Solubility of Volatile Electrolytes in Multicomponent Solutions with

Chapter 5

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on February 28, 2016 | http://pubs.acs.org Publication Date: December 7, 1990 | doi: 10.1021/bk-1990-0416.ch005

Solubility of Volatile Electrolytes in Multicomponent Solutions with Atmospheric Applications 1

2

Simon L. Clegg and Peter Brimblecombe 1

Plymouth Marine Laboratory, Citadel Hill, Plymouth PL1 2PB, United Kingdom School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, United Kingdom

2

Thermodynamic Henry's law constants are given for the strong acids HNO , HCl, HBr and HI (KH/mol kg atm ), and for weak electrolytes HF, HCOOH, CH3COOH and N H (K' /mol kg atm ) from 0 - 40°C. Use of the Pitzer thermodynamic model for the calculation of gas solubilities is evaluated, contrasting the behavior of HCl with new work on NH (as an example of a weak electrolyte). Agreement between measurements and model calculations is good for both gases. The effects of dissolved salts, association equilibria, and temperature variations on gas partial pressure are illustrated. The incorporation of non-electrolytes into the model and the estimation of salt effects on neutral species are briefly discussed. 3

2

-2

-1

-1

3

-1

H

3

To calculate gas solubility in natural geochemical systems, basic thermodynamic properties such as the Henry's law constant and, in the case of weak electrolytes the dissociation constant, must be combined with a thermodynamic model of aqueous solution behavior. An analogous approach has been used to predict mineral solubilities in concentrated brines (1). Such systems are also relevant to the atmosphere where very concentrated solutions occur as micrometer sized aerosol particles and droplets, which contain very small amounts of water relative to the surrounding gas phase. The ambient relative humidity (RH) controls solute concentrations in the droplets, which will be very dilute near 100% RH, but become supersaturated with respect to soluble constituents (such as NaCl) below about 75% RH. The chemistry of the aerosol is complicated by the non-ideality inherent in concentrated electrolyte solutions. THEORY

The equilibrium of a strong acid HX between aqueous and gas phases is represented by: HX( ) = H g

2

+ ( a q )

- 2

+X-

( a q )

,

2

K = mH+ mX" y± /pHX

(1)

H

1

where K H (mol k g atnr ) is the thermodynamic Henry's law constant, prefix 'm' represents molality, y± is the stoichiometric mean activity coefficient of H and X" ions in solution and pHX the equilibrium partial pressure of HX. While the undissociated acid molecule must exist in solution, the equilibrium is expressed in the form of Equation 1 in order to be consistent with the thermodynamic convention of treating all strong electrolytes as completely dissociated (2). A different treatment of the solubility of weak electrolytes is required, where two clearly separable reactions are involved: +

0097-6156/90/0416-0058$06.00/0 c 1990 American Chemical Society

In Chemical Modeling of Aqueous Systems II; Melchior, Daniel C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

5.

C L E G G & BRIMBLECOMBE HY(g) = H Y HY

( a q )

= H+

( a q )

,

(aq)

59

Solubility of Volatile Electrolytes

K ' H = THY mHY/pHY +Y-

( a q )

(2)

2

,

Kdiss = y± mH+ m Y ' / Y H Y mHY

(3)

where y± is the mean activity coefficient of the/ree aqueous ions and Y H Y that of the neutral molecule. Here the overall reaction is represented by a Henry's law constant ( K ' H / mol k g atnr ), which describes the equilibrium between the gas phase weak electrolyte and aqueous neutral molecule, and a dissociation constant Kdj (mol kg ). Note that we adhere to the convention of using the 'atmosphere' as the unit of pressure (for conversion to S.I. units, atm = 101325 Pa), and also that K H is equivalent to K'nKdiss where the dissociation reaction is considered separately from that of dissolution. The term 'thermodynamic Henry's law constant' is used to distinguish K H and K ' H from the purely empirical constants that are often employed Q). Strictly, gas phase concentrations should be expressed as fugacities. However, for the range of conditions encountered in the earth's atmosphere, deviations from ideal behavior in the gas phase are not significant. Partial pressures are therefore used throughout. To calculate the partial pressures of volatile electrolytes above solutions of known composition, values of the activity coefficients of the dissolved components are needed in addition to the appropriate Henry's law constants. In this work activity coefficients are calculated using the ioninteraction model of Pitzer (4). While originally formulated to describe the behavior of strong electrolytes, it is readily combined with explicit recognition of association equilibria (1,5), and may be extended to include neutral solutes (4,©. The model has previously been used to describe vapor-liquid equilibria in systems of chiefly industrial interest (7). In Pitzer's model the Gibbs excess free energy of a mixed electrolyte solution and the derived properties, osmotic and mean activity coefficients, are represented by a virial expansion of terms in concentration. A number of summaries of the model are available (1,4,&). The equations for the osmotic coefficient ((j)), and activity coefficients (y) of cation (M), anion (X) and neutral species (N) are given below: 1

1

-1


ss

(

(•-i) =

/ 2

AV 2>. l o 7 7 w r ? ? ^ " 2

-

m

+ 11 c and those for anions, contain parameters (0 - and 0 -) for interactions between ions of like sign and an unsymmetrical mixing term. The parameters \ | / ' and Ycaa account for interactions between one ion of one sign, and two dissimilar ions of opposite sign. Double summation indices c7 mol k g ) , there may be considerable errors at lower concentrations. The thermodynamically calculated value of 7.06x10 mol kg" atnr may therefore be preferred for such systems, particularly if the activity coefficients of Macaskill and Bates (17) are used. Similar considerations apply to H N O 3 . Recently Tang et al. (24) have made P H 2 O and P H N O 3 measurements at 25°C and have used these to derive activity coefficients which differ from those of Hamer and Wu (14). These were used, together with other published partial pressure data, to calculate K H equal to 2.66xl0 m o ^ k g ^ a t m . This is greater than the value derived by Brimblecombe and Clegg (19) by approximately one standard deviation. The Henry's law constant of Tang et al. (24) should only be used with the set of corresponding activity coefficients. In terms of absolute accuracy (predicting P H N O 3 ) there appears to be little to choose between the two studies. However, work in progress by the authors using mole fraction based activity coefficient models of Pitzer (25), shows that at concentrations >10 mol k g there are systematic errors in the mean osmotic and activity coefficients derived by both Hamer and Wu Q4) and Tang et al. (24). This is largely due to the nature of the fitting equations used (extended polynomials in molality), and results in a poorer correlation of the data at high concentrations than might otherwise be achieved. 9

1

s

2

2

6

1

1

-1

W E A K E L E C T R O L Y T E S . The Henry's law constants of these solutes (Table II) have been estimated in the same way as those of the strong acids, relying mainly upon partial pressure data.


5.

C L E G G & BRIMBLECOMBE

63



Dissociation is slight at the aqueous concentrations for which partial pressures have been measured, and where it has been calculated, a simple Debye-Huckel expression was used to obtain ion activity coefficients. Formic and Acetic Acids. The solubility equilibrium of these weak acids js treated as the two stage process described by Equations 2 & 3. The dissociation constants of both acids are well known and are given as functions of temperature in Table III. While there are several studies of the thermodynamics of aqueous acetic acid, e.g. (2£), and of formic acid (27), there are relatively few data for dilute aqueous solutions at 25°C (28-31). The chemistry of these acids is complicated by dimerisation Qi-22) and higher association reactions Q4) in both aqueous and gas phases. Using an aqueous phase dimerisation constant of 0.149 kg mol" Q2), a gas phase constant of 1.26xl0 atm Q l ) , and assuming unit activity coefficients for uncharged species the quotient mCH3COOH/pCH3COOH was calculated at 25°C for available partial pressure data, see Figure 1. At low aqueous phase concentrations values decrease sharply. Extrapolating the higher concentration data back to zero yields K ' H for C H 3 C O O H of 5.24xl0 mol kg" atm , lower than that calculated from thermodynamic data (8.6xl0 ) (22). Note that the vapor phase dimerisation constant of Chao and Zwolinski (25) is greater than that obtained by earlier workers. Use of a value of 0.000484 atm" (2£) yields K ' H equal to 5.8xl0 mol kg" atm at 25°C. The temperature variation of K ' H was estimated using Equation 9 and published enthalpies (22) and heat capacities (2236). 1

3

-1

3

1

-1

3

1

3

1

-1

Table III. Dissociation Constants of Weak Electrolytes from 0 - 40°C, given by: (Kdiss) = a + b/T + cT where T/Kelvin. ln

Species HF

4

6.71xl0" 1.774xl0" 1.772xl0" 1.754xl0"

5

NH3

HCOOH

4

5

CH3COOH

Ref.

a

b

c

-12.535 16.9732 13.2948 7.4850

1558.334 -4411.025 -3258.651 -2724.347

0 -0.0440 -0.03691 -0.03118

Kdiss(25°)

0

(11,12) OS) 09) (4Q)

(a) Hamer and Wu (H) adopt a value of 0.000684 at 25°C, as did the authors in recent calculations of HF solubility (41).

1

For formic acid an aqueous phase dimerisation constant of 0.00775 kg mol" (32), and a gas phase value of 345.0 atm" (33) were used together with three partial pressure measurements (29) to estimate a K ' H of 5.2xl0 mol kg" atm at 25°C, Table II. While the data are scattered, this estimate is in good agreement with the thermodynamically calculated value. It should be noted that the treatment presented here is not exhaustive, and data for very high aqueous phase concentrations and/or high temperatures have not been included. 1

3

1

-1

Ammonia. The solubility of N H 3 is described in two stages, as dissolution (Equation 2) followed by base dissociation: +

NH (aq) + H 0 = NH4 (aq) + O H " 3

2

( a q )

(10)

Henry's law constants of N H 3 are readily available over a range of temperatures (6,7), so partial pressure data were used to evaluate YNH3 and the neutral interaction parameters from 0° to 40°C. Fits were restricted to mNH3 proposed by Felmy and Weare (9). If individual ion molalities are used in place of salt concentration we then obtain: m

2

(YNH3) = 2mNH3^NN + 3mNH3 |iNNN + 2mM A N M + 2mX + 6mNH (mM }1NNM +

M

X

3


where:

1 2

M-NNX) + mM mX £ N M X

( )

CNMX = 6 ^ N M X + 3(IZXI/ZM)M-NMM + 3(ZM/IZXDM-NXX

and z[ is the charge on ion T. If the triplet parameters in Equations 11 & 12 are neglected, then the similarity to the various formulations of the empirical Setchenow equation (48) becomes clear, there being only a self interaction term (ANN) and salting coefficient (V+ANM + V-ANX)Where the neutral species is present at sufficiently high concentration, its influence on the activity coefficients of dissolved salts and the osmotic coefficient of the solution must be considered. The equation for the mean activity coefficient of salt M X . dissolved in an aqueous solution containing N H 3 (and neglecting dissociation) is given by: a

v +

v

2

vln(y ) = {ion terms) + 2mNH (v A M + V.ANX) + 3mNH (v |iNNM + v.p-NNX) ±

3

+

N

3

2

+

2

+ 6 m N H . m M X . ( v | i N M M + 2v+v_fl MX + v . ^ N X X ) 3

v+

v

+

(13)

N

where the bracketed 'ion terms' are the appropriate multiples of the summations for charged species given in Equations 5 & 6. The constraint of electrical neutrality means that only the parameter sums bracketed together in Equations 11-13 are observable. In order to assign values to individual parameters for N H 3 interactions we have set A N , O and M-N,N,C1 to zero. Although the choice of convention does not affect calculated values of YNH3 ion activity coefficients, inconsistencies could arise when estimating conventional single ion activity coefficients using neutral-ion parameters from different sources. For example Harvie et al. (I) set Aco2,H equal to zero in their investigations of the carbonate system. Ion-NH3 parameters of geochemical interest determined by the authors are listed in Table IV. First derivatives of A M with respect to temperature at 25°C are also given for a few ions. Some parameters, in particular those of the alkaline earths, are subject to considerable uncertainty. Further details are given in the original text (©. Triplet parameters listed in Table IV are chiefly of the form M-NNi (where i is an ion). Because of the high degree of separation of ions of like sign, it was thought that triplet parameters involving two such ions would be negligible and could be set to zero. Hence the final term in Equations 11 & 13 involves only M-NMX- There is some observational justification for this assumption. When fitting solubilities of NaCl and KC1 in the systems Na/Ca/Cl/NH3/H20 and K/Ca/Cl/NH3/H20, it was found that the only additional term required (to those determined in systems not containing C a ) was JiN,Ca,Cl- Its value was found to be the same in both cases, implying that the parameters |iN,Na,Ca and M-N,K,Ca ere either very similar or negligible. In general the term JiNMX s rarely required for N H 3 . The N H 3 - ion interaction parameters listed in Table IV have been obtained from a variety of different data types. Do the results form a coherent whole? In Figure 2 all the available experimental data for KCI/NH3 aqueous solutions at 25°C are compared in terms of the quantity mK AN,K, obtained by the manipulation of the appropriate equations for partial pressure (PNH3 data), activity (aqueous phase partitioning data) and activity product (KC1 solubility data). While there is some scatter, particularly at low salt concentrations, agreement in terms of A N , K (slope) is generally good. There is also consistency in |IN,N,K> since the value of this parameter, found to be necessary for the Baldi and Specchia P N H 3 data (49) in Figure 2, was obtained from salt solubility measurements (6). These results confirm the utility of the approach adopted here. More importantly, they illustrate the advantage of a thermodynamically based model, when treating different aspects of the system properties, over the purely empirical expressions that are often used. o r

m

e

a

n

2+

w

w a

+



66

CHEMICAL MODELING O F AQUEOUS SYSTEMS II

Figure 1. The quotient mCH COOH/pCH COOH calculated using partial pressure data from the following sources: dots - Fredenhagen and Liebster (2&); triangles - Kaye and Parks (29); squares Campbell et al. Ql); open diamonds - Zarakhani and Vorob'eva (5Z); closed diamond - Wolfenden 3

3

(20).

Figure 2. Comparison of the salt effect of KC1 on N H obtained from different data sets at 25°C: circle - H 0 / C H C 1 partitioning data Q&); open diamonds - KC1 solubility in N H ) (59); closed diamonds p N H (60); dots - p N H (56); triangles - p N H for systems containing >10 mol k g N H (42), and including M-N,N,K Equation 11; small open triangles - as previous data set but neglecting MN,N,Kslope of the full line is equal to 0.0454 (Table IV). The influence of M-N,N,K significant only for pNH data (4°0, and salt solubility data (59). 3

2

3

3 ( a q

3

3

1

3

m

3

w

a

s

3


5.

CLEGG & BRIMBLECOMBE


67

TABLE IV. Interaction parameters for N H (N) at 25°C (6) 3

Species i

M-N,N,i

"NH Ug *Ca ^a^ d+ *NH4

_

3

b

1+

2+


K

+

0.01472 -0.21 -0.081 0.0175 0.0454 0.0

Species i

wsr,N,i 0.0 -0.000437 0.000625

0.091 0.0 -0.022 -0.051 0.103 -0.01 0.140 0.180

F" ciBr r OHN03" /so C0 "

-0.000311 -0.000321 -0.00075

2

4

2

3

(a) Temperature variation over the range 0 - 40°C given by the equation: A = 0.033161 - 21.12816/T + 4665.1461/T where T/K. (b) Derived from single data point only. (c) Partial pressure and solubility data suggest Ajsr.Na is equal to about 0.031. (d) 3AN,K/

Solubility of Volatile Electrolytes in Multicomponent Solutions with

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