 (1947). (13) LANGE, E. W., A N D DURR,F.: 2. physik. Chem. 121, 361 (1926). (14) LANGE,E. W . , AND ROBINSON, A. L . : Chem. Revs. 9, 89 (1931). (15) LEOPOLD, H . G., A N D JOHNSTON, J.: J. Am. Chem. SOC.49, 1974 (1927). (16) OSBORNE, N. J., STINSON, H. F., A N D GINNINGS, D. C.: J. Research Natl. Bur. Standards 1s, 197 (1939). (17) RICHARDS, T. W., A N D GUCKER, F. T.: J. Am. Chem. SOC.47, 1876 (1925). (18) ROBINSON, R. A,: Trans. Faraday SOC. 41, 756 (1945). (19) SEIDELL,A,: Solubilities of Inorganic and Metal OTganic Compounds, 3rd edition, Vol. I. D. Van Nostrand Company, Inc., New York (1940). (20) THIERS,R. E . , AND BEAMISH, F. E.: Anal. Chem. 19, 434 (1947). (21) UNIVERSITY OF, PENNSYLVANIA THERMODYNAMICS RESEARCH LABORATORY: Progress Report for March, 1947, Section on Project G-8. (22)WILLARD,H. H., AND FURWAN, N. H.: Elementary Quantitative Analysis, 3rd edition. D. Van Nostrand Company, Inc., New York (1940). (23) WORTHING, A. G., A N D GEFNER,J. : Treatment of E z p e r i m a h l Data. John Wiley and Sons, Inc., New York (1943).
