M. 1. Sanders and R. R. Beckell Novol Regional Medical Center Puget Sound Naval Shipyard Brernerton, Washington 98314
The Mercury-Water System A deviation from Raoult's law
A fallacious assumption often encountered in the laboratory is that covering liquid mercury with water will "keep it from vaporizing." In fact, a recently published criteria document (1) proposes that in order to control mercury vapor the surface of mercury must be covered with an aqueous layer maintained at a temperature below its boiling point. In reality, the mercury will continue vaporizing as if the aqueous layer was not even present. This phenomenon provides an interesting example for illustrating the practical utility of classical thermodynamics. Raoult's law tells us that when one liquid is dissolved in another, the partial pressure of each over the liquid-vapor interface is reduced. The reasoning for this can be seen if we assume two ideal liquids A and B with molecules of the same size and without the complicating effects of any chemical interaction. If the liquids are mixed in some molar fraction (A/B), then for any given volume within the mixture the molar ratio (A/B) will be found and at the liquid-vapor interface any given area will also produce LA/B). (This situation would be visibly analogous to the simple physical mixing of two differently colored dry powders.) Therefore, the escaping tendency, and thus the partial pressure, of each of the constituents will simply depend on (A/B). In general,
where Pi = partial pressure of component i in solution; pi = vapor pressure of pure i; and X, = mole fraction of component i in solution. However, we know that molecules do have finite and differing volumes and that the average solution is a cornucopia of chemical interactions. It is not surprising that Raoult's law is violated far more often than not and large deviations are encountered-particularly with aqueousorganic combinations. In using Raoult's prediction, it is assumed tbat A-B attraction is such that complete liquid miscibility occurs. If conditions change so that A-A and B-B combinations are also found then partial miscibility occurs and deviations from prediction set in. Finally, if intra-component attraction becomes stronger than inter-component attraction, immiscibility results and the moieties separate into two liauid . ohases. This behavior can be visualized witb boiling point composition diagrams. Increasingly positive deviations result in skewed curves and finallv low-boiling azeotropes. In the limit of very large positive deviations
.
VaDor Pressure (mm Ha)
Temp ("C)
Pure H1O
Pure CS.
Sum
Mixture
from Raoult's law the two components are completely insoluble and each component will vaporize independently of the other to give a constant total vapor pressure tbat is simply a sum of the individual vapor pressures. This was first shown experimentally by H. V. Regnault (2) in 1854 with the system CS2-H20; his measurements are shown in the table. This is such a common phenomenon that it is often exploited in the procedure known as steam distillation. Many water-insoluble organic compounds may be effectively collected this way. Recall tbat the phase rule predicts that a three-phase, two-component system has only one degree of freedom and vaporization will occur a t a constant temperature as long as two phases are present. If the vapor pressures of the two components are known at various temperatures, the distillation temperature and the com~ositionof the distillate are easily found ara~hicallv - . by plotting the vapor pressure curve of each component and makina a summation curve. The steam distillation temperature will be the temperature at which the vapor pressure summation is equal to atmospheric pressure. Using Dalton's law of partial pressures one can then calculate the composition of the distillate a t that temperature. Therefore, for the immiscible and trinary system mercury-water-vapor, the phase rule predicts there will be only one variance possible-either temperature or pressure; thus the mercury will continue vaporizing unabated irrespective of the presence of the aqueous layer. A simple experiment will confirm this: introduce 1 ml of mercury carefully (via hypodermic syringe) into a 1M)O-ml Erlenmeyer flask half filled with distilled water. Purge the air inside the flask gently with compressed air and stopper the flask. Using a portable ultraviolet spectrophotometer (e.g., Bacharach Instrument Company J-W model MV-2 mercury-vapor meter) or a 10-cm quartz cell in conjunction witb an atomic absorption spectrophotometer, one can show tbat within a few hours the mercury vapor concentration approaches 13 mg/M3-the theoretical maximum for free vaporization of mercury at Z09C and 1 atm pressure (3). The only limiting parameter is the diffusion rate of the mercury through the water.
Volume 52, Nomber2, February 1975 / 117
Deviations are usually handled from an engineering standpoint by considering non-ideality of the gaseous and liquid states of the system. Lewis and Randall (4) first suggested that the fugacity of a component in a mixture was equal to the mole fraction of the component in the mixture times the fugacity of the pure component at the same temperature and total pressure as the mixture. Since a t equilibrium, fugacity,.,,r, = fugacityli,,l,, then
the vapor satisfies the perfect gas law, the Duhem equation predicts that
where Xi = mole fraction of component i; P r = total pressure of mixture; and f* = fugacity of pure liquid a t temperature T under total pressure P,r. This equation is not identical to Raoult's law and f* is not in general equal to p,, the vapor pressure of pure i a t temp T, because the liquid is under a different pressure than p , . This can he evaluated by recalling that for isothermal changes d in f = VdPIRT, so that
Robinson and Gilliland (5) have described in detail the treatment of non-ideal liquid-vapor equilihria for real systems. Like all real systems, however, the mercury-water system is not a completely immiscible one. Mercury is actually soluble in water to the extent of M (-.05 ppm) (6) so that if the mole-fraction abscissa were greatly expanded, vapor-liquid equilihrium behavior would be seen approximating Raoult's prediction at a mercury mole fraction corresnonding to less than lo-' M and a water mole fraction 'corresponding to less than the solubility limit of water in mercuw because of establishment of normal solution behavior. An article appearing recently in this Journal (7) and an extensive literature review (8) regarding direct and synergistic effects of mercury in the hiosystem lends credence To the ldea that a laho;atory situation need nnt he exotic or esoteric before it assumes relevance. The commoness of an event sometimes lulls us into accepting that event as fundamental veracity: that luxury is not allowed if science is to remain "a state of learning."
/*
= f , exp
J,,: ' V
~ /RT P
where f , = fugacity of component i a t temperature T and pressure Pi and V = molal volume of component i in solution. Over the pressure range usually encountered, V is essentially constant and f* = f,exp V(Pr - Pi)/RT. It should be noted that these equations differ from Raoult's law by the exponential term and fl instead of Pi. These terms are small and can usually he neglected; however in high pressure equilihria even an ideal solution would not obey Raoult's law because: (1) The various components are under a different total pressure than they would he as isolated Dure components; and (2) The fugacity of the pure liquid is not equal to its vapor pressure. Thermodynamic relationships are available for the liquid phase but their application is not nearly so well developed as for the vapor phase. In general,
(a in f,) X , ( U P . ~ , T X,XP,T
ax,
+
+
and lumping all the liquid deviations together the prohlem becomes one of evaluating the activity coefficients
Literature Cited Recommended Standard-Occupatiand Exposure to Inorganic Mercury, HSM 13-11024. National lnsfifufe far Occupations1 Safety and Health. 1973.
(1) Criteria for a
p.9.M.
12) Glasstone, S., and Van, D.. "Textbmk of Physical ChemiaUy." D. Van Nmtrand Ca.. Inc. NewYork, 1943, p. 124. (31 Nelson. G. 0.. "Controlled Test Atmospheres: Principles and Techniques." Ann ArborSeisnecPub.Inc., 1911, p. 114. (41 Levis end Randall. "Thermadmamics." MeGraw-Hill Book Co.. Inc. Now York. 1923.p.228.
I51 Robinson, C. S.. end Gillilsnd. E. R.. "Elements of Fraetionsl Distillation," 4th Ed.. Chemical Engineering Series. MeGraw-Hill Bmk Co.. Ine.. New York. 1950. I81 Sykos, A. G.. "Kinetics of Inorgsnb Reactions." Poigaman Preu, London, 1966, p. 146.
so that for a binary mixture, if the pressure is such that
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Journal ofChemical Educafion
(11 Sfmn&L.E..I.CHEM. EDUC.,49.28l19121. (8) Voatal, .J..J, andClark8on. T.W . J . Oer. M d 8. €49 11913).
