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Journal of Thermodynamics
Volume 2011, Article ID 432132, 4 pages
doi:10.1155/2011/432132

Research Article
Vapor Pressure of Saturated Aqueous Solutions of
Potassium Sulfate from 310 K to 345 K

Matias O. Maggiolo, Francisco J. Passamonti, and Abel C. Chialvo

Programa de Electroquı́mica Aplicada e Ingenierı́a Electroquı́mica (PRELINE), Facultad de Ingenierı́a Quı́mica,
Universidad Nacional del Litoral, Santiago del Estero 2829, 3000 Santa Fe, Argentina

Correspondence should be addressed to Abel C. Chialvo, achialvo@fiq.unl.edu.ar

Received 29 June 2011; Accepted 11 September 2011

Academic Editor: Angelo Lucia

Copyright © 2011 Matias O. Maggiolo et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.

The experimental evaluation of the vapor pressure of saturated aqueous solutions of potassium sulfate was carried out in the range
of temperatures 310 K ≤ T ≤ 345 K. The experimental data were used to determine the corresponding values of the water activity
in such solutions. The analytical expressions as a function of temperature of both, vapor pressure and water activity, were obtained
from the correlation of the experimental results. The vapor pressure expression was also extrapolated to a different temperature
range in order to make a comparison with the results obtained by other authors.

1. Introduction manometer (F) and to a vacuum pump (H) through the

valve (G). The flask, the manometer, and the connecting
The dependence on temperature of the vapor pressure of tubes are immersed in an isothermal water bath (B), which
saturated aqueous solutions has been already determined temperature is controlled by a Lauda Thermostat UB20 Ultra
for most of the inorganic salts, particularly halides, sulfates, (E), thermostated to within ±0.01 K. To ensure the unifor-
and nitrates [1–3]. However, for the case of potassium mity of the bath temperature, a recirculation pump (D) was
sulfate the available information is surprisingly scarce and used with a flow rate of 4 dm3 min−1 . Moreover, a magnetic
restricted to the temperature range 273 K ≤ T ≤ 323 K stirrer (C) was used in order to ensure the highest mass
[4–7] plus one evaluation at 374 K [8]. On this context, transfer rate between the liquid and vapor phases and also
the present work studied experimentally the vapor pressure the temperature uniformity inside the equilibration flask.
of saturated aqueous solutions of potassium sulfate from The temperature was measured by a digital thermometer
310 K to 345 K and evaluated from these data the dependence Lauda R46, with a Pt resistance of 100 Ω which precision
of the water activity on temperature. For this purpose, an is ±0.01 K. The pressure was measured by an open U-tube
isothermal static apparatus has been constructed and the mercury manometer and the manometric readings were
reliability of the methodology employed was verified through made with a cathetometer to ±0.1 mm (±0.015 kPa). The
the determination of the vapor pressure of pure water. reading performed at the temperature of each experiment
was corrected according to the thermal expansion coefficient
of mercury [10] and referred to 273.15 K. The atmospheric
2. Experimental Section pressure was measured by a calibrated barometer.
2.1. Equipment. The apparatus used for the vapor pressure 2.2. Reagents. Potassium sulfate was analytical grade reagent
measurements, which is a modified version of the device manufactured by Merck and was used in the experiments
employed by Kim et al. [9], is shown in Figure 1. It consists without further purifications. The solutions were prepared
of a round-bottom flask (A) of 125 cm3 which contains the with ultra-pure water (PureLab, Elga LabWater). Solid
solution to be evaluated. It is connected to a U-tube mercury K2 SO4 and the saturated solutions were degassed at room
2 Journal of Thermodynamics

Table 1: Measured and standard(a) values of vapor pressure of pure

water and relative deviation.
H
T/K Pw /kPa Pws (a) /kPa (ΔPw /Pws ) × 100
308.10 5.62 5.612 −0.140
313.35 7.46 7.465 0.067
G
318.70 9.87 9.870 0.000
323.2 12.38 12.382 0.016
327.95 15.63 15.612 −0.120
327.95 15.61 15.612 0.013
B 333.35 20.13 20.132 0.010
A 333.65 20.40 20.413 0.064
337.55 24.38 24.378 −0.008
D 338.00 24.87 24.875 0.020
338.05 24.93 24.931 0.004
C
338.25 25.15 25.155 0.020
F
343.80 32.06 32.089 0.090
348.45 39.12 39.083 −0.094
348.50 39.16 39.164 0.010
348.50 39.17 39.164 −0.015
353.25 47.61 47.607 −0.006
353.45 48.00 47.994 −0.012
(a) [11].

3. Results
Figure 1: Device for vapor pressure measurements. (A) Equilibra- 3.1. Vapor Pressure of Pure Water. Before the evaluation
tion flask; (B) isothermal water bath; (C) magnetic stirrer; (D) recir- of the vapor pressure of the saturated aqueous solution
culation pump; (E) thermostat; (F) U-tube mercury manometer; of K2 SO4 at different temperatures, the dependence of the
(G) valve; (H) to condenser and vacuum pump.
vapor pressure of pure water on temperature was measured
in order to verify the adequate operation of the apparatus,
through the comparison of the results obtained with values
temperature into a vacuum oven previously to be put into reported in the literature [8]. Table 1 shows the values of the
the equilibration flask. s(exp)
vapor pressure of pure water (Pw ) measured in the range
307 K ≤ T ≤ 353 K. The corresponding values obtained
2.3. Procedures. In each experiment, a volume of approxi- from the correlation proposed by Wagner and Pruß [11]
s(ref)
mately 80 cm3 of the saturated solution of potassium sulfate (Pw ) are also illustrated. It can be appreciated that the
at room temperature was put into the flask (A) together s(exp)
average value of the relative deviation, evaluated as (Pw −
with an amount of solid K2 SO4 , high enough to ensure the s(ref) s(ref)
Pw )100/Pw , is 0.04%, while the highest value is 0.14%.
saturation condition at the temperature of the experiment, These results demonstrate the correct functioning of the
and a magnetic bar. Then the system was vacuumized experimental device and the applied methodology.
through the valve (G) during two hours, with a vigorous
and continuous agitation of the solution, ensuring that the
boiling point is reached. This process produces the complete 3.2. Vapor Pressure of K2 SO4 -Saturated Solutions. Table 2
displacement of air by water vapor. After this stage, valve illustrates the values of the vapor pressure of saturated solu-
(G) is closed and the water bath (B) begins to be heated tions of K2 SO4 (Pw ) measured at different temperatures. The
relationship between ln Pw and the inverse of temperature
is shown in Figure 2 (). These experimental values were
through the thermostat (E) and the recirculation pump (D).
The solution is continually agitated to facilitate that the
system could reach the equilibrium state, which is verified correlated employing the equation proposed by Apelblat
through the invariance of the manometric pressure. The and Korin [12], through the use of nonlinear least squares
presence of solid salt is also verified in order to ensure the regression, and the resulting expression was as follows:
saturation of the solution. In these conditions, the values 5293.806
of the temperature (T) and the vapor pressure (Pw ) are ln(Pw /kPa) = 23.22469 − − 0.75463 ln(T/K).
(T/K)
obtained. The same procedure is used to verify the correct (1)
proper functioning of the equipment through the evaluation
of the dependence of the vapor pressure of pure water on This analytical dependence is illustrated in Figure 2 (contin-
temperature. uous line). The quality of the correlation can be appreciated
Journal of Thermodynamics 3

Table 2: Vapor pressure and water activity of saturated aqueous 3.5

solutions of potassium sulfate.

T/K Pw /kPa aw 3
313.25 7.27 0.9787
313.65 7.43 0.9788 2.5
314.80 7.88 0.9768
315.95 8.56 0.9759

ln (Pw /kPa)
2
317.55 9.07 0.9741
318.75 9.63 0.9732
320.45 10.48 0.9710 1.5
321.60 11.08 0.9690
322.90 11.81 0.9682 1
323.25 12.02 0.9680
324.60 12.82 0.9667 0.5
325.75 13.56 0.9661
326.90 14.30 0.9639
0
327.75 14.92 0.9645 280 290 300 310 320 330 340
329.35 16.05 0.9615 T (K)
330.75 17.15 0.9615
Figure 2: Dependence of the vapor pressure of saturated solutions
331.90 18.08 0.9601 of potassium sulfate on temperature. () experimental; (—) data
333.25 19.23 0.9592 correlation; () [4]; () [5]; () [6]; ( ) [7].

335.75 21.51 0.9569
338.45 24.25 0.9551
341.00 27.10 0.9535 given in Table 2. The correlation of these values leads to the
342.45 28.84 0.9524 following equation:
579.361
ln aw = −10.2654 − − 1.4607 ln(T/K). (3)
by the average value of the relative deviation, which is (T/K)
0.147%. The regression line was extrapolated to lower values
Figure 3 shows the experimental values (symbols) and the
of temperature in order to be compared with experimental
continuous line is the corresponding simulation with (3). It
results obtained from the literature (the results of [4–7]).
can be observed that this equation describes accurately the
water activity of saturated solutions of potassium sulfate in
3.3. Water Activity in the K2 SO4 -Saturated Solutions. From the temperature range 310 K ≤ T ≤ 345 K. The quality of the
the experimental values of the vapor pressure of saturated water activity correlation can be appreciated by the average
solutions of K2 SO4 given in Table 2, the corresponding values value of the relative deviation, which is equal to 0.028%.
of the water activity can be evaluated. In order to perform
this calculation, it is proposed that the deviation from the
ideal behavior of the vapor pressure can be appropriately 4. Discussion
described by the virial equation of state, considering only The experimental evaluation of the vapor pressure of
the second virial coefficient B(T). In this case, the logarithm saturated aqueous solutions of potassium sulfate was carried
of the water activity can be evaluated from the following out in the range of temperatures 310 K ≤ T ≤ 345 K.
expression [13]: In this range the solid phase corresponds to the anhydrous
 
P (T) Pw (T) − Pws (T)   salt [16]. From the correlation of the experimental results,
ln aw = ln ws + Bw (T) − vwo (T) , the corresponding analytical dependence was derived, which
Pw (T) RT
(2) is given by (1). The results obtained were compared with
the vapor pressure data reported by Leopold and Johnston
where Pw (T) is the vapor pressure of saturated solutions [4], Foote et al. [5], and Adams and Merz [6]. There were
of K2 SO4 , values given in Table 2. The values of the vapor also included vapor pressure values obtained from dew
pressure of pure water Pws (T) were calculated from the point measurements evaluated by Wexler and Hasegawa [7].
equation proposed by Wagner and Pruß [11]. The second These data, which correspond to the temperature range
virial coefficient for water vapor Bw (T) was evaluated with 280 K ≤ T ≤ 323 K, are included in Figure 2. To carry
the equation proposed by Harvey and Lemmon [14]. Finally, out the comparison, the dependence given in (1), obtained
the molar volume of liquid water vwo (T) was calculated from the correlation of the ours experimental results, was
from the relationship between water density and temperature extrapolated up to 280 K. There can be observed in Figure 2
given by Kell [15]. The values of the water activity for the a good agreement between the extrapolation of the correla-
saturated solutions of K2 SO4 evaluated experimentally are tion (continuous line) and the values of the vapor pressure
4 Journal of Thermodynamics

References
−0.02
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5. Conclusions
aqueous solutions of sodium chloride, sodium bromide,
The experimental evaluation of the vapor pressure of sodium nitrate, sodium nitrite, potassium iodate, and rubid-
saturated aqueous solutions of potassium sulfate was carried ium chloride at temperatures from 227 K to 323 K,” Journal of
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This work was supported by ANPCyT (PICT 541) and [16] A. Seidell and F. W. Linke, Solubilities of Inorganic and Metallo-
CONICET (PIP 1556), Argentina. M. O. Maggiolo thanks the Organic Compounds, vol. 2, American Chemical Society,
scholarship granted by the Universidad Nacional del Litoral Washington, DC, USA, 1965.
(Argentina).
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