Thermodynamic Model of the System H NH Na SO NO Cl HO at K

Transcription

1 Article Subscriber ccess provided by the University of Wyoming Librries + Thermodynmic Model of the System H NH N SO NO Cl HO t K Simon L. Clegg, Peter Brimblecombe, nd Anthony S. Wexler J. Phys. Chem. A, 1998, 102 (12), DOI: /jp973043j Downloded from on Februry 7, 2009 More About This Article Additionl resources nd fetures ssocited with this rticle re vilble within the HTML version: Supporting Informtion Links to the 13 rticles tht cite this rticle, s of the time of this rticle downlod Access to high resolution figures Links to rticles nd content relted to this rticle Copyright permission to reproduce figures nd/or text from this rticle The Journl of Physicl Chemistry A is published by the Americn Chemicl Society Sixteenth Street N.W., Wshington, DC 20036

2 J. Phys. Chem. A 1998, 102, Thermodynmic Model of the System H + -NH 4 + -N + -SO NO 3 - -Cl - -H 2 O t K Simon L. Clegg* nd Peter Brimblecombe School of EnVironmentl Sciences, UniVersity of Est Angli, Norwich NR4 7TJ, U.K. Anthony S. Wexler Deprtment of Mechnicl Engineering, UniVersity of Delwre, Newrk, Delwre ReceiVed: September 17, 1997; In Finl Form: December 2, 1997 A multicomponent mole-frction-bsed thermodynmic model of the H + -NH 4+ -N SO 4 -NO 3- -Cl - - H 2 O system is used to represent queous-phse ctivities, equilibrium prtil pressures (of H 2 O, HNO 3, HCl, nd NH 3 ), nd sturtion with respect to 19 solid phses ((NH 4 ) 2 SO 4(cr), (NH 4 ) 3 H(SO 4 ) 2(cr),NH 4 HSO 4(cr),NH 4 - NO 3(cr), NH 4 Cl (cr), N 2 SO 4 10H 2 O (cr), N 2 SO 4(cr), N 3 H(SO 4 ) 2(cr), NHSO 4 H 2 O (cr), NHSO 4(cr), NH 3 - (SO 4 ) 2 H 2 O (cr), NNO 3(cr), NCl (cr),nh 4 HSO 4 NH 4 NO 3(cr), (NH 4 ) 2 SO 4 2NH 4 NO 3(cr), (NH 4 ) 2 SO 4 3NH 4 NO 3(cr), (NH 4 ) 2 SO 4 N 2 SO 4 4H 2 O (cr),n 2 SO 4 NNO 3 H 2 O (cr), 2NNO 3 NH 4 NO 3(cr) ). The model is vlid for concentrtions from infinite dilution to sturtion (with respect to the solid phses) nd to bout 40 mol kg -1 for cid sulfte systems which cn remin liquid to concentrtions pproching the pure cid. Prmeters for H 2 - SO 4 -H 2 O interctions were dopted from previous study, nd vlues for other binry (wter-electrolyte) nd ternry (wter nd three ions) interctions were determined from extensive literture dt for slt solubilities, electromotive forces, osmotic coefficients, nd vpor pressures. The model is compred with solubility mesurements for the quternry ion systems H + -N SO 4 -Cl - -H 2 O nd NH 4+ -N SO 4 -Cl - - H 2 O. 1. Introduction Acid mmonium sulfte erosols, with dditions of nitrte nd se slt, re ubiquitous in the lower troposphere. 1-3 They re n importnt influence on urbn ir qulity, for exmple in the Los Angeles bsin, 4 nd there hve been numerous chemicl modeling studies of such erosols over the pst decde nd more. 5,6 Mixing rules such s tht of Meissner nd Kusik 7 hve generlly been used to estimte ion nd solvent ctivities in queous erosols, s the presence of highly soluble mmonium slts nd cid sulftes enbles very high queous concentrtions to be ttined t low reltive humidity. These concentrtions re too gret to llow the ppliction of potentilly more ccurte methods of clculting ctivities, such s the ion interction model of Pitzer, 8,9 which hs been widely used in brine chemistry. 10 However, mny of the concentrtion limittions of the mollity-bsed ion interction model re overcome by the Pitzer, Simonson, nd Clegg (PSC) pproch, 11,12 which hs the dvntges over mixing rules tht ssocited ionic species nd ternry interctions between ions cn be treted explicitly. This is importnt, for exmple, for modeling the effects of bisulfte formtion in cidic sulfte solutions. In the ccompnying publiction (herefter referred to s pper 1) Clegg et l. 13 pply the mole-frction-bsed PSC model to the system H + -NH + 4 -SO 2-4 -NO - 3 -H 2 O to high supersturtion (low reltive humidity) nd tempertures up to 330 K. This system of equtions hs lso been used to predict the behvior of low-temperture cid solutions relted to strtospheric erosols. 14 A comprehensive model of inorgnic tropospheric erosols should predict ctivities, prtil pressures, nd slt solubilities in H + -NH 4+ -N + -SO 2-4 -NO 3- -Cl - -H 2 O mixtures over wide rnge of temperture. The ddition of the ions N + nd Cl - (to the system in pper 1) llows clcultions to be crried out for erosols contining se slt component, though omitting Mg 2+ (present t bout one-ninth the concentrtion of N + in sewter) nd other minor constituents. Aqueous solutions of composition H + -NH + 4 -N + -SO 2-4 -NO - 3 -Cl - -H 2 O hve the potentil to form seven cid sulfte or double slts t K in ddition to those discussed in pper 1. Equilibrium constnts for the formtion of severl of these re poorly known, s estimtes of their vlues require knowledge of the ctivity coefficients of the constituent ions in the concentrted solution mixtures in which they form. Idelly, the properties of supersturted solutions should lso be represented by models intended for tmospheric pplictions, s erosols re believed to occur in this stte. 15 However, dt for supersturted solutions, especilly mixtures, re fr from comprehensive even t K. In previous studies we hve successfully pplied the PSC equtions to the systems H + -NH + 4 -SO 2-4 -H 2 O nd N + - SO 2-4 -NO 3- -Cl - -H 2 O t K, including dt for supersturted solutions, 16,17 lthough there remin difficulties in representing ccurtely the thermodynmic properties of some electrolytes, prticulrly queous N 2 SO 4, t extreme concentrtion. These my need to be overcome by refinements in the model equtions or by ssuming the formtion of species such s ion pirs in solution. This is resonble given often smll mounts of wter vilble for hydrtion of the ions in supersturted solutions, but represents complicting fctor s there re few dt with which the concentrtions of such species cn be directly constrined. In this work we present model of the full H + -NH 4+ -N + - SO 2-4 -NO - 3 -Cl - -H 2 O system t K, restricted to substurted nd sturted solutions. The purpose of this model S (97) CCC: $ Americn Chemicl Society Published on Web 02/27/1998

3 2156 J. Phys. Chem. A, Vol. 102, No. 12, 1998 Clegg et l. is (1) to determine equilibrium constnts of cid sulfte slts nd other double slts tht form in solution mixtures nd provide more ccurte method of exploring phse equilibrium reltionships for these inorgnic erosols thn hs hitherto been vilble; (2) to estblish the bsis for temperture-dependent model for solutions up to sturtion with respect to dissolved slts; nd (3) to provide reference to id comprisons between different methods of estimting ctivity coefficients used in erosol models. It will lso llow the requirements for ccurcy in the thermodynmic clcultions to be ssessed reltive to uncertinties in erosol composition, tmospheric conditions (temperture, reltive humidity, nd the prtil pressures of soluble gses), nd physicl trnsport processes in typicl tmospheric modeling pplictions. For these purposes the prmeteriztion of the ctivity coefficient equtions for ech component electrolyte hs been limited to mximum concentrtion within which the vilble mesurements re represented to within, or close to, experimentl precision. For ll slts this is t or bove the concentrtion t which ech binry solution becomes sturted. The model should provide more ccurte method of predicting the properties of the system t K (principlly HNO 3, HCl, NH 3, nd H 2 O prtil pressures nd solid/liquid phse equilibrium) thn currently vilble. It is vlidted by comprisons with mesured slt solubilities in two quternry ion systems. 2. Theory In the model, ll liquid-phse concentrtions nd ctivity coefficients re expressed on the mole frction scle. The mole frction x i of species i is given by x i ) n i /( j n j ), where n i is the number of moles of component i nd the summtion j is over ll solution components including the solvent. The ctivities i of ll components i re given by i ) f i x i where f i is the ctivity coefficient. The reference stte for the ctivity coefficients of solute species is one of infinite dilution with respect to the solvent, identified by subscript 1, nd ctivity coefficients on this bsis re denoted f i *; thus f i * f 1sx 1 f 1. The reference stte for the ctivity coefficient of the pure solvent is the pure liquid, so tht f 1 f 1sx 1 f 1. The reltionship between mole frction nd mollity-bsed ctivity coefficients nd equilibrium constnts, nd definitions of moll (φ) nd rtionl (g) osmotic coefficients, re given in eqs 2-4 of pper (1). The present model is similr to tht in pper (1) in tht conventionl strong electrolytes re treted s fully dissocited in solution, but the dissocition of the bisulfte ion (HSO 4- )is considered explicitly (eq 5 nd eq 6 of pper 1). Equilibrium expressions for the formtion of solid phses, nd for vpor-liquid equilibrium, re the sme s those given in pper (1), nd re summrized below Formtion of Solid Phses. For slt M ν+ X ν- zh 2 O (cr) in equilibrium with n queous solution contining ction M nd nion X, M ν+ X ν- zh 2 O (cr) h ν + M (q) + ν - X (q) + zh 2 O (l) x K S ) M ν+ X ν- 1 z /(M ν+ X ν- zh 2 O (cr) ) (1) (1b) where M ν+ nd X ν- re the mole frction ctivities of M nd X, nd 1 is the wter ctivity. Becuse the ctivity of the pure solid phse (M ν+ X ν- zh 2 O (cr) ) is by definition unity, only the ctivity product of the ions nd solvent in eq 1b is significnt. Solubility dt for ll the systems studied hve been used to constrin the model, nd vlues of the equilibrium constnts themselves, consistent with the modeled ctivities, hve lso been determined here Vpor-Liquid Equilibrium. The solubilities of the voltile cids HNO 3 nd HCl in queous solution re expressed s the equilibrium HX (g) h H + (q) + X- (q) x K H ) xh + f H *xx - f X */phx (2) where phx (tm) is the prtil pressure of cid gs HX. (For conversion to SI units, tm ) P.) The Henry s lw constnts of HNO 3 nd HCl re nd tm -1, respectively, t K. 14,18 The solubility of NH 3 is described in terms of the equilibrium between the gs-phse molecule nd queous H + nd NH 4 + ions: NH 3(g) + H + (q) h NH + 4 (q) x K H ) xnh 4 + f NH4 */(xh + f H *pnh 3 ) (2b) (3) (3b) where x K H (tm -1 ) is equivlent to the conventionl Henry s lw constnt for NH 3 (K H, for NH 3(g) h NH 3(q) ) divided by the cid dissocition constnt of NH + 4 (K, for NH + 4 (q) h H + (q) + NH 3(q) ). At K, x K H is equl to tm , The Model. Equtions for solute nd solvent ctivity coefficients in liquid mixture re presented in generl form by Clegg et l., 12 nd re given for the cse of single solute in wter in pper 1. The model contins interction prmeters whose vlues must be determined from empiricl dt. For single ionic solute M ν+ X ν- in wter there re prmeters B MX, W 1,MX, U 1,MX, nd V 1,MX tht ccount for interctions between the solvent nd ions M nd X. The ction-nion coefficients R MX my either be set to fixed vlues or, where necessry, fitted together with the prmeters for solvent-ction-nion interctions noted bove. In multicomponent solutions bsed on single solvent nd contining severl ctions nd nions, there lso rise mixture prmeters of type W ii j, Q 1,ii j nd U ii j, where i nd i re dissimilr ctions or nions nd j is n ion of opposite sign. These hve the gretest influence in very concentrted solutions nd re typiclly determined from vpor pressures, electromotive forces (emfs), or slt solubilities for three-ion mixtures. The determintion of prmeter vlues for pure (single-solute) queous solutions nd mixtures is summrized in the following section. 3. Prmeteriztion of the Model The present model does not, in generl, extend to supersturted solutions. However, it represents the thermodynmic properties of queous mixtures up to, nd including, sturtion with respect to nineteen possible solid phses t K. Prmeteriztion of the model over such restricted rnge of concentrtions leds to n increse in ccurcy t low to moderte concentrtion compred, for exmple, to the extended fits of Clegg et l. 17 Figure 1 shows the reltionship between wter ctivity (reltive humidity) nd concentrtion for ech of the binry solutions, in most cses up to the sturtion mollity. There is wide diversity of behvior. For exmple, 25 mol kg -1 solutions of NH 4 NO 3 nd H 2 SO 4 re in equilibrium with reltive

4 Thermodynmic Model of H + -NH 4 + -N + -SO NO 3 - -Cl - -H 2 O J. Phys. Chem. A, Vol. 102, No. 12, TABLE 1: Fitted Binry Model Prmeters for the System H + -NH 4+ -N + -SO NO 3- -Cl - -H 2 O t K prmeter vlue prmeter vlue prmeter vlue B H NO B H Cl e B NH4 HSO h R H NO R H Cl 15.0 e R NH4 HSO h W 1,H NO W 1,H Cl e W 1,NH4 HSO h U 1,H NO U 1,H Cl e U 1,NH4 HSO h V 1,H NO V 1,H Cl e V 1,NH4 HSO h B NH4 SO b B NH4 NO f B NH4 Cl i R NH4 SO b R NH4 NO3 7.0 f R NH4 Cl 15.0 i W 1,NH4 SO b B 1 NH4 NO f W 1,NH4 Cl i U 1,NH4 SO b R 1 NH4 NO f U 1,NH4 Cl i V 1,NH4 SO b W 1,NH4 NO f V 1,NH4 Cl i U 1,NH4 NO f B N HSO c V 1,NH4 NO f B N NO j R N HSO c R N NO3 5.0 j W 1,N HSO c B N SO g B 1 N NO j U 1,N HSO c R N SO g R 1 N NO j V 1,N HSO c W 1,N SO g W 1,N NO j U 1,N SO g U 1,N NO j B N Cl d V 1,N SO g V 1,N NO j R N Cl 5.0 d W 1,N Cl d U 1,N Cl d V 1,N Cl d Prmeters for H + -HSO 4- -SO H 2O (queous H 2SO 4) interctions re given by Clegg nd Brimblecombe. 21 The interction prmeters bove were determined from dt for the following systems: () HNO 3-H 2O; (b) (NH 4) 2SO 4-H 2O; (c) N 2SO 4-H 2SO 4-H 2O; (d) NCl-H 2O; (e) HCl-H 2O; (f) NH 4NO 3-H 2O; (g) N 2SO 4-H 2O; (h) (NH 4) 2SO 4-H 2SO 4-H 2O; (i) NH 4Cl-H 2O; (j) NNO 3-H 2O. Figure 1. Reltionship between wter ctivity ( 1) nd mollity (m/ mol kg -1 ) for single-solute solutions t K. Numbered solutes: (1) H 2SO 4(q); (2) HNO 3(q); (3) HCl (q); (4) (NH 4) 2SO 4(q); (5) NH 4NO 3(q) (sturtion occurs t 26 mol kg -1 ); (6) NH 4Cl (q); (7) N 2SO 4(q) (lies between the curves for (NH 4) 2SO 4(q) nd NH 4Cl (q)); (8) NNO 3(q); (9) NCl (q). humidities of 62% nd only 4%, respectively. The mounts of wter tken up by tmospheric erosols re thus highly dependent upon composition, especilly t low reltive humidities where the curves for the individul electrolytes in Figure 1 diverge. In the following subsections, the prmeteriztion of ech binry nd ternry system is summrized. All model prmeters re listed in Tbles 1 nd 2, nd equilibrium constnts for the formtion of solid phses in Tble 3. For queous mixtures tht hve been modeled in previous studies, for exmple in pper 1, fits of the present model to the vilble dt re generlly not shown here. In other cses they re given in Figures 24-42, with summry digrms contined in the min text. The quntities φ nd f ( *, shown in Figures 2-9, re differences between the experimentl nd fitted vlues of the osmotic nd men ctivity coefficient, respectively H 2 SO 4 -H 2 O, HNO 3 -H 2 O, nd HCl-H 2 O. For queous H 2 SO 4 the prmeteriztion of Clegg nd Brimblecombe 21 is used, s for the model in pper 1, to represent ctivity Figure 2. Fit of the model to men ctivity coefficients of HNO 3 (f (*) in HNO 3(q) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Clegg nd Brimblecombe 18 (evluted dt from mny sources). Lines: solid, model of Crslw et l.; 14 dshed, eqution of Hmer nd Wu. 22 Figure 3. Fit of the model to men ctivity coefficients of HCl (f (*) in HCl (q) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Crslw et l. 14 (evluted dt from mny sources). Lines: solid, model of Crslw et l.; 14 dshed, eqution of Hmer nd Wu. 22 nd osmotic coefficients to 40 mol kg -1 ( reltive humidity of 0.59%). For HNO 3 -H 2 O, criticlly evluted ctivity dt

5 2158 J. Phys. Chem. A, Vol. 102, No. 12, 1998 Clegg et l. TABLE 2: Fitted Ternry Model Prmeters for the System H + -NH 4+ -N + -SO NO 3- -Cl - -H 2 O t K prmeter vlue prmeter vlue prmeter vlue W H NH4 HSO h W H N Cl n W HSO4 NO3 NH s Q 1,H NH4 HSO h Q 1,H N Cl n Q 1,SO4 NO3 NH t W H NH4 SO h W NH4 N SO o U SO4 NO3 NH t U H NH4 SO h Q 1,NH4 N SO o W SO4 NO3 N u W H NH4 NO k W NH4 N NO p Q 1 SO4 NO3 N u Q 1,H NH4 NO k Q 1,NH4 N NO p U H NH4 NO k U NH4 N NO p U SO4 Cl NH v Q 1,SO4 Cl NH v W H NH4 Cl l W NH4 N Cl q Q 1,H NH4 Cl l Q 1,NH4 N Cl q W SO4 Cl N w Q 1 SO4 Cl N w W H N HSO c W HSO4 SO4 NH h Q 1,H N HSO c Q 1,HSO4 SO4 NH h W NO3 Cl NH x U H N HSO c U HSO4 SO4 NH h Q 1,NO3 Cl NH x W H N SO c Q 1,H N SO c Q 1,HSO4 SO4 N c W NO3 Cl N y Q 1 NO3 Cl N y W HSO4 NO3 H r W H N NO m U HSO4 NO3 H r U H N NO m W SO4 NO3 H r Prmeters W ii j nd Q 1,ii j re symmetricl; thus W i ij ) W ii j nd Q 1,i ij ) Q 1,ii j. However, U i ij )-U ii j. The interction prmeters bove were determined from dt for the following systems: (c) N 2SO 4-H 2SO 4-H 2O; (h) (NH 4) 2SO 4-H 2SO 4-H 2O; (k) HNO 3-NH 4NO 3-H 2O; (l) HCl- NH 4Cl-H 2O; (m) HNO 3-NNO 3-H 2O; (n) HCl-NCl-H 2O; (o) (NH 4) 2SO 4-N 2SO 4-H 2O; (p) NH 4NO 3-NNO 3-H 2O; (q) NH 4Cl-NCl- H 2O; (r) HNO 3-H 2SO 4-H 2O; (s) NH 4HSO 4-NH 4NO 3-H 2O; (t) NH 4NO 3-(NH 4) 2SO 4-H 2O; (u) NNO 3-N 2SO 4-H 2O; (v) (NH 4) 2SO 4-NH 4Cl- H 2O; (w) (N) 2SO 4-NCl-H 2O; (x) NH 4NO 3-NH 4Cl-H 2O; (y) NNO 3-NCl-H 2O. TABLE 3: Equilibrium Constnts for Solid Phses for the System H + -NH 4+ -N + -SO 2-4 -NO 3- -Cl - -H 2 O t K solid phse ln( x K S) solid phse ln( x K S) (NH 4) 2SO NH 3(SO4) 2 H 2O (NH 4) 3H(SO 4) NNO NH 4HSO NCl NH 4NO NH 4HSO 4 NH 4NO NH 4Cl (NH 4) 2SO 4 2NH 4NO N 2SO 4 10H 2O (NH 4) 2SO 4 3NH 4NO N 2SO (NH 4) 2SO 4 N 2SO 4 4H 2O N 3H(SO 4) N 2SO 4 NNO 3 H 2O NHSO 4 H 2O (NH 4NO 3 2NNO 3) NHSO This solid my be metstble (see section 3.15); its formtion is consistent with the ternry prmeters W NH4 N NO3 ) , Q 1,NH4 N NO3 ) , nd U NH4 N NO3 ) , which should be substituted for the vlues in Tble 1. Figure 5. Fit of the model to moll osmotic coefficients of NH 4NO 3(q) (φ, left-hnd scle) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Wishw nd Stokes; 60 pluses, Hmer nd Wu; 22 open circles, Kirgintsev nd Luk ynov. 47 Lines: solid, model 1; dshed, eqution of Hmer nd Wu; 22 dotted, chnges in wter ctivity ( 1, right-hnd scle) for n error in the osmotic coefficient of (0.01. Figure 4. Fit of the model to moll osmotic coefficients of (NH 4) 2- SO 4(q) (φ, left-hnd scle) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Wishw nd Stokes; 56 pluses, Goldberg; 57 open circles, Plmer nd Milioto; 58 open squres, Filippov et l.; 59 open dimonds, Tng nd Munkelwitz; 59 crosses, Clegg et l. 23 Lines: solid, model 1; 23 dshed, model of Clegg et l.; 58 dotted, chnges in wter ctivity ( 1, right-hnd scle) for n error in the osmotic coefficient of (0.01. Figure 6. Fit of the model to moll osmotic coefficients of NH 4Cl (q) (φ) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Grnsey nd Prue; 61 open circles, Wishw nd Stokes; 60 pluses, Kirgintsev nd Luk ynov; 62 crosses, Shul ts et l. 63 Lines: dshed, eqution of Hmer nd Wu; 22 dotted, chnges in wter ctivity ( 1, right-hnd scle) for n error in the osmotic coefficient of (0.01.

6 Thermodynmic Model of H + -NH 4 + -N + -SO NO 3 - -Cl - -H 2 O J. Phys. Chem. A, Vol. 102, No. 12, Figure 7. Fit of the model to moll osmotic coefficients of N 2SO 4(q) (φ) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Rrd nd Miller; 64 open circles, Indelli; 65 open squres, Pltford; 66 open tringles, Downes nd Pitzer; 67 pluses, Rndll nd Scott; 68 solid inverted tringles, Gibson nd Adms; 69 open dimonds, Chn et l. 24 (dynmic experiments); solid tringles, Chn et l. 24 (sttic experiments); crosses, Tng nd Munkelwitz. 70 Lines: solid, model of Clegg et l.; 17 dotted, chnges in wter ctivity ( 1, right-hnd scle) for n error in the osmotic coefficient of (0.01. Figure 8. Fit of the model to moll osmotic coefficients of NNO 3(q) (φ) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, Robinson; 25 open circles, Kirgintsev nd Luk ynov; 71,62 pluses, Bezboruh et l.; 26 open tringles, Kngro nd Groeneveld; 72 solid tringles, Perce nd Hopson; 73 crosses, Tng nd Munkelwitz. 70 Lines: dshed, evlution of Wu nd Hmer; 74 dotted, chnges in wter ctivity ( 1, right-hnd scle) for n error in the osmotic coefficient of (0.01. (Clegg nd Brimblecombe, 18 see their Tble 1) re fitted using the mole frction equtions (eq 14 of pper 1) up to mole frction ionic strength (I x ) of 0.5, equivlent to 27.5 mol kg -1. Figure 2 shows tht the dt re represented to within experimentl precision, with n improvement in ccurcy compred to both the extended fit of Crslw et l. 14 nd the erlier compiltion of Hmer nd Wu. 22 Sources of thermodynmic dt for queous HCl re listed in Tble 7 of Crslw et l. 14 For this model the representtion of osmotic nd ctivity coefficients of the pure queous cid is limited to 8 mol kg -1, nd the fit is shown in Figure 3. Although the dt (electromotive force mesurements) re quite scttered bove bout 2.5 mol kg -1, it is cler tht the present model better represents the men ctivity coefficients of HCl within the fitted rnge thn the 0-20 mol kg -1 fit of Crslw et l., 14 which ws obtined chiefly in order to predict HCl solubilities in highly cidic solutions t strtospheric tempertures (NH 4 ) 2 SO 4 -H 2 O. Avilble thermodynmic dt for this system re listed in Tble 4 nd consist of isopiestic nd Figure 9. Fit of the model to moll osmotic coefficients of NCl (q) (φ) t K, plotted ginst the squre root of mollity (m/mol kg -1 ). Symbols: dots, criticl evlution of Archer; 27 open circles, Tng et l.; 28 open squres, Chn et l. 24 (sttic experiments); crosses, Chn et l. 24 (dynmic experiments); pluses, Cohen. 29 Lines: solid, model of Clegg et l.; 17 dshed, eqution of Hmer nd Wu; 22 dotted, chnges in wter ctivity ( 1, right-hnd scle) for n error in the osmotic coefficient of (0.01. TABLE 4: Sources of Activity Dt t K for (NH 4 ) 2 SO 4 -H 2 O Solutions m b min mx used c dt type d source yes iso Wishw nd Stokes yes iso Filippov et l no iso Frolov nd Nsonov yes iso Clegg et l yes edb Clegg et l yes edb e Tng nd Munkelwitz 70 As in previous work, 58 osmotic coefficients of queous K 2SO 57 4 were used to constrin the model below 0.1 mol kg -1. b Mollity. c Used in the fit of the model. d Type of mesurement: iso, isopiestic mesurement; edb, electrodynmic blnce mesurements of the wter ctivity/concentrtion reltionship for supersturted solutions. e Dt restndrdized using osmotic coefficients for substurted solutions. blnce (edb) mesurements crried out by severl different groups. Here, the mximum mollity of fit ws restricted to 8 mol kg -1 (bout 2 mol kg -1 bove the sturtion concentrtion), nd the result is shown in Figure 4. There is n improvement in ccurcy over the extended fit of Clegg et l., 23 used for the model in pper 1 (herefter referred to s model 1). Figure 4 lso shows the error in equilibrium reltive humidity tht corresponds to chnge of (0.01 in φ (right-hnd scle). The edb dt re uncertin by t lest this mount, equivlent to (0.25% in reltive humidity. The reltive humidity in equilibrium with sturted solution of (NH 4 ) 2 SO 4 t K is 80.2% NH 4 NO 3 -H 2 O. The thermodynmic dt for this system re listed in Tble 3 of pper 1. The fit of the model is here limited to mximum of mol kg -1 nd includes only isopiestic mesurements. The result is shown in Figure 5, where it is compred with both model 1 nd the erlier criticl evlution of Hmer nd Wu. 22 The devitions between model 1 nd the present fit correspond to mximum differences of bout 0.2% in equilibrium reltive humidity. The equilibrium reltive humidity bove sturted solution of NH 4 NO 3 t K is 61.2% NH 4 Cl-H 2 O. Sources of ctivity dt for this system re listed in Tble 5 nd consist of freezing point dt (which were converted to osmotic coefficients t K) nd isopiestic nd edb mesurements. The dt were fitted to mximum mollity of 7.5 mol kg -1 (pproximtely the sturtion mollity), with the edb determintions excluded nd with

7 2160 J. Phys. Chem. A, Vol. 102, No. 12, 1998 Clegg et l. TABLE 5: Sources of Activity Dt t K for NH 4 Cl-H 2 O Solutions m min mx used b dt type c source yes iso Wishw nd Stokes yes iso Shul'ts et l yes iso Kirgintsev nd Lukynov yes fp d Grnsey nd Prue no e edb Ling nd Chn 92 Mollity. b Used in the fit of the model. c Type of mesurement: iso, isopiestic mesurements; fp, freezing point depression; edb, electrodynmic blnce mesurements of the wter ctivity/concentrtion reltionship for supersturted solutions. d Converted to osmotic coefficients t K using vilble therml dt. e Not used, s the fit ws restricted to substurted solutions only. prmeter V 1,NH4 Cl fixed to The result is shown in Figure 6, where it is lso compred with the previous criticl ssessment of Hmer nd Wu. 22 The sctter of the isopiestic dt, bout (0.002 in φ, corresponds to n uncertinty of only (0.04% in reltive humidity. The equilibrium reltive humidity bove sturted solution of NH 4 Cl t K is 77.2% N 2 SO 4 -H 2 O, NNO 3 -H 2 O, nd NCl-H 2 O. Aqueous solutions of these slts nd their mixtures hve been modeled to high supersturtion by Chn et l. 24 nd by Clegg et l. 17 Sources of ctivity dt for queous N 2 SO 4 re summrized in Tble 3 of Clegg et l. 17 In the model of Clegg et l. 17 the osmotic nd ctivity coefficients of queous N 2 SO 4 re represented to bout 14 mol kg -1 (compred to sturtion with respect to N 2 SO 4 10H 2 O (cr) t only 1.97 mol kg -1 ), lthough ccepting quite lrge devitions of the fitted model from the experimentl dt. In prticulr, rising trend in wter ctivity is predicted for mollities bove bout 12 mol kg -1, which is not relistic (see Figure 3 of Clegg et l. 17 ). In this work we use dt from sources listed by Clegg et l., 17 but restrict the mximum mollity of fit to 6 mol kg -1. The result is plotted in Figure 7. The model represents the dt to within experimentl precision over the concentrtion rnge fitted, with worthwhile improvement in ccurcy over the extended fit of Clegg et l. 17 The equilibrium reltive humidity of sturted solution of N 2 SO 4 t K is 93.6%. The work of Clegg et l. 17 shows tht the reltive humidity/ concentrtion reltionship for queous NNO 3 t K cn be represented by the model to mollities exceeding 100 mol kg -1 (for which the wter ctivity is 0.2), to bout the sme precision s the mesurements. Sources of thermodynmic dt re listed in Tble 2 of Clegg et l. 17 Here we hve tken the opportunity to restndrdize the osmotic coefficients of Robinson 25 nd Bezboruh et l. 26 to new vlues for the queous KCl isopiestic stndrd (D. G. Archer, personl communiction, 1997) nd hve refitted to the sme mximum mollity of mol kg -1. The result is shown in Figure 8 nd is compred with the evlution of Hmer nd Wu 22 for substurted solutions. The uncertinty in the edb mesurements of (0.01 to (0.02 in φ corresponds to mximum chnge of bout (0.25% in equilibrium reltive humidity. The reltive humidity bove sturted solution of NNO 3 t K is 73.9%. Sources of ctivity dt t K for queous NCl re listed in Tble 1 of Clegg et l. 17 Here, osmotic coefficients from the criticl evlution of Archer 27 nd the edb studies of Tng et l., 28 Cohen, 29 nd Chn et l. 24 hve been fitted to mollity of 8 mol kg -1. The result is shown in Figure 9, where it is lso compred with the results of Clegg et l. 17 (for compositions including some supersturted solutions) nd the evlution of Hmer nd Wu (1972). The improvement in ccurcy for substurted solutions, compred to the work of Clegg et l., 17 is up to bout 0.6% in equilibrium reltive humidity. The reltive humidity bove sturted solution of NCl t K is 75.3% H 2 SO 4 -HNO 3 -H 2 O, H 2 SO 4 -HCl-H 2 O, nd HNO 3 - HCl-H 2 O. These mixed cid systems hve been modeled by Crslw et l., 14 who list sources of ctivity dt in their Tbles 11 nd 13. A lrge number of thermodynmic mesurements, including freezing points nd equilibrium phno 3 nd ph 2 O mesurements, re vilble for H 2 SO 4 -HNO 3 -H 2 O solutions. Crslw et l. 14 hve determined prmeters W HSO4 NO3 H, W SO4 NO3 H, nd U HSO4 NO3 H s functions of temperture from these dt. In the bsence of mesurements t K, their vlues (t this temperture) re dopted for the present study nd re listed in Tble 2. Solubilities of HCl (g) in queous H 2 SO 4 hve been determined from to 343 K. 30,31 Stisfctory greement with the model ws obtined with ll ternry interction prmeters set to zero for the mixed solution (see Figure 12 of Crslw et l. 14 ), nd these null vlues re retined here. There pper to be no stisfctory ctivity dt for HNO 3 - HCl-H 2 O solutions for the compositions nd tempertures of interest to tmospheric chemists, nd becuse of this, it is necessry to set the ternry interction prmeters to zero. However, comprisons of model predictions with prtil pressures over H 2 SO 4 -HNO 3 -HCl-H 2 O solutions t low temperture mesured by Elrod et l. 32 show excellent greement, which gives confidence in these prmeter vlues H 2 SO 4 -(NH 4 ) 2 SO 4 -H 2 O, HNO 3 -NH 4 NO 3 -H 2 O, (NH 4 ) 2 SO 4 -NH 4 NO 3 -H 2 O, nd NH 4 HSO 4 -NH 4 NO 3 -H 2 O. Sources of ctivities for these systems re listed in Tbles 4-7 of pper 1. The dt hve been refitted for the present model using the pure (single-solute) prmeters listed in Tble 1. For the H 2 SO 4 -(NH 4 ) 2 SO 4 -H 2 O system it ws possible to retin fit extending into the supersturted region; for exmple the edb dt of Spnn 33 for queous NH 4 HSO 4 re fitted to just over mol kg -1 ( reltive humidity of 19.4%) nd cid mmonium slt solubilities to bout 27 mol kg -1 H 2 SO 4,sis shown in Figure 20 of pper 1. Due to the optimiztion of NH 4+ -SO 2-4 interction prmeters for substurted solutions, it is likely tht the present model is more ccurte for such concentrtions, t lest for mixtures in which (NH 4 ) 2 SO 4 is the mjor component. For solutions contining chiefly H 2 SO 4 the liquid phse extends essentilly to the pure cid, which is beyond the limit of either model (40 mol kg -1,nH 2 SO 4 mole frction of 0.419). Nonetheless, both the present model nd tht in pper 1 represent the solubility curve to reltive humidities of <10%. Clculted reltive humidities bove solutions simultneously sturted with respect to (NH 4 ) 2 SO 4(cr) nd (NH 4 ) 3 H(SO 4 ) 2(cr) re 68.6% (model 1) nd 68.8% (the present model), nd for solutions sturted with respect to (NH 4 ) 3 H(SO 4 ) 2(cr) nd NH 4 - HSO 4(cr) they re 36.7% (model 1) nd 36.8% (the present model). For HNO 3 -NH 4 NO 3 -H 2 O mixtures the solubilities of NH 4 - NO 3 (Tble 5) hve been fitted to mximum mollity of 20 mol kg -1 HNO 3 here, compred to 25 mol kg -1 for model 1. This slightly reduced concentrtion is consistent with the lower mximum mollity of fit for queous HNO 3 used in the present model. The dt for the pk *ofnh + 4 in queous NH 4 NO 3 re represented to bout the sme level of ccurcy for both models (see Figure 9 of pper 1 for the model 1 result). The clculted reltive humidity, bove 10 mol kg -1 HNO 3 solution sturted with NH 4 NO 3 is 45.7% (model 1) nd 45.8% (the present model), indicting good consistency. The difference

8 Thermodynmic Model of H + -NH 4 + -N + -SO NO 3 - -Cl - -H 2 O J. Phys. Chem. A, Vol. 102, No. 12, TABLE 6: Sources of Activity Dt t K for H 2 SO 4 -N 2 SO 4 -H 2 O Solutions m min mx used b dt type c source >100 yes sol Silcock yes sol Foote yes φ Rrd 75, yes emf Covington et l yes emf Hrned nd Sturgis yes emf Rndll nd Lngford >100 yes edb Tng nd Munkelwitz 70 Totl mollity (mh 2SO 4 + mn 2SO 4). b Used in the fit of the model. c Type of mesurement: sol, slt solubility; φ, osmotic coefficient from isopiestic experiments; emf, electromotive force determintion of H 2SO 4 ctivity; edb, electrodynmic blnce mesurements of the wter ctivity/concentrtion reltionship for supersturted solutions. rises to 2% t 20 mol kg -1 HNO 3, the limit of the present fit. It is likely tht model 1 is more ccurte t this nd higher concentrtions, becuse of the lrger rry of ternry dt used in the prmeteriztion nd lso the extended rnge of fit of the two binry components. In the prmeteriztion of the model for (NH 4 ) 2 SO 4 -NH 4 - NO 3 -H 2 O mixtures (see Tble 7 of pper 1 for sources of dt), the wter prtil pressure mesurements of Emons nd Hhn 34 t K were included in the dt set, nd the edb mesurements of Chn et l. 35 for supersturted solutions were omitted. As comprison between the models, the clculted reltive humidities bove solutions simultneously sturted with respect to (NH 4 ) 2 SO 4(cr) nd (NH 4 ) 2 SO 4 2NH 4 NO 3(cr) re 63.5% (model 1) nd 66.2% (the present model), for (NH 4 ) 2 SO 4 2NH 4 - NO 3(cr) nd (NH 4 ) 2 SO 4 3NH 4 NO 3(cr) they re 64.5% (model 1) nd 63.5% (the present model), nd for (NH 4 ) 2 SO 4 3NH 4 NO 3(cr) nd NH 4 NO 3(cr) they re 60.4% (model 1) nd 60.1% (the present model). The differences for the first two trnsitions mostly reflect vritions in the predicted concentrtions of the sturted solutions, which re within the uncertinty of the dt (Figure 22 of pper 1). However, there remin differences of bout 0.4% in reltive humidity between the model predictions when the sme solution compositions re used, due to vritions in the clculted ctivities. For the NH 4 HSO 4 -NH 4 NO 3 -H 2 O system, for which there re mesurements of the solubility of NH 4 HSO 4 NH 4 NO 3(cr), NH 4 HSO 4(cr), nd NH 4 NO 3(cr) (Tble 8 of pper 1), the sme dt were fitted for both model 1 nd the present model, lthough here only results for K were used. At this temperture the equilibrium constnts x K S (NH 4 HSO 4 NH 4 NO 3 ) for the two models differ by bout 45%. Model 1 is likely to be more ccurte for clculting the properties of this system becuse of the very high queous-phse concentrtions t which solid phses precipitte. Clculted reltive humidities bove solution sturted with respect to both NH 4 HSO 4(cr) nd NH 4 - HSO 4 NH 4 NO 3(cr) re very similr (29.8% for model 1, nd 29.3% for the present model), lthough the compositions of the sturted solutions differ (46.6 mol kg -1 NH 4 HSO 4 nd mol kg -1 NH 4 NO 3 for model 1; 41.1 mol kg -1 NH 4 HSO 4 nd 15.8 mol kg -1 NH 4 NO 3 for the present model) H 2 SO 4 -N 2 SO 4 -H 2 O. Sources of dt vilble for this system re listed in Tble 6 nd comprise extensive mesurements of osmotic coefficients, nd emf studies which yield the H 2 SO 4 ctivity, slt solubilities, nd edb mesurements of wter ctivity. The solubility curve of this mixture is complex, with the following series of solids precipitted t K s queous H 2 SO 4 concentrtion is incresed: N 2 - SO 4 10H 2 O (cr),n 2 SO 4(cr),N 3 H(SO 4 ) 2(cr), NHSO 4 H 2 O (cr), nd Figure 10. Phse digrm of H 2SO 4-N 2SO 4-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) N 2SO 4 10H 2O (cr); (2) N 2SO 4(cr); (3) N 3H(SO 4) 2(cr); (4) NHSO 4 H 2O (cr); (5) NHSO 4(cr). Contours: equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. NHSO 4(cr) within the fitted rnge of the model. In solutions contining over 21 mol kg -1 H 2 SO 4(q) hydrted nd nhydrous forms of NH 3 (SO 4 ) 2 occur. The solid N 3 H(SO 4 ) 2 H 2 O (cr) hs been climed to occur from bout 3 to 5.5 mol kg -1 H 2 SO 4(q), 36 but ppers to be metstble t best. Following Hrvie et l., 37 we hve excluded it from the model. The H 2 SO 4 -N 2 SO 4 -H 2 O mixture contins four ions; consequently there re four possible sets of triplet interction prmeter within the model in ddition to the unknown binry N + -HSO - 4 terms. Figure 24 shows slt solubilities t K, together with the rnge of compositions for which osmotic coefficients hve been determined. The coverge is extensive, except for solutions contining mostly H 2 SO 4, nd the lrge number of mesurements is sufficient to constrin the model well. Electromotive force dt were converted from interntionl volts to volts, nd stndrd emfs (E ) were determined s described by Hrvie et l. 37 The osmotic coefficients nd emf mesurements were fitted by the model to mximum totl mollity of 15 mol kg -1 nd slt solubilities to 23 mol kg -1 in order to determine the equilibrium constnt for NHSO 4 formtion. The result of the fit is shown in Figures nd shows excellent greement with the mesured solubilities nd emfs (here shown s f H2SO4 *) nd only smll devitions in the cses of the osmotic coefficients (Figure 26). Using dt tbulted in the Gmelin hndbook, 38 we hve lso determined tenttive vlue of x K S (NH 3 (SO 4 ) 2 H 2 O); see Tble 3. The clculted solubility curve nd contours of wter ctivity re shown in Figure 10 nd exhibit mrkedly different behvior from electrolyte systems in which there is little or no ion ssocition. Here, for H 2 SO 4 mollities between bout 7 nd 10 mol kg -1, wter ctivity is lmost invrint with N 2 SO 4 concentrtion (to 6 mol kg -1 of slt, the limit shown in the figure). Furthermore, for cid mollities bove bout 10 mol kg -1 the ddition of N 2 SO 4 increses the equilibrium reltive humidity bove the solution. This behvior is qulittively similr to tht of H 2 SO 4 -(NH 4 ) 2 SO 4 -H 2 O nd confirms the importnce of the explicit recognition of the HSO - 4 (q) h H + (q) + SO 2-4 (q) equilibrium within the model in order to represent the observed behvior of the system HNO 3 -NNO 3 -H 2 O. The only sources of ctivity dt for this system (Tble 7) re slt solubilitiessthough over wide rnge of temperturesnd very few prtil pressure

9 2162 J. Phys. Chem. A, Vol. 102, No. 12, 1998 Clegg et l. TABLE 7: Sources of Activity Dt t K for HNO 3 -NNO 3 -H 2 O Solutions m min mx used b dt type c source yes sol d Gmelin Hndbook yes sol Kurnkov nd Nikolev yes phno 3, ph 2O e Fltt nd Benguerel no f phno 3 Clegg nd Brimblecombe 93 Totl mollity (mhno 3 + mnno 3). b Used in the fit of the model. c Type of mesurement: sol, solubility of NNO 3; phno 3, equilibrium prtil pressure of HNO 3; ph 2O, equilibrium prtil pressure of H 2O. d Vlues in the Gmelin Hndbook re bsed upon Kurnkov nd Nikolev 82 nd other work by the sme uthors. e Dt were converted to men ctivity coefficients of HNO 3 nd to wter ctivity. f Only single prtil pressure ws mesured. Figure 11. Phse digrm of HNO 3-NNO 3-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubility of NNO 3 in HNO 3(q); contours, equilibrium wter ctivities with vlues s mrked. Contours re dotted for supersturted solutions. TABLE 8: Sources of Activity Dt t K for HCl-NH 4 Cl-H 2 O Solutions m min mx used b dt type c source d yes sol Silcock yes emf e Robinson et l yes emf e Chn et l yes emf e Downes et l yes pk * f Med et l yes g phcl Silcock no h phcl Clegg nd Brimblecombe 94 Totl mollity (mhcl + mnh 4Cl). b Used in the fit of the model. c Type of mesurement: sol, solubility of NH 4Cl, emf, electromotive force mesurement of HCl ctivity, pk *, cid dissocition constnt of NH 4+ in queous NH 4Cl. d Mollity rnge of queous HCl. e Converted to men ctivity coefficients of HCl. f Converted to the reciprocl of NH 4+ nd H + ctivity coefficients using γ NH3 from the work of Med et l. 42 g Only single mesurement ws used (out of totl of four). h Only one composition ws mesured. mesurements for solutions contining low mollities of NNO 3. Interction prmeters W H N NO3 nd U H N NO3 were determined from the dt, nd the results re shown in Figures 28 nd 29. The clculted solubility curve nd equilibrium wter ctivities re shown in Figure HCl-NH 4 Cl-H 2 O. Sources of ctivity dt for this system re listed in Tble 8 nd comprise NH 4 Cl (cr) solubilities, emf determintions of HCl ctivities, the pk *ofnh + 4 (q) (from potentiometric titrtion), nd very few prtil pressure mesurements. Activity coefficients of HCl were clculted from the emf mesurements of Robinson et l. 39 using their listed stndrd emfs (E ) nd tken directly from the tbultions of Chn et l. 40 nd Downes et l. 41 At K the properties of this system re comprtively Figure 12. Phse digrm of HCl-NH 4Cl-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubility of NH 4Cl (cr) in HCl (q); contours, equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. TABLE 9: Sources of Activity Dt t K for HCl-NCl-H 2 O Solutions m min mx used b dt type c source yes sol Silcock yes emf Hwkins yes emf Hrned yes emf Mcskill et l yes emf Chn et l no d phcl Clegg nd Brimblecombe 94 Totl mollity (mhcl + mncl). b Used in the fit of the model. c Type of mesurement: sol, solubility of NCl; emf, electromotive force mesurement (yields γ HCl); phcl, equilibrium prtil pressure of HCl. d Only single prtil pressure ws mesured. well studied. The fits of the model to the emf mesurements nd slt solubilities (see Figures 30 nd 31) gree well with the dt over the full rnge of compositions nd concentrtions. The pk * determintions of Med et l. 42 were not included in the fit, but re compred with predictions in Figure 32 s test. For this purpose they were first converted from [K γ NH4 / (γ H γ NH3 )] to f NH4 */f H * using the known thermodynmic dissocition constnt 43 nd ctivity coefficients of NH 3 derived by Med et l. 42 Agreement with the model is stisfctory, lthough the reson for the smll positive offset of the dt nd the fct tht they do not pper to extrpolte monotoniclly to unity t zero ionic strength is not known. Figure 12 shows the clculted solubility curve with contours of equilibrium reltive humidity superimposed HCl-NCl-H 2 O. Dt for this system, Tble 9, consist chiefly of emf mesurements of HCl ctivity (which extend over wide rnge of tempertures) nd NCl solubilities in queous HCl. The emfs of Mcskill et l. 44 were converted to f HCl * s described by Clegg nd Whitfield, 20 nd vlues of the men ctivity coefficient given in the other studies were used directly. Mesured nd fitted ctivity coefficients from ll sources re compred in Figure 33 nd gree well over the full rnge of ionic strength to 6 mol kg -1. The observed solubilities re lso represented well, Figure 34. The clculted solubility curve, with contours of wter ctivity superimposed, is shown in Figure (NH 4 ) 2 SO 4 -NH 4 Cl-H 2 O. Dt for this system consist of solubilities of (NH 4 ) 2 SO 4(cr) nd NH 4 Cl (cr), nd sources re listed in Tble 10. The mesurements were used to determine vlues of Q 1,SO4 Cl NH4 nd U SO4 Cl NH4, nd the result of the fit is shown in Figure 35. Clculted solubilities, together with contours of wter ctivity, re shown in Figure 14.

10 Thermodynmic Model of H + -NH 4 + -N + -SO NO 3 - -Cl - -H 2 O J. Phys. Chem. A, Vol. 102, No. 12, Figure 13. Phse digrm of HCl-NCl-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubility of NCl in HCl (q); contours, equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. TABLE 10: Sources of Activity Dt t K for (NH 4 ) 2 SO 4 -NH 4 Cl-H 2 O Solutions m min mx used b dt type c source yes sol Silcock d yes sol Hill nd Loucks 85 Totl mollity (m(nh 4) 2SO 4 + mnh 4Cl). b Used in the fit of the model. c Type of mesurement: sol, slt solubility. d A single mesurement of simultneous sturtion with respect to both solid phses. Figure 14. Phse digrm of (NH 4) 2SO 4-NH 4Cl-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) (NH 4) 2SO 4(cr); (2) NH 4- Cl (cr). Contours: equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. TABLE 11: Sources of Activity Dt t K for NH 4 NO 3 -NH 4 Cl-H 2 O Solutions m min mx used b dt type c source yes sol Silcock no edb Ling nd Chn (unpublished) Totl mollity (mnh 4NO 3 + mnh 4Cl). b Used in the fit of the model. c Type of mesurement: sol, slt solubility; edb, electrodynmic blnce mesurements of the wter ctivity/concentrtion reltionship for supersturted solutions NH 4 NO 3 -NH 4 Cl-H 2 O. The vilble dt for this system, Tble 11, comprise solubilities of NH 4 NO 3(cr) nd NH 4 - Cl (cr) nd unpublished edb mesurements of wter ctivities for very concentrted solutions (which re not used in this model). Mesured nd fitted slt solubilities re shown in Figure 36, with clculted contours of wter ctivity superimposed. Note tht, when the model prmeters were determined, the ctivity product of NH 4 NO 3(cr) ws djusted to the mesured solubility for pure queous NH 4 NO 3 shown in Figure 36 in order to void Figure 15. Phse digrm of NH 4NO 3-NH 4Cl-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) NH 4Cl (cr); (2) NH 4NO 3(cr). Contours: equilibrium wter ctivities, with vlues s mrked (nd dotted for supersturted solutions). TABLE 12: Sources of Activity Dt t K for (NH 4 ) 2 SO 4 -N 2 SO 4 -H 2 O Solutions m min mx used b dt type c source yes sol Silcock yes sol Sborgi et l yes sol Filippov et l yes φ Filippov et l no φ Kotlyr-Shpirov nd Kirgintsev no edb d Tng 96 Totl mollity (m(nh 4) 2SO 4 + mn 2SO 4). b Used in the fit of the model. c Type of mesurement: sol, slt solubility; φ, isopiestic mesurement of wter ctivity; edb, electrodynmic blnce mesurements of the wter ctivity/concentrtion reltionship for supersturted solutions. d Presented s fitted equtions. bis in the result. This solubility (26.22 mol kg -1 ) is slightly lower thn found in other studies (see Figure 40 nd lso pper 1) nd greter thn the vlue used to determine the equilibrium constnt in Tble 3 (26.79 mol kg -1 ). The clculted solubility curve nd equilibrium wter ctivities re shown in Figure (NH 4 ) 2 SO 4 -N 2 SO 4 -H 2 O. Tble 12 lists sources of ctivity dt for this system, which include osmotic coefficients, solubilities of (NH 4 ) 2 SO 4(cr),N 2 SO 4(cr), nd the double slt (NH 4 ) 2 SO 4 N 2 SO 4 4H 2 O (cr), nd edb mesurements for supersturted solutions (not used for the present model). The results of the fit re shown in Figures 37 nd 38, with good greement between the model nd both types of dt. An ctivity product ( x K S ) of for the double slt ws determined in the fit. The clculted solubility curve, with wter ctivities superimposed, is shown in Figure NH 4 NO 3 -NNO 3 -H 2 O. Osmotic coefficients nd NH 4 NO 3(cr) nd NNO 3(cr) solubilities hve been determined for this system; see Tble 13. Bergmn nd Shulyk 45 nd Timoshenko 46 hve found double slt, NH 4 NO 3 2NNO 3(cr), which occurs in solutions concentrted with respect to both NH 4 - NO 3 nd NNO 3. However, this phse ws not noted in either of the vpor pressure studies listed in Tble 13, nor does it pper to hve been found t other tempertures except by Bergmn nd Shulyk. 45 In the principl fit of the model, on the bsis of the osmotic coefficients of Kirgintsev nd Lukynov 47 nd slt solubilities, we hve ssumed tht the doubleslt compositions re in fct NNO 3(cr) (see Figures 39 nd 40). However, the possibility remins tht the double slt is metstble or even stble solid phse, nd the fit hs therefore been repeted nd the ctivity product of NH 4 NO 3 2NNO 3(cr)

11 2164 J. Phys. Chem. A, Vol. 102, No. 12, 1998 Clegg et l. Figure 16. Phse digrm of (NH 4) 2SO 4-N 2SO 4-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) N 2SO 4 10H 2O (cr); (2) N 2SO 4 (NH 4) 2SO 4 4H 2O (cr); (3) (NH 4) 2SO 4(cr). Contours: equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. TABLE 13: Sources of Activity Dt t K for NH 4 NO 3 -NNO 3 -H 2 O Solutions m min mx used b dt type c source yes sol Silcock yes d sol Bergmn nd Shulyk no e sol Shpunt yes f sol Timoshenko yes φ Kirgintsev nd Lukynov no edb Ling nd Chn (unpublished) st. g no ph 2O Dingemns nd Dijkgrf 48 st. g no ph 2O Prideux 49 Totl mollity (mnh 4NO 3 + mnno 3). b Used in the fit of the model. c Type of mesurement: sol, slt solubility; φ, isopiestic mesurement of wter ctivity; edb, electrodynmic blnce mesurements of the wter ctivity/concentrtion reltionship for supersturted solutions; ph 2O, equilibrium wter prtil pressure. d The double slt tht hs been found by some workers (including Bergmn nd Shulyk) ws ssumed to be NNO 3(cr) in the principl fit of the model. e Only single mesurement t K. f Only two compositions listed, double-slt found. g An queous solution simultneously sturted with respect to NNO 3(cr) nd NH 4NO 3(cr). TABLE 14: Sources of Activity Dt t K for NH 4 Cl-NCl-H 2 O Solutions m min mx used b dt type c source yes sol Silcock d yes sol Sborgi nd Frnco yes φ Kirgintsev nd Lukynov yes φ Med et l. 89 Totl mollity (mnh 4Cl + mncl). b Used in the fit of the model. c Type of mesurement: sol, slt solubility; φ, isopiestic mesurement of wter ctivity. d A single mesurement of simultneous sturtion with respect to both solid phses. Figure 18. Phse digrm of NH 4Cl-NCl-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) NCl (cr); (2) NH 4Cl (cr). Contours: equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. Figure 19. Phse digrm of N 2SO 4-NNO 3-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) NNO 3(cr); (2) NNO 3 N 2- SO 4 H 2O (cr); (3) N 2SO 4(cr); (4) N 2SO 4 10H 2O (cr). Contours: equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. Figure 17. Phse digrm of NH 4NO 3-NNO 3-H 2O t K nd equilibrium wter ctivities for both substurted nd supersturted solutions. Compositions re given s mollities. Lines: solid (hevy), solubilities of the following solid phses: (1) NNO 3(cr), (2) NH 4NO 3(cr); dotted (hevy), (3) 2NNO 3 NH 4NO 3(cr). Contours: equilibrium wter ctivities, with vlues s mrked. Contours re dotted for supersturted solutions. determined. The solubility curve for NH 4 NO 3 2NNO 3(cr) is lso shown in Figure 40, nd there is, for this cse, improved greement between the mesurements nd fitted solubilities nd lso the osmotic coefficients (not shown). However, the equilibrium prtil pressures of wter over solutions stted s being sturted with respect to both NH 4 NO 3(cr) nd NNO 3(cr) (Tble 13) re more consistent with these two slts being the equilibrium solid phses. The model yields 1 ) (equivlent to prtil pressure of mmhg) for solution sturted with respect to NH 4 NO 3(cr) nd NNO 3(cr), compred with mesured vlues of 11.7 mmhg 48 nd 11.6 mmhg. 49 For solutions sturted with respect to NH 4 NO 3(cr) nd NH 4 NO 3 2NNO 3(cr) the clculted equilibrium prtil pressure of wter would be higher, becuse of the lower totl concentrtion of slts in the queous phse. The model prmeters obtined in the principl model fit re listed in Tble 2, nd those obtined for the cse of double-slt formtion given in the notes to Tble 3. Figure 17 shows the clculted solubility curves for the system, with wter ctivities superimposed. Here the scle for NNO 3(q) is extended, s the