Determination of Water Activity in Ammonium Sulfate and Sulfuric Acid Mixtures Using Levitated Single Particles

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1 Aerosol Science and Technology ISSN: (Print) (Online) Journal homepage: Determination of Water Activity in Ammonium Sulfate and Sulfuric Acid Mixtures Using Levitated Single Particles Yong Pyo Kim, Betty K.-L. Pun, Chak K. Chan, Richard C. Flagan & John H. Seinfeld To cite this article: Yong Pyo Kim, Betty K.-L. Pun, Chak K. Chan, Richard C. Flagan & John H. Seinfeld (1994) Determination of Water Activity in Ammonium Sulfate and Sulfuric Acid Mixtures Using Levitated Single Particles, Aerosol Science and Technology, 20:3, , DOI: / To link to this article: Published online: 12 Jun Submit your article to this journal Article views: 708 View related articles Citing articles: 24 View citing articles Full Terms & Conditions of access and use can be found at

2 Determination of Water Activity in Ammonium Sulfate and Sulfuric Acid Mixtures Using Levitated Single Particles Yong Pyo ~im,' Betty K.-L. ~un,"hak John H. Seinfeld* Department of Chemical Engineering, California Institute of Technology, Pasadena, CA K. Chan,' Richard C. Flagan, and Water activities of ammonium sulfate-sulfuric acid termiued relative to the known properties at RH about mixtures with ammonium to sulfate molar ratios be The data were compared with other meatween 0 and 2 were measured by a spherical void surements and the estimates from the Zdanovskiielectrodynamic levitator at relative humidities (RH) of Stokes-Robinson (ZSR) method and SCAPE, a newly Since the composition of the solid particles developed gas-particle equilibrium model, and generis subject to uncertainty, solution properties were de- ally were found to be in good agreement. INTRODUCTION Ammonium and sulfate are important components of atmospheric particles of various origins (Heintzenberg, 1989). Therefore, the thermodynamics of the H,O-(NH,),SO,-H,SO, system is important in understanding the properties of atmospheric aerosols (Stelson and Seinfeld, 1981; Bassett and Seinfeld, 1983, 1984; Saxena et al., 1986; Pilinis and Seinfeld, 1987; Wexler and Seinfeld, 1991; Kim et al., 1993a, b), one of which is the relation between ambient relative humidity 'Present address: Environment Research Center, Korea Institute of Science and Technology, Seoul, Korea. 'Present address: Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA "resent address: Department of Chemical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. "To whom correspondence should be addrcssed. and equilibrium composition. The equilibrium state of the system is dependent on the water activity or water content. In general, water activity data are essential to the understanding of the behavior of concentrated aerosol systems. Such data for multicomponent aqueous solutions, however, are limited. Tang and coworkers (Tang and Munkelwitz, 1977; Tang et al., 1978) have measured water uptake and deliquescence relative humidities (RHDs) of mixed ammonium sulfate and sulfuric acid solutions with a [NH~]/[SO:~] molar ratio in the range of 1 to 2 by measuring the diameter increase of monodisperse particles in a flowing system. Spann and Richardson (1985) measured the water cycle in levitated mixed NH; -H+-SO:- single particles with the [NH;]/[SO:-] ratio also of 1 to 2 from the water vapor pressure in a vacuum system. They compared their results with the predictions of the modified Zdanovskii-Stokes-Robinson (ZSR) Aerosol Science and Technology 20: (1994) C> 1994 Elsevier Science Inc.

3 Y. P. Kim et al. method (Stokes and Robinson, 1966) and the Meissner and Kusik method (Meissner and Kusik, 1972). The (NH,),SO,-H,SO, system can form various salts, (NH,),SO, (ammonium sulfate), NH,HSO, (ammonium bisulfate), and (NH,),H(SO,), (letovicite). Tang et al. (1978) constructed a phase diagram of the system at 30 C. However, the thermodynamic properties of these salts in multicomponent solution, especially concentrated solutions, are not well established. Conventional techniques using bulk solutions have inherent problems in studying supersaturated solutions, including heterogeneous nucleation on wall surfaces. Levitated single particle techniques have been used to circumvent these problems. An advantage of the levitated single particle techniques is that the exact mass change of a droplet can be measured. These techniques have been widely used to study solution thermodynamics and chemistry of single component solutions (Tang and Munkelwitz, 1977, 1984; Rubel, 1981; Richardson and Kurtz, 1984; Richardson and Spann, 1984; Tang et al., 1986; Cohen et al., 1987a; Chan et al., 1992) and multicomponent solutions (Tang et al., 1978; Spann and Richardson, 1985; Cohen et a]., 1987b; Chan et al., 1992). As noted earlier, in most water activity measurements of sulfate/ammonium systems, solutions with the [NH:]/[S0:-] molar ratio ranging from 1 to 2 have been investigated. As shown in Table 1, for example, atmospheric aerosol frequently belongs to that concentration ratio range. As shown in Table 1, in the intensive study in Uniontown, PA, during the summer of out of 97 3-hour Harvard EPA annular denuder system (HEADS) measurements were in the range of [NH;]/ [SO!-] < 1 (Saxena et al., 1993). For solutions in this range, few water activity measurements have been carried out. Also note that for about two thirds of the samples, the RH range was below 80%, the RHD of (NH,),SO,. In this work we report measurements of water activity of levitated single particles of ammonium sulfate-sulfuric acid mixtures with the [NH~]/[so~-] molar ratio ranging from 0 to 2 and the RH ranging between 18% and 90%. Water activity data for multicomponent solutions, especially at low RH, are rare and thermodynamic models are frequently used in their place The ZSR method is used to calculate the water activity up to the supersaturated range (or lower RH). A gas-particle equilibrium model, SCAPE (simulating composition of atmospheric particles at equilibrium; Kim et al., 1993a, b), is also used to simulate the measurements up to the saturated range including solid-liquid equilibrium. WATER ACTIVITY MEASUREMENTS A flow system with a spherical void electrodynamic levitator (SVEL) as reported by Chan et al. (1992) is used to trap and levitate single particles and measure the water activity and the mass of the particles. Detailed descriptions of the experimental system used here have been giv- TABLE 1. Distribution of [NH,f]/[SO;-] Molar Ratios R in Aerosol Samples Taken at Uniontown, PA during the Summer of 1990 (Saxena et al., 1993) R<1 1 lir< R 0 Total 2 40 < RH 40 < RH < < RH < < RH Total

4 Water Activity in (NH,),SO,-H,SO, Mixtures 277 en previously (Cohen et al., 1987a; Chan et al., 1992). A charged droplet is trapped in the SVEL by controlling the a.c. field, and the d.c. field is then adjusted to balance the weight of the particle. A fraction of dry and ultrapure air flows through a bubbler to adjust the RH of the air and then flows through the SVEL. The RH is measured by a dew point meter (911 Dew-All digital humidity analyzer) and the particle mass is obtained from the d.c. field voltage. At each RH, about min are required for the particle to establish equilibrium. The levitated particle, illuminated by a helium-neon laser (Aerotech LS4P), is viewed through a microscope. In this way, dry particles can be identified. The temperature range during the measurements was between 23.6 and 2S.S C; for individual measurements the temperature variation was within 0.4"C. Experiments were carried out for five solutions, with molar ratios of ammonium to sulfate of 0 (pure sulfuric acid), 2:3, 1, 4:3, and 2 (pure ammonium sulfate). During an experiment, the RH of the system was reduced from about 75% to 90% to 19% to 3376, depending on the molar ratio of the solution. For the resultant solid particles with [NH~]/[SO;- 1 ratios of 4:3 and 2, the RHs are increased up to the saturated solution range. These results are denoted as the solid data points in Figures 1 and 5 and will be discussed subsequently. A potential problem associated with measuring the water activity of ammonium sulfate-sulfuric acid solutions is the volatility of ammonium sulfate. Equilibrium calculations by SCAPE show that for sulfuric acid and mixed solutions little evaporation occurs, but for pure ammonium sulfate solution up to 20% of the ammonium can evaporate when the system is in equilibrium. Estimation of the evaporation rate, however, indicates that for the particle size and the temperature range used here only about 1% of the ammonium will evaporate during the five hours that is the average time required to obtain a complete set of data for each particle. Experimentally, no significant mass loss over the period of measurement was noted. For the ammonium sulfate solution, in which ammonium is most volatile, the RH was decreased gradually from about 90% to about 62% and then increased to about 86%, and both measurements of particle mass at about 86% were the same. The same verification procedure was used for particles of other solutions and no mass loss was observed. Another problem in the experimental deliquescence cycle, as pointed out by Cohen et al. (1987a, b) and Chan et al. (1992), is that the solid particles formed by drying a levitated droplet may not be the most thermodynamically stable form and the resulting uncertainties in the dry state composition may lead to errors in the estimated solution concentration at high solute mass fraction. We adopt the following approach to address this problem. First, the mass fraction of solute (mfs) at a high RH range is calculated based on the assumption that the solid particle is the most thermodynamically stable form and contains no water. Second, the mfs value is compared with other measurements, if available, and with the value estimated by the ZSR method at a high RH range. If these values agree within a reasonable range, the aforementioned assumption is deemed to be a reasonable one and the mfs based on the dry particle assumption is used. This is the approach followed by Cohen et al. (1987a). If that is not the case, we follow the approach adopted by Chan et al. (1992) in estimating solution concentration. That is, to employ a wet state at high RH as a reference state and calculate the mfs value at that state from which the concentration of the solution at lower RH is determined. If there are several consistent lit-

5 278 Y. P. Kim et al. erature data, these are used to calculate the reference state. Since water activity data for multicomponent aqueous solutions are quite limited, thermodynamic models are valuable tools in estimating water activity. Based on various comparisons as will be discussed in the next section, the ZSR method is chosen as the water activity estimation method to calculate the reference state. WATER ACTMTY The chemical potential of water in the gas phase is equal to that in the liquid phase at equilibrium (Denbigh, 1981), showed that there are no major differences in accuracy among them. Cohen et al. (1987b) compared the ZSR, Reilly- Woods-Robinson (RWR), and Pitzer methods, and Chan et al. (1992) compared the ZSR, Kusik and Meissner (K-M), and Pitzer methods, and also concluded that there are no major differences in accuracy among them, although in the RWR and Pitzer methods the cooperated interactions between ions, e.g., between NO, and SO:- are omitted. Since the ZSR method is relatively easy to use it is chosen as the water activity estimation method for concentrated and supersaturated solutions. The ZSR method can be expressed as, where p;,, and p;.x are the standard state chemical potentials in the liquid and gas phases, respectively. R is the gas constant and T is the absolute temperature. p, and po are the water vapor partial pressure and that at the saturation at temperature T, respectively. Ideal gas behavior is assumed and the Kelvin effect is neglected since the particles used here are about pm in diameter. Since p:,, = PO,,^, Eq. 1 reduces to where RH is expressed as a fraction. Thus, the water activity of an aqueous particle in equilibrium with water vapor can be determined by measuring the ambient dew point and temperature. Several water activity estimation methods for multicomponent solutions have been developed (Stokes and Robinson, 1966; Meissner and Kusik, 1972; Bromley, 1973; Pitzer and Kim, 1974; Pitzer, 1986; Kusik and Meissner, 1978). Saxena and Peterson (1981) compared four methods, two versions of the Lietzke and Stoughton, Bromley, and ZSR methods, and they where m, is the molality of species i in a multicomponent solution and mlo(a,) is the molality of the binary solution at the desired water activity, a,, of the multicomponent solution. The basis of this method is the assumption that the interactions between solutes are absent or small. From the definition of molality, m, = MJW, where M, is the molar coqcentration of species i in the air (mole/m3 air) and W is the mass concentration of water in the aerosol (kg water/m3 air). The water content is given by, For ammonium sulfate, the water activity estimation formula of Chan et al. (1992) is used, and for sulfuric acid the data compiled by Staples (1981) are used. The gas-particle equilibrium model, SCAPE, is used to simulate measurements (Kim et al., 1933a, b). In SCAPE, gas-liquid-solid concentrations in equilibrium are calculated by solving a set of nonlinear equations; mass balances, equilibria, and the electroneutrality condition

6 Water Activity in (NH,),SO,-H,SO, Mixtures are solved by the bisectional and the combined bisectional-newton methods. The ZSR method is also used in SCAPE for water content calculation. The main difference between SCAPE and the ZSR method is that the ZSR method simulates an aqueous phase, only, while SCAPE simulates both the aqueous and solid phases and their mixtures. Thus, for systems containing no solid components, the ZSR method and SCAPE predict the same result. RESULTS AND DISCUSSION Water activities of pure ammonium sulfate and sulfuric acid solutions were first measured to check the reliability of the measurements and models against another reported measurements and previous data. In Figure 1, the measured mass fraction of solute (rnfs) based on the dry particle assumption is compared with model estimates and other reported data. Parameters used in the ZSR method for (NH,),SO, solution are valid for the RH range > 47.48% below which no solution state exists (Chan et al., 1992), and the prediction for this range is denoted as ZSR1 in Figure 1. But since (NH,!,SO, may exist in a multicomponent solution as a liquid phase for RHs lower than that, the ZSR method is extrapolated to the lower RH range (the result is denoted as ZSR2 in Figure 1). The good agreement between the mfs based on the dry particle assumption and that by the ZSR method implies that the solid particle may not contain water and is the stable form for the (NH,),SO, single component solution. Cohen et al. (1987a) observed a similar result. The ZSR method also predicts the water activity of the supersaturated solution, as shown in Figure 1, down to RH = SCAPE also predicts the behavior of the solution in the equilibrium state, including the RHD that is about WATER ACTIVITY (a,) FIGURE 1. Water activity data for ammonium sulfate solutions at 298 K (Tang et al., 1978). Other measurements by Spann and Richardson (1985) and Cohen et al. (1987a) also agree with our data and estimate as shown in Figure 1. Figure 2 shows water activities for H,SO, solutions. Since no solid particle can be formed for this system, the mfs value estimated by the ZSR method at 79.4% RH is used as the reference point. In this case the ZSR method predicts a saturated solution, and SCAPE is basically the same as the ZSR method since no solid exists. Both estimates agree well with the data. From these single cornponent results, it is confirmed that the parameters used in the ZSR method and SCAPE for (NH&SO, and H2S0, single component solutions are accurate and reliable. Next, the water activity of solutions with different [NHfr]/[SO:-] molar ratios was measured. For the system with [NHi]/ [SO:-] = 2/3 or [H2S041/[(NH4)2S041 = 2, no solid particle was observed.

7 Y. P. Kim et al. C Particle 1 A Partlcle 2 0 Particle 3 - ZSR method, SCAPE WATER ACTIVIFf (a,) FIGURE 2. Water activity data for sulfuric acid solutions. Therefore the rnfs value estimated at about 80% RH by the ZSR method is used as the reference value. As shown in Figure 3, the cstimate by the ZSR method at the lower RH range agrees well with the data for two particles. No comparable 0 0 A Particle 2 - ZSR method... SCAPE C WATER ACTIVITY (a,) FIGURE 3. Watcr activity data for mixcd solutions of ammonium/sulfate molar ratio of 2:3. water activity measurement is available for the solution at this molar ratio. In the solubility diagram for this system at 30 C (Tang et al., 1978) the solid species at this molar ratio is NH,HSO, and solid is formed for the RH < 0.40 with the rnfs value of about In agreement with this, SCAPE estimates the presence of solid at about 23% RH, the mfs value of 0.74, with NH,HSO, being the solid species. One concludes that ZSR method and SCAPE predict the data quite well for this system which is not highly nonlinear. The mixed solution with [NH;]/[SO~-] molar ratio of 1.0 can be considered as a single component solution of NH,HSO,, ammonium bisulfate. For this system, no solid particle is observed except at the lowest RH value of 25%. Spann and Richardson (1985) also observed no solid particles for this system down to 10% RH. Thus we compared the rnfs values based on the reference state estimated by the ZSR method and those based on the reference state estimated from literature data. Tang and Munkelwitz (1977) and Spann and Richardson (1985) measured water activities for this system, NH,HSO, single component solutions, and their results agree as shown in Figure 4. These literature data agree with the measured rnfs based on the reference state mfs from Tang and Munkelwitz (1977) except at 25% RH where a solid particle was observed. On the contrary, the measured rnfs values based on the reference state rnfs calculated from the ZSR method do not agree with thc literature data (they fall between the literature data and the ZSR method prediction) and are not shown in Figure 4. Note that the estimates from the ZSR method and SCAPE deviate from other measurements, especially at the low RH range. Tang and coworkers reported that the RHD for NH,HSO, is about 39.5% with the rnfs value of The rnfs values predicted

8 Water Activity in (NH,),SO,-H,SO, Mixtures O Th~s work - Spann and Richardson (1985) 0 Tang and Munkelwttz (1977) - ZSR method... - SCAPE + C Stelson et al (1984) I I WATER ACTIVITY (a,) FIGURE 4. Water activity data for mixed solutions of ammonium/sulfate molar ratio of 1. by SCAPE for all the RH range are, however, less than Thus, the simulated solution remained unsaturated even if all other thermodynamic properties used in SCAPE are accurate, and SCAPE would not predict the presence of solid species for this solution. Stelson et al. (1984) predicted water activity for this system by using the Kusik and Meissner activity coefficient estimation method (Kusik and Meissner, 1978) and the Gibbs-Duhem equation in which the HSO; ion is explicitly considered in addition to SO:-, NH:, and Hi ions. Their estimate, shown in Figure 4, fits this measurement and other literature data well, better than the ZSR method. Note that the K-M method used by Stelson et al. (1984) is different from that used by Chan et al. (1992), which is similar to the ZSR method, an empirical mixing rule using water activity data of two single component solutions without activity coefficients. From these considerations, it is apparent that the present form of the ZSR method is not appropriate for this highly nonlinear system. This point will be discussed later. Data for the mixed solution with [NH:]/[SO:-] molar ratio of 4/3 are shown in Figures 5 and 6. Unlike other mixed solutions, solid particles are observed for a wide range of RH. Comparison of the mfs result with the dry particle assumption and that with the reference state estimated by the ZSR method at about 80% RH in Figure 5 shows a distinct deviation. Also plotted in Figure 5 are the interpolated values from the data of Spann and Richardson (1985) which were also obtained with the dry particle assumption, and these agree well with the measured result based on the dry particle assumption. Since (1) no other literature water activity data are available; (2) Spann and Richardson's result is also based on the dry particle assumption; (3) the mfs values with the dry particle assumption do [NH,']~[so,~]=~I~, PARTICLE 1 2 Dry particle ZSR method Spann and Richardson \ O WATER ACTIVITY (a,) FIGURE 5. Comparison of watcr activity data based on the dry particle assumption and the ZSR method estimation for mixed solution of ammonium/sulfate molar ratio of 4:3.

9 Y. P. Kim et al I.O WATER ACTIVITY (a,) FIGURE 6. Water activity data for mixed solution of ammonium/sulfate molar ratio of 4:3. not agree with Tang et al.'s solubility data (1978); and (4) the SCAPE result fits solid-liquid equilibrium mfs values well (the last two items will be discussed shortly), we present the data based on the reference state estimation by the ZSR method (Figure 6). Also shown in Figure 6 is the SCAPE estimate. An interesting point is that SCAPE predicted no solid species for RH > 0.50 while solid particles were observed at about RH = According to the solubility diagram of Tang et al. (1978) a solid can be formed for this system between 60% and 70% RH with an mfs value of about At about 50% RH, an mfs value of about 0.80 and (NH4),H(S04), (letovicite) is the solid species, and when RH decreases to about 39.5% the solid phase becomes a mixture of letovicite and ammonium bisulfate. In both cases, the liquid phase also exists, supporting the idea that the solid particle is not completely dry. SCAPE predicted the presence of solid up to about 49% RH with an mfs value about Letovicite is the solid species down to about 25% RH and then a mixture of letovicite and ammonium bisulfate forms. Thus, SCAPE predicted the literature data quite well except for failing to predict a solid particle at RH higher than about 50%. Also note that Tang et al.'s data do not agree with the mfs values under the dry particle assumption. Based on these considerations, the probable cause of inaccuracy of SCAPE in predicting the presence of solid is inaccuracy of the thermodynamic property values used in SCAPE. The existence of solid species in SCAPE is mainly determined by three thermodynamic properties: (1) the equilibrium constant of letovicite, (2) the water content data of (NH4),S04 and H,S04 and the accuracy of the ZSR method, and (3) activity coefficients of NH;, H+, HSO;, and SO:- ions. Water activity prediction by the ZSR method was good as shown in Figure 6, and the activity coefficient estimation method used, the Pitzer method, is shown to be more accurate than other available methods, including the K-M method (Kim et al., 1993a). Therefore, it seems reasonable to suspect the equilibrium constant is the source of uncertainty. The equilibrium constant of letovicite used in SCAPE is from Bassett and Seinfeld (1983), who calculated the equilibrium constant from the saturated solution data of Tang et al. (1978) by using the K-M method. The resulting value is about 29.3 at 298 K. We recalculated the equilibrium constant using the Pitzer method from the same data of Tang et al. (1978) and also from other solubility data (Linke and Seidell, 1965). The Pitzer method predicted 40.0 for the data of Tang et al. and generally larger values than that for other solubility data. The effect of an increased equilibrium constant value is expansion of the no-solid existence range to lower RH values. Thus, at this stage, the source of

10 Water Activity in (NH,),SO,-H,SO, Mixtures 283 the inaccuracy of SCAPE in predicting the solid presence for the system with the [NH;]/[SO;-] ratio of 4/3 is uncertain. The ZSR method accurately predicts water activities for single-component solutions ([NH;]/[SO;-] = 0, 2) and mixed solutions of which molar ratios are close to those of single component solutions ([NH:]/[so,~~] = 2/3, 4/3), but predicts poorly for mixed solution between the two single-component solutions ([NHI I/ [S0zp] = 1). This trend can be explained by the nonlinearity of the system while the estimation method is a linear model, though other variables may affect this trend. As the deviation of the mixed solution from the single component solutions increases, the accuracy of the prediction decreases. Spann and Richardson (1985) also noted this deviation, even with the addition of a term that accounts for the solute-solute interaction and suggested that with the ZSR method the H,O-H,SO,-(NH,),SO, system be considered as one of mixed NH,HSO,- (NH,)3H(S0, 1, or (NH,)3H(S04),- (NH,),SO, ([NHIl/ [SO;- I = 1-2) instead of NH,HSO,-(NH,),SO,. Thus, for the mixed solution considered here ([NH;]/[SO;-I= 0-2), the system would be considered as one of H,S04-NH, HSO, or NH,HSO,-(NH,),H(SO,), or (NH,),H(SO,),-(NH,),SO,. In other words, the system should be divided into three domains instead of one domain to account for thermodynamically stable solid salts, letovicite, and ammonium bisulfate. The HSO; ion should be explicitly considered to estimate thermodynamic properties of multicomponent systems including sulfate. The importance of the HSO, ion in considering multieomponent systems is well documented (Pitzer et al., 1977; Kim et al., 1993a, b; Saxena et al., 1993). Note that the K-M method shown in Figure 6 explicitly includes the HSO; ion with better predictions than the ZSR method. Unfortunately, appro- priate data for NH,HSO, and (NH,),H(SO,), solutions are lacking. CONCLUSIONS Water activities of the H,O-H,S04- (NH,),SO, system with [NH;]/[SO;~] molar ratios of 0, 2:3, 1, 4:3, and 2 for a wide range of RH were measured using an electrodynamic balance. The ZSR method and SCAPE, a gas-aerosol equilibrium model, were used to interpret the data. The ZSR method generally predicted measurements well, but deviated considerably from measurement and literature data for the mixed solution with [NH,+l/[S0,2-] ratio of 1. The ZSR method has an inherent limitation in not including a formalism for solute activity coefficients that are necessary for modeling of chemical equilibrium (Chan et al., 1992). Furthermore, during the application of the ZSR method, HSO; was not considered explicitly. The importance of treating the HSO; ion explicitly for this system has been demonstrated p;eviously and clearly shown in the comparison with the K-M method that included HSO, and solute activity coefficients. To use the ZSR method for this system, water activity data for NH4HS04 and (NH,),H(SO,), solutions should be known and the system should be further divided to account for these thermodynamically stable solid salts. SCAPE generally estimated the behavior of mixed solutions well. For the mixed solution with [NH;]/[so~~] ratio of 1, however, due to the inaccuracy of the ZSR method, its prediction also deviated from the data and did not predict the existence of solid particles for RH < 0.4. It also failed to predict the presence of solid for the mixed solution with [NHI]/[S0,2-] ratio of 4:3. These problems demonstrate the need for additional data on thermodynamic properties of con-

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