solid-liquid equilibria in concentrated aqueous salt solutions—systems with a common ion

Desalina!ion. 15 ( 1974) 225-24 I @ Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

SOLID-LIQUID EQUILIBRIA IN CONCENTRATED AQUEOUS SALT

SOLUTIONS - SYSTEMS WITH A COMMON ION

RICARDO VEGA ASP EDWARD W. FUNK*

Uniwrsidad Ttknica dri Ertudo. Santiago (Chile)

(Received May 17, 1974: in rwiscd form July 5. 19’1)

A thermod.namic correlation is presented for solid-liquid equilibtia in

concentrated aqueous salt systems containing a common ion. It is assumed that

no solid solutions are formed. although the solid phase can be a pure salt. a

multiple salt or a hydrate. Predictions of solid-liquid equilibria in multicomponent

systems are made using parameters calculated from solid-liquid equilibrium data

for the constituent binary and ternary systems.

Parameters tire given for the prediction of solid-liquid equilibria in the

aqueous system containing Na’, K -. MgC &. N03-, Cl-, SO,- - from O-50°C.

These parameters correlate the available solid-liquid equilibrium data for ternary

systems with an error in liquid-phase composition of less than 2 grams salt/100

grams H,O. Errors are similar in the estimation of solid-liquid equilibria in four-

component systems such as NaNO,-NaCl-Na,SO1-H,0.

SYMBOIS

a -

A,, Aji -

A,B,C,D -

f: fT -

activity

salt-salt interaction parameters used to calculate activity co-

efficients in ternary solution empirical constants used in Tables I to IV fugacity of pure solid i

standard-state fusacity for activity coefficient of salt i in aqueous solution Henry’s constant

Solubility product for double saIt ij

Solubility product for hydrate of salt i

molality

temperature

l Corporate Research Laboratory. Exxon Research and Engineering, Linden, NJ. 07036. U.S.A.

226 R. VEGA AND E. W. FUNK

- mole fraction of salt i calculated as though the salt did not

dissociate - mole fraction of salt i at saturation in binary system - fraction of tota salt in solution existing as i - mean ionic activity coefficient

- activity coefficient of salt i alone in solution (see Eq. 4) - activity coefficient of salt i in multicomponent solution - activity coetficient of water in solution with salt i

- activity coefficient of \\ater in ternary solution of salts i and j - chemical potential

ISTROIiUCTlON

Solid-liquid equilibrium data for aqueous salt solutions are necessary for

the design of crystaihzation processes and equipment for the treatment of sea \vater and metallurgical \\astes. There are numerous solid-liquid equilibrium data (I.?) for binary and ternary aqueous salt systems. However. there are few data for

the multicomponent systems of industrial interest. The six-component aqueous salt system containing the ions Na’. K’,

Mg’-. NO;.CI-,andSO;-‘- f’ d IS o In ustrial interest in the production of commer-

cial salts. This is the basic system considered in the production of Chilean nitrate. Van3 Hoff (3) began the experimental study of the solid-liquid equihbria in this

system and numerous \\orkers (4, 5, 6) have continued the study. Nevertheless, solid-liquid equilibrium data are still only partially complete. Estimates of the equilibria in this system are often required for the rational design of leaching and crystallization processes.

We present in this paper a general thermodynamic correlation for solid- liquid equilibria in aqueous salt systems; as an example, the correlation has been applied to the system described above. The idea of the correlation is to consider the salts themselves as the components. This approach appears reasonable since we are considering phase equilibria involving macroscopically neutral salts, and not transport phenomena which depend upon the actual ionic components. Once the neutral salts are considered as the components. solid-liquid equilibria in aqueous salt systems become similar to multicomponent phase equilibria involving nonelectrolytes. Hence, it is possible that phase equilibria for multicomponent aqueous salt systems can be predicted from phase-equilibrium data for the constituent binary and ternary systems; much progress toward this goal has already been made for nonelectrolyte systems. The present correlation uses a simple model from nonelectrolyte solution theory to predict solid-liquid equilibria in the common-ion systems, for example, NaCI-KCI-M&I,-HzO.

The derived phase-equilibrium relations are limited to systems that do not

SOLID-LIQUID EQUILIRRIA 227

form solid solutions, although the salt may appear in the solid phase as a pure salt, multiple salt, or hydrate. Equations and tables of required parameters are presented u hich allow the estimation of solid-liquid equilibria from 0 to 50% for the common-ion subsystems of the six-component system described above.

The correlation is presently limited to those systems which contain a common ion. Extension to systems without a common ion is difficult. As an example, consider the four-component system having the ions Na’. Kf. Cl-. and NO; in aqueous solution. This is a simple reciprocal salt system since the four pure salts only exist ns the solid phases: there are no multiple salts or hydrates. The system is often represented by the metathesis reaction

NaCI + KN03 = NaNO, + KCI

and can be completely described in terms of the three salts. Therefore. the salt components can not be selected in an unambiguous manner. Also it is possible to choose NaCI. NaNO, and KNO, as the components for ;L par!icular solution composition which has KCI appearing as a solid phase. Difficulties are still greater in other systems where the total molality can depend upon the choice of components. Probably the best approach for these systems is lo introduce an equilibrium constant for the metathesis reaction, through which all four salts are included.

However, for immediate application, there are many systems of practical interest which can be considered as common-ion systems. Also, development of new computer-design methods for crystallization processes can effectively use a simple analytical correlation of solid-hquid equilibria_

THERMODYNAMICS OF SOLID-LIQUID EQUILIBRI4

Experimental evidence indicates that for the six-component system of

interest, no solid solutions are formed. Therefore. phase-equilibrium relations are required only for the solid phase as a pure salt, a multiple salt, or a hydrate.

The equilibrium relation can be expressed in terms of the solubility product for each of the three types of solid-liquid equilibria. With a pure salt, for example NaN03. as the solid phase the equation of equilibrium is

where& is the fugacity of pure sodium nitrate, s, the liquid-phase mole fraction of sodium nitrate, Tz the liquid-phase activity coefficient of the salt and fi the

standard-state fugacity for the activity coefficient. The ratio of fugacities, f;/’ can be considered the solubility product for sodium nitrate and is a function of the temperature, but not the liquid-phase composition.

With the solid phase a multiple salt, agin the equilibrium is conveniently

22s R VEGA ASD E. W. EUNK

expressed using the solubihty product. For darapskite (NaNO, - NazSO,) as the solid phase, the solubihty product is:

Kto = x,x,rJ* (2)

where subscript 2 refers to sodium nitrate and 4 to sodium sulfate. The equiLibrium relation for a hydrate as the soiid phase is similat to &at

for the multiple salt. For example, the solubihty product for Glnuber’s Salt fNa,SO, - 10H20) as the solid phase can be expressed

K14 = 10

a-4r1 (3)

?vhere rr is the activity coefficient of water. Eq. 3 is only an approximate expression and is discussed in the Appendix.

The solubility product K, -s is not rigorously independent of the solution composi-

tion; however, for practical purposes, K14 is assumed to be a function only of the temperature.

Eqs 1 to 3 show *hat the principal problem in the description of solid-

liquid equilibria is the estimation of activity coeKcients in highly concentrated aqueous salt solutions.

LIQUID-PHME ACnVlTY COEFFIClEhXS

Solid-liquid equilibrium calculations based on Eqs. I to 3 require estimates of the activity coefficients of salts near or at saturation; never are required the activity coefficients of salts in dilute solutions. Since we are only interested in the concentrated region, it is not convenient to use the activity coefficients defined in terms of the ionic components. These ionic components are very useful in the Debye-Hiickel theory and in the description of transport phenomena, however do not aid in the analysis of sohd-liquid equilibria in aqueous salt systems. Instead, the activity coefficient of the salt is defined directly in terms of the salt concentra-

tion.

The activity coefficient of the salt is thus defined as though it were a nonelectrolyte. This new activity coefficient can be related to the conventional mean ionic activity coefficient y& by equating expressions for the liquid-phase fugacity written in terms of each of the activity coefficients. For NaNO,, the relation between the activity coefficients is

(4)

when:

r~31.0 aS Xi+XT (5)

The molality of NaNOs is m, and the standard state for yA is I-I, Henry’s

SOLID-LIQUID EQUILIRRIA 229

constant. Lewis .md Randall (7) discuss expressions for the right-hand side of

Eq. 4 \vith salts of more complex charge type. The activity coefftcient of the salt

alone in aqueous solution, i-p. is normalized such that it becomes unity at _I-;.

the mole fraction of the salt at saturation in the binary solution. Thus, the activity

coefficient of N,tNO, is unity at a molality of 10.8 for the NaNO,-H,O system

31 25-c.

The standard state of the salt at saturrition has the conceptual advantage

that no salt entering into solid-iiquid equilibrium calculations is far from its

standard state. and the xtivity coefiicients are neclr unity and easily interpretable.

There are also two practical advantages to the standard state at saturation. First.

In 7r rerws composition is usu~llly a highly nonlinear function: it is dilhcult to

tit analytically. However. lnfP WTSIIS mole fraction of salt can easily be fit from

low concentration up to baturation. Second. normalizing the activity coe%cients

at s,tturation ailo\\s the calculation of solubility products using only solubility

d<tta.

The utrlity of the standard state for a s.dt ai saturation has been previously

discussed b> M~hccvtc (8) who gives several e\dmples of it apphcation. Also, the

prcscnt author (9) h,tb used this stand,ud stdte in the treatment of vapor-liquid

equilibria in the NaCl-HCI-H,O system.

Table I gives an equation and the required constants for the calculation of

the saturation mole fraction _I-: for each of the nine salts that comprise the qstem of interest. For those salts of Table I that appear in the solid phase as a pure salt.

the mole fraction at saturatton is equal to the solubility product defined by Eq.

I due to the normalizztlon of the activity coefficient_ Therefore_ the equation

of Table I serves to calculate both the saturation mole fraction and the solubility

product. Fig. I shows that these solubility products are linear functions of the

temperature.

Data for ;‘* at 25°C as a function of molality (10-12) were used with Eqs.

4 and 5 to calculate rg as a function of mole fraction. Fig. Z sho\\s In rq as a

function of _I-;-s, for several salts of interest. Near saturation InI-: is a linear

function of x1 -xi and for some salts, such as MgCI,. it is a linear function from

dilute solution up to the saturation point. The activity coefficient l-g for each of

the nine salts alone in aqueous solution can be described usins the empirical

equation

In l-p = A(xt - Xi) + B exp [C(O - Si)]

where ii, B. C. D are empirical constants fit such that the second term would only

be important at low salt concentrations. Table IL gives the constants of Eq. 6.


TARLE 1

PARAMETERS FOR THE CALCULAllOX OF THE SATURATIOS MOLE FRACTIOV OF SALTS IS DISARY

AQUEOUS SYXF.MS

XL’ = A + B(fjl0) A C(r;lo)‘. t. “C

_.__._-_ ___.- -.---.. ._. --. ---_-.-._. _..._ -._. .~.__.______ --__

Solid phase A B c -- - ---- .-- - _ .- ..-_. .-. .._ _._ . .- - -. ._. . . _ __-_ __

1 NaCl 0.0990 0.000’8 - 1 NaNO? 0. I337 0.01 I44 - 3 NaTSOa* 0.0627 -0.0012 -

4 KCI 0.0625 0.0066 - 5 KNOX 0.0232 0.0119 0.00155 6 KzSOi 0.0075 0.0019 - 7 MgCIz .6H10 0.0909 0.OtX-I - 8 Mg(NO&. .6H20 0.0715 0.0036 -

9 MgSOa - 7H:O 0.0380 0.0062 -

l These constant5 express the solubility of the pure salt and are based on cvrapolated values of the solubility below 31.5X.

I

R3. 1. Solubility product as function of temperature for pure salts and hydrates.

SOLID-LIQUID EQUlLll3HlA 231

tn r:

Fig 2. Activity coctlicisnts of aIts ils a function of composition for hinary aqueous salt solutions.

TABLE II

PARAWXERS FOR THE C4LCUt.ATIOL OF ACTtVtTY COEFFtClthTS 13, Bl?cARY 4QUEOUS SALT

!iOLunOhS

InI’,0 I= A(xP - A-I) T Bcxp[C(D--x,1]

Sah

1 NaCl 2 NaNOa 3 Na!sOa 4 KC1 5 KNOJ 6 KzS0.a 7 ,U&CI, 8 MdNO& 9 MgsOl

.4 --___ .--_ -_ -_ ._-..

- 30.25 - 4.88 - 13.85 - ! 7.42

5.85 - 88.5’ -200.00 - 140.00 - 49.15

_.--. --- _- B

- --.__..-

-0.0436 -00310

00 -0.0375 -0.0363

0.0

-z !i86 0:088s

C - -.--___-.

50.0 so.0 0.0

100.0 100.0

0.0 0.0

50.0 100.0

D -.-- -..-- .._._ ,___

0.0594 0.0850 0.0 0.0125 0.04'1 0.0

E47 0:03 14

___. ---__


Deviations of calculated from experlmental activity coefficients are only significant at low salt concentrations.

Eq. 6 and the Gibbs-Duhem equation can bc used to calculate ry,,,. the activity coefficient of water, for each of the binary systems. For a binar) aqueous salt solution. the Gibbs-Duhcm equation is written

where l-y,,, is normalized such that it becomes unity when the activity coefficient of the sait, l-y, is unity. ‘Fig. 3 shows the graphical integration of Eq. 7 for the

!UaNO,-H,O system at 25T and also the approximate integration using values bf l-p calculated using only the first term of Eq. 6. The approximate integration gives exceilent values of I-:(,, at high salt concentrations with only moderate

20 I I 1 I 1 I

18 - i

16-

- e*ocrmental

14 - ------ CakUloted using

l2-

06-

04-

Fig. 3. Graphical calculation of the activity coeflicient of NaN03 for the system NaNOs- Hz0 at 25 ‘C.

!WLID-LIQUID EQUILIBRIA 233

t OO

I 1 I

004 008 012 016 ,

rdok fratm of Naq

3

Fis. 4. Calculated and eqxrimcnt~l achit> co&iitents of NaN03 at 0. 25 and 50°C for the system NaNOa-Hz0

deviations occurring at low concentritttons where the second term of Eq. 6 contrib- utes to l-7. Since Eq. 3 requires activity coeffkients of water at high salt concen- trdtions, these values ccin be accurately calculated by analytically integrating Eq. 7 using only the first term of Eq. 6. The result is

. In r~ci, = A (ST - Xi) + A In $ (8)

1

where X; is the mole fraction of water when salt i is at saturation in the binary

solution. Values of A are given in Table II. The parameters for the calculation of the activity coerticicnts have been

determined at 25°C; unfortunately. there are few experimental data for activity coefficients of salts in aqueous solution at temperatures removed from 25°C. For this correlation, the best procedure is to assume that the constants in Table II

are independent of temperature. This assumption has no justification, and errors

‘34 K. VEGA AND E. W. FUNK

in the estimated activity coeflicicnts must be absorbed in other parameters of the

correlation. Thus. with the parameters in Table II constant, the activity coeficicnts

changz with temperature due to the change in the saturation composition.

This method of estimating activity coefficients from 0-5O’C can be partially

tested using the vapor-pressure data for NablO,--H,O and NaCI-H20 (17).

Activity coelficients of water were calculated directly from the vapor-pressure data

and the Gibbs-Duhem equation \\;ts used to calculate the activity coefficients of

the salt. Fig. 4 shows the experimental and calculated activity coefficients of

NaNO, wrsus mole fraction of salt at 0. 3 and SO’C: Fig. 5 shows the activity

coeflicients of water at the same temperatures. Eqs 6 and S \\ere found to give reasonable estimates of the activity co-

efficients from 0-50-C for both the NaibO,-H,O and NaCI-Hz0 systems.

The proposed method of estimatin g the effect of temperature on the activity

coetlicients is not intended for quantitative application. Within the framwork of

Fig. 5. Calculated and experimental actkity coefficients of H?O at 0, 25 and 5O’C for the system NaNa-H=O.

SOLID-LIQUID EQUlLIi3RlA 235

the present correlation, errors in the estimates of the activity coefficients will be

absorbed in the interaction parameters and solubility products.

The solubility product for all the hydrates. except NalSO - 10HzO. is

equal to sr due to the normalization of the activity coefficients. This is the same

result as found for the solubility products of the pure salts. Fig. I shows that these

solubility products arc linear functions of temperature_

Sodium sulfate is the only one of the nine salts that exists in the solid phase

as both hydrate and pure salt. Since the activity coefficient of Na+O_, was normal

ized to be umty at the XI values of Table I for the pure salt, the activity,coefficients

in Eq. 3 will not be unity for the calculation of the solubility product of Na,SO, - IOH20. The necessar? activity coedicicnts were calculuted using Eqs. 6 and 8 and

the values of the solubility product are presented in Table IV.

ACTIVITY C0FFFlCIE~l-S Ih -I‘ERS-\RY SYSTEVS

For a ternary system of salts i and j. the follo\king semiempirical equations

are proposed to describe the activity coetticients

In r, = in 1-F + Ailsi (9)

In rj = In l-7 + Aj,Si (10)

(11)

where T,ci.lB is the activity coctficient of water in the ternary solution. The activity

coefficient ry,,, is calculated using Eq. 8 and the mole fraction of water and salt i

in the ternar! solution: the activity coefficient l-g is calculated using the mole

fraction of sait i in the ternary solution, not using the total salt mole fraction. The

fraction of total salt present as salt i is Y,. and the parameters rii,, Aji characterize the in:cractions between the two different salts.

The rp terms of Eqs. 9 and 10 express the excess Gibbs energy due to the

salts not being at their respective standard-state concentrations. The terms con-

taining the interaction parameters give the contribution to the excess Gibbs

eneqy due to interactions between salts i and j. Positive values of the interaction

parameters lead to an excess Gibbs energy greater than zero and decreased solubility

of the salts. Thus, the interaction parameters can be considered similar to the

salting-out parameters used in the study of the solubility of none!ectrolytes in

salt solutions_

Eq. I1 expresses the activity coetiicicnt of water using only data for the

binary systems. Therefore, it can not be expected to give precise estimates of the

activity coeffkient of water in the ternary system; errors in the activity coefficient

of water can, however, be absorbed in the interaction parameters. The standard-

‘36 R. VEGA 4hD E. W. f:USK

state fugacity for r,ci_i, changes with solution composition since the stmdard- state fugacity of water is different in each binary system. Numerical values nf the

standard-state fugacity of water are not required for the correlation; however,

it is rcasonablc to assume ii rcintion similar to Eq. I I for the composition depend-

ence of the standard-state fugacity.

Eqs. 9. IO and I I are based on a very simple model of concentrated salt

solutions. Nevertheless. the equations can be extended without further assumptions

to solutions containing more than two salts.

f)ATA REf~UCTIOh FOR TEREARY AQUEOUS SALT SYSTEMS

Solid-liquid equilibrium data for the IS termuy subsystems were used \\ith

Eqs. 1 and 3 to calculate the interaction parameters of Eqs. 9 and IO. The planes

of Figure 6 tllustmtc the types of ternary systems which were analyzed. In addition

to correhtting the solid-liquid equilibrium data for ternary systems. the calcuiatcd

Sfdr (i)-Sulf (j) ____-._. -. --__. -.-

f NaCf-NazSOa

2 NaCI-NaNOz 3 Na&Oa-NaN03

4 KCI-K&O I 5 KCI-KNOa 6 KzSOr-KNO 1 7 MgCl~Mg(N0s)z a MgClz-MgSO: 9 hlgSO+hlg(NO.,)z

10 NaCI-KCl 11 NaCI-MgCIz II KCI-MgCIz I3 NaNCh-KN03 I4 NaN03-Mg(NO& I5 KNO.s-Mg(NO& I6 KISOF-M~SO.I 17 NazSO s--MgSOa 18 Na&O I-KzSO~

_-_ d-1 4,

A -__. .

45 53

16.30 !5.30

(11.80 5’.‘3

Go 23.75

520 0 194.7

18.5 23.37 79.66 37.90

- 1.00 30.98 19.39

- 15.76 36.30

(_&IO

B __ -

0 37

-0.018 _-

-0.190)+ - - -

- ‘7.0

-0.58 - -

0.39 0.077

- - -

-0.477 -

I x0*

15.60 (14.70

14 00 12 35

45.48 6.41 6.36

~08.0 31.6

298.0 ‘0 22

160.10 I‘mo.0 - 0.45

80.7 101 0

38.0 6.90

-

ii --- - _._. ._ _._

0.0’ -- 0.21)*

- 0.078 -

- - -

0.73 -

-’ 4 85 -

44s -

0.014 -

- 0.56 -

0.43 -

.- T<Wp_

runsy .._.__

a-50 O--W O-50 O-50 O-50

25-50 O-15 o-25 O-50 o-15 %50 o-15 o-25 &‘5 O-50 o-25 o-15 O-50 o-so

-

O-50

* These interaction parameters must bc used with Na-SO . IOf-kO as the solid phase. They are not equal to those for Na~S0r as a solid due to the arbmary extrapolation of XP for NazSOa.

SOLID-LIQUID lQUILIBRIA 237

interaction parameters are useful for estimating solid-liquid equilibria in four nnd

ti~ecomponenl systems.

For ;i pure wit 2s the solid phase. the cxpcrimental activity coeflicient of

salt i is equal to the mole fraction of the salt :rt snturation in the binary solution.

XT_ divided by the mole fr,iction of the salt in the ternary solution. The inter,tztlon

parameter is then directly calculated usins Eqs. 6 and 9. Table III presents the

the intersction parsmeters cdculated from solid-liquid equilibrium d‘lta for pure

salts as the solid ph,w>. These parameters vxxe found to be independent of the

solution composition: lsherc there arc sufliclent experimental data. Table III gives the temperature dependence of the intcrwtion pnrumeters.

For ;s hydrate ;IS the solid phase. the solubility product equation. CJ.~. Eq. 3.

is used to calculate the activity cocllicicnt of the s:ili from solid-liquid equilibrium

data.

The c,dculrttcd activity cocflicients are not true c\penment,d values since

Eq. I I must be used to cstlmatc the actibit? coefficient of wuter. Forturwcly.

activity coefclents of \\ater crrlculuted by Eq. I I are ulunys very near unity and

term> such us r,” ilrc not large. This is an advantage of having the standard-state

fugacity of fvater change \\ith wlutlon composition.

Table 111 prcscnts the interxtion paramctcrs dctcrmmcd from solid-hquid

cquihbrium data for hydrates .ls the solid phases. These interxtion parameters

are independent of solution composition. ho\\ever arc weak functions of the tem-

perature. Two ditkrent sets of interxtion parameters are required for sodium sulfate: one for the pure salt as the solid phase and the other for NaISO, - IOH,O

as the solid. The two sets of parameters are different smce the activity coetlicients citlculatcd from both Eqs. I and 3 arc not true cxpcrm~cntal vzlucs: those from

Eq. 1. for temperatures belo\\ 32.5.C. depend on the extrapolation of.\-:. and those

from Eq. 3 depend on Eq. I I to estlmatc the activit) coefficient of water. Therefore.

T9RLE I\’

P,xRAs,ETtlU H,R THE CALCCLATIO% OF ‘ItiF. SOLCUILIT~ f’ROI>l:CTS OE b~L’LlII’1 t S\LlS AhI> SOI)IUhl

SULFAfE

In K :-= A t B I 1. c

Solid srrlr .4 B

1 NarS01 - IOH- -5.651 0.096 2 NazSO I - NaNO I” --5.877 0.009 3 Na2S0.~. M&O, _ 4H~0” - I.100 I .600 4 NazSO I . 3K2SO ac - I .450 -- 0.001 5 MgSOa. KzS0.r. 6H10” - l.mo -- 0.002 6 MgSOs. KzSOI 4KzOe .- 0 650 -0.001

Common names for salts: a Darapshlrc. ” Astrahanitc, ’ Glascrlte. 11 Schocnite. e Leoncte.

238 R. VEGA AhD E. W. FUNK

pcltticular care is required to select the proper Interaction paramercrs for equilib-

rium calculations involving Na$!GO,.

The parameters of Table 111 generally correlate experimental solid-liquid

equilibrium data for ternary salt systems with errors in the liquid-phase composi-

tion of less than 2 grams salt/100 grams H20. As expected, the correlation is better

for equilibria with pure salts as the solid phase. Maximum errors of &- 6 prams

salt/l00 grams Hz0 are found for equilibria with hydrates at temperatures near

0 -C.

No interaction parameters chn be calculated from equilibrium points where

the only *,olid phase is a multiple salt. However. Eq. 2 and the interaction para-

meters dcriv?d from other equilibrium points can be used to calculate the solubility

products o!‘ double and multiple salts. Table IV presents an empirical equation and the neccssnv constants to calculate these solubility products from 0 to 5O’C.

Erro;s in predicted liquid-phase compositions arc similar to those for solid-liquid

equilibria uith hydrates ;LS the solid phases.

Fig. 6. The four-component system NaNO3-NaCl-NazSOa at 25 “C.

SOLID-LIQUID EQUILIBRIA 239

FOUR-COMPOSEST SYSTEMS

The parameters in Tables f-f V can be used to predict solid-liquid equilibria

in the following four-component systems

1. NaCI-KCI-MgCl,-.L120 3 _. IN~~SO,-K~SO_,-M~SO,-H~O 3 _ . NaNOJ-KNO,-,Mg(NO,),-HZ0

4. NaCI-Ni~~SO,-NaNO,-H~O

5. KC&-K,SO,-KNOj-H,O

6. MgCl,-MgSO,-Mg(NO3)2-Hz0 \\ here each system JWC .m ion in common. Availrthlc data for these systems have

been sumnwized &II I7Ans (I). however the data arc wry incomplete. Experimental solid-liqwd equilibrium data for the system NaN03-NKI-

NJ~SO,-H~O (1.3) tit 15 -C are shown In Fig. 6. Experimental phase-equilibrium data for this system an be compared \\ith predicted v.~lues. Errors in the predicted

liquid-phase cornpositIon* \\ere found to be similar to those of ternary systems.

The predictions arc most rchable for equilibria involving pure salts as the sohd

phases. Maximum errors arc encountered In the prediction of equilibria involving

hydrates near O’C.

Phase-equillhrium rAttons are prchenttd to describe solid-liquid equilibria

in aqueous salt systems for the solid phase his iI pure salt. hydrate. or multiple salt: rt is assumed that no solid solutions are formed. The activity coefficient of

a salt in the phase-cquihbrium rAtions hns been defined as though it were LI

nonelectrolyte. This new activity cocflicient is easily related to the familiar mean

ionic activity coefficient and alkws a simple descriptions of solid-liquid equilibria.

Activity coefficients at 25 -C in conccntratcd binary aqueous salt solutions

are \\ell described using simple empirical expressions: these some expressions can

be used to estimate activity coefficients from 0 to SO’C. The solubility products of

pure salts and hydrates are calculated directly from solubilit> dittrt for the binary

s> stems.

Eqs. 9, 10 and II describe the activity coetlicients at high concentriltions

in ternary aqueous salt solutions. The equations for the activity coefkients of

the salts contain two interaction parameters which must be determined using solid-liquid equilibrium data for the ternary systems. The activity coeffkient of

water is estimated using only data for the binary systems.

The proposed correlation of solid-liquid equilibria has been applied to the

binary and ternary subsystems of the six-component system of Na +. K +. Mg * -.

Cl-, NO,-, SO,--, and H20. Table I presents the solubility products of the

240 R. VEGA AND E. W. FUBK

pure salts and hydrates. and Table 2 the required constants to calculate the activity coefficients in binary systems. The interaction parameters calculated from ternary

solid-liquid equilibrium data NC independent of solution composition and are only weak functions of temperature: Table III is used to calculate these interaction

parameters. Solubility products for common multiple salts have been calculated rind itre presented in Table IV. Tables I to IV can be used to calculate solid-liquid

equilibria in the binary and ternary systems from 0 to 50°C with errors in the liquid-phase composition of less than Z grams salt/ 100 grams H,O. Good estimates of solid-liquid equilibria can be made for the four-component systems containing a common ion using only parameters determined from binary and ternary data.

The purpose of this paper has been to present a general description of a new correlation for solid-liquid equilibria in aqueous salt systems. The basic idea has been to apply to these equilibria those thermodynamic methods developed

for the correlation of phase equilibria data involving multicomponent non-

electrolyte systems. Although the correlation has been applied to a particular six- component system of practical interest, there hds been no detailed discussion of the experimental datci for the subsystems or quantitative results sho\ving the success or failure of the correlation in specific situntions. This would be ;1 difficult

task. The experimental data for these systems differ greatly in quality. along with their tendency to form supersaturated solutions. metastable equilibria. and unex-

petted multiple salts. Logically. the success of the proposed correlation varies

considerably from subsystem to subsystem and the expected errors given above are only very approximate values. It is assumed that for practical application the correlation \\ould be used very cautiously and in conjunction with available

experimental data for the equilibria in question.

Since this work v\ds completed. Meissner and coworkers (11-16) have

presented a correlation of the activity coefficients of strong electrolytes in concen-

trated aqueous solutions u hich can be used to estimate phase equilibria in salt systems. Their correlation is of different form than that proposed here and depends

upon an empirical extrapolation of activity coefficients to very concentrated

solutions. Their estimates of solid-liquid equilibria involving pure solid salts are

very sood. and rhc method appears especially promising for .I simple treatment of

equilibria involving hydrates.

ACRKOWLEDGEbWNT

The authors are grateful to “Sociedad Quimica y Minera de Chile” for financial support and to ECOM for the use of their computational facilities. The senior author further acknovvledSes the financial support of Latin American Teaching

Fellowships. Fletcher School of Lava and Diplomacy, Tufts University.

SOLID-LIQUID EQUILIBRIA 241

REFERENCES

I. A. SEIVELL. Solubilitrer of Or~anrc artd Metal Orgmic Con~pot~nds, Third Edition, Volume 1. D. Van Nostrand. New York, N.Y., 1940.

2. H. B. SUHR, Eqwhbrium Data on the Six-component System: Water and the Chlorides. Sulfates and Nitrates of Sodium, Potassium and Magnesium. Tcchnicul Report. Socicdad Quimica y Mincra de Chile, 1969.

4. E. CORSEC AND H. KROVACH. Ann. CXifn.. IO (1929) X3. 5. W. C. BLASDALE, Eqcdibria in Sutrcrated Suit Sdcttions. The Chemical Catalogue Co..

New York. N.Y.. 1917. 6. J. E. TEEPLE, The fndudriui Dr~efoprent of Seatke~ fake Brrnes, The Chemical Cr:aloguc

Co.. New York, N.Y . 1919. 7. G. N. LE~VIS nsn M. RAXDALL, T/lerro~~~nof~,rcs. Scxond Edition, Rcviscd by K. S. PITTER

A~I> L. BREWLR. McGra\\-Hdl. NC\\ York. N.Y., 1961. 8. B. MILICEVIC, HeIs. Chitn. Actu, 46 (1963) 1466. 9). E. W. Fuse. Iml. i2.r. Clrem. Process Drsrgn Dovelop.. m prcs.

IO. R. A. Roetssov -\NI) R. H. STOKES. Ekctrol~tc Solrrtions. Second Editton, Buttcrworths. London. 1959.

Edltion. Reinhold, New York (I’)%). 11 fnrrmorrmul Crrricul TuhleA. Lot. 3, McGr.aw-Hill. Nca York. N.Y.. 1926. 13. A. CHK~TLE~, Colrc/rr. 1 I (1929) IUS. t4_ H. P. X~EISSYER AXD C. L. KUSIK. A. 1. C/I. E. Jouma/. 18 (1971) 19-L 15. H. P. MEISS~ER. C. L. KUSIK AXV J. W. TESIER. rhrcl., 661. 16. H. P. MEISSSFR AW> J. W. TFSTER. hi. Eng. Chetm Procers Design De~eIop.. t t (1971) 1128.

APPENDIX

The solid-liquid equilibrium reMion of a hydrate. for example Na,SO, - IOH?O, c.m be written in terms of the chemical potentials

/I NazSO, - lOH,O = ~1 Na,SO, + 10/c Hz0 (la)

Introducing the activity u, and combining the standard-state chemical

potentials, Eq. la becomes

which is the usual expression for the solubility product K. HowcQer, since the standard-state fugacity of water changes with solution composition, the standard- state chemical potentiai of water also changes. Therefore. the solubility product of Eq. 2a is not strictly independent of solution composition. Nevertheless, for practical application, it is assumed that changes in the standard-state chemical potential of water with solution composition are too small to change significantly

the value of the solubility product, and thus K is effectively only a function of temperature.

solid-liquid equilibria in concentrated aqueous salt solutions—systems with a common ion

Documents