2886
J. Phys. Chem. 1981, 85, 2886-2895
the dye laser (6022.3 A) experiment was to monitor the equilibrium concentration of Na and Na2 by exciting the 5s level of Na through the two-photon process on the one hand and by looking at the A-X fluorescence of Na2 on the other. The dye laser (6022.3 A) excites u’ = 34, J’ = 50 by pumping the u” = 10,J” = 49 level. This means that our optically pumped Naz laser (pumped at 5682 A) can
be readily used for 3s
-
5s two-photon experiments.
Acknowledgment. We thank Dr. Robert F. Ferrante for his assistance and Professor Lowell Cross for the loan of his Krf laser. Support received from the National Science Foundation is gratefully acknowledged.
ARTICLES High-Temperature Thermodynamic Properties of Aqueous Sodium Sulfate Solutions P. S. Z. Rogers and Kenneth S. Pltzer” University of California and Lawrence Berkeley Laboratory, Berkeley, California 94720 (Received: March 3 1, 198 1;
In Final Form: June 4, 1981)
A flow calorimeter has been used to measure the heat capacities of aqueous sodium sulfate solutions from 30 to 200 “C at 1bar, or the saturated vapor pressure, and at 200 bar. The heat-capacitydata have been integrated as a function of temperature to obtain values of the apparent molal enthalpy, the osmotic coefficient, and the mean activity coefficient. Osmotic coefficients obtained in this manner are in good agreement with available literature data over the entire temperature range. These results indicate that heat-capacity measurements can be used reliably to obtain the high-temperature activity properties of electrolyte solutions, provided the enthalpy and Gibbs energy are known at 25 “C.
Introduction The thermodynamic properties of electrolyte solutions have been studied extensively at room temperature and pressure. However, comparatively little is known about the behavior of aqueous electrolytes at higher temperatures and pressures. While sodium chloride solutions have been studied at high temperatures, much less information is available on electrolytes of charge type other than 1-1. We have determined the high-temperature thermodynamic properties of aqueous sodium sulfate because it provides an example of a higher charge-type salt. The thermodynamic properties of aqueous solutions are of interest for research and engineering design in such areas as desalination, geothermal energy development, geopressurized brine exploration, and hydrothermal ore deposition. The number of electrolyte solutions of interest at high temperatures is large, so that a method of obtaining thermodynamic properties from a minimum amount of experimental data is desirable. Heat-capacity measurements are ideal for this purpose, since the data can be integrated to yield enthalpy and activity information by using literature data available at room temperature to evaluate the integration constants. We have constructed a flow calorimeter to measure the heat capacities of aqueous solutions at high temperatures and pressures. Sodium chloride, the most abundant component of natural brines, has been studied previously by a number of investigator^.'-^ Sodium sulfate was chosen (1)L. F. Silvester and K. S. Pitzer, J. Phys. Chem., 81, 1882 (1977).
(2) K. S. Pitzer, D. J. Bradley, P. S. Z. Rogers, and J. C. Peiper, Lawrence Berkeley Laboratory Report No. 8973, 1979. (3) D. Smith-Magowan and R. H. Wood, submitted to J. Chem. Thermodyn. 0022-3654/81/2085-2886$01.25/0
for this study because it is also a major component of natural brines. In addition, osmotic coefficients for sodium sulfate solutions, derived from the heat-capacity measurements, can be compared with isopiestic data available at high temperatures. Sodium sulfate also is of interest in studies of ion-pair formation at elevated temperatures and as an example of a 2-1 charge-type salt. Experimental Section Flow calorimetry has many features which make it ideal for use at high temperature. Since the experimental fluid flows through the calorimeter, it is possible to keep the calorimetric temperature constant while changing samples. There is no vapor phase, hence no correction for vaporization. Fluid flowing through the calorimeter can also be kept at constant pressure, allowing measurements along isobars rather than along the saturated vapor pressure curve. The capability to extend measurements to high pressures is limited only by the fluid pump and the back-pressure regulation system. The fast response and the high sensitivity which make flow calorimetry powerful at room temperature also are advantageous at high temperatures. The high-temperature flow calorimeter is an adaptation of a design used by Picker, Leduc, Philip, and Desnoyers4 at room temperature. It has been described in detail elsewhere; in addition, Smith-Magowan and Wood3 have constructed a similar flow calorimeter for use a t high temperatures. The calorimeter, illustrated in Figure 1, is (4) P. Picker, P.-A. Leduc, P. R. Philip, and J. E. Desnoyers, J. Chem. Thermodyn., 3, 631 (1971). ( 5 ) P. S. Z. Rogers, Doctoral Dissertation, University of California, Berkeley, CA, 1981.
0 1981 American Chemical Society
The Journal of Physical Chemistty, Vol. 85,
Properties of Aqueous Sodium Sulfate Solutions c
No. 20, 198 1 2887
When water is flowing through both sides of the calorimeter, the power in the heaters can be adjusted to equalize the temperature rise in both sides. The temperature rise in the working side is given by
P, - L
T=-
fWCP,
I
//////////A
/,
Y
Flgure 1. High-temperature flow calorimeter: (A) stainless-steel jacket;
(B)copper cylinder; (C) vacuum; (D) heater; (E)temperature sensor; (F) supporting tube containing electrical leads and vacuum connection.
constructed of small, thin-walled tubing (0.150-cm outside diameter by 0.023-cm wall stainless steel). A high-pressure, liquid-chromatography pump (Altex Model 100) being used, solution is forced through the tubing and past a heater where it is heated -3 K. The heater is made of 1 m of Thermocoax insulated nichrome heating wire (Amperex Electronics) which has a resistance of 50 0 m-l and is wound around the tubing to form a helix -5 cm long. The heated solution then flows through a 2-cm long spiral in the tubing, which surrounds a temperature sensor. Both the inconel-clad heating wire and the thin-walled, stainless-steel thermometer well are silver soldered to the tubing for good thermal constant. The temperature sensor is a four-lead, 1000-0 platinum resistance thermometer (Rosemount No. 146MA) which is cemented into the well with high-temperature ceramic cement. A second, identical unit of the calorimeter contains pure water flowing in series with the solution. In practive, only pure water is fed through the chromatography pump and the reference side of the calorimeter. The water then displaces an equal volume of solution, contained in a sample exchange loop thermostated at 25 "C, through the working side of the calorimeter. The calorimeter is supported on and surrounded by a large copper cylinder, which serves as thermal mass and adiabatic shield. The copper cylinder is contained in a stainless-steel vacuum jacket, and the whole assembly is heated in a fluidized bath, which is controlled with an iron-constantan thermocouple sensor and an Electromax I11 controller (Leeds and Northrup) to f O . l K. The large thermal mass of the copper cylinder provides temperature stability of better than 0.01 K during the course of a measurement. Because both sides of the calorimeter are equally affected by temperature fluctuations, the temperature difference between reference and working sides is stable to 0.005 K. This temperature difference is measured directly by using a calibrated, G-2 Mueller bridge with a microvolt amplifier (Leeds and Northrup) and a recorder serving as a galvanometer. The temperature of the copper cylinder is measured by using a calibrated, 25-9 platinum resistance thermometer (Burns Engineering) and the Mueller bridge. The system pressure is monitored to f l bar with a pressure transducer calibrated against a Bourdon tube pressure gauge (Ashcroft Digigauge Model 7781).
-
where P, is the total power dissipated by the heater, L is the power loss, f , is the mass flow rate of the water, and cp, is the specific heat capacity of pure water. The total power to the heater (P,) is determined by measuring the voltage drop across the heater and across a 30-0 standard resistor in series with the heater, using a calibrated, 5.5place digital voltmeter (Systron Donner Model 7205). The power lost through conduction, convection, and radiation (L) is determined directly by measuring the temperature rise, the power input, and the mass flow rate of water, the heat capacity of water being known. Because the percentage power loss is large (increasing from 5% at room temperature to 15% at 200 "C), it is measured between every two or three heat-capacity determinations. When a sample solution is flowing through the working side, the heater power can again be adjusted so that the temperature rise of the solution matches the unchanged temperature rise of water in the reference side. If one assumes that the power loss depends only on absolute temperature and the temperature rise
where the power input, the flow rate, and the heat capacity are those of the sample solution. The ratio of the heat capacity of the solution to that of pure water is then given by
P, - L 2S°C
where the density ratio is taken at 25 "C and the system pressure. Here the density ratio can replace the mass flow rate ratio because the water displaces an equal volume of solution, at 25 "C, in the solution exchange loop. The total uncertainty in the experimental ratio (P,L)/(P, - L),resulting from uncertainties o f f 0.01 K in the temperature rise, f 0.001 g min-l in the flow rate, the f 0.001 K in temperature matching, can be estimateds as f 0.0005. This is equivalent t o a maximum uncertainty of 1.7% in the value of (P, - P,)/(P, - L). When this estimate for the uncertainty in the experimental ratio is used, the maximum precision of a specific heat capacity measurement is roughly f 0.002 J g-' K-l. The solutions used in this study were prepared from Baker reagent-grade anhydrous sodium sulfate, which was dried overnight at 180 "C and cooled in a vacuum desiccator. All solutions were prepared by weight, and all weights were corrected for air buoyancy. At room temperature (22 "C) sodium sulfate solutions are saturated at 1.56 m.6 Since supersaturated solutions of sodium sulfate are relatively stable, a few attempts were made to load the solution exchange loop with samples at high concentrations. These attempts were not entirely successful, and the few data points reported above 1.5 m should be used with caution. (6) W. F. Linke, "Solubilities of Inorganic and Metal Organic Compounds", Val. 11,4th ed., American Chemical Society, Washington, DC, 1965.
2888
The Journal of Physical Chemistry, Vol. 85,
No. 20, 1981
Rogers and Pltzer
0
Figure 2. Comparison of apparent molal heat capacity values obtained In this study wlth those published by Likke and Bromley.''
Results The results of heat-capacity measurements of sodium sulfate solutions from 30 to 200 " C are given in Table I. The values listed for the heat capacity of pure water below 95 "C were taken from Stimson,' while those above 95 "C were taken from the steam tables of Haar, Gallagher, and Ke11.8 The density of water at 25 "C was taken as 0.997 047 g cm-3 at 1 bar and as 1.0059 g cm-3 at 200 bar.8 Densities of sodium sulfate solutions at 25 "C and 1bar were taken from the literature."12 Those at 200 bar were taken from Chen, Emmet, and Millero13 below 0.33 m; above 0.33 m they were estimated from values of the bulk compressibility to 1000 bar.14 Heat-capacity data along the vapor saturation curve were analyzed by assuming that the ratio (p.Jp,+,) at 25 "C does not vary over the small pressure range from 1 to 16 bar. Likke and Bromley15 have published the only comprehesive study of the heat capacities of sodium sulfate solutions at high temperatures. Their data are compared with those of the present study in Figure 2, where the error bars shown for the 180 "C data were calculated by using the uncertainty of fO.O1 J g-' K-l (in the specific heat capacity) given by Likke and Bromley. The two sets of data are in agreement well within the stated uncertainty. However, the greater precision of the present measure(7)H.F. Stimson, Am. J. Phys., 23,622 (1955). (8)L. Haar, J. Gallagher, and G. S. Kell, "Proceedingsof the International Association for the Properties of Steam", Sept 1979,pp 1-14. (9)I. V. Olofosson, J. J. Spitzer, and L. G. Hepler, Can. J. Chem., 56, 1871 (1978). (10)G.Perron, J. D. Desnoyers,and F. J. Millero, Can. J. Chem., 53, 1134 (1975). (11) R. E. Gibson, J. Phys. Chem., 31,496 (1927). (12)C.-T. A. Chen., J. H. Chen, and F. J. Millero,J. Chem. Eng. Data,
25., - - (19901. ~. ~ ~ - - - , -
307
(13)C.-T.Chen, R.T. Emmet, and F. J. Millero, J. Chem. Eng. Data, 22,201 (1977). (14)R. E.Gibson, J. Am. Chem. SOC.,56,4 (1933). (15)S.Likke and L. A. Bromley, J. Chem. Eng. Data, 18,189(1973).
IO
2.0
Mola 11 t y
Figure 3. Comparison of apparent molal heat capacities at 1 and 200 bar, at 50 OC.
14OOC
Molality
Flgure 4. Comparison of apparent molal heat Capacities at 4 and 200 bar. at 140 OC.
ments is evident at the lower concentrations. No literature data on sodium sulfate heat capacities are available at pressures greater than the saturated vapor pressure. The 200-bar data at 50 and 140 "C are compared with lowpressure data in Figures 3 and 4. The pressure dependence of the apparent molal heat capacity of Na2S04at
The Journal of Physical Chemistry, Vol. 85, No. 20, 198 1 2889
Properties of Aqueous Sodium Sulfate Solutions
-100
50 OC is twice as large as that reported by Smith-Magowan and Wood3 for NaC1.
0
Calculations Review of Equations. To calculate high-temperature activity properties, the heat-capacity data must be fitted to a temperature-dependent equation, and the fitting equation must be integrated twice by using enthalpy and activity data at 25 "C to evaluate the integration constants. The system of equations chosen to complete this calculation for sodium sulfate solutions was developed by Pitzer and c o - ~ o r k e rand s ~ ~was ~ ~found to describe successfully the properties of sodium chloride solutions at high temperatures.lp2 The basic equations for the osmotic and acticity coefficients (q5 and rh),the apparent molal enthalpy ("), and the apparent molal heat capacity (+Cp)have been derived by Pitzerm and are summarized in Table 11. Here p(O), p(l), and C+ are the virial coefficients related to short-range interionic forces whose temperature dependence will be determined from the heat-capacity data. Also, the additional symbols p(o)Land p(0)Jare defined as
p(o)L= (ap(O) / anp p@)J= ( a p ( y d T ) ,
+ (z/T)p@)L
(144
aT)p
U4b)
This study
0
I
I 100
0
I
2( 3
Flgure 5. Comparison of values of the apparent molal heat capacity at infinite dilution. The solid line represents values obtained from the parameters listed in Table 111. Squares represent the data of Gardner, Jekel, and Cobble,** and dots represent values obtained in this study.
-
Values of +Cp- C,O at all temperatures, including literature data at 25 0C19J023were then used simultaneously in a linear least-squares routine to determine the optimum temperature-dependent equations for p(0)J,P(l)J, and CN:
= ( a p c o ) / d r )sat - (apc0)/dP) T ( ~ Pa T/) s a t (15)
Extensive volumetric data at high temperatures and pressures are required to evaluate the last term in eq 15; in this study, it has been assumed to be negligibly small. This assumption is probably reasonable below 200 "C, but it could lead to significant error at higher temperatures. Temperature Dependence of the Heat Capacity. The low-pressure, heat-capacity data were first fitted to eq 8 at constant temperature to evaluate These values of Cp,O were combined with those reported by Gardner, Jekel, and Cobble22in a least-squares fitting routine to determine their temperature dependence. The two sets of Cp: values and the smooth curve given by the fitting equation
Go.
Cpz" = U1 + U2T + U3P + U4/(T - 263)
(16)
are shown in Figure 5. The coefficients of eq 16 are given in Table 111. The values c," were fixed by this equation for the rest of the calculations. (16) K. S. Pitzer, J. Phys. Chem., 77,268 (1973). K. S. Pitzer and G. Mayorga, J. Phys. Chem., 77,2300 (1973). K. S. Pitzer and G. Mayorga, J. Solution Chem., 3,539 (1974). K. S. Pitzer and J. J. Kim, J. Am. Chem. Soc., 96, 5701 (1974). K. S. Pitzer in "Activity Coefficients in Electrolyte Solutions", Vol. I, R. M. Pytkowicz, Ed., CRC Press, Boca Raton, FL, 1979, Chapter (17) (18) (19) (20)
7.
c
Temperature, "C
with similar definitions for p(l)L,C4L, and C". Values of the Debye-Huckel (D-H) slopes have been calculated by using the equation for the dielectric constant of pure water ( D ) given by Bradley and Pitzer21and values for the density of pure water (d,) given by Haar et al.s Use of eq 8 to describe the low-pressure sodium sulfate heat capacities as a function of temperature requires one approximation. The definitions of p(o)J and the other parameters require temperature derivatives at constant pressure. However, the heat-capacity data have been taken near the saturated vapor pressure curve, so that above 100 "C the required first derivative of pcO)is
(apn/
-400
(21) D. J. Bradley and K. S. Pitzer, J . Phys. Chem., 83, 1599 (1979). (22) W. L. Gardner, E. C. Jekel, and J. W. Cobble, J. Phys. Chem., 73, 2017 (1969).
The factors (T - 263)-3and (680 were chosen for convenience as factors which vary rapidly at low and high temperatures, respectively. The values of 263 and 680 have no theoretical significance. Predicted values of the osmotic coefficient were calculated from a straightforward, albeit lengthy, integration of the equations for p S J , p('lJ, and CN to obtain p a , and C+, The required integration constants are simply values of pC0),p(l), and C+,and their first derivatives with temperature, conveniently evaluated at 25 "C. Improved values of $O), O(l), and C+ for sodium sulfate at 25 "C have recently been calculated by Rard and Miller24from their isopiestic data; they are listed in Table 111. The remaining integration constants were evaluated by fitting literature data available at 25 0C2Er27 with eq 5. They differ slightly from the values determined previously by Silvester and (23) (24) (25) (1941). (26) (27)
M. Randall and F. D. Rossini, J.Am. Chem. Soc., 51, 323 (1929). J. A. Rard and D. G . Miller, J. Chem. Eng. Data, 26, 33 (1981). W. E. Wallace and A. L. Robinson, J. Am. Chem. SOC.,63, 958
E. Lange and H. Streeck, 2.Phys. Chem., 167,1 (1931). P. T. Thompson, D. E. Smith, and R. H. Wood, J . Chem. Eng. Data, 19,386 (1974).
2890
The Journal of Physical Chemistry, Vol. 85, No. 20, 1981
Rogers and Pitzer
TABLE I: Heat Capacity of Aqueous Sodium Sulfate molality
(cPs/cPw)T(Ps~Pw)2s O c
P,(
25 C), g/cm3 O
cp,, J g-I
K-'
@ C p ,J mol-' K-'
T = 304.62K (31.47"C)
0 0.0528 0.0528 0.0995 0.2491 0.4986 0.7486 0.9995 1.9407
P = 1.01 bar
P = 1.01 bar
P = 1.01bar
P = 1.01 bar
1.0000 0.9978 0.9977 0.9960 0.9917 0.9884 0.9878 0.9891 0.9939
0.997047 1.0038 1.0038 1.0097 1.0279 1.0572 1.0853 1.1125 1.2060
4.1780 4.1408 4.1403 4.1092 4.0188 3.8946 3.7913 3.7036 3.4329
-116 -126 - 108 -68.3 -15.2 22.0 51.4 103.7
T = 324.00K(50.85"C) 0
0.0500 0.1092 0.2832 0.2832 0.4995 0.4995 0.7487 1.0089 1.4430 2.0394
P = 1.01bar
P = 1.01 bar
P = 1.01bar
P = 1.01 bar
1.0000 0.9980 0.9966 0.9935 0.9937 0.9911 0.9916 0.9910 0.9921 0.9967 1.0064
0.997047 1.0034 1.0109 1.0320 1.0320 1.0573 1.0573 1.0854 1.1135 1.1581 1.2152
4.1807 4.1457 4.1095 4.0128 4.0137 3.9073 3.9093 3.8058 3.7139 3.5873 3.4522
-111 -68.3 - 22.9 -19.6 7.6 11.9 39.8 64.8 98.3 133.1
P = 1.01 bar
T = 349.18K (76.03" C ) 0 0.0500 0.1092 0.2832 0.4995 0.7487 1.0089 1.4430 2.0394
P = 1.01 bar
P = 1.01bar
P = 1.01bar
1.0000 0.9984 0.9970 0.9944 0.9927 0.9920 0.9929 0.9974 0.9947
0.997047 1.0034 1,0109 1.0320 1.0573 1.0854 1.1135 1.1581 1.2152
4.1932 4.1600 4.1233 4.0285 3.9254 3.8211 3.7280 3.6006 3.4222
- 73 - 54 - 9.4
21.4 45.8 68.4 100.8 108.0
T = 413.90 K (140.75" C ) 0
0.0528 0.0995 0.2491 0.4986 0.7486 0.9995 1.9407 2.6294
P = 5 bar 1.0000 0.9976 0.9961 0.9922 0.9874 0.9850 0.9834 0.9841 0.9936
P = 3.69bar
P = 3.69 bar
P = 3.69 bar
0.997047 1.0038 1.0097 1.0279 1.0572 1.0853 1.1125 1.2060 1.2673
4.2901 4.2510 4.2200 4.1288 3.9950 3.8820 3.7810 3.4903 3.3537
-137 -105 -61.1 - 24.4 6.3 27.7 83.6 120.2
T = 450.41K (177.26" C ) 0
0.0528 0.0995 0.2491 0.4986 0.7486 0.9995 1.9407
P = 10 bar 1.0000 0.9967 0.9940 0.9883 0.9814 0.9766 0.9731 0.9677
P = 9.40 bar 0.997047 1.0038 1.0097 1.0279 1.0572 1.0853 1.1125 1.2060
P = 9.40bar 4.3934 4,3494 4.3123 4.2117 4.0664 3.9417 3.8315 3.5149
P = 9.40bar
P = 16.04 bar 4.4966 4.4449 4.4056 4.2953
P = 16.04bar
- 215 - 203 - 131 - 78.2 -43.5 - 17.9 46.6
T = 474.68K (201.53"C) 0
0.0528 0.0995 0.2491
P = 17 bar 1.0000 0.9952 0.9922 0.9848
P = 16.04 bar 0.997047 1.0038 1.0097 1.0279
- 348 -
289 198
The Journal of Physical Chemistry, Vol. 85,No. 20, 1981 2891
Properties of Aqueous Sodium Sulfate Solutions
TABLE I (Continued) molality
( C p s l C p w ) T ( P s l P w ) * sO
P = 207.2 bar
C
~ ~ ("C), 2 5 dcm'
P = 199.2 bar
P = 200 bar
1.0059 1.0126 1.0126 1.0184 1.0184 1.0362 1.0362 1.0650 1.0928 1.1196 1.2121
4.1379 4.1044 4.1044 4.0769 4.0761 3.9960 3.9952 3.8805 3.7826 3.6976 3.4020
-42 - 2.0 - 5.4 34.9 62.7 84.7 104.0
T = 414.20 K(131.05"C) P = 200 bar
P = 200 bar
P = 200 bar
1.0059 1.0126 1.0184 1.0362 1.0650 1.0928 1.1196 1.2121
4.2363 4.1991 4.1689 4.0824 3.9568 3.8472 3.7509 3.4696
1.0000 0.9978 0.9963 0.9927 0.9889 0.9866 0.9855 0.9869 0.9913
0 0.0528 0.0995 0.2491 0.4986 0.7486 0.9995 1.9407 2.6294
120-c .61
\
inn ' r
\
\
@Cp,J mol-' K-l
T = 323.81 q50.66"C) P = 200 bar
1.0000 0.9985 0.9985 0.9975 0.9973 0.9948 0.9946 0.9929 0.9931 0.9946 0.9907 0.9756
0 0.0528 0.0528 0.0995 0.0995 0.2491 0.2491 0.4986 0.7486 0.9995 1.9407 2.6294
c p s , J g-' K-I
\o
1.69
\ \
q69
z-%j,65
P = 200 bar - 51 - 51 - 34
- 108
- 85 -38.0 1.5 26.7 47.1 97.8
from 45 to 120 "C in Figure 6, where the osmotic coefficients predicted from this fit are shown by the solid line at low concentrations progressing to the dashed line at high concentrations. Below 100 "C, the agreement of data and prediction is excellent, even to concentrations above the 1.5 m range of the fitting equation. Since the parameters chosen as the integration constants reproduce the osmotic coefficient to high concentrations, this agreement above 1.5 m, a t low temperatures, is not too surprising. These results indicate that high-temperature, heat-capacity data, in combination with known values of the enthalpy and activity at room temperature, are sufficient to obtain accurate activity properties as a function of temperature. The temperature-dependent equations for the thermodynamic properties of sodium sulfate solutions can now be improved by including the osmotic-coefficient data available below 120 O C in a simultaneous fit with the heat-capacity data. This serves to extend the concentration range for activity properties calculated from the fitting equations from 1.5 to 2.5 m. The form of the equations for @(o)J, @(lV,and CU are unchanged, and the parameters U,-Ul, obtained from this combined fit are listed in Table 111. (Values for the parameters obtained in the fit of the heat-capacity data alone are available in ref 5.) Osmotic coefficients calculated from the combined fit are shown by the solid line in Figure 6. The parameters determined in the combined fit reproduce the heat-capacity measurements to A3 X J g-' K-l, in good agreement with the estimated precision of the data. They can be used to calculate apparent molal heat capacities to 200 "C, at concentrations up to 1.5 m. Values of the apparent molal enthalpy can be calculated, with an estimated uncertainty of 2%,at concentrations up to 2 m
LU .?-' 0
0
0
O O O
1.0 M o l a l i t y
0
.65 2.0
Flgure 6. Comparison of predicted values of the osmotic coefficient with literature data. Osmotlc Coefficients have been Calculated from published isopiestic referenced to NaCl solutions by using the tabulated values of 4 Nacl given by Pitzer, et ai.'
P i t z e P in that the value of the Debye-Huckel slope, AH, has been improved.21 Osmotic coefficients calculated by using the heat-capacity data alone are compared with literature (28)L.F. Silvester and K.S. Pitzer, J. Solution Chem., 7,327(1978). (29)K.L. Hellams, C. S. Patterson, B. H. Prentice 111, and M. J. Taylor, J. Chem. Eng. Data, 4,323 (1965).
(30)W.T.Humphries,C. F. Kohrt,and C. S.Patterson,J. Chem. Eng. Data, 13,327 (1968). (31)J. T.Moore, W. T. Humphries, and C. S. Patterson, J. Chem. Eng. Data, 17,180 (1972). (32)C. S. Patterson, L. 0. Gilpatrick, and B. A. Soldano, J. Chem. SOC.,2730 (1960). (33)B. A. Soldano and C. S Patterson, J. Chem. Soc., 937 (1962). (34)Gy. Jakli, T.C. Chan, and W. A. Van Hook, J.Solution Chem., 4,71 (1975).
2892
The Journal of Physical Chemistry, Vol. 85, No. 20, 1981
-
Rogers and Pitzer
Osmotic Coefficient of Na2S04
Predicted from Fit of Cp ond 9 Dolo 0 L I U and Lindsay
9
50
5
10
15
Molality
Figure 7. Comparison of osmotic coefficients for Na2SO4solutions. S o l i llnes represent osmotic coefficients predicted from the combined fit of heat-capacity and osmoticcoefficient data below 120 OC. Points are the data of Llu and which were not included in the combined fit.
below 120 "C and to 1.5 m above 120 "C. Calculation of osmotic and activity coefficients above 120 O C is limited to concentrations below 1.5 m because they are predicted solely from the heat-capacity data. The estimated uncertainty in the calculated values for these quantities is also 2%. Calculated values of the mean activity coefficient are given in Table IV. Other data are provided as supplementary material. (See paragraph at end of text regarding supplementary material.)
Discussion Additional comparisons of thermodynamic properties calculated with the fitting equations and literature data are shown in Figures 7-9. High-temperature values of the osmotic coefficient are in substantial agreement with the data of Lindsay and Liu,%as illustrated in Figure 7. Figure 8 shows that the predicted values of the apparent molal enthalpy are in general agreement with the data of Snipes, Manly, and E n s ~ between r ~ ~ 40 and 80 OC, although the difference between calculated and experimental values is in some cases as large as 8% of the calculated value. At high temperatures, predictions of the apparent molal enthalpy are in good agreement with values reported by Mayrath3' a t low concentrations. A t concentrations between 0.5 and 1.0 m, the values of Mayrath are substantially smaller than those obtained in the present study, as shown in Figure 9. In addition, low-temperature activity coefficients calculated from the electromotive-force data for sodium-amalgam electrode cells of Harned and Hecker38are in good agreement with the predicted values at (35) C-T. Liu and W. T. Lindsay, Office of Saline Water Research and Development Progress Report No. 722, Int-OSW-RDPR-71-722,1971. (36) H. P. Snipes, C. Manly, and D. D. Ensor, J.Chem. Eng. Data, 20, 287, (1975). (37) J. E. Mayrath Ph.D. Thesis, University of Delaware, Newark, DE, 1980.
(38) H. S. Harned and J. C. Hecker, J.Am. Chem. SOC.,66,650 (1934).
-2
t
I
,
I
1.0
0
2.0
Mololity
Figure 8. Comparison of values of the apparent molal enthalpy. SolM lines represent values predicted from the comblned fit of heatcapacity and osmotic-coefficient data. Points are the data of Snipes, Manly, and EnsorS3'
1
I 1.0 Molal it y
I 0
Figure 9. Comparison of apparent molal enthalples at hlgh temperatures. Solid lines represent values predicted from the comblned fit of heat-capacity and osmotic-coefficient data. Points are the values reported by Ma~rath.~'
high concentrations but differ by as much as 2% a t concentrations below 0.1 m. Some literature sources contained data that were not totally consistent with the heat-capacity and osmotic-
The Journal of Physical Chemistty, Vol. 85, No. 20, 1981 2893
Properties of Aqueous Sodium Sulfate Solutions
TABLE 11: Pitzer's Equations for t h e Thermodynamic Properties o f an Aqueous Electrolyte Solution' Osmotic Coefficient
Appa.rent Molal Enthalpy
Apparent Molal Heat Capacity
Debye-Huckel Slopes
(11)
A @=
(12)
AH = 4 R T Z ( a A a / a T ) ,
(13)
A J = (aAH/aT),
(2nN,d,/10O0)'/'[e2/(DhT)] 'I2
Definitions of symbols: 01 = a constant with value 2.0; p~x(O), p ~ x ( l )'and , C M X @are fitting parameters; m = molality of t h e s o l u t e ; I = ionic strength ( l / l z i m i Z i z )v; = t o t a l n u m b e r o f ions f o r m e d from dissociation of salt MX ( V = vM + v X ) ; Z M a n d zx are charges o n ions M a n d = apparent molal h e a t capacity of the solute a t infinite dilution.
x;Tlo
0
100 Temp. 'C
1
200
-601
0
,
,
I00
,
Temp, "C
,
]
200
FI ure 10. Temperature dependence of the fltting parameters Po), @IL, and
PRL, and $ l ) J .
coefficient data chosen for this study. High-temperature osmotic coefficients obtained from the isopiestic data of Soldano and c o - w o r k e r ~ ~are ~ @substantially larger than those predicted from the fit of the heat-capacity data.
Heat of dilution data at 50 "C reported by Gritsus, Akhumov, and Zhilina41 also are not in agreement with the predicted values. Osmotic coefficients calculated from the vapor pressure difference measurements of Fabuss and
(39)B. A. Soldano and M. Meek, J. Chem. SOC.,4424 (1963). (40)B. A. Soldano and P. B. Bien. J. Chem. SOC.A, 1825 (1966).
(41)B. V. Gritsus, E. I. Akhumov, and L. P. Zhilina, Zh.Prikl. Khim. (Leningrad), 44,186 (1971).
FI
w e 11. Temperature dependence of the flttlng parameters @'),
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The Journal of Physical Chemistty, Vol. 85,
No. 20, 1981
Rogers and Pitrer
TABLE 111: Values of the Fitting Parameters for the Heat Capacity of Na,SO, as a Function of Temperature Integration Constants at T = 298.15 K p(') = 0.01869 p ( o ) L = 0.002349 p ( ' ) = 1.0994 p(')L = 0.005958 C @= 0.005549 C@L = -0.00479
-
Parameters for Cp,"
U , = - 990.405 U, = 6.79636
U , = -.0117779 U,= -6518.67
Parameters of Eq 14-16 for Fit of Heat-Capacity and Osmotic-Coefficient Data U , = - 1.03611 X U , , = - 1.88769 X l o z U , = 3.00299 X l o w 2 U,, = - 2.05974 X 10.'
U,=-1.43441 X 10' U,=-6.66894 X lo-' U, = -3.23550 X U,,= 5.76552X lo-'
U,,= 1.46744 x l o 3 U,, = 5.14316 X l o w 5 U , , = 3.45191 X 10-1
Flgure 12. Temperature dependence of the fitting parameters d , dL, and d J .
K o r o ~ behave i ~ ~ erratically at low concentrations, indicating that the precision of the measurements is not sufficient to provide a test of the osmotic-coefficient predictions. The temperature dependences of the parameters, as determined from the combined fit, are shown in Figures 10-12. The general pattern of behavior of each of the parameters P ( O ) , P(l),and C4 for Na2S04is similar to that for NaCl! If substantial ion pairing were occurring, and P(l) would decrease to negative values; no such tendency is evident. The triple interaction parameter C+ does become negative, but small, which suggests a mild tendency toward ion triplet formation. The magnitude of this effect even at 200 "C, however, is small in comparison with that for electrolytes such as ZnClz at 25 "C. Apparently, the electrostatic effects of the decrease in the dielectric constant of water with increasing temperature are well accounted for in the DebyeHuckel term since the remaining short-range interactions between Na+ and SO-: ions, described by ( 3 0 and P(l), remain small.
Conclusion The quality of the heat-capacity data obtained in this study and their agreement with literature data indicate that flow calorimetry is a valuable technique for hightemperature studies. The successful prediction of osmotic coefficients from a temperature-dependent fit of the heat-capacity data shows that heat-capacity measurements can be used reliably to obtain activity properties of electrolyte solutions a t high temperatures. One limitation to the use of flow calorimetry at high pressures should be mentioned. Reduction of the flow measurements to obtain specific heat capacities requires density data at room temperature and the system pressure. High-pressure volumetric data, even at room temperature, are available for only a few electrolyte solutions over a very limited concentration range. In addition, integration of high-pressure, heat-capacity data to obtain activity prop(42)
B. M.Fabuss and A. Korosi, Desalination, 1, 139 (1966).
00000000000
J. Phys. Chem. 1981, 85, 2895-2897
erties requires enthalpy and activity data at the same pressure to evaluate the integration constants. These are most easily obtained by using density and expansivity data, as a function of pressure, to adjust activity and enthalpy data at 1bar to the higher pressure. Thus, a full treatment of flow-calorimetry data requires volumetric properties, as a function of pressure, over a small temperature range. It is hoped that current interest in high-pressure flow calorimetry will encourage further work in the determination of these important volumetric properties.
Acknowledgment. We thank Professor R. H. Wood for
2895
sharing his results in advance of publication and for valuable discussions. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, US. Department of Energy, under Contract W-7405-ENG-48.
Supplementary Material Available: Values for the osmotic coefficient, the apparent molal enthalpy, the apParent molal heat Capacity, and the specific heat capacity are given a t rounded concentrations and temperatures in Tables V-VII(4 pages). Ordering information is available on any current masthead page. -
Solvent Dependence of the Nonradiative Decay Rate of Methyl Salicylate Kevln K. Smitht and Kenneth J. Kaufmann" Depaftment of Chemistry, University of Illinois, Urbana, Illinois 6 180 I (Received: April 29, 198 1)
Proton translocation in the singlet excited state of methyl salicylate results in fluorescence at 450 nm. The fluorescence lifetime of the 450-nm emission was studied as a function of solvent. Hydrogen bonding of the solvent to the molecule does not appear to play a major role in the nonradiative deactivation of the excited state that fluoresces at 450 nm. An empirical relationship exists between the nonradiative deactivation of the excited singlet state and the dielectric strength of the solvent.
Introduction Methyl salicylate is structurally similar to o-hydroxybenzophenone. Both molecules have a phenolic hydroxyl group. This hydroxyl group may be intramolecularly hydrogen bonded to a carbonyl group which receives resonant electronic donation from the adjacent benzene ring after excitation of the molecule. Both molecules make identical six-member rings through the formation of the intramolecular hydrogen bond. A great deal of effort has been expended trying to discover the decay kinetics of ohydroxybenzophenone, an excellent polymer protection agent.l* This work has been primarily concerned with the anomalously rapid nonradiative deactivation of ohydroxybenzophenone and the absence of any triplet products. Examination of the excited-state properties of methyl salicylate might allow some insight into the rapid deactivation of o-hydroxybenzophenone, since for both methyl salicylate and o-hydroxybenzophenone it has been well established that the anomalous nonradiative decay results from translocation of the proton across the intramolecular hydrogen bond that is present in the ground state. When methyl salicylate is excited to the first excited singlet state, the appearance of a large Stokes shift in the emission signals the translocation of the proton. This emission has a maximum at 450 nm, while molecules for which the proton remains in its initial ground-state position fluoresce a t 340 nm. The unusual fluorescence properties of methyl salicylate and some of its derivatives have been studied extensi~ely.~-l~ These studies have established that the 340- and 450-nm emissions of methyl salicylate are due to at least two ground-state species. These studies have also shown that the molecular conformations responsible for the 340- and 450-nm emission 'Tektronix, P.O. Box 500, Mail Station 50-289,Beaverton, OR 97077.
do not equilibriate in the excited singlet state. Other experiments have shown that the ground-state population of the two molecular conformations can be affected by both the temperature and solvent. Most of these experiments lack the time resolution necessary to study excited-state kinetics. Picosecond studies can yield additional information concerning the effect of temperature and solvent on the excited state. We undertook this work in an attempt to elucidate the mechanism for the nonradiative deactivation of the 450-nm emission in methyl salicylate. Several papers had suggested that the hydrogen-bonding strength of various solvents caused dramatic changes in the fluorescence s p e ~ t r a . ~ ,Picosecond ~J~ studies allowed us to determine that one of the major causes for these changes was due to the influence of the dielectric strength of the solvent on the nonradiative decay rate of the excited singlet state of the zwitterionic form of methyl salicylate.
Experimental Section The picosecond apparatus used in this study has been previously described.15 Most of these experiments were (1) A. Beckett and G. Porter, Tram. Faraday SOC.,69,2051 (1963). (2)A. A. Lamola and L. J. Sharp, J. Phys. Chem., 70, 2634 (1966). (3)J. E.A. Otterstedt, J. Chem. Phys., 58,5776 (1973). (4)W. Klopffer, J. Polym. Sci., 57, 205 (1976). (5)W. Klopffer, Adu. Photochem., 10,311 (1977). (6)S.-Y. Hou, W. M. Hetherington, 111, G. M. Korenowski, and K. B. Eisenthal, Chem. Phys. Lett., 68,282 (1979). (7)A. Weller, 2.Electrochem., 60,1144 (1956). (8)W. Klopffer and G. Naundorf, J. Lumin., 8, 457 (1974). (9)K. Sandros, Acta Chem. Scand., Sect. A, A30, 761 (1976). (IO) E.M. Kosower and H. Dodiuk, J . Lumin., 11, 249 (1975). (11)I. Yu Martynov, B. M. Uzhinov, and M. G. Kuz'Min, Khim. Vys. energ., 11, 443 (1977). (12)A. U. Acuna, F. Amat-Guerri, J. Catalan, and F. Gonzalez-Tablas, J. Phys. Chem., 84,629 (1980). (13)W. Klopffer and G. Kaufmann, J.Lumin., 20,283 (1979). (14)H. Beena, K. H. Grellman, M. Gurr, and A, H. Weller, Discuss. Faraday SOC.,39, 183 (1965).
0022-365418112085-2895$01.25/0 0 1981 American Chemical Society
