SATURATION THERMODYNAMIC FUNCTIONS FOR BISMUTH CHLORIDE
2389
The Saturation Thermodynamic Functions for Bismuth Chloride from 2 9 8 ° K to the Critical Point'
by Daniel Cubicciotti, H. Eding, F. J. Keneshea, and J. W. Johnson Stanford Research Institute, Menlo P a r k , California 94036
(Received February 14, 1966)
The saturation enthalpy increments above room temperature for BiC13 in its condensed phases were determined with a drop calorimeter to within 75" of the critical point. These were combined with previously determined enthalpies of vaporization to obtain values for the saturated vapor, and the data were extrapolated to the critical point. Saturation entropies for vapor and condensed phases were calculated from the enthalpies. The internal energy departures of the gas from ideal values were evaluated and compared with similar data for molecular fluids.
Introduction Earlier reports from this laboratory have presented the vapor pressures2 and the volume changes3 on vaporization for BiC13 up to its critical point and the enthalpies2 of vaporization calculated from them. To extend this work, we have measured the heat evolved by samples of BiC13when cooled from the liquid at high temperature to room temperature. From the heat evolved, the enthalpy and entropy increments above room temperature are calculated for the condensed phases under saturation conditions. From these and the enthalpies of vaporization, the functions for the saturated gas phase are derived.
Measured Heat Increments Experimental Details Samples of BiC13 sealed in quartz glass ampoules were heated to various temperatures, some as high as lllO°K, then dropped into a Parr calorimeter at room temperature to measure the heat evolved. The details of the calorimeter are described in an earlier paper.4 The samples were sealed in heavy-walled quartz glass ampoules to withstand the vapor pressure of the BiC13, which reached as much as 70 atm in some of the measurements. Because of the large amount of glass required for strength, only a fraction of the heat liberated from the samples originated from the BiC13; the rest was from the quartz glass. Therefore, the accuracy of the measurements was limited. The
amounts of quartz glass and BiC13 in each of the six samples are given in Table I. A small part of the heat liberated by the sample was due to the condensation of BiC13 from the vapor. The amount of heat from that source was calculated for each drop from the known liquid and vapor densities, the volumes of t'he ampoules, and the known enthalpy of vaporization. It was assumed that all the vapor condensed a t the drop temperature. Since the maximum correction was less than 0.5% of the total heat, the exact calculat'ion using Table I : Details of Samples Used
Sample no.
1 2 3 4 5 6
I 3
quartz, g
Internal vol. of ampoule, cc
3.8088 4.6110 4,7463 4.9224 4.8405 9.4603
6.1521 5.9856 5.9236 6.1514 6.1879 3.8254
1.7120 1.7224 1.6638 1.7688 1.7082 3.1743
W t of BiCla,
W t of
Symbol used in Figure 1
0 0
0
fR 0 0
(1) This work was made possible by financial support from the Research Division of the U. S. Atomic Energy Commission under Contract No. AT(04-3)-106. (2) J. W. Johnson, W. Silva, and D. Cubicciotti, J . Phys. Chem., 69, 3916 (1965). (3) J. W. Johnson and D. Cubicciotti, ibid., 68, 2235 (1964). (4) D. Cubicciotti and H. Eding, ibid., 69, 2743 (1965).
Volume 70,Number 7 J u l y 1966
D. CUBICCIOTTI, H. EDING, F. J. KENESHEA, AND J. JOHNSON
2390
the integrated heat of condensation was considered superfluous. For drops from temperatures below about 800°K this correction was negligible. The heat liberated by the quartz ampoules was obtained from measurements on samples of quartz glass from the same batch of glass used to make the ampoules. The enthalpy increments measured for that quartz glass were very close to those obtained by Lucks, et aL5 An equation which fits both sets of data within about 1% from 290 to 1130°K is
(HT - HTg8)(cal/g)
+ 3.229 X 10-5~2+ 7.619 + 1 0 3 / ~- 97.39
Enthalpy Increments The heat evolved by a sample in equilibrium with its vapor when cooled from T to 298'K is equal to the integralg
The temperature derivative of that quantity gives C,, the saturation heat capacity. The quantity C, is related to the saturation enthalpy by
bH
=
40 35 30
= 0.2313T
The material used was reagent grade BiCla which was distilled into the ampoules in a stream of dry oxygen at 300"; the oxygen was removed by evacuation and the ampoules were sealed off under vacuum. The resultant heat increments for BiCL in condensed phases (Le., heat liberated when cooled from T to 298°K) are shown as circles in Figure 1. The different types of circles refer to different samples which are identified in Table I. The data obtained in the present work agree quite well with those reported by Topol, Mayer, and Ransoms and those of Bredig.? The results of Walden and Smithla however, are substantially lower. We feel that the purity of the material used by these last workers is questionable, as they used reagent grade BiC13 without purification. Since BiC1, is very hygroscopic, we suspect their values were low because of an impurity-possibly BiOCl.
(SF)
45
c, + v(%)
c
For ordinary liquids below the boiling point the last term is negligible and drop calorimeter measurements give the enthalpy increments at constant pressure as well as the saturation enthalpy increments. A t temperatures well above the boiling point, the differThe Journal of Physical Chemistry
15
0 t TOPOL et a1 0 WALDEN AND SMITH 0 PRESENT DATA
300
400
500
I
I
I
I
1
I
600
700
800
900
1000
1100
1200
TEMPERATURE--'K
Figure 1. Enthalpy of BiC13 above 298'K. Data points are heats evolved in calorimeter. Different types of circles refer to different samples in present data (see Table I). Dotted curve and full curve a t lower temperatures are smoothed representation of heats evolved. Full and dashed curve represents derived saturation enthalpies. Dotrdash curve represents calculated standard enthalpy of ideal gas. Reference state is solid BiCla at 298°K. Critical point is shown by cross.
ences become significant, although small. Since we have no information about the compressibility of the liquid, we are not able to evaluate the constant pressure heat capacity or enthalpy increments. We can only evaluate the saturation quantities. The heats evolved for drops from various temperatures are shown as data points in Figure 1. The enthalpy increments above 298"K, derived from the data, are given in Table 11. Below 800°K the data were well represented by two straight lines (one for the solid and another for the liquid). In that range C, and C, are the same within an experimental error. The values obtained from our data for C, (or C,) were 25.6 eu (5) C.F. Lucks, J. Matoloch, and J. A. VanVelzor, U.S. Air Force Technical Report 6145,Part 111, March 1954 (AD 95406). (6) L. E.Topol, S. W. Mayer, and L. D. Ransom, J. Phys. Chem., 64,862(1960). (7) M.A. Bredig, ibid., 63,978 (1959). (8)G.E. Walden and D. F. Smith, U. S. Bureau of Mines, Report of Investigations No. 5859,Mines Bureau, Pittsburgh, Pa., 1961. (9) For a discussion of thermodynamics under saturation conditions see: E. A. Guggenheim, "Thermodynamics," 3rd ed, North-Holland Publishing Co., Amsterdam, 1957,p 149; or J. S.Rowlinson, "Liquid and Liquid Mixtures," Academic Press, Inc., New York, N. Y . . 1959,p 16 ff.
SATURATION THERMODYNAMIC FUNCTIONS FOR BISMUTH CHLORIDE
for the solid and 32.6 eu for the liquid. Topol, Mayer, and Ransom found 26.1 and 34.3, respectively. The enthalpy of fusion obtained from our data was 5.71 f 0.1 kcal/mole, in good agreement with 5.68 =t 0.08 reported by Topol, Mayer, and Ransom and 5.50 f 0.15 reported by Bredig.
Table I1 : Standard Thermodynamic Functions of BiCls in Condensed Phases below 800°K"
-
OK
HOT - H a m , kcal/moleb
SOT, eu
-(FoT H"d/T, eub
298 350 400 450 500 506.7 (6) 506.7(1) 550 600 650 700 750 800
... 1.33 2.61 3.89 5.17 5.34 11.05 12.47 14.10 15.73 17.36 18.99 20.62
41.70 45.82 49.24 52.25 54.95 55.30 66.57 69.25 72.08 74.68 77.10 79.35 81.45
41.70 42.01 42.70 43.59 44.60 44.74 44.74 46.56 48.57 50.48 52.26 54.03 55.67
T,
Below 800°K the saturation values (ie., values for the substance under its own vapor pressure only) are the same, within experimental error, as the standard-state values (ie., under 1 atm pressure). The precision quoted in the table is greater than the accuracy of any one value but it is useful for differences between values. The reference state for all values in the second and fourth columns is the solid a t 298°K.
Above about 800"K, the heats evolved were better represented by a curved line, although the scatter of the data near 1100°K makes the curve difficult to draw. The curve is shown in Figure 1 as a full line from 800 to 950°K (where it is not sensibly different from the enthalpy curve) and as a dotted line from 950 to 1100°K. The slope of that curve at any temperature was taken as C,, the saturation heat capacity, according to the discussion above. The saturation enthalpy increment (HT- HOzgg),was obtained by a summation of eq 2. That is, for 10" intervals from 800 to 1100"K, the quantity V(dp/dT),, evaluated from our earlier measurements of density and vapor pressure, was added to C,, and the sum was multiplied by 10 and added to the value of ( H , - H"298)for the preceding temperature. The resulting values of (H,H02g8),are shown as the full line in Figure 1 and for specific temperatures in Table 111. For the gas phase, the enthalpy was calculated relative to the solid a t 298°K. At 298°K the quantity
2391
(H",(g) - H0298(S)) is equal to the enthalpy of evaporation and was taken from the evaluation of vaporization datal0 as 27.3 kcal/mole. The enthalpy increments for the ideal gas, as calculated by Kelleyll and by Sundaraml2 from molecular constants, were used to establish the ideal standard-state curve for the gas shown in Figure 1. From 950 to 1100°K the enthalpies of evaporation, given by Johnson, et a1.,2 were added to the enthalpies of the liquid to give the saturation enthalpies of the gas (relative to the solid at 298"K), shown as a full curve in Figure 1. The curve was extended to join the ideal gas curve smoothly in the neighborhood of the boiling point because the vapor pressure data indicated that the gas was behaving ideally there. In that region the curve is shown dashed to indicate its interpolated nature. A value of (H, - H0298($)), at the critical point was estimated from data for other substances. To do this, a plot of reduced enthalpy increments for both liquid and vapor vs. reduced density was constructed for severalla substances: Ar, COz, NH3, and HsO. These formed a family of curves that were relatively close together for the liquid. Comparison of the values of ( H , - Hoz9&and reduced density for BiC13 in the range 1000 to 1100°K with the family of curves led to a value for BiC13 at of 37,500 cal/mole for ( H , - H0298)o the critical point. The enthalpy increments for the saturated liquid and vapor from 1100°K to the critical point (1178°K) were then drawn so that they met at the critical value and so that their separation was equal to the enthalpy of vaporization given by Johnson, et aL2 Values for the saturation quantities are given in Table 111. Entropies and Free Energy Functions For the condensed phases, the absolute entropy at 298°K was taken from the evaluation by Cubicciotti. lo The heat capacities for the solid and the liquid up to 800°K were constant, as reported above, and the entropy increments above 298°K were calculated from the integral of C J T . These were added to the absolute entropy at 298°K and the resulting values are shown in Table 11. Standard free energy functions were calculated from them and the enthalpy increments by the relation (10) D. Cubicciotti, to be published. (11) K. K. Kelley, U. S. Bureau of Mines Bulletin 584, U.S. Govern-
ment Printing Office, Washington, D. C., 1960. (12) S. Sundaram, 2. Physik. Chem., 34,233 (1962). (13) Data for these substances were taken from F. Din, "Thermodynamic Functions of Gases,'' Vol. 1-3, Butterworth and Co. Ltd., London, 1961-1962.
Volume 70, Number 7 July 1966
2392
D. CUBICCIOTTI, H. EDINQ,F. J. KENESHEA, AND J. JOHNSON
Table I11 : Thermodynamic Functions for BiCls under Saturation Conditions to the Critical Point
T, OK
800 850 900 950 1000 1050 1100 1150 1170 1178 (crit. pt.)
HT - Hales, kcal/molea
ST, eu
20.62 22.25 23.86 25.40 26.93 28.62 30.5 33.3 35.4 37.5
81.45 83.43 85.26 86.92 88.47 89.93 91.3 93.7 95.4 97.3
-(FT
-
H029S)/
T,
-
Gas
Liquid
c
cu,
V,
eua
eu
cc/moleb
55.67 57.25 58.75 60.18 61.54 62.67 63.6 64.7 65.1 65.5
32.5 32.5 31 30 32 35 40 78 140
97.8 102 107 112 119
...
(dp/dT), atm/degc
HT
128
-
ST,
Hazes, kcal/mole"
0.050 0.084 0.132 0.195 0.277 0.378 0.500 0.648 0.704
138 165 190 261
-(FT
9.65 10.56 11.68 12.10 12.77 13.40 13.5 12.9 12.0 10.2
...
-
eu
HOzss)/T, eua
V, cc/moleb
101.7 101.6 101.6 101.6 101.6 101.4 100.7 99.7 99.1 97.3
89.6 89.2 88.6 88.9 88.8 88.6 88.4 88.5 88.8 88.6
10,300 5 360 3,220 2,080 1 380 915 558 407 461
Reference state for second and fourth columns is the solid in its standard state at 298"K, and for eighth and tenth columns the gas in its standard state a t 298°K. Data in the sixth and eleventh columns calculated from the equations given in ref 3. Data in this column calculated from the equations given in ref 2.
I 130
These values are also given in Table 11. In the higher temperature range of these measurements, C, and C , are sensibly different. To evaluate the difference, data on the compressibility are required (see eq 3), and these are not available at present. Therefore, above 800"K, we report only the saturation values of the thermodynamic functions. Up to 110O0K, the saturation entropies were obtained by integrating the saturation heat capacity (ie., the slope of the curve of measured heat evolved in the calorimeter) divided by temperature. From 1100°K to the critical point, the slope of the enthalpy curve was reduced by the quantity V(dp/dT), to evaluate C, and this was integrated to give the entropy increments. The values obtained are reported in Table 111 and Figure 2. For the vapor, the standard entropy for the ideal gas has been calculated by Kelley and by Sundaram from molecular constant data. This is shown as a broken line in Figure 2. The standard entropy refers to the gas in the hypothetical state of 1 atm pressure and equals the saturation entropy only at the normal boiling point (unlike the enthalpy increments which are essentially equal at all temperatures below the boiling point). Below the boiling point the saturation entropies were calculated by subtracting R In p (vapor pressure in atmospheres) from the standard, ideal gas entropy . The saturation entropy for the vapor above the boiling point was calculated from the value for the liquid plus the entropy of evaporation (equal to the The JOUTTXZ~ of Physical Chemistry
I20
110
I
I
I
1
I
I
I
1
1
t\
-
m
; 100 u 0
> i g E
>-
90 80
K
5 70
6o
I-
I
-t'/ '
40
I
300
400
500
I
600 700 800 TEMPERATURE - O K
I
1
1
900
1000
1100
I: )O
Figure 2. Absolute entropy of BiCla. Full and dashed curve represents saturation entropy of vapor (upper curve) and condensed (lower) phases. Dot and dash curve is standard entropy of ideal gas. Cross shows critical point.
enthalpy of evaporation divided by t,emperature). The resulting values are shown in Figure 2 as full lines, or dashed lines where extrapolations of the enthalpy data were involved. The fact that the saturation entropy curves for the vapor above and below the boiling point join smoothly indicates consistency of the data because of the two different methods used for evaluating the curve. From
SATURATION THERMODYNAMIC FUNCTIONS FOR BISMUTH CHLORIDE
2393
Gas Imperfection Energy. The difference between the internal energy of the ideal gas and that of the real gas @'Tidea1 - ETrea1)is approximately equal to the net average energy (of attraction) per mole between molecules. (There is a contribution to (ETidealETrea1)from intramolecular energy differences between the ideal and real gas. This is assumed to be small and is neglected in the present discussion.) The quantity Etdea1- Erealis, then, the gas imperfection energy and can be calculated from the enthalpies given above by the relation
0.8
0.9
1.0
REDUCED TEMPERATURE
Figure 3. Energy departure from ideal gas values for several substances.
about 800 to 1000°K the saturation entropy of the vapor is almost independent of temperature. In that region there are two competing factors that influence the entropy. The increasing vapor pressure acts to decrease the entropy, and the increasing internal thermal motions of the molecules increases it. Apparently, these factors tend to balance one another with the result that the saturation entropy is essentially independent of temperature. Above about 1100"K, a factor that reduces the entropy becomes important and leads to the pronounced drop to the critical point. Presumably, this factor is a correlation of molecular positions and momenta over regions including several molecules (and might be considered as "clustering"). The saturation values for the free energy functions were calculated as for the condensed phases.
The quantity is equal to RT, and (PV)real was calculated from the saturation vapor pressures and volumes. The quantity E;dea1 - ETreal can be converted to a function of reduced properties by dividing by the critical temperature. l4 Comparison of (Eidea1 - Ereal)/Tofor several substanceP is made in Figure 3. The gas imperfection energy for BiC4 is seen to lie below those of HzO, N H , and COSand above that of Ar. Thus this property of BiCL also falls among those of molecular fluids. It was shown earlier that the reduced density of the liquid fell between the values for H20and Ar. Examination of reduced vapor pressures shows that it also falls between HaOand Ar. It appears, then, that in the thermodynamics of its vaporization BiC& acts like a molecular fluid. This suggests either that the species that give rise to its ionic conductivity are of small concentration or that the thermodynamic quantities associated with their recombination to neutral, molecular species are small compared to the quantities associated with vaporization.
(14) See 0. A. Hougen, K. M. Watson, and R. A. Ragatz, "Chemical Process Principles, Part 11, Thermodynamics," 2nd ed, John Wiley and Sons, Inc., New York, N. Y ., 1959, p 611.
Volume 70, Number 7 July 1966
