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276
Step 3: the absorbance of HDO measured in cells with a 5 X em. path length was found to be 0.012 at 3635 cm.-l for the YO-H band of HDO in DzO and 0.010 at 2680 cm.-l for the YO-Dband of HDO in
H2O. Step 4 : from the values in steps 1and 3, we calculate the concentration of “free O-H groups’’ for HDO in D20 (0.7 M ) to be 0.048 M or about 7% (mole fraction 0.07). The concentration of “free 0-D groups” for HDO in H2O (0.55 M ) is found to be 0.0694 M or about 13% (mole fraction 0.13). Measurements of the absorbance values in step 3 as a function of temperature show that the mole fraction of non-H-bond 0-H groups of HDO in DzO liquid roughly doubles between 25 and 62”. The validity of this procedure rests on several
points. The procedure assumes that all the intensity measured in step 3 is due to a band located at the position assumed for the free vO-H or v0-D band. This is probably not true. If bands due to H-bonded 0-H and O-D groups (which have absorption maxima at lower frequencies) are broad enough to contribute absorbance at 3635 and 2650 cm.-l, then the estimates for free O-H and O-D will be too large. It is therefore necessary to regard the estimates of part 4 as maximum values for free O-H and O-D. It is stressed that the estimates made in steps 1 and 2 may be far from the true values, and, therefore, the values for the mole fraction or mole per cent of free O-H and O-D groups may be in error.
Acknowledgment. The author wishes to thank Mr. Arthur L. Strickland for expert technical assistance
Association in Vapors of Ionic Salts. Vapor Densities and Vapor Pressures of Potassium Bromide
by K. Hagemark, M. Blander, and E. B. Luchsinger North American Aviation Science Center, Thousand Oalca, California 91960 (Received August 64,1966)
Vapor densities and vapor pressures of KBr were measured using a liquid gold isoteniscope similar to that of Datz, Smith, and Taylor. The values of the dimerization constant, K2, for the equilibrium 2KBr G K2Br2calculated from the vapor density measurements fit the equation log K2(M-l) = -3.407 8378/T. The standard free energy and energy and entropy of dimerization are found to be in excellent agreement with predicted values from the dimensional theory of association in ionic salt vapors.
+
Zntroduction Previously, Datz, Smith, and Taylor1 have published vapor density data for NaCI, NaBr, NaI, KC1, KI, RbCI, and CsCI. The deviations from ideal gas behavior could be accounted for by assuming monomers and dimers in the vapor phase. Blander2 has found the calculated dimerization constants to be in excellent agreement with a dimensional theory of association in ionic vapors. T h J W T of~ Physical Chemistry
In this paper we will discuss measurements of the vapor densities and vapor pressures of KBr. Apparent molecular weights in the vapor phase were determined by direct measurements of the pressure-temperature relation of the vapor at constant volume. The ap(1) 8. Datz, W. T. Smith, Jr., and E. H. Taylor, J. C h m . Phys., 34, 558 (1961).
( 2 ) M. Blander, ibid., 41, 170 (1964).
ASSOCIATION IN VAPORS OF IONIC SALTS
277
paratus used for these measurements was a modific+ tion and a simplification of the liquid gold isoteniscope of Datz and Smitha and Datz, Smith, and Tay1or.l In order to set limits on the range of pressures which could be measured in our apparatus we also made measurements of the vapor pressure of molten KBr. The dimerization constants calculated from our vapor density data are in excellent agreement with predictions of the dimensional theory.
for examplethe theory leads to several relationships between the dimerization constant for a comparison salt (Kzo)in which the internuclear separation is do and the dimerization constant of an arbitrary salt ( K z )in which the internuclear separation is d. These relations are: (1)A law of corresponding states
Association Constants The deviations of alkali halide vapors from ideal gas behavior have successfully been interpreted in terms of associations of salt molecules, nKBr Ft (KBr),, where the association constants K , are expressed in units of (M-I)n-l and K,(p) in units of atm.l*. The total pressure, PT ,under these assumptions is
In K2(T) =
where p, is the partial pressure of an n-mer. We may define an “ideal pressure,” P i d , as that pressure which one would find if there were no association pid =
wRT --- CnPn MIV n
(2)
where w is the weight of the salt with a monomeric molecular weight M 1in a volume V at a temperature T (OK.). If, as is indicated by mass spectrometric4 studies, only monomer and dimer are present in significant amounts, then one may calculate association constants for dimerization, K2, from measurements of p~ for a fked weight of salt in a measured volume and at a measured temperature. Thus
- PT p1 = 2pT - pid p2
= pid
(3)
(4)
where p l and p2 are the partial pressures of monomer and dimer, respectively. Thus
where R in eq. 2 and 5 is in liter atm./deg. mole.
The Dimensional Theory of Association for Pure Salts The dimensional theory of association of ionic salts is derived from a dimensional analysis of the partition functions for vapor molecules. It leads to relationships for relative values of association constants for the formation of polymeric salt species in terms of the relative internuclear separations of different monomeric molecules. For the simplest association-dimerization,
In Kz(Todo/d)
+ 3 In (dold) = In K ~ o ( T o ) (6)
(2) Isothermal relationships
- 3 In (&/a) + In Kzo(T)2 0 do - 1) + ACT =(;t do - 1y +
-(-
a
. (7)
RT d AS2 = ASzO - 3R In
(&/a)
AE2 = (do/d)AEzo
(8) (9)
The subscripts 2 and 20 signify the value of the thermodynamic quantity for the dimerization of the arbitrary salt and the comparison salt, respectively. The energy entropy ( A s ) , and heat capacity (ACT) changes are the changes of the standard values of these quantities for the dimerization. Similar simple relationships exist for higher polymers. The theory allows one to make relative calculations for many molecules in a simple manner and circumvents computations which are so complex and dficult that they have been attempted only for dimerizations. The theory is approximate and should apply best to ionic salts such as the alkali halides. Theoretical calculations have been shown to be in excellent agreement with the limited data available for the alkali halides which supports the potential usefulness of the theory in making predictions for unknown ionic systems. This paper provides data on a pure salt for further comparison with the theory and describes an apparatus which can provide data for testing aspects of the theory which have not been examined adequately.
(a),
Experimental Method The construction of the apparatus and the experimental procedure were essentially identical with that reported by Datz, et a l . , l l a except for the changes described below which simplified construction. A schematic of the apparatus is shown in Figure 1. A cylindrical vessel of fused silica, about 20 cm. long and made of tubing with a 60-mm. 0.d. (56-mm. i.d.), was connected by 10-mm. 0.d. (7-mm. i.d.) tubing to one arm of a U tube filled with liquid gold. The other arm of the U tube was connected to a mercury manometer and a needle valve, through which the compensat(3) 9. Dats and W. T. Smith, Jr., J. Phys. Chem., 63, 938 (1959). (4) J. Berkowits and W. A. Chupka, J. Chem. Phys., 29, 653 (1968).
Volunte 70,Numbw 1 Januarg 1.966
K. HAQEMARE, M. BLANDER, AND E. B. LUCESINGER
278
Schematic of, Vapor Density Apparatus Vacuum
Liquid Geld
TO Argon Leak
r
/yL - - - Salt vapor
-\
,,TheJ:::IocoypI* \
Constriction For Sealing
Figure 1. Schematic diagram of the vapor density apparatus.
ing pressure in this side of the U tube was adjusted by opening stopcocks either to a vacuum manifold or an argon reservoir. I n our initial experiments we constructed a doublewalled, vacuum-jacketed vessel such as applied by Datz, et al.’ An apparent leakage into the vessel observed by Datz was also observed in our case. This apparent leak ultimately was traced to the seemingly unlikely distillation of mercury into the molten gold through more than 1 m. of tubing with several bends. Since the gold-mercury solution is less dense than pure gold, an apparent pressure was observed even when there was no real pressure difference. This difficulty was corrected by interjecting a Dry Ice trap and a stopcock between the mercury manometer and the U tube and by opening the stop cock only briefly during the measurements. Consequently, we were able to use a single-walled vessel which was considerably simpler to fabricate. Contrary to the findings of Datz, et al.,’J we found no measurable leakage of air into the singlewdled fused silica vessel even after operation of the vessel for more than 24 hr. at high temperature including more than 4 hr. of operation above 1350°K. The elimination of the doublejacketed vessel not o d y simplified construction but also allowed us to seal a fused silica thermocouple “well” about 19 cm. long to the bottom of the vessel.
As in the apparatus of Datz, et al., the upper and lower furnaces were multitap Marshall furnaces each separately controlled to *lo by a West Gardsman saturable reactor controller. The two furnaces were separated by a small auxiliary furnace about 85 mm. long consisting of a Variac controlled cylindrical heating element (Kanthal windings) surrounded by insulating firebricks. Temperatures measnred at four levels alongside the vessel were the same as those measured by a single movable thermocouple inserted a t the same levels inside the thermocouple “well.” Consequently, in the final experiments, measurements of temperature were made at four levels inside the “well” with the average temperature being utilized for the calculations. Differences of temperature at different points in the vessel were held to less than 5” by shunts across the furnace taps. In the vapor pressure measurements thermal gradients were adjusted so that the liquid was in the coolest region. The temperatures given are those of the liquid. Potassium bromide was Mallinckrodt analytical reagent grade which was predried under vacuum at 400”. For the vapor density measurements a weighed sample of dried salt was placed in the fused-silica vessel of known volume. The salt was outgassed for several houn at 3WOO”, the vessel was sealed, and the temperature was raised until all of the salt was completely vaporized. The pressure of the salt inside the vessel was observable as a difference of height of gold in the two arms of the U tube. This pressure waa counterbalanced by an equal pressure of argon in the other arm of the U tube. A cathetometer was used to observe the levels in the gold U tube and mercury manometer. The pressure was meamred to about 0.05 mm. and was reproducible to about 0.10 mm. At the end of each experiment the temperature was lowered to about 500” so that the salt had a negligible vapor pressure. Within the precision of the measurements, the pressure was always zero indicating a negligible quantity of water in the sample which had been introduced into the vessel. We observed that, upon cooling, it waa important to condense the salt in the vessel and not in the connecting tubmg. Since the tubing very often waa broken open and fused together between experiments, the salt contaminated and corroded the silica badly if this precaution was not taken. Further details of the measurements are as given by Datz, Smith, and Taylor.’
Measarements Data from the vapor pressure measurements are plotted in Figure 2. Included are also the vapor pres-
279
ASSOCIATION IN VAPORS OF IONIC SALTS
I \
60-
I A
2.26.10-4 mole/liter
0
3.2O.1Oe4 mole/liter
I
/ * @
I I.
a 3.86,10-4 mole/liter
50-
A
5.18.10-~ mole/liter
I I
7.79.10-"
I
---
mole/liter vapor presjure from separate run
; I
A
I I
40-
I I
A
I
I
I
I
7.0
7.5
80
8.5
90
I04/T["K)
Figure 2. Vapor pressures of potassium bromide. A least-squares treatment of the points shown fits the equation log p(mm.) = 22.159 - 10,824/T 3.966 log T,which, when plotted, is indistinguishable from the line shown (JANAF).
T("K)
sures obtained from the vapor density experiments when the salt had not been completely evaporated. In this case the lowest temperature of the vessel is recorded. A least-squares treatment of the data w a ~ made using calculated values of ACp5 for vaporization at 1300°K. The analysis leads to the equation
Figure 3. Data obtained from the vapor density experiments. When the salt w&s not completely vaporized the points fell on the dashed line which represents the vapor pressures. These points are also plotted in Figure 2.
A 2.26.
IO-^ mole/liter mole/liter
0 3.20
3.86.10-4 mole/liter
log p(".)
=
22.159
-- 3.966 log T T
which is in excellent agreement with the vapor pressures calculated from the "JANAF Tables" [log ~(IIXII.)= 22.258 - 10,937/T - 3.966 log TI. In Figure 3 is given a plot of the pressure of KBr us. temperature for the vapor density measurements mole/l at 2.26, 3.20, 3.86, 5.18, and 7.79 X of KBr. The dashed curve represents data from the separate vapor pressure measurements. Values of log K2 calculated from the data in Figure 3 (where dl of the salt was in the vapor phase) are plotted in Figure 4. A least-squares analysis of the data leads to the equation
mote/liier
A 5.18
(10)
t o I
t
1 , p,
I .o 6.8
-
7.0
Z2
, , -$ , 7.4
7.6
7.8
E
IO4/T('K)
Figure 4. The calculated association constants for the equilibrium 2KBr & KJ3r2.
(K2 in units of M-I). 1.1 x 10-1.
The standard deviation is
(6) "JANAF Thermochemical Tables," The Dow Chemical Go., Midland, Mich., Dee. 1961.
Volume '70,Number 1
January 1966
K. HAGEMARK, M. BLANDER, AND E. B. LUCHSINGER
280
Discussion In Table I are given values of the thermodynamic properties of KBr predicted from the dimensional theory using NaI as the test salt as in ref. 2. These are compared with the values determined in this work. The agreement is excellent and lends further support to the predictive value of the dimensional theory.
+
Predicted
Measured
2.99
2.93
3.10 -38.6 -26.6
3.04 -38.3 -26.9
S. H. Bauer and R. F. Porter in “Molten Salt Chemistry,” M. Blander, Ed., Interscience Publishers, Inc., New York, N. Y., 1964, p. 642. The standard states for ASzP are the ideal gas a t 1 atm. = 2,7115 and d = 2.8207:
The dimerization constants determined in this work are only slightly higher than the estimated data in the “JAXAF Tables” and thus confirm the approximations made in making the JANAF estimate^.^ (At 1300°K. log K2 = 3.04 in our case compared to log K2 = 2.94 from JANAF. However, this difference will lead to only a small change in the values for the thermodynamic quantities of monomer and dimer estimated in the “JANAF Tables.”) A point of potential interest is the possibility of trimer formation. Mass spectrometric results4p6indicate the presence of a small amount of trimer. If trimer were formed, then the association constants calculated from our data would be apparent associ& tion constants (Kz(app.)) which would be a function of density. This can be seen as follows.
The Journal of Phgcicd Chemistry
+
As an illustration let us compare a vapor of total mole/l. 2p2 3pa = p) of 2.86 X density (PI of KBr with one having a total density of 7.68 X mole/l. of KBr containing the following assumed fractions of monomer, dimer, and trimer.
+ +
Table I : Predicted and Measured Values of the Thermodynamic Properties of KBr
Log Kd1365dold) 3 log (dold)” Log K:: (1300’K.) AEz, kcal./mole ASzp, cal./deg. moleb
The density of monomers, dimers, and trimers is and pa, respectively. By interpreting the deviation from ideality as being due to dimers only, one finds apparent values of monomers and dimers to be given by dapp.) = PI - pa and a(app.1 = pz 2~3,and the dimerization constant is given by PI, p2,
pl = 2.0 X
mole/l.
pl =
4.0 X
mole/l.
= 0.4 X
mole/l.
p2 =
1.6 X
mole/l.
p2
pa =
0.02 X 10-4 mole/l.
=
0.16 X
mole/l.
The calculated value of log K2(app.) at the low density is 3.05, and at the high density it is 3.11 as compared to the true value of 3.00. The scatter of the calculated association constants plotted in Figure 4 appears to be nonrandom. If there are no systematic errors in the measurements, this may be a result of the presence of trimer. However, the scatter in the data are of the same magnitude as the differences in K2(app.) so that more refined data would be necessary to obtain the fairly small corrections to K2(app.) if higher polymers were present.
Acknowledgments. The authors wish to thank Mr. Dennis Hengstenberg, who performed some of the measurements, and Mr. Desmond Radnoti, whose patience and helpfulness in constructing the fusedsilica apparatus were essential. (6) The maas spectrometric measurements were made at lower temperatures and at much lower pressures than our measurements. A crude extrapolation of the small relative amount of trimer (4.1%) to the conditions of our experiments indicate that the fraction of trimer could be as high aa 6%.
