Pergamon

_I. Aemsol Sci. Vol. 29, Suppl. I, pp. S379-S380, 1998 0 1998 Published by Elsevier Science Ltd. All rights reserved

Rimed in Great Britain 0021-8502/98 $19.00 + 0.00

THERMODYNAMICS FOR HIGHLY CONCENTRATED WATER - AMMONIUM SULFATE SOLUTIONS

P. Korhonen, A. Laaksonen*, E. Batris and Y. Viisanen

Finnish Meteorological Institute, Sahaajankatu 20 E 00810 Helsinki, Finland.

*University of Kuopio,Department of Applied Physics,P.O.Box 1627, 70211 Kuopio, Finland.

KEYWORDS

Activity coefficient, surface tension, ammonium sulfale, ammonium bisulfate, supersaturated solution.

Ammonium sulfate ((NH&So& which dissolves to ammonia (N&+) and sulfate (S042- ) ions in aqueous solutions, is a common substance in the atmospheric aerosol particles. At lower ambient relative humidities aerosol particles may be highly concentrated. Hysteresis effect allows even the existence of the supersaturated aqueous salt particles in the atmosphere, which according to Rood et al. (1989) can be common in the atmosphere. Thus, one needs various thermodynamical data also for the supersaturated aqueous salt solutions, for example, when the nucleation of the aerosol particles is studied with numerical models. In order to determine the vapor pressures of ammonia and sulfuric acid above the aqueous ammonium sulfate solution particle one needs the mean ionic activity coefficient of the solute (e.g. Bassett and Seinfeld, 1983). We present here an equation for the mean ionic activity coefficient of aqueous (NH&S04 valid up to 26.8 mol/kg (the saturated solution ca. 5.834 mol/kg). We also present the mean ionic activity coefficient of aqueous ammonium bisulfate (NH4HS04). When the particles are small one needs in addition the surface tension of the solution against air. The data for the aqueous (NH4)2SO4 surface tension is presented only for moderate concentrations. We present here an estimation for the surface tension of highly concentrated water - ammonium sulfate solution. In the following the thermodynamic properties are presented at 298.15 K. The mean ionic activity coefficient of aqueous ammonium sulfate in the molality scale is obtained by solving first the osmotic coefficient from the water activity presented by Tang and Munkelwiz (1994). They have given a fitting for water activities of aqueous ammonium sulfate at the concentrations from 0 to 26.8 mol/kg (O-78 mass %). The osmotic coefficient was then fitted to the expanded Bromley’s osmotic coefficient model presented e.g. by Saxena and Peterson (198 1) who included third order polynomial terms in the model. We have included polynomial terms to model up to 9th order terms. The mean ionic activity coefficient is then

obtained by using Gibbs-Duhem equation. The mean ionic activity coefficient (r&) as a function of ionic strength (I) can be calculated from

log,,(y,) = -0.5108~2+2-Ifi + (0.06+0.6B,)(Z+Z-11 + ;B,Ii.

(I+&) (i +aZ)’ I (1)

i=l

Here z’ and Z refers to the charge of ions present in the solution. The fitting coefficients are following: Bl=-3.50390944E-2, B2= 3.73770098E-3, B3=-2.10301983E-4, B4=7.18178119E-6, Bs = - 1.58509094E-7, B6 = 2.275843 lOE-9, B7 = -2.05355438E-11, Bs = 1.0576675 lE- 13 and Bg= -2.37107320E-16. Here E-X equals to 10.‘.

s379

S380 Abstracts of the 5th International Aerosol Conference 1998

Figure 1 .The activity coefficients of ammonium sulfate and ammonium bisulfate calculated with equation 1 (lines) and calculated with the equation presented by Jacobson et al. (1996).

The same approach is used for the mean ionic activity coefficient of aqueous ammonium

bisulfate. Our fitting for aqueous Nl&HSOh is valid at the concentration range from 0 to 270.0 mol/kg (0 - 96.9 mass %). The obtained fitting coefficients are following: B1=1.953416731E- 2, B2 = -9.764358756E-4, Bs=-2.152588991E-5, Bq= -2.811506513E-7, B5= 2.298668607E-9, Bg = -l.l84459425E-11, B7 = 3.729677698E-14, Bs = -6.545729067E-17 and Bs = 4.09 14 13234E-20 In figure 1. the activity coefficients are compared with coefficients presented by Jacobson et al. (1996). The surface tension of aqueous (NH&S04 solution against air for the mass fractions 0 to c 1.0 of ammonium sulfate is estimated from Gibb’s adsorption isotherm with numerical integration. The isotherm is fitted by using the water activity and surface tension (from ICT, (1960)) data for the concentrations from zero to the saturated solution. We have fitted the obtained surface tension (cr) in the following polynomial form

CT = iAiX; (2) i=O

where X,,, is the mass fraction of salt. The fitting coefficients are AO = 0.07 19121335 1, Ai = 0.02238717151, A2 = -0.07996064682, A3 = 0.6985161142, & = -2.361475486, A5 = 4.291669494, A6 = -3.664358167 and A7 = 1.143836868.

REFERENCES

Bassett M. and Seinfeld J.H., 1983: Atmos.Env., Vol. 17, pp. 2237-2252. ICT (International Critical Tables), 1960, Vol. 3, McGraw-Hill, New York. Jacobson M.Z., Tabazadeh A., Turco R.P., 1996: J. Geophys. Res., Vol. 101, pp. 9097-9091. Saxena P. and Petersson T.W., 198 1: J. Colloid. Interf. Sci., Vol. 79, pp. 496-5 10. Rood M.J., Shaw M.A., Larson T.V. & Covert D.S., 1989: Nature, Vol. 337, pp. 537-538. Tang I.N. and Munkelwiz H.R. , 1994: J. Geophys. Res., Vol. 99, pp. 18801-18808.