NaCl-NaAlO4活度系数

doi:10.1016/S0016-7037(03)00133-9

Isopiestic measurement of the osmotic and activity coef?cients for the NaOH-NaAl(OH)4-H 2O system at 313.2K

J UN Z HOU ,1,*Q I Y.C HEN ,1J IE L I ,1Z HOU L.Y IN ,1X IA Z HOU ,2and P ING M.Z HANG 1

1

Institute of Physical Chemistry,College of Chemistry and Chemical Engineering,Central South University,Changsha,Hunan,410083,

People’s Republic of China

2

English-teaching Group,Hunan Police College,Changsha,Hunan,410006,People’s Republic,China

(Received September 3,2002;accepted in revised form February 5,2003)

Abstract —By using a specially designed and constructed isopiestic apparatus,we measured the osmotic coef?cients at 313.2K for the NaOH-NaAl(OH)4-H 2O system with the total alkali molality,m NaOHT (m NaOH ?m NaAl[OH]4),from 0.05mol/kg H 2O to 12mol/kg H 2O and ?K (m NaOHT /m NaAl(OH)4)from 1.64to 5.53.The mean standard deviation of the measurements is 0.0038.Several sets of the Pitzer model parameters for NaOH-NaAl(OH)4-H 2O system were then obtained by regressing the measured osmotic coef?cients with the Pitzer model and the Pitzer model parameters for NaOH(aq).One set of the results is as follows:?(0)NaOH :0.08669,?(1)NaOH :0.31446,?(2)NaOH :?0.00007367,C ?NaOH :0.003180,?(0)NaAl(OH)4:0.03507,?(1)NaAl(OH)4:0.02401,C ?NaAl(OH)4:?0.001066,?OH ?Al(OH)4?:0.08177,?Na ?OH ?Al(OH)4?:?0.01162.The mean standard difference between the calculated and the measured osmotic coef?cients is 0.0088.With the obtained Pitzer model parameters,we calculated the values of K ??(?NaAl(OH)4,cal 2·m Al(OH)4?,exp )/(?NaOH,cal 2·m OH ?,exp )for the gibbsite solubility.The results show that the obtained Pitzer model parameters are reliable,and the relative error of the calculated activity coef?cients should be ?2.1%.We also compared the calculated gibbsite solubility data among several activity coef?cients models over a range of m NaOHT at various temperatures.The comparison indicates that our activity coef?cients model may be approximately applied in the ranges of temperature from 298.2to 323.2K and m NaOHT from 0to 8mol/kg H 2O.We also calculated the stoichiometric activity coef?cients of NaOH and NaAl(OH)4and the activity of H 2O for the NaOH-NaAl(OH)4-H 2O system,and these calculations establish their variations with m NaOHT and ?K .These variations imply that the strengths of the repulsive interactions among various anions are in the following sequence:Al(OH)4?-Al(OH)4??Al(OH)4?-OH ??OH ?-OH ?,and the attractive interaction between Al(OH)4?and H 2O is weaker than that between OH ?and H 2O.Copyright ?2003Elsevier Ltd

1.INTRODUCTION

The physico-chemical properties of sodium aluminate solu-tions are quite different from those of normal electrolytes,especially the abnormally high metastability of the supersatu-rated solution.Thus,the rate of the deposition process of the solution is very slow.It results in this process to be the bottleneck in the production of Al 2O 3by the Bayer method (Yang,1993),in which the sodium hydroxide is used for the extraction of aluminum from several of its ores.Unfortunately,there are many discrepancies in the views about the mechanism of the deposition process and the structure of the solution (Yang,1993;Li,2001).The physico-chemical properties of sodium aluminate solutions are also the important components in the system involving aluminum.Aluminum is the third most abundant element in the Earth’s crust.Many of the active Earth processes of interest to geoscientists,such as ore formation,geothermal alteration,sedimentary diagenesis,the remediation of the high level nuclear wastes in leaking underground storage tanks,geochemical transport of the aluminum,and so forth,involve the physico-chemical properties of aluminum in natural systems,especial the aqueous chemistry of dissolved alumi-num.However,the aqueous chemistry of dissolved aluminum remains a controversial subject (May et al.,1979;Apps et al.,

1988;Wesolowski,1992,2002).Moreover,it has been neces-sary to substitute concentrations for activities in the thermody-namic analysis of sodium aluminate solutions in most cases,because of the lack of the reliable activity coef?cients.But this kind of substitution could result in wrong conclusions.In addition,the osmotic and activity coef?cients can provide a theoretical and experimental thermodynamic foundation for the studies of the solubilities of aluminum hydroxides or oxides in solutions,of the deposition processes,and of the structures of sodium aluminate solutions.Therefore,the determination of the osmotic and activity coef?cients for the sodium aluminate solution system,especially for the supersaturated solution,is needed for practical and theoretical applications.However,this aim is much more dif?cult to achieve than for many other electrolytes.Because the forms of existing various species of aluminate anions are very complex and NaOH is very corro-sive,an effective reversible electrode responding to the alumi-nate anion,which could be used to directly determine the activity coef?cients of the component NaAl(OH)4,is not avail-able.The cryoscopic method is dif?cult to be employed,be-cause the deposition or precipitation of the sodium aluminate solution is prone to occur as the temperature is lowered.Even for the isopiestic method,which has wide applicability and great ?exibility,the tendency of the hydroxide to absorb atmo-spheric carbon dioxide,the high viscosity of the solution,and many other disadvantageous properties,make experiments be-come dif?cult.Atranovskiy (1970),Apps et al.(1988),Apps

*Author to whom correspondence should be addressed

(zhouj_csu@https://www.wendangku.net/doc/412317564.html, or

zhouj_csu@https://www.wendangku.net/doc/412317564.html,).

Pergamon

Geochimica et Cosmochimica Acta,Vol.67,No.18,pp.3459–3472,2003

Copyright ?2003Elsevier Ltd

Printed in the USA.All rights reserved

0016-7037/03$30.00?.00

3459

and Neil(1990),Zeng(1993),and Pokrovskii and Helgeson (1995)had presented complete reports of the accrued research involving aluminum.Despite of the wealth of experimental

data for the system NaOH-Al

2O

3

-H

2

O,few direct studies of the

osmotic and activity coef?cients are available.By modeling the

solubility of gibbsite with the Pitzer ion interaction treatments, Wesolowski(1992,2002)gave a set of approximate values of the pure electrolyte Pitzer model parameters for NaAl(OH)

4

(aq)at various temperatures,as well as the mixing

parameters for Al(OH)

4

?with OH?and OH??Na?.Park and Englezos(1999)measured the osmotic coef?cients for

NaOH-NaAl(OH)

4-NaCl-H

2

O system from(m

NaOH

?0.85,

m

NaAl[OH]4

?0.05,m NaCl?0.15)(mol/kg H2O)to(m NaOH?

2.6,m

NaAl(OH)4

?0.35,m NaCl?1.04)(mol/kg H2O)at298.15 K by an isopiestic method,and modeled the experimental data with the Pitzer model.The temperature of the practical interest to industry for sodium aluminate solutions is usually?313to 353K(Yang,1993).In here,we measured the osmotic coef-

?cients for the NaOH-NaAl(OH)

4-H

2

O system at313.2K with

our isopiestic apparatus.This isopiestic apparatus was specially designed and constructed to be applicable to the NaOH-

NaAl(OH)

4-H

2

O system and other unstable systems(Zhou and

Chen,in press).The experimental data were then modeled with the Pitzer model to give the Pitzer model parameters.The obtained Pitzer model parameters were then used to analyze the solubilities of aluminum hydroxide in the aqueous solution. The activity coef?cients were also calculated.These values re?ect the interactions between the species in solutions.

2.EXPERIMENTAL

2.1.General

Each of experimental data is usually given with a uncertainty fol-lowing the datum.The uncertainty is expressed in integer forms with the right-hand digit in the same order as the right-hand digit of the experimental datum.The standard deviation of a calculated datum was calculated from the individual standard deviations of all used data according to the usual propagation of errors method as follows:

y?y?x1,x2,x3,······?,(1)??y?2???y/?x1?2·??x1?2???y/?x2?2·??x2?2?······,(2) where?is the standard deviation.

Electronic balances of Satorius BP190S(??0.0001g)and Satorius BS2000S(??0.01g)were used in our experiments.They were always calibrated before used.Each weighing was repeated for at least three times,and the average weight was taken as the result.For all weights, except for those of containers,vacuum correction was made when the relative errors arising from air buoyancy were?1/8000.

2.2.Apparatus

The apparatus mainly contains four small silver cups for the refer-ence standard solution samples and one big cup for the sample being investigated.It has been described in detail by Zhou and Chen(in press).Experiments showed that,not only the apparatus was able to ensure a good consistent equilibrium temperature among the samples, but also it had a favorable reliability and stability during the equilibra-tion process.Experiments also showed that the apparatus possessed a fairly fast rate of equilibration,and it was easy and effective to decide when the equilibrium is achieved.Therefore,the apparatus is suitable for complex or unstable solutions that are sluggish to equilibrate or have other disadvantageous properties for the measurements.

The isopiestic apparatus was put on a platform that was rotating during the equilibration process.The platform was in a thermostat.The thermostat was inclined by??/36,and the temperature was electri-cally controlled to313.2K with a maximum drift of??0.5K over

24h.Although this kind of temperature was not so precise as usual (??0.01K),our previous work has shown that good results could be obtained with our apparatus(Zhou and Chen,in press).

2.3.Chemical Reagents and the Preparation of the Stock

Solutions

Water was prepared by distillation of tap water.A small amount of KMnO

4

and NaOH had been added into the tap water to get rid of organic substances and inorganic acids.The temperature of the distilled water in the outlet was controlled to348to358K during the distilla-tion.The distilled water was stored in a big glass container,which is connected to a gas-washed bottle?rst with NaOH solution in it and

then a gas-dried tower with soda-lime in it to eliminate CO

2

and the dust in the admitting air.

The concentrated stock solution of reference standard NaCl solution is the same as described by Zhou and Chen(in press).It was prepared by dissolving reagent grade NaCl(GR grade GB1266-86)in the puri-?ed water.The density of the NaCl stock solution was measured to be 1191.675?22g/dm3at?287.6K.The impurities in the stock solution were analyzed by using inductive-coupled plasma atomic emission spectroscopy(ICPAES).It was found that the contents of the impurities were:K:0.000642mol/mol NaCl;S:0.000555mol/mol NaCl;Zn: 0.000033mol/mol NaCl;each of the remainder:?0.000043mol/mol NaCl.These impurities were neglected in our experiments,and the solute was assumed to be only NaCl in the calculation of molalities. The effective molar mass of NaCl was taken to be58.443g/mol.The density of the crystalline NaCl was calculated by Archer’s(1992) equation to be2165g/dm3at298.15K.The molality of the NaCl stock

solution was analyzed to be5.7690?11mol/kg H

2

O(the mass percentage is25.2146?49%)by the dehydration method.The dehy-dration method was similar to that used by Rard and Archer(1995)and that presented in the Handbook of Analytical Chemistry(Analytical Chemistry Editor Group,Hangzhou University,1997).The details of the analysis have been described by Zhou and Chen(in press).

The concentrated stock solution of the reference standard CaCl

2 solution was prepared by the reaction between primary standard CaCO

3 (GB12596-90)and reagent grade aqueous HCl(GR grade GB622-89). The method was similar to that used by Rard and Miller(1981).The prepared CaCl

2

solution was stored in contact with excess CaCO

3

for

several days,and the excess CaCO

3

was then?ltered off to yield the

?nal CaCl

2

stock solution.The density of the stock solution was measured to be1361.415?49g/dm3at?290.0K.The impurities of

the CaCl

2

stock solution were analyzed by ICPAES method:K:

0.000741mol/mol CaCl

2

;S:0.000245mol/mol CaCl

2

;Ba:0.000060

mol/mol CaCl

2

;each of the remainder:?0.000011mol/mol CaCl

2

.All impurities were neglected so that the solute could be assumed to be

only CaCl

2

in the calculation of molalities.The effective molar mass of

CaCl

2

was taken to be110.984g/mol.The density of the solid CaCl

2 is2150g/dm3at room temperature(Dean,1985).The molality of the CaCl

2

stock solution was analyzed to be5.3030?12mol/kg H

2

O (mass percentage37.0496?74%)by the direct dehydration method, which has been discussed by Rard and Miller(1981).The details of the analysis were similar to those of the NaCl stock solution analysis. The NaOH used was of reagent grade(GR grade GB629-81[84]),its molar mass is taken to be39.9971g/mol.The NaOH stock solution was prepared by the method similar to those used by Stokes(1945),Si-monson et al.(1989),and Handbook of Analytical Chemistry(Analyt-ical Chemistry Editor Group,Hangzhou University,1997).The prep-aration method was described in detail by Zhou and Chen(in press). The density was measured to be1456.6?15g/dm3at?291.6K. According to the method of GB629-81(84)(Quality Monitoring Center for Chemical Reagents,Chemical Department of China,1996),the

content of Na

2

CO

3

in one sample was analyzed.This sample was prepared from the stock solution and had been stored for?1month.

The analysis showed that the presence of1/2(Na

2

CO

3

)was equivalent to0.177?70mol.%of the total alkali.In Stokes’s(1945)opinion,the presence of0.2%carbonate is not likely to affect the isopiestic molality

ratios of m

H2SO4

/m

NaOH

by?0.0005in isopiestic experiments.There-

fore,the presence of Na

2

CO

3

was ignored in our experiments.The NaOH contents in the stock solutions were analyzed by an improved titration method,which was described in detailed in the reference

3460J.Zhou et al.

(Zhou and Chen,in press).The analyses yielded the follows:stock solution I:NaOH%?42.640?37,m NaOH ?18.586?20mol/kg H 2O,?NaOH ?1456.6?15g/dm 3at ?291.6K;stock solution II:NaOH%?43.115?46,m NaOH ?18.950?25mol/kg H 2O,?NaOH ?1465.9?15g/dm 3at ?286.0K.

The Al wire is of ultrapure grade ?99.999%(Q/CYDZ-184-97,lot number Shanghai SCR-F990506).The density is 2.6989g/cm 3at 293K (Weast and Astle,1983).Molar masses of Al and Al(OH)3are taken to be 26.98154g/mol and 78.0036g/mol,respectively.

Sodium aluminate stock solutions were prepared in the following steps:(1)According to the method similar to that used in GB32571-82(The National Standard of the People ’s Republic of China,1982),a certain amount of Al wires was ?rst boiled in aqueous HCl (1:1)for at least 5to 10min.Then they were washed with distilled water for at least ?ve times and with CH 3CH 2OH for at least three times.Subse-quently,they were blown to be completely dry by a hair dryer and cooled in a desiccator.Finally they were accurately weighed.(2)An amount of the NaOH stock solution in a 500-cm 3measuring ?ask was accurately weighed.The measuring ?ask had been weighed accurately in advance.(3)The lower part of the measuring ?ask was inserted into a water bath,whose temperature was controlled in the range of 353to 373K.Then the Al wires,along with an appropriate amount of water,were added to the NaOH solution gradually.At the same time,the measuring ?ask was being wagged in the water bath so that the temperature of the sodium aluminate solution in it was approximately equal to that in the water bath.(4)The prepared sodium aluminate solution was adjusted to a ?xed volume of 500cm 3by adding some water.Subsequently,the sodium aluminate solution was mixed thor-oughly and weighed accurately,and then transferred into an 800-cm 3polyethylene bottle.(5)After being capped hermetically and weighed,the bottle was stored in a desiccator containing soda-lime.The bottle was always re-weighed before used.The weight difference from that when the bottle was placed in the desiccator should be ?0.01g.By this experimental technique,we can calculate the compositions of the stock solutions accurately and avoid chemical analyses of the alumi-num contents of the solutions.According to the standard chemical analysis methods described in GB32571-82(The National Standard of the People ’s Republic of China,1982)and ISO 6994-1986(1)(1986),the relative error is nearly 0.5%.However,accurate analyses of the stock solutions are very important for isopiestic measurements as pointed out by Rard and Platford (1991).

The obtained compositions of the prepared sodium aluminate stock solutions are given in Table 1.

The compositions of the stock solutions,except for number 4,are approximately in the stable regions according to the phase diagrams of Na 2O-Al 2O 3-H 2O systems (Atranovskiy,1970).Number 4was pre-pared from number 2and the NaOH stock solution several days before the isopiestic experiments.They were always examined carefully to check whether there was any deposition before use.In our experiments,no deposition was found.

The Si contents of the sodium aluminate stock solutions were ana-lyzed by spectrophotometry.We had found that when the lower part of the measuring ?ask was not inserted into the water in step (3)of the preparation of an aluminate solution,the temperature of the aluminate solution was ?393K while the Al wires were being dissolved into the NaOH solution.When the time of dissolving Al is ?6to 12h,the Si

content of the solution is ?111mg/dm 3.Therefore,the lower part of the measuring ?ask was always inserted into the water during the preparation of the stock aluminate solutions.For number 3,the water in the water bath was controlled to be 373K,and the time of dissolving Al wires was ?6to 12h.The Si content was found to be 32.8mg/dm 3(0.00013mol/mol NaOH).For stock solution 2,the temperature of the water was controlled to ?353K,and the time was ?4h,and the Si content was found to be ?1mg/dm 3(0.000004mol/mol NaOH).For number 1,the water was controlled to 353K,and the time was ?10h.The Si content was assumed to be ?32.8mg/dm 3(0.00013mol/mol NaOH).One sample was prepared from stock aluminate solution 3by mass dilution.The molality of NaOH was 0.88360?88mol/kg H 2O.The impurities were analyzed by ICPAES:S:0.000636mol/mol NaOH,Si:0.0000584mol/mol NaOH,each of remainder:?0.0000289mol/mol NaOH.These impurities should be equivalent in the other stock aluminate solutions.All these impurities,including Si,were neglected in our experiments.2.4.Array of the Experimental Molalities

As we know,one important reason for the measurement of the osmotic coef ?cients ?is to calculate the activity coef ?cients of solutes.For the binary system of water and the solute i ,there is

In ?i ?

?

m i

d ??

?

m i

??–1?d ln m i ,

(3)

where ?i is the activity coef ?cient of the solute i ,the m i is the stoichiometric molality.From Eqn.3,it can be seen that the relative error in ?i depends on the absolute error in ?,and the error in the second part of the right side,which is an integration error.The array of the experimental molalities was designed basically according to Eqn.3,being more closely spaced in the dilute solutions and more widely spaced in the concentrated solutions.2.5.Experimental Procedure

The adopted experimental procedure was the same as described in detail by Zhou and Chen (in press).(1)The experimental solutions were prepared by mass dilution from the stock solutions.Two small cups were used for the reference standard solutions of higher initial molality,the other two small cups were used for the solutions of lower initial molality.The relative difference between the higher and lower initial molalities was ?25%.The masses of the reference standard solutions were 0.2to 1.0g.About 100cm 3sodium aluminate solution was put into the big cup.(2)All cups were put into the isopiestic apparatus,then,the isopiestic apparatus was closed and evacuated with our evacuation system.(3)The whole apparatus was put on the plat-form in the thermostat,and the equilibration experiment commenced.In general terms,the water activity of the initial sodium aluminate solution was easily maintained between those of the reference standard solutions of the higher and lower initial molalityies because of the great relative difference in the initial molalities of the reference standard solutions.As the equilibration progressed,the higher and lower initial molalities approached together.In the end of the equilibration process,

Table 1.The obtained compositions of the sodium aluminate stock solutions (NaOH ?NaAl(OH)4-H 2O).

Number

123

4

?K a

1.6481?18

2.1951?23

3.2500?28 5.5236?45NaOHT (%)b 26.571?2827.477?2925.883?223

4.520?27Al(OH)3(%)

31.4434?5524.4119?5515.53125?3112.1881?29m NaOHT (mol/kg H 2O)c 15.823?2014.279?1711.0044?10416.195?15?(g/dm 3)

1505.3?151466.3?151388.5?141454.3?15(302.0K)

(293.0K)

(289.0K)

(298.2K)

a

?K ?m NaOHT /m Al(OH)3?m NaOHT /m NaAl(OH)4.

b

NaOHT denotes the total alkali which includes the free alkali NaOH and the alkali NaOH in NaAl(OH)4(namely the alkali NaOH reacting with the aluminum hydroxide A1[OH]3).c

m NaOHT ?m NaOH ?m NaAl(OH)4.

3461

Osmotic and activity coef ?cients for NaOH-NaAl(OH)4-H 2O

the mean molality of all reference standard solution samples was accepted as the equilibrium molality.The?nal standard deviation was calculated from the individual standard deviations of all molalities used in the calculation and the limit difference of all molalities.The sodium aluminate solutions were always examined carefully,and only those experiments,in which there was no evidence of precipitation,were accepted as the equilibrium results.More experimental details can be found in our paper(Zhou and Chen,in press).

3.RESULTS AND DISCUSSION

3.1.Osmotic Coef?cient Measurements

Results of the isopiestic molalities of the equilibration ex-periments are listed in Table2.

In experiments29,30and31,a small amount of sodium-D-gluconate(C

6

H

11

O

7

Na)of25mg/dm3,15mg/dm3,and16

mg/dm3,respectively,was added into the sodium aluminate

solutions during their preparation,as C

6

H

11

O

7

Na can effec-tively inhibit the crystallization of gibbsite from the sodium aluminate solution according to Watling et al.(2000)and

Watling(2000).Because the amounts of C

6

H

11

O

7

Na added were very small in comparison with the main compositions of the solutions,they would have little effect on the whole ther-modynamic properties of the solutions.

The osmotic coef?cients of the NaOH solutions,which were prepared from the same NaOH stock solutions to those de-scribed in this paper,were measured at298.2K,and the measured osmotic coef?cients were basically within the range

Table2.Isopiestic molalities of the equilibration experiments for NaOH-NaAl(OH)

4-H

2

O system at313.2K.

Experiment

m

NaOHT

a,b

(mol/kg H

2

O)

m

NaAl(OH)4

a

(mol/kg H

2

O)?K c

m

NaCl

a

(mol/kg H

2

O)

m

CaCl2

a

(mol/kg H

2

O)

10.10416?160/0.10398?28/

2 2.9704?340/ 3.0603?20/

3 5.1849?470/ 5.5150?78 2.7777?78

49.7215?91 2.9911?14 3.2500?28/ 4.4246?25

5 6.4286?58 1.97800?65 3.2500?28/ 3.1522?19

6 4.6166?40 1.42048?46 3.2500?28 4.6251?25 2.4106?26

7 3.1680?270.97475?30 3.2500?28 3.1427?29/

8 1.5053?130.46315?16 3.2500?28 1.5043?16/

9 1.01702?880.31292?11 3.2500?28 1.01777?65/

100.50388?430.155034?59 3.2500?280.50358?35/

110.26342?230.081050?34 3.2500?280.26329?19/

120.105245?910.032382?14 3.2500?280.10480?12/

130.052547?450.0161679?71 3.2500?280.05236?19/

1411.755?14 5.3548?34 2.1951?23/ 4.7969?37 158.5922?101 3.9141?21 2.1951?23/ 3.7718?47

16 5.9247?67 2.6991?12 2.1951?23/ 2.8404?31

17 3.9204?43 1.78589?74 2.1951?23 3.7988?34/

18 2.5622?29 1.16717?48 2.1951?23 2.4967?33/

19 1.4663?160.66799?27 2.1951?23 1.4382?20/

200.9988?110.45499?18 2.1951?230.9834?14/

210.46922?540.213758?88 2.1951?230.46162?104/

220.23753?250.108207?44 2.1951?230.23405?52/

230.098104?1110.044693?19 2.1951?230.09675?35/

2410.337?12 6.2725?37 1.6481?18/ 4.1095?48 250.45190?490.274239?97 1.6481?180.44201?84/

260.23919?260.145136?52 1.6481?180.23389?263/

270.095199?1060.057762?23 1.6481?180.09359?29/

280.047406?550.028763?12 1.6481?180.046482?46/

29d0.97152?1060.58950?20 1.6481?180.94096?134/

307.5502?83 4.5813?20 1.6481?18/ 3.2852?41 31e 2.5533?28 1.54928?52 1.6481?18 2.4093?61/

32f 1.4931?160.90600?30 1.6481?18 1.4275?55/

339.4308?85 1.7074?16 5.5236?45/ 4.4848?84 347.2377?62 1.31033?50 5.5236?45/ 3.5773?28

35 5.5417?48 1.00328?43 5.5236?45 5.6871?67/

36 4.0179?340.72740?27 5.5236?45 4.0580?89/

37 2.5116?220.45470?17 5.5236?45 2.4952?93/

38 1.4574?130.26384?10 5.5236?45 1.43861?488/

390.96454?840.174621?65 5.5236?450.9498?14/

400.46274?410.084314?33 5.5236?450.45654?62/

410.23858?210.043194?18 5.5236?450.23311?37/

420.096064?830.0173912?75 5.5236?450.09457?12/

a All m values are the stoichiometric molalities.

b m

NaOHT is the molality of total alkali,i.e.,m

NaOHT

?m NaOH?m NaAl(OH)4.

c?K?m NaOHT/m NaAl(OH)4.

d Th

e sodium-D-gluconate(C

6H

11

O

7

Na)content is25mg/dm3(see text).

e The sodium-D-gluconate(C

6H

11

O

7

Na)content is15mg/dm3(see text).

f The sodium-D-gluconate(C

6H

11

O

7

Na)content is16mg/dm3(see text).

3462J.Zhou et al.

of the various reference values (Zhou and Chen,in press).Table 3gives the osmotic coef ?cients of the NaOH solutions and CaCl 2solutions,which were measured at 313.2K with the NaCl solution as the reference standard solutions.

From Table 3,we can draw the conclusion that our measured osmotic coef ?cients are reliable.It further implies that the analyzed molalities of the stock solutions are reliable and consistent with each other.

Table 4lists the measured osmotic coef ?cients ?meas for the NaOH-NaAl(OH)4-H 2O system.The standard deviations of the measured osmotic coef ?cients are usually ?0.001to 0.005,and the mean standard deviation is calculated to be 0.0038.The value of ?meas was usually calculated according to the osmotic coef ?cient of NaCl reference standard solution.The osmotic coef ?cient of NaCl solution was calculated with the equations and parameters given by Archer (1992).For an experiment,where only the CaCl 2reference standard solution was em-ployed,the value of ?meas was calculated from the average osmotic coef ?cient of the CaCl 2reference standard solution.The average osmotic coef ?cient of the CaCl 2solution was the average of those values calculated with the sets of parameters given by Phutela and Pitzer (1983),Ananthaswamy and Atkin-son (1985),and M ?ller (1988).The difference among those reference osmotic coef ?cients of CaCl 2solution was consid-ered in the calculation of the standard deviation of the average value.

3.2.Modeling of the Osmotic Coef ?cients for the NaOH-NaAl(OH)4-H 2O System With the Pitzer Model It is known that aluminum in sodium hydroxide solutions occurs as various kinds of species,such as Al(OH)4?,Al(OH)4?OH ?,Al 2O(OH)62?,AlO(OH)2?,(Al[OH]4)66?,NaAl(OH)40,and so forth.According to the research of Lip-pincott et al.(1952),Mal ’tsev et al.(1965),Moolenaar et al.(1970),Zambo (1986),and Barcza and Palfalvi-Rozsahegyi (1989),it is generally accepted that the tetrahedral Al(OH)4?ion is the only important species in hydroxide solutions of less than moderate concentration (2–4mol/kg H 2O)below 373K.On the basis of the possible equilibria among the various species,the Al(OH)4?ion would be the only possible alumi-num species in an in ?nitely dilute hydroxide solution.As a

result,in many recent studies,such as those of Wesolowski (1992,2002),Verdes et al.(1992),Zeng (1993),and Park and Englezos (1999),the Al(OH)4?ion is assumed to be the major species in dilute sodium aluminate solutions.Here,we adopted NaAl(OH)4,NaOH and H 2O as the basic components of the sodium aluminate system.These components can be consistent in formula with the actually existing species of Na ?,Al(OH)4?,OH ?,and H 2O in an in ?nitely dilute sodium alu-minate solution.The molalities of these components are stoi-chiometric molalities.Only on this basis,we can use the Pitzer model to regress the experimental osmotic coef ?cients.

According to the equation of Pitzer (1991),the osmotic coef ?cient ?of the NaOH-NaAl(OH)4-H 2O system is given by ?–1?–A ?m 1/2/?1?bm 1/2??

?1?1/?k ?m ??NaOH

?0???NaOH ?1?

exp ?–?1m 1/2???NaOH

?2?exp ?–?2m 1/2??mC NaOH ?

???m /?k ??NaAl(OH)4

?0???m /?k ?exp ?–?1m 1/2??NaAl(OH)4?1?

??m /?k ?exp ?–?2m 1/2??NaAl(OH)4?2?

?

?m 2/?K ?C NaAl(OH)4??1–1/?k ??1/?k ?m ?OH –Al(OH)4–

??1–1/?k ??1/?k ?m 2?Na ?OH –Al(OH)4–

(4)

where m ?m NaOHT ?m NaOH ?m NaAl(OH)4;?K ?m NaOHT /

m NaAl(OH)4;A ?is Debye-Hu ¨ckel limiting-law slope equal to

0.4023(kg mol ?1)1/2

at 313.15K (Pitzer,1991);b is a univer-sal parameter generally considered to be 1.2(kg mol ?1)1/2(Pitzer,1991);?1and ?2are also universal parameters usually taken as 2.0(kg mol ?1)1/2and 8.0(kg mol ?1)1/2,respectively,and these values were also previously used by Simonson et al.(1989)for sodium hydroxide solutions.(?(0)NaOH ,?(1)NaOH ,?(2)NaOH ,C ?NaOH )and (?(0)NaAl[OH]4,?(1)NaAl[OH]4,C ?NaAl[OH]4)are the Pitzer model parameters for NaOH and NaAl(OH)4,respectively.?OH ?Al(OH)4?and ?Na ?OH ?Al(OH)4?are the Pitzer model mixing parameters.For symmetrical mixed solutes,the Pitzer model mixing terms e ?(I),e ??(I)are taken to be zero (Pitzer,1991);therefore,they do not appear in Eqn.4.After two sets of the values of (?(0)NaOH ,?(1)NaOH ,?(2)NaOH ,C ?NaOH )were calculated from the equations and the parame-ters given by Simonson et al.(1989)and Pabalan and Pitzer

Table 3.The osmotic coef ?cients of CaCl 2and NaOH solutions at 313.2K and 0.1MPa.

Experiments 1

236

NaCl m

0.10398?28 3.0603?20 5.5150?78 4.6251?25?Archer (1992)0.930625?39 1.06218?14 1.23383?56 1.16999?18?·m a 0.09677?26 3.2506?25 6.8046?127 5.4111?40CaCl 2

m // 2.7777?78 2.4106?26?meas

// 1.6331?65 1.4965?22?Phutela,Pitzer (1983)

// 1.6337 1.49832?Ananthaswamy,Atkinson (1985)// 1.6371 1.49928?M ?ller (1988)/

/

1.6374

1.50130NaOH

m 0.10416?16 2.9704?34 5.1849?47/?meas

0.9290?29 1.09433?151 1.3124?27/?Pabalan,Pitzer (1987,1991)

0.93156 1.0990 1.3209/?Simonson,Mesmer,Rogers (1989)0.93265 1.0893 1.3067/?Holmes,Mesmer (1998)

0.93262

1.0899

1.3080

/

a

The standard deviation is calculated from the greatest and the smallest values of ?·m corresponding to m with the standard deviation.

3463

Osmotic and activity coef ?cients for NaOH-NaAl(OH)4-H 2O

(1987,1991),the?

meas

values in Table4were regressed

according to Eqn.4by the least-squares linear method with the

standard deviations of?

meas

as the weights.In the regression

analysis,?(2)

NaAl(OH)4

was taken to be zero.The regression analysis readily gave the Pitzer model parameters for

NaAl(OH)

4

and the mixing parameters.These parameters are given in Table5.

Table4illustrates the comparison between the measured

osmotic coef?cients?

meas and the osmotic coef?cients?

cal

calculated with set1of Pitzer model parameters in Table5.

From Table4,the mean standard difference between?

meas and

?cal was calculated to be0.0088.It is obviously larger than the mean standard deviation of the measured osmotic coef?cients that is0.0038.The situation is similar when set2of Pitzer model parameters in Table5is used.We have also regressed

the experimental data with consideration of?(2)

NaAl(OH)4,and

the value of the mean standard difference was still?0.0087.

Generally speaking,the differences,?,are usually?0.01.This

is adequate for most applications.More important,the?t of the

Pitzer model to our experimental data at313.2K extends to

almost?m

NaOHT

?10mol/kg H2O,so it would appear that, not only our experimental data are fully consistent with the

current thermodynamic model,but also the current thermody-

namic model is valid over broader ranges of NaOH-

NaAl(OH)

4

-H

2

O system than expected.In addition,it is rea-sonable to suppose that the Pitzer model could be applied to the

sodium aluminate solution at other temperatures.That is very

bene?cial to the study on the sodium aluminate solution at

other temperatures,since the Pitzer model parameters could be

obtained by various methods.

Wesolowski(1992,2002)had proposed a set of equations to

calculate the Pitzer parameters for NaAl(OH)

4

(aq)at various

Table4.The osmotic coef?cients for the NaOH-NaAl(OH)

4-H

2

O system and the comparison between the measured osmotic coef?cients and the

calculated osmotic coef?cients at313.2K and0.1MPa.

Experiment m

NaOHT a(mol/kg H

2

O)?K b?meas?cal,1c?1d?cal,3e

49.7215?91 3.2500?28 1.5487?46 1.54060.0081 1.5577

5 6.4286?58 3.2500?28 1.3079?37 1.29910.0088 1.2887

6 4.6166?40 3.2500?28 1.1721?13 1.16710.0051 1.1531

7 3.1680?27 3.2500?28 1.0591?15 1.0654–0.0063 1.0548

8 1.5053?13 3.2500?280.9665?140.96090.00560.9608

9 1.01702?88 3.2500?280.9434?100.93600.00740.9396 100.50388?43 3.2500?280.9230?100.91750.00550.9239 110.26342?23 3.2500?280.9209?100.91670.00420.9227 120.105245?91 3.2500?280.9266?130.9277–0.00110.9316 130.052547?45 3.2500?280.9381?340.9398–0.00160.9423 1411.755?14 2.1951?23 1.4750?82 1.4876–0.0126 1.5473 158.5922?101 2.1951?23 1.3282?53 1.3397–0.0116 1.3520

16 5.9247?67 2.1951?23 1.1935?35 1.1956–0.0021 1.1884

17 3.9204?43 2.1951?23 1.0776?17 1.0797–0.0021 1.0712

18 2.5622?29 2.1951?230.9995?19 1.0016–0.00210.9991

19 1.4663?16 2.1951?230.9452?180.94400.00120.9499 200.9988?11 2.1951?230.9267?170.92360.00310.9332 210.46922?54 2.1951?230.9077?230.9093–0.00160.9209 220.23753?25 2.1951?230.9084?220.9123–0.00390.9220 230.098104?111 2.1951?230.9188?340.9261–0.00730.9322 2410.337?12 1.6481?18 1.2806?46 1.27840.0022 1.3228 250.45190?49 1.6481?180.9021?200.90000.00210.9180 260.23919?26 1.6481?180.9015?1010.9062–0.00470.9206 270.095199?106 1.6481?180.9164?290.9236–0.00720.9321 280.047406?55 1.6481?180.9251?140.9383–0.01320.9434 290.97152?106 1.6481?180.9097?170.90770.00200.9263 307.5502?83 1.6481?18 1.1939?44 1.18880.0051 1.2033

31 2.5533?28 1.6481?180.9627?300.9712–0.00840.9797

32 1.4931?16 1.6481?180.9207?400.9256–0.00480.9410 339.4308?85 5.5236?45 1.6346?75 1.6467–0.0121 1.6539 347.2377?62 5.5236?45 1.4397?50 1.43640.0033 1.4298

35 5.5417?48 5.5236?45 1.2790?23 1.2825–0.0035 1.2709

36 4.0179?34 5.5236?45 1.1414?33 1.1529–0.0115 1.1414

37 2.5116?22 5.5236?45 1.0189?45 1.0370–0.0180 1.0298

38 1.4574?13 5.5236?450.9512?360.9676–0.01640.9658 390.96454?84 5.5236?450.9253?160.9410–0.01570.9420 400.46274?41 5.5236?450.9102?150.9220–0.01180.9251 410.23858?21 5.5236?450.9008?160.9210–0.02020.9241 420.096064?83 5.5236?450.9175?140.9312–0.01370.9333

a m

NaOHT is the molality of total alkali,i.e.,m

NaOHT

?m NaOH?m NaAl(OH)4.

b?K?m NaOHT/m NaAl(OH)4.

c?cal,1is calculated with set1of Pitzer parameters in Table5.

d?1??meas–?cal,1.

e?cal,3is calculated with Pitzer parameters generated from Wesolowski’s(1992,2002)equations coupled with NaOH equations of Simonson et al.(1989).

3464J.Zhou et al.

temperatures,as well as the mixing parameters for Al(OH)4?with OH ?and OH ??Na ?.Those equations were obtained by modeling his own experimental data of gibbsite solubilities and those of Russell et al.(1955).We can then generate a set of Pitzer model parameters for NaAl(OH)4at 313.2K and 0.1MPa from Wesolowski ’s (1992,2002)equations,coupled with the equations given by Simonson et al.(1989).This set of Pitzer model parameters is also given in Table 5.The compar-ison between our Pitzer model parameters (set 1in Table 5)and those derived from Wesolowski (1992,2002)(set 3in Table 5)shows that there is actually a reasonable agreement between the two sets of values of ?(0)NaAl(OH)4and C ?NaAl(OH)4,although the value of ?(1)NaAl(OH)4and the mixing parameters from two studies are fairly different.Table 4also includes the compari-son between the measured osmotic coef ?cients and the osmotic coef ?cients calculated with set 3Pitzer parameters.The mean standard difference is 0.0187.In fact,this magnitude of differ-ence should be acceptable as the sodium aluminate solution is quite complicate.

After the Pitzer model parameters for NaOH-NaAl(OH)4-H 2O are obtained,the gibbsite solubilities in sodium hydroxide solutions can be discussed.The dissolving reaction between gibbsite and sodium hydroxide solutions can be expressed as follows:

Al(OH)3(cr)?NaOH(aq)?NaAl(OH)4(aq).

(5)

The equilibrium constant K is

K ?a NaAl(OH)4,equ 2?NaOH,equ 2??NaAl(OH)42m Na ?,equ m Al(OH)4?,equ

?NaOH 2

m Na ?,equ m OH ?,equ

??NaAl(OH)42

?1/?K,equ ?

?NaOH 2

?1–1/?K,equ ?

.(6)

According to the Pitzer equation,there is

ln ?NaAl(OH)4,cal –ln ?NaOH,cal ?m ??NaAl(OH)4

(0)–?NaOH (0)

??m 2?1–?1??1m 1/2?exp ?–?1m 1/2????1m 1/2?2

??NaAl(OH)4(1)

–?NaOH (1)

??m 2?1–?1??2m 1/2?exp ?–?2m 1/2????2m 1/2?

2

??NaAl(OH)4(2)

–?NaOH (2)

???m 2/2??C NaAl(OH)4

?–C NaOH ?

?–??m ?1/?K ?–m ?1–1/?K )]–??/2)[m 2?1/?K )–m 2(1–1/?K )],

(7)

where the symbols are similar to those in Eqn.4.We can then

use the solubility data of gibbsite in hydroxide solution and Eqn.6and 7to calculate the equilibrium constant.However,due to deviations in the experimental solubility data and the calculated activity coef ?cients from the true values,the “cal-culated equilibrium constant ”from solubility data will not be exactly equal to the true equilibrium constant.So we represent these calculated values by K ?.The K ?is de ?ned by Eqn.8as

K ???NaAl(OH)4,cal 2m Al(OH)4–,exp ?NaOH.cal 2

m OH –,exp ??NaAl(OH)4,cal 2?1/?K ,exp ??NaOH,cal 2?1–1/?K ,exp )

(8)

For the solubility data of gibbsite in sodium hydroxide solu-tions at 313.15K given by Russell et al.(1955)and Ikkatai and

Okada (1963)the values of K ?are calculated and given in Tables 6and 7.

From Table 6it can be seen that there is a generally good consistency among the values of K ?1calculated from the dif-ferent molalities of the solubility experiments.However,num-bers (1,2,and 9)are somewhat smaller than the others.The regularity of K ?3is similar.The same phenomena also occured in the analysis of these solubility data performed by We-solowski (1992,2002)and Pokrovskii and Helgeson (1995).As pointed out by Wesolowski (1992,2002)and Atranovskiy (1970),it might be due to the lack of complete equilibration in some experiments of Russell et al.(1955),especially at low ionic strengths.Therefore the mean value of K ?in Table 6does not include the numbers (1,2,and 9).In fact,the mean value of K ?1,0.1074?23,is in the range of the equilibrium constants given by different references:0.097(Russell et al.,1955),?0.091(calculated from the tabulated values given by Apps and Neil,1990,with an interpolation method;the error of the calculation is estimated to be ?1–2%),0.114(Wesolowski,1992,2002),0.119(Verdes et al.,1992).Most of these inves-tigators have also used the solubility data of Russell et al.(1955)in their analyses;therefore,our mean value of K ?1should be reasonable.Since our Pitzer model parameters are used in the calculation of K ?1,the good consistency among the values of K ?1from the different molalities of the solubility experiments and the mean value of K ?1in the range of the various reference equilibrium constants indicate that our Pitzer model parameters are reliable.The standard variance of the mean value of K ?1is 0.0023,and the relative error is 2.1%.It may imply that the relative error of the calculated activity

Table 5.The Pitzer model parameters for NaOH-NaAl(OH)4-H 2O system at 313.2K and 0.1MPa.

Set

1

2

3a

NaOH b NaAl(OH)4?c NaOH d NaAl(OH)4?c NaAl(OH)4?(0)0.086690.035070.051620.092570.039590.052980.05109?(1)0.314460.024010.290450.283390.070360.213030.31446?(2)–7.367?10–50e

/

0e

/

C ?

0.003180–0.001066

0.004246

0.002636–0.001268

0.003904

–0.002080?OH –A1(OH)4–

0.081770.058480.014?Na –OH –A1(OH)4–

–0.01162

–0.009934

–0.0048

a Generated from Wesolowski ’s (1992,2002)equations coupled with the equations given by Simonson et al.(1989).

b

The Pitzer model parameters for NaOH are calculated from the equations and parameters given by Simonson et al.(1989).c

??parameter (NaOH)–parameter (NaAl[OH]4).d

The Pitzer model parameters for NaOH are calculated from the equations and parameters given by Pabalan and Pitzer (1987,1991).e ?(2)

NaAl(OH)4is taken to be zero in the regression analysis.

3465

Osmotic and activity coef ?cients for NaOH-NaAl(OH)4-H 2O

coef?cients of NaAl(OH)

4

and NaOH with our Pitzer model

parameters may be?2.1%.

In Table7there is also a generally good consistency among the values of K?calculated from the different molalities.How-ever,the mean values of K?in Table7are obviously greater than those in Table6.The same phenomenon occurred in the treatments of these solubility data performed by Wesolowski (1992,2002)and Pokrovskii and Helgeson(1995).Wesolowski

(1992,2002)calculated the values of log(m

OH?

/m Al(OH)4?)with the parameters obtained by regressing the solubility data from his own experiments and those of Russell et al.(1955).The

comparisons between the calculated values of log(m

OH?

/

m

Al(OH)4?

)and the experimental values of Russell et al.(1955) and Ikkatai and Okada(1963),respectively,showed that the calculated values agreed well with most of the values of Russell et al.(1955);however,the values of Ikkatai and Okada(1963) were obviously smaller than the calculated values.Pokrovskii and Helgeson(1995)modeled all of the previous experimental

work with HKF model,and calculated out log(Q·a

w

2),which is equivalent to log K?in our paper.The results showed that the

values log(Q·a

w

2)of Russell et al.(1955)were greater than those of Ikkatai and Okada(1963).Therefore,there is indeed some kind of difference between those two sets of solubility data.

From Tables6and7,we could see that there are some differences between the values of K?calculated by us and those derived from Wesolowski(1992,2002).However,the differ-ences are generally within0.05log units.Pokrovskii and Helgeson(1995)have reported that the predicted solubilities of gibbsite in concentrated NaCl?NaOH solution in their anal-ysis were within?0.05log units.So we consider that the difference of0.05log units in our analysis would be acceptable.

When the Pitzer model parameters for NaOH-NaAl(OH)

4

-

H

2

O system and the equilibrium constant for the dissolving

Table6.The values of K?for the solubility data at313.2K of Russell et al.(1955).

Number

m

NaOHT,exp

a

(mol/kg H

2

O)?K,exp a,b K?1c,d log K?1c,d K?3c,e log K?3c,e

10.501610.350.09592 1.01810.10420.9822

2 1.25010.550.08797 1.05570.09720 1.0123

3 2.2958.2250.10720.96980.11770.9290

4 2.5657.9090.10970.95980.12000.9207

5 3.0577.6870.10900.96280.11800.9280

6 4.0927.0600.10860.96410.11570.9366

7 5.068 6.4510.10700.97060.11320.9463

87.888 4.3990.10270.98860.11590.9358

910.75 3.0920.08387 1.07640.11080.9556 Mean//0.1074?23f0.9693?94f0.1168?22f0.9328?81f

a Calculated from the values of Na

2O(g/dm3),density,and Al

2

O

3

/Na

2

O(g/g)given in the reference(Russell et al.,1955).

b?K,exp?m NaOHT,exp/m NaAl(OH)4,exp.

c K?is de?ne

d by Eqn.8.

d Calculated with our Pitzer model parameters(th

e set1in Table5).

e Calculated with the Pitzer model parameters derived from Wesolowski(1992,2002)(the set3in Table5).

f The calculation of the mean value of K?does not include the numbers(1,2,and9)value(see text).

Table7.The values of K?for the solubility data at313.2K of Ikkatai and Okada(1963).

Number

m

NaOHT,exp

a

(mol/kg H

2

O)?K,exp a,b K?1c,d–log K?1c,d K?3c,e–log K?3c,e

1f 1.2717.120.1279?68h0.8930.1431?78h0.8444 2g 1.2607.84

3f 2.5647.10.1317?87h0.8800.1463?105h0.8348 4g 2.559 6.28

5f 3.993 6.260.1314?72h0.8810.1436?89h0.8428 6g 3.924 5.68

7f 5.439 5.240.1366?103h0.8650.1515?135h0.8196 8g 5.284 4.62

Mean//0.1319?89i0.87980.1461?109i0.8354

a Calculated from the values of Na

2O(g/L),density,and Al

2

O

3

/Na

2

O(mol/mol)given in the reference(Ikkatai and Okada,1963).

b?K,exp?m NaOHT,exp/m NaAl(OH)4,exp.

c K?is de?ne

d by Eqn.8.

d Calculated with our Pitzer model parameters(th

e set1in Table5).

e Calculated with the Pitzer model parameters derived from Wesolowski(1992,2002)(the set3in Table5).

f Measured by dissolution.

g Measured by crystallization.

h The average value of K?is calculated from the corresponding experimental data of(f)and(g),respectively,and the deviation is calculated from the greater and smaller values.

i The deviation is calculated from variation of all K?and their individual deviations.

3466J.Zhou et al.

reaction (Eqn.5)are known,gibbsite solubilities can be calcu-lated by solving Eqn.6and 7with the help of computer.The compare of the calculated gibbsite solubilities over a range of m NaOHT ?m NaOH ?m NaAl(OH)4between our activity coef ?-cients model and that derived from Wesolowski (1992,2002)at 313.2K is then obtained.In addition,though our Pitzer model parameters for NaOH-NaAl(OH)4-H 2O system are at 313.2K,which is an industrially important but very speci ?c tempera-ture,we are able to estimate the NaAl(OH)4(aq)Pitzer model parameters at other temperatures basing on our results.As pointed out by Wesolowski (1992,2002),the OH ?/Al(OH)4?activity coef ?cient ratio for the isocoulombic reaction (Eqn.5)is nearly independent of the temperature in the 273.15to 373.15K range,namely,these values,?(0)NaOH -?(0)NaAl(OH)4,?(1)NaOH -?(2)NaAl(OH)4,C ?NaOH -C ?NaAl(OH)4,would be nearly unchangeable at least in the 273.15to 373.15K range.There-fore,we could approximately calculate the NaAl(OH)4(aq)Pitzer model parameters at other temperatures by using our difference quantities (?)in Table 5,coupled with the NaOH Pitzer model parameters.The mixing parameters could be taken as those at 313.2K.Therefore,we can then carry out the comparison at other temperatures between our activity coef ?-cients model and that derived from Wesolowski (1992,2002),as well as the activity coef ?cients model of Park and Englezos (1999),to see what range of temperature our activity coef ?-cients model is able to apply to.All these comparisons are given in Table 8and Figure 1.

From Table 8and Figure 1,it can be found that the values of m NaAl(OH)4(III)are systematically larger than those of m NaAl(OH)4(I),and the differences between the two sets of values increase with increasing m NaOHT and temperature.How-ever,the agreement between the two sets of values is within 10%when the molality extends to 6mol/kg H 2O at 323.2K.Even when m NaOHT extends to 8mol/kg H 2O,the agreement is within 20%.The values of m NaAl(OH)4(II)are systematically smaller than those of m NaAl(OH)4(I)from 298.2to 323.2K.However,when the temperature reaches 333.2K or the higher,m NaAl(OH)4(II)turns to larger than m NaAl(OH)4(I).At 298.2K,m NaAl(OH)4(III)agrees well with m NaAl(OH)4(I),and the values of m NaAl(OH)4(III)are between those of m NaAl(OH)4(I)and m NaAl(OH)4(IV).Therefore,we estimate that our activity coef-?cients model may be effective from 298.2K or lower tem-peratures to 323.2K.

3.3.Stoichiometric Activity Coef ?cients of NaOH and

NaAl(OH)4and the Activity of H 2O According to the equation given by Pitzer (1991),the fol-lowing equations for NaOH-NaAl(OH)4-H 2O system are de-rived:

ln ?NaOH,cal ?–A ??m 1/2/?1?bm 1/2???2/b ?ln ?1?bm 1/2??

?m ?

?

NaOH ?0???NaOH

(1)2?1–?1??1m 1/2?exp ?–?1m 1/2??

??1m 1/2?2

??NaOH

(2)2?1–?1??2m 1/2?exp ?–?2m 1/2??

??21/2?2

??1–1/?K ???NaOH (0)??NaOH (1)

exp ?–?1m 1/2?

??NaOH (2)

exp ?–?2m 1/2??

??1/?K ???NaAl(OH)4(0)??NaAl(OH)4(1)

exp ?–?1m 1/2?

??NaAl(OH)4(2)

exp ?–?2m 1/2??

?m ??1/2?1–1/?k ?C NaOH ???1/?K ?C NaAl(OH)4?

]

??1/?K ???OH –Al(OH)4–??1–?1/?K ?/2?m ?Na ?OH –Al(OH)4–]}

(9)

ln ?NaAl(OH)4,cal ?–A ??m 1/2/?1?bm 1/2???2/b ?ln ?1?bm 1/2??

?m ?

?NaAl(OH)4(0)??NaAl(OH)4

(1)

2?1–?1??1m 1/2?exp ?–?1m 1/2??

??11/2?2

??

NaAl(OH)4

(2)

2?1–?1??2m 1/2?exp ?–?2m 1/2??

??21/2?2

??1–1/?K ???NaOH (0)??NaOH (1)

exp ?–?1m 1/2?

??NaOH (2)

exp ?–?2m 1/2??

??1/?K ???NaAl(OH)40??NaAl(OH)4(1)

exp ?–?1m 1/2?

??NaAl(OH)4(2)

exp ?–?2m 1/2??

?m ??1/2?1/?K ?C NaAl(OH)4???1–1/?k ?C NaOH ?

]

??1–1/?K ???OH –Al(OH)4?

??1–?1–1/?K ?/2?m ?Na ?OH –Al(OH)4–]}

(10)

where the symbols are similar to those in Eqn.4.The relation between ?and the activity of water a w for NaOH-NaAl(OH)4-H 2O is

??–

m w lna w

2m NaOHT

(11)

where m w is equal to 55.508mol/kg H https://www.wendangku.net/doc/412317564.html,ing set 1of Pitzer model parameters in Table 5and Equations 4,9,10,and 11,we calculated the stoichiometric osmotic and activity coefficients for the NaOH-NaAl(OH)4-H 2O system.The relative errors of the calculated stoichiometric activity coefficients of NaOH and NaAl(OH)4are expected to be ?2.1%.The results are given in Table 9and Figure 2.

From Table 9and Figure 2the following conclusions can be obtained

1.With the decreasing value of ?K ,namely the increase in the NaAl(OH)4content in the total alkali m NaOHT ,the activity of water a w at constant m NaOHT increases.It implies that the attractive interaction between Al(OH)4?and H 2O may be weaker than that between OH ?and H 2O.

2.Initially the stoichiometric activity coef ?cients of NaOH,r NaOH ,decrease steeply with the increasing molality of the total alkali m NaOHT .When m NaOHT is ?1mol/kg H 2O,?NaOH turns to increase with m NaOHT up to high concentra-tions.The value of r NaOH at the higher ?K is greater than the corresponding r NaOH value at the lower ?K ,and the extent of the increase in ?NaOH in concentrated solutions is more

3467

Osmotic and activity coef ?cients for NaOH-NaAl(OH)4-H 2O

obvious at the higher?

K

.These observations imply that the

repulsive interaction between OH?and OH?may be stron-

ger than that between OH?and Al(OH)

4

?.

3.Initially the stoichiometric activity coef?cients of

NaAl(OH)4,?

NaAl(OH)4

,decrease steeply with the increas-

ing molality of the total alkali m

NaOHT .At the lower?

K

,

?

NaAl(OH)4turns to increase when m

NaOHT

is?2to5mol/kg

H

2

O.However,the extent of the increase is small in contrast

to that of?

NaOH .With increasing?

K

,the molality,at which

the minimum occurs,decreases to the lower m

NaOHT of?1

to2.5mol/kg H

2

O.The extent of the increase in?

NaAl(OH)4 in the region of high concentration is also enlarged.The

values of?

NaAl(OH)4

at higher?

K

are greater than the

corresponding values at lower?

K

in a similar manner to that

of r

NaOH

.These regularities show that the repulsive inter-

action between OH?and Al(OH)

4

?may be greater than

that between Al(OH)

4

?and Al(OH)

4

?,from the other point of view,the attractive interaction between OH?and

Al(OH)

4

?may be weaker than that between Al(OH)

4

?and

Al(OH)

4

?.

Table8.The comparison of the calculated gibbsite solubility data between several activity coef?cients models over a range of the molality of the total alkali and at various temperatures.

T(K)m

NaOHT a m

NaAl(OH)4

(exp)b m

NaAl(OH)4

(I)c m

NaAl(OH)4

(II)d m

NaAl(OH)4

(III)e m

NaAl(OH)4

(IV)f

298.20.10.0067420.0051970.0069340.007243 298.20.50.034380.027720.037020.04681 298.20.51420.035330.035380.028550.038130.04855 298.210.070750.057740.077250.1232 298.2 1.0190.07250.072170.058910.078820.1267 298.220.15180.12170.16360.3808 298.2 3.0450.24900.25320.19660.26520.7929 298.240.36730.27740.3754 1.263 298.260.70790.52090.7077 2.398 298.28 1.2690.9664 1.310 3.617 298.210 2.174 1.833 2.440 4.855 313.20.10.010240.010020.01053

313.20.50160.048480.052370.053740.05649

313.2 1.2500.11850.13630.14260.1500

313.2 2.2950.27900.27010.27950.2944

313.2 2.5650.32430.30860.31790.3349

313.2 3.0570.39760.38420.39230.4134

313.2 4.0920.57960.57000.57330.6048

313.2 5.0680.78560.78760.78850.8323

313.27.888 1.793 1.765 1.873 1.974

313.210.75 3.475 3.527 4.228 4.407

313.26 1.045 1.054 1.112

313.210 2.979 3.469 3.631

323.20.10.013360.011810.01374

323.20.50220.066550.068440.063490.07391

323.20.51430.069410.070130.065110.07580

323.2 1.0190.14260.14290.13530.1577

323.2 1.27060.17150.18100.17180.2005

323.2 3.0450.49760.49630.46490.5464

323.26 1.331 1.262 1.490

323.28 2.260 2.304 2.695

323.210 3.590 4.023 4.573

333.20.10.017230.015890.01770

333.20.50360.086010.088450.085810.09562

333.2 1.25720.22240.23040.23020.2570

333.2 2.31780.47620.45650.45910.5144

333.2 2.61090.54910.52590.52880.5931

333.2 3.08310.67280.64530.64900.7288

333.2 4.09940.98430.93930.9492 1.0681

333.26 1.666 1.748 1.966

333.28 2.757 3.121 3.465

333.210 4.240 5.130 5.550

a m

NaOHT ?m NaOH?m NaAl(OH)4.

b m

NaAl(OH)4(exp)is the experimental gibbsite solubility data taken from Wesolowski(1992,2002)and Russell et al.(1955).

c Calculate

d with th

e Pitzer model parameters(set3in Table5)and the equilibrium constant o

f the dissolvin

g reaction(Eqn.5)given by Wesolowski(1992,2002).

d Calculated with our Pitzer model parameters(set1in Table5)and th

e equilibrium constant o

f the dissolvin

g reaction(Eqn.5)given by Apps

and Neil(1990),while for T?313.2K,the equilibrium constant is taken as0.1074,from the mean value of K?

1in Table6.

e Calculated with our Pitzer model parameters(set1in Table5)and the equilibrium constant o

f the dissolvin

g reaction(Eqn.5)given by Wesolowski(1992,2002).

f Calculated with the Pitzer model parameters proposed by Park and Englezos(1999)and the equilibrium constant of the dissolvin

g reaction(Eqn.5) given by Wesolowski(1992,2002).

3468J.Zhou et al.

4.CONCLUSION

1.The osmotic coef ?cients at 313.2K were measured for the NaOH-NaAl(OH)4-H 2O system with the total alkali molal-ity,m NaOHT (m NaOH ?m NaAl(OH)4),from 0.05to 12mol/kg H 2O and ?K (m NaOHT /m NaAl(OH)4)from 1.64to 5.53.The measurement covers most range of the composition of the supersaturated sodium aluminate solutions in the production of Al 2O 3.The standard deviations of the measured osmotic coef ?cients are usually ?0.001to 0.005,and the mean standard deviation is 0.0038.

2.The Pitzer model was used to regress the measured osmotic coef ?cients with two sets of reference Pitzer model param-eters for NaOH from different references.One set of the obtained Pitzer model parameters for NaOH-NaAl(OH)4-H 2O system are in the following:?(0)NaOH :0.08669,?(1)NaOH :0.31446,?(2)NaOH :?0.00007367,C ?NaOH :0.003180,?(0)NaAl(OH)4:0.03507,?(1)NaAl(OH)4:0.02401,C ?NaAl(OH)4:?0.001066,?OH ?Al(OH)4?:0.08177,?Na ?OH ?Al(OH)4?:?0.01162.The mean standard difference between the calculated osmotic coef ?cients ?cal and

the

Fig.1.The comparison of the calculated gibbsite solubility data between several activity coef ?cients models over a range of the molality of the total alkali and at various temperatures.m NaOHT ?m NaOH ?m NaAl(OH)4.m NaAl(OH)4(exp)is the experimental gibbsite solubility data taken from Wesolowski (1992,2002)and Russell et al.(1955).m NaAl(OH)4(I)is calculated with the Pitzer model parameters (set 3in Table 5)and the equilibrium constant of the dissolving reaction (Eqn.5)given by Wesolowski (1992,2002).m NaAl(OH)4(II)is calculated with our Pitzer model parameters (set 1in Table 5)and the equilibrium constant of the dissolving reaction (Eqn.5)given by Apps and Neil (1990),while for T ?313.2K,the equilibrium constant is taken as 0.1074,from the mean value of K ?1in Table 6.m NaAl(OH)4(III)calculated with our Pitzer model parameters (set 1in Table 5)and the equilibrium constant of the dissolving reaction (Eqn.5)given by Wesolowski (1992,2002).m NaAl(OH)4(IV)is calculated with the Pitzer model parameters proposed by Park and Englezos (1999)and the equilibrium constant of the dissolving reaction (Eqn.5)given by Wesolowski (1992,2002).(a)298.2K;(b)313.2K;(c)323.2K;(d)333.2K.

3469

Osmotic and activity coef ?cients for NaOH-NaAl(OH)4-H 2O

measured osmotic coef ?cients ?meas is 0.0088.With the data for the gibbsite solubility in sodium hydroxide solu-tions and the obtained Pitzer model parameters,we calcu-lated the values of K ?1?(?NaAl(OH)4,cal 2m Al(OH)4?,exp )/(?NaOH,cal 2m OH ?,exp ).The mean value of K ?1is in the range of the various reference equilibrium constants for the dis-solution reaction of gibbsite.The relative standard deviation of the calculated values of K ?1is only 2.1%,which implies that the relative error of the calculated activity coef ?cients could be ?2.1%.These results indicate that our Pitzer model parameters are reliable.We also estimated the NaAl(OH)4(aq)Pitzer model parameters at other tempera-tures and calculated the gibbsite solubility data with several activity coef ?cients models over a range of the molality of the total alkali and at various temperatures.The comparison

between these activity coef ?cients models indicates that our activity coef ?cients model may be approximately applied to the temperature from 298.2to 323.2K and m NaOHT ?m NaOH ?m NaAl(OH)4from 0to 8mol/kg H 2O.

3.The stoichiometric activity coef ?cients of NaOH and NaAl(OH)4and the activity of H 2O for the NaOH-NaAl(OH)4-H 2O system were calculated with our Pitzer model parameters,respectively.The results show the regu-larities of the activity coef ?cients with the m NaOHT and ?K .All of these regularities imply that the strengths of the repulsive interactions among various anions follow the se-quence of Al(OH)4?-Al(OH)4??Al(OH)4?-OH ??OH ?-OH ?,and the attractive interaction between Al(OH)4?and H 2O is weaker than that between OH ?and H 2O.

Table 9.The osmotic and activity coef ?cients for the NaOH-NaAl(OH)4-H 2O system calculated with set 1of Pitzer model parameters at 313.2K and 0.1MPa in Table 5.m NaOHT (mol/kg H 2O)a

?K b ?cal a w,cal ?NaOH,cal ?NaAl(OH)4,cal

0.0011c 0.98780.999960.9640.9640.011c 0.96460.999650.8990.8950.11c 0.91260.996720.7670.7420.51c 0.86630.984510.6720.59311c 0.85440.969680.6590.5311.51c 0.85380.954900.6710.50021c 0.85780.940060.6940.48231c 0.87150.910100.7560.46251c 0.90580.849430.9190.45271c 0.93920.78909 1.1120.455101c 0.97920.70270 1.4140.4660.001 1.50.98790.999960.9640.9640.01 1.50.96580.999650.8990.8960.1 1.50.92120.996690.7700.7490.5 1.50.89550.984000.6770.6131 1.50.90170.968030.6630.5621.5 1.50.91680.951660.6730.5392 1.50.93530.934820.6930.5293 1.50.97630.899850.7540.5245 1.5 1.05910.826300.9260.5427 1.5 1.13310.75143 1.1500.57010 1.5 1.21810.64475 1.5740.6080.00130.98800.999960.9640.9640.0130.96670.999650.9000.8970.130.92810.996660.7730.7570.530.91620.983630.6820.634130.93340.966930.6670.5951.530.95830.949520.6760.583230.98680.931360.6970.58433 1.04970.892740.7610.60253 1.18610.807610.9620.67273 1.32630.71569 1.2680.761103 1.53340.57550 1.9930.9020.00150.98810.999960.9640.9640.0150.96710.999650.9000.8980.150.93040.996650.7740.7600.550.92210.983520.6840.643150.94180.966640.6690.6091.550.96890.948980.6780.60225 1.00020.930460.6990.60835 1.07030.890750.7660.63855 1.22950.801320.9860.73975 1.40340.70191 1.3410.87010

5

1.6810

0.54570

2.272

1.095

a m NaOHT ?m NaOH ?m NaAl(OH)4.b

?K ?m NaOHT /m NaAl(OH)4.c

A pseudo-state which presumes that all solutes are NaAl(OH)4.

3470J.Zhou et al.

4.The calculated osmotic and activity coef ?cients,and the obtained Pitzer model parameters for the NaOH-NaAl(OH)4-H 2O system provide a reliable thermodynamic basis for the theoretical analysis of the solubilities of alu-minum hydroxides or oxides in solution,the thermodynamic calculations of the deposition process from the supersatu-rated sodium aluminate solutions,and the study on the structure of the solution.

Acknowledgments —We would like to express our great thanks to Dr.David J.Wesolowski for providing much useful information and ad-vice,and we would also like to express our great thanks to three anonymous reviewers for their thorough reviews and useful comments.All of their work has given us great help in preparing the ?nal version.We should also express our thanks to Yong Zhou and Jinju Chen for their friendly help in the ?nal editing.This research is supported by the National Priority Development Project Fundamental Research (project number G1999064902).

Associate editor:D.J.Wesolowski

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三元物系活度系数计算公式

三元物系活度系数计算公式 一、威尔逊公式 1、适用：互溶物系，特别是适用于极性和非极性混合物的活度系数计算 2、关系式 ①???? ??A ++A -+A +A ++A +=323221121 1332121 12213321211)ln(ln x x A x A x x x x A x x x γ ??? ? ??++-+++332231131 1331221133x A x A x A A x A x x A x ②???? ??A ++A -++A +++=313122112 233221 121123322112)ln(ln x A x x A x x A x x A x x A x γ ??? ? ??++-+++332231132 2332211233x A x A x A A x x A x A x ③???? ??A ++A -++A +++=313122113 332231 131133223113)ln(ln x A x x x A x A x x x A x A x γ ??? ? ??++-+++23 3221123 3322311322A x x A x A x A x A x A x 其中：?? ? ??Λ-= RT V V A L L 122 112exp ?? ? ??Λ-= RT V V A L L 211 221exp

??? ??Λ-= RT V V A L L 133 1 13exp ?? ? ??Λ-= RT V V A L L 311 331exp ? ? ? ??Λ-= RT V V A L L 233 223exp ?? ? ??Λ-= RT V V A L L 322 3 32exp --L i V 物系液相摩尔体积，kmol m /3 ； --R 热力学常数，8.314； --T 热力学温度，K ； --Λ威尔逊参数，λλ-=Λ12 λλ-=Λ21 12A 、--21A 端值常数 二、NRTL 公式 1、适用：液液部分互溶物系； 2、一般式 ∑ ∑∑∑∑∑======????? ? ?? ???? ?????? ? ?-+ = C j C k k kj C k kj kj k ij C k k kj ij j C k k ki C j j ji ji i x G G x x G G x x G x G 1 111 1 1ln τττ γ ) exp(ji ji ji a G τ-= RT g g jj ij ij /)(-=τ

Pitzer活度系数模型研究与开发

龙源期刊网 https://www.wendangku.net/doc/412317564.html, Pitzer活度系数模型研究与开发 作者：韩莎莎郑俊强孙晓岩项曙光 来源：《当代化工》2020年第01期 Research and Development of Pitzer Activity Coefficient Model HAN;Sha-sha，ZHENG;Jun-qiang，SUN;Xiao-yan，XIANG;Shu-guang （Process Systems Engineering Institute， Qingdao University of Science and Technology，Shandong Qingdao 266042， China） 自然界、生命体和工业过程中普遍存在着电解质溶液，是化工行业中的重要组成部分，也是众多过程处理的对象，目前逐渐成为许多有机物和無机物反应的良好媒介，因此对电解质溶液的理论研究、电解质溶液的热力学性质的研究及电解质过程模拟研究具有重要的工业实用价值和理论意义。 其中在电解质溶液理论及含电解质溶液体系的热力学性质方面，Debye[1]、Meissner[2]、Bromley[3]、Chen[4]、陆小华[5]、左有祥[6，7]、Loehe[8]、李以圭[9]和杜艳萍[10]等都做出了很大的贡献。目前Pitzer是用于计算水电解质溶液体系（尤其是离子强度为6摩尔以下的强电解质体系）的活度系数等热力学性质较为准确的电解质活度系数模型，也是应用最为广泛的电解质溶液理论。最初1973年，Pitzer修正了D-H理论[1]，得到了经典的半经验Pitzer模型[11]，但适用的浓度较低。随后为了扩大浓度适用范围，用Margules方程修正了短程项，得到了Pitzer[12]（1980年）模型。之后，Bromley[3]（1973年）简化的Pitzer模型、Pitzer[13]（1975年）添加的静电非对称混合项、Fürst和Renon[14]（1982年）研究的多种参数对模型用于1-1型电解质固 液平衡的影响、李以圭[15，16]（1986年）的Pitzer-Li方程、Simonson等[17]（1986年）的Pitzer-Simonson方程、Kim等[18，19]（1988年）回归的高浓度体系参数、Clegg等[20，21]（1992年）的Clegg-Pitzer模型、李以圭等[22，23]（1994和1997年）的Li-Mather模型、Pitzer[24]（1999年）以及Chen等[25]（2008年）都对Pitzer模型做了相应的修正和完善。因此，参照Fortran语言编程如Zemaitis[26]中实现含电解质体系的模拟计算过程，也可通过Visual C++编程语言开发Pitzer模型，实现被已有的支持CAPE-OPEN标准的大型通用化工模拟软件所调用，从而对工业中含电解质溶液过程进行设计、模拟、计算和优化，更好地解决较复杂的工程问题。 本文主要是根据Pitzer修正的水电解质溶液体系活度系数计算模型[13]（1975年模型）进行开发并通过对一些应用实例的模拟计算并验证结果对该开发的Pitzer活度系数模型进行分析、讨论和评价。 1 ;Pitzer活度系数模型

液相活度系数方程总结

液相活度系数方程总结 1、Wohl 模型 Wohl 模型是一个普通模型，可以概括Margules 方程（1895年）、Van Laar 方程（1910年）以及Scatchard-Hamer 方程（1953年）。 Whol 在1946年提出将超额自由焓E G 表示为有效容积分率的函数，并展开成为Mc Laurin 级数： +++=∑∑∑∑∑∑∑∑∑∑i j k l ijkl l k j i i j k ijk k j i i j ij j i i i i E a Z Z Z Z a Z Z Z a Z Z x q RT G （1-1） 式中：i Z ——混合物中i 组分的有效容积分率：1=? = ∑∑i i i i i i i i Z x q x q Z ； i x ——i 组分的摩尔分数； i q ——i 组分的有效摩尔体积； ij a ——i-j 两组分之间的交互作用参数，称为二尾标交互作用参数； ijk a ——i-j-k 三组分之间的交互作用参数，称为三尾标交互作用参数； ijkl a ——i-j-k-l 四组分之间的交互作用参数，称为四尾标交互作用参数； 略去四分子以上集团相互作用项，将式（1-1）用于二元系统时变为： () 1222 2111222112212211332a Z Z a Z Z a Z Z x q x q RT G E ++=+ （1-2） 令： ()12212132a a q A += ()11212232a a q B += 代入上式，根据() j n p T i E i n RT nG ,,ln ? ?? ?????=γ将式（1-2）对i n 进行偏微分，经整理得： ??? ?? ????? ??-+=A q q B Z A Z 2112 2 12ln γ （1-3a ） ??? ?? ????? ??-+=B q q A Z B Z 1222122ln γ （1-3b ） 式（1-3）中包括三个参数A 、B 与12q q ，其值必须用实验值来确定。 2、Scatchard-Hamer eq ． 用纯组分的摩尔体积l V 1及l V 2代替有效摩尔体积1q 及2q ，则式（1-3a ）和式（1-3b ）就变为：

强电解质溶液的活度与活度系数

5.3 强电解质溶液的活度和活度系数 5.3.1 电解质溶液的活度和活度系数 对于非理想溶液，其溶质的化学位可表示为： m a RT ln +=*μμ，m a m γ= m a — 活度（有效浓度） * μ — 标准状态时的化学位，即1a m =时的化学位。 m — 溶质的质量摩尔浓度 γ — 活度系数 对于强电解质溶液，由于电解质在溶剂中解离为离子，故m a m γ=关系不适用于溶质的整体，但对离子本身仍然适用，即： +++γ=m a ，---γ=m a 设某电解质 -+ννA M 在溶液中电离： --++ννν+ν→-+z z A M A M 这时：+* +++=a RT ln μμ， -* --+=a RT ln μμ 而： --++*+=+=μνμνμμa RT ln 又： * --* ++* μν+μν=μ 故： -+ν -ν +?=a a a 因为溶液是电中性的，各种离子的γ、m 无法通过实验测定，而引出“平均离子活度”的概念。 令： -+ν+ν=ν 定义：平均离子活度 ( )νν- ν+ ±-+?=1a a a 平均离子活度系数 ( ) ν ν- ν+±-+γ ?γ =γ1 平均离子浓度 ( ) ν ν- ν+ ±- +?=1m m m 又： m m ++ν=，m m --ν= 得： ① ±±±γ=m a ② ( )ν ν - ν+ν±- +ν?νγ=m a

表格1 298K 时一些1－1价型电解质溶液中TlCl 饱和溶液的±γ 5.3.2 离子强度 由下表可知，当21m m +＜0.021 kg mol -?时，TlCl 的±γ只与（21m m +）有关而 与外加电解质的种类无关。1921年，路易斯（Lewis ）等人在研究了大量不同离子价型电解质对活度系数的影响之后，总结出一个经验规律：在稀溶液中，电解质离子的平均活度系数±γ与溶液中总的离子浓度和电荷有关，而与离子的种类无关。总的离子浓度和电荷对±γ的影响可用公式描述： I z z A -+±-=γlg ——德拜-休克尔（Debye-H ückel ）极限公式 A 是一个只与温度和溶剂性质有关的常数，对于25℃的水溶液，A=0.509kg/mol ；+z 和-z 分别为正负离子的价数；I 为离子强度，它被定义为 ∑= i i i z m I 221 i m 和i z 分别为离子i 的质量摩尔浓度和价数。上述活度系数计算公式适用于I ＜0.01的 稀溶液。对于离子强度更大的浓电解质溶液上述公式需要校正。 5.3.3 溶解度法测定溶液中电解质的±γ 设难溶盐-+ννA M 的饱和溶液存在着下面的平衡： ()s -+ννA M →--+++z z A M νν () () ()() ν ν ν ννγ?? ? ??===±±±-+- + m m a a a K sp

活度系数计算

电解质溶液活度计算理论进展 【摘要】：由于溶液大多数不是理想溶液，需要用活度来代替浓度。活度系数 又是描述活度与浓度的差异程度，因此活度系数的计算对于反应过程相当的重要。近几年，随着活度系数理论模型的不断发展，活度系数的计算方法也在不断的提高、创新。本文在回顾电解质溶液热力学经典理论的基础上，对活度系数计算做了综述。 【关键词】：活度系数活度模型热力学模型活度计算 Electrolyte solution activity in recent years, progress in computational theory Abstract：Solution is not ideal because most of the solution need to replace the concentration of activity. Activity coefficient is described differences in degree of activity and concentration, so the calculation of activity coefficients for the reaction process was very important. In recent years, with the activity coefficient of the continuous development of theoretical models, the calculation of activity coefficients are also constantly improving and innovation. In this paper, recalling the classical theory of thermodynamics of electrolyte solution, based on calculations made on the activity coefficient is reviewed. Keywords: Activity coefficient, Activity Model, Thermodynamic model, Activity calculation 1、活度与活度系数 绝大多数的反应都有溶液（固溶体、冶金熔体及水溶液）参加，而这些溶液经常都不是理想溶液，在进行定量的热力学计算和分析，溶液中各组分的浓度必须代以活度。活度的概念首先由刘易斯(G.N.Lewis)于1907年提出，迅速被应用于电化学,以测定水溶液中电解质的活度系数。活度不能解决冶金熔体的结构问题。它能指出组分在真实溶液与理想溶液中热力学作用上的偏差，但不能提供造成偏差的原因。

活度系数实验报告

实验三 色谱法测定无限稀释溶液的活度系数 一、实验目的 1. 用气液色谱法测定苯和环己烷在邻苯二甲酸二壬酯中的无限稀释活度系数。 2. 通过实验掌握测定原理和操作方法。熟悉流量、温度和压力等基本测量方法。 3. 了解气液色谱仪的基本构造及原理。 二、基本原理 采用气液色谱测定无限稀释溶液活度系数，样品用量少，测定速度快，仅将一般色 谱仪稍加改装，即可使用。目前，这一方法已从只能测定易挥发溶质在难挥发溶剂中的 无限稀释活度系数，扩展到可以测定在挥发性溶剂中的无限稀释活度系数。因此，该法 在溶液热力学性质研究、气液平衡数据的推算、萃取精馏溶剂评选和气体溶解度测定等 方面的应用，日益显示其重要作用。 当气液色谱为线性分配等温线、气相为理想气体、载体对溶质的吸附作用可忽略等 简化条件下，根据气体色谱分离原理和气液平衡关系，可推导出溶质i 在固定液j 上进 行色谱分离时，溶质的校正保留体积与溶质在固定液中无限稀释活度系数之间的关系式。 根据溶质的保留时间和固定液的质量，计算出保留体积，就可得到溶质在固定液中的无 限稀释活度系数。 实验所用的色谱柱固定液为邻苯二甲酸二壬酯。样品苯和环己烷进样后汽化，并与 载气2H 混合后成为气相。 当载气2H 将某一气体组分带过色 谱柱时，由于气体组分与固定液的相互 作用，经过一定时间而流出色谱柱。通 常进样浓度很小，在吸附等温线的线性 范围内，流出曲线呈正态分布，如右图 所示。 设样品的保留时间为r t （从进样到样品峰顶的时间），死时间为d t （从惰性气体空气 进样到其峰顶的时间），则校正保留时间为： d r r t t t -=' （1）

温度、配合物对活度与活度系数的影响

温度、配合物对活度与活度系数的影响 一、温度对活度与活度系数的影响 通常给出的活度系数是在25℃（298K）时的值，对于其他温度下的活度系数，Meissner 提出了如下方程修正q o值 （1） 式中，△t＝t－25；a和b的值对硫酸盐分别为－0.0079和－0.0029，对其他电解质为－0.005和－0.0085。此外，式（2）中的Г值必须改变以修正含有依赖温度的变量D的德拜－体克尔参数。 （2） 二、配合物对活度与活度系数的影响 （一）配合物的形成 德拜－休克尔极限定律对浓度大于10－3mol∕L的强电解质溶渣发生的偏差表明，在这些溶液中，离子间的静电引力不再在决定G ex值时占主导地位。在扩展德拜－休克尔极限定律的各种尝试中，虽然以不同的方式考虑了短程作用，但它们都假定没有因离子间的电子作用形成化学键，也没有新的物质生成。由于目前尚无方法计算这类电子间作用对G ex值的影响，只能作这种假定。对于溶液中各组分之间，不论是离子与离子之间或者离子与中性分子之间反应生成的新化合物，都无法计算其生成自由能。而这类反应对于过程化学和湿法冶金都是十分重要的，为了处理这些反应，过程化学和湿法冶金学家则从另一个角度，即将它们作为化学平衡来处理，用实验测得的平衡常数来定量描述它们。 考虑含一价阴离子L－的溶液中的一个z＋价的金属离子M z＋。它们间发生作用时假定L －是作为配位体，产物称为配合物。配合物分级形成，每一级都由一个平衡常数控制： 与M z＋形成配合物的L－离子的最大数目n称为M z＋的配位数。总的平衡常数β（称为不稳定常数）为 一般形式，累计不稳定常数 βn＝K1K2K3…Kn 若配位体为不带电荷的分子，如氨，平衡亦按同样的方式处理，则每个配合物的电荷数为z＋。

实验二气相色谱法测定无限稀释活度系数(精)

实验二 气相色谱法测定无限稀释活度系数 用经典方法测定汽液平衡数据需消耗较多人力、物力。如果有无限稀释活度系数，则可确定活度系数关联式中的常数，进而可推算出全组成范围内的活度系数。采用气相色谱法测定无限稀释溶液活度系数样品用量少，测定速度快，将一般色谱仪稍加改装即可使用。这一方法不仅能测定易挥发溶质在难挥发溶剂中的无限稀释活度系数，而且已扩展到测定挥发性溶剂中的无限稀释活度系数。 一．实验目的 1．用气相色谱法测定苯和环己烷在邻苯二甲酸二壬酯中的无限稀释活度系数； 2．通过实验掌握测定原理和操作方法。 二．实验原理 1．活度系数计算公式 液相活度系数可以用Wilson 方程来计算，对于二元体系： ln γ1=－ln(x 1+Λ12x 2)+x 2(212112x x Λ+Λ －1 21221x x Λ+Λ) （1） ln γ2=－ln(x 2+Λ21x 1)+x 1(212112x x Λ+Λ －1 21221x x Λ+Λ) （2） 对于无限稀释溶液，则有 )1(ln ln 21121Λ-+Λ-=∞γ （3） )1(ln ln 12212 -Λ+Λ-=∞γ （4） 式中：∞1ln γ——组分1的无限稀释活度系数 ∞2ln γ——组分2的无限稀释活度系数 通过实验测得了∞1ln γ、∞2ln γ，便可求得配偶参数Λ12、Λ21。 2．平衡方程 LittleWood 认为在气相色谱中，载体对溶质的作用不计，固定液与溶质之间有气液溶解平衡关系。 把气体（载气和少量溶质）看成是理想气体，又由于溶质的量很少（只有4-5微升），可以认为吸附平衡时，被吸附的溶质i 分子处于固定液的包围之中，所以有： L L i i i i i i N n r P x r P P ∞∞==00 （5）

电解质溶液活度系数的测定

实验目的 测定不同浓度盐酸溶液中的平均离子活度系数，并计算盐酸溶液中的活度。 实验原理 将理想液体混合物中一组分B 的化学势表示式中的摩尔分数 代之以活度，即可表示真实液体混合物中组分B 的化学势。 /B B B f a x = B f 为真实液体混合物中组分B 的活度因子。真实溶液中溶质B ， 在温度T 、压力P 下，溶质B 的活度系数为： /(/)B B B a b b θ?= 其中B ?为活度因子（或称活度系数）。 电池：Ag ，AgC l|HCL |玻璃|试液||KCL （饱和）| 22Hg Cl Hg ψ膜 L ψ（液接电势） 玻璃电极 | | 甘汞电极 A /gCl Ag ψ ψ ψ=+膜 玻璃 22L H /g Cl Hg ψ ψ= 上述电池的电动势： L E ψ ψ ψ =+-玻璃 Hg Cl /Hg 22 （1） 其中：K+0.059lg a ψ=膜 （K 是玻璃膜电极外、内膜表面性质决定的常数） 当实验温度为250C 时 0.11831lg L E K a ψ ψψ=++--AgCl/Ag Hg Cl /Hg 22 0.11831lg K a =-

K-0.1183lg m γ=±± （2） 上式可改写为： K-0.1183lg -0.1183lg E m γ =± ± 即 lg (0.1183lg )/0.1183K E m γ=--±± 根据得拜——休克尔极限公式，对1——1价型电解质的稀溶液来说，活度系数有下述关系式 0/(/)B B B a b b γ= lg m A γ±=- 所以 (0.1183lg )/0.1183K E m A m --=-± 或 0.1183lg 0.1183E m K A m +=+ 若将不同浓度的HCl 溶液构成单液电池，并分别测出其相应的电动势E 值，以0.11831gm 为纵坐标，以m 为横坐标作图，可得一曲线，将此曲线外推，即可求得K 。求的K 后，再将各不同浓度m 时所测得的相应E 值代入（2）式，就可以算出各种不同浓度下的平均例子活 度系数γ±，同时根据2 2HCL a a ()H Cl a a m γ+-±±±===之关系，算出各溶液中 HCl 相应的活度。 三、仪器药品 仪器: 离子活度计、干电池、移液管若干支； 药品: 0.1mol/L 盐酸溶液。 四、试验步骤 1、溶液配制 分别配置0.005mol/L 、0.01mol/L 、0.02mol/L 、0.05 mol/L 及0.1 mol/L 溶液50mL 2、不同浓度的盐酸溶液的电动势测定

实验讲义- 活度系数电极充放电

活度系数的测定 实验五电解质溶液活度系数的测定 一、实验目的 1、掌握用电动势法测定电解质溶液平均离子活度系数的基本原理和方法。 2、通过实验加深对活度、活度系数、平均活度、平均活度系数等概念的理解。 二、基本原理 活度系数是用于表示真实溶液与理想溶液中任一组分浓度的偏差而引入的一个校正因子，它与活度a、质量摩尔浓度m之间的关系为： (1) 在理想溶液中各电解质的活度系数为1，在稀溶液中活度系数近似为1。对于电解质溶液，由于溶液是电中性的，所以单个离子的活度和活度系数是不可测量、 无法得到的。通过实验只能测量离子的平均活度系数，它与平均活度、平均质量摩尔浓度之间的关系为： (2) 平均活度和平均活度系数测量方法主要有：气液相色谱法、动力学法、稀溶液依数性法、电动势法等。本实验采用电动势法测定ZnCl2溶液的平均活度系数。其原理如下： 用ZnCl2溶液构成如下单液化学电池： 该电池反应为： 其电动势为：(3) (4)

根据：(5) (6) 得：(7) 式中：，称为电池的标准电动势。 可见，当电解质的浓度m为已知值时，在一定温度下，只要测得E 值，再由标准电极电势表的数据求得，即可求得。 值还可以根据实验结果用外推法得到，其具体方法如下： 将代入式（7），可得： (8) 将德拜-休克尔公式：和离子强度的定义： 代入到式（8），可得： (9) 可见，可由图外推至时得到。因而，只要由实验测出用不同浓度的ZnCl2 溶液构成前述单液化学电池的相应电动势E值， 作图，得到一条曲线，再将此曲线外推至m=0，纵坐标上所得的截距即为。 三、仪器及试剂 仪器LK2005A型电化学工作站（天津兰力科化学电子公司），恒温装置一套，标准电池，100 ml容量瓶6只，5 ml和10 ml移液管各1支，250 ml和

活度系数

化工专业实验报告 实验名称：色谱法测定无限稀释溶液的活度系数 实验人员：徐继盛同组人：赵乐、陈思聪 实验地点：天大化工技术实验中心620室 实验时间：2014年4月22号 年级2011 ；专业化学工程与工艺；组号10 ；学号3011207115 指导教师：陈艳英 实验成绩： 天津大学化工技术实验中心印制

一．实验目的 1. 用气液色谱法测定苯和环己烷在邻苯二甲酸二壬酯中的无限稀释活度系数。 2. 通过实验掌握测定原理和操作方法。熟悉流量、温度和压力等基本测量方法。 3. 了解气液色谱仪的基本构造及原理。 二．实验原理 采用气液色谱测定无限稀释溶液活度系数，样品用量少，测定速度快，仅将一般色谱仪稍加改装，即可使用。目前，这一方法已从只能测定易挥发溶质在难挥发溶剂中的无限稀释度系数，扩展到可以测定在挥发性溶剂中的无限稀释活度系数。因此，该法在溶液热力学性质研究、气液平衡数据的推算、萃取精馏溶剂评选和气体溶解度测定等方面的应用，日益显示其重要作用。 当气液色谱为线性分配等温线、气相为理想气体、载体对溶质的吸附作用可忽略等简化条件下，根据气体色谱分离原理和气液平衡关系，可推导出溶质i 在固定液j 上进行色谱分离时，溶质的校正保留体积与溶质在固定液中无限稀释活度系数之间的关系式。根据溶质的保留时间和固定液的质量，计算出保留体积，就可得到溶质在固定液中的无限稀释活度系数。 实验所用的色谱柱固定液为邻苯二甲酸二壬酯。样品苯和环己烷进样后汽化，并与载气H2混合后成为气相。 当载气H2将某一气体组分带过色谱柱时，由于气体组分与固定液的相互作用，经过一定时间而流出色谱柱。通常进样浓度很小，在吸附等温线的线性范围内，流出曲线呈正态分布，如图1所示。 设样品的保留时间为t r（从进样到样品峰顶的时间），死时间为t d（从惰性气体空气进样到其峰顶的时间），则校正保留时间为： （） 校正保留体积为： （） 式中，——校正到柱温、柱压下的载气平均流量，m3/s

电解质溶液活度系数的计算方法

电解质溶液活度系数的计算方法 【摘要】：本文综述了近二十年电解质溶液活度系数计算方法的进展情况。电解质溶液 活度是溶液热力学研究的重要参数，它集中反映了指定溶剂中离子之间及粒子与溶剂之间的相互作用，对离子溶剂化、离子缔合及溶液结构理论的研究具有重要意义【1】。因此，了解电解质溶液活度系数的计算方法意义非凡。 【关键词】：活度系数 ； 电解质溶液 ；计算方法 Abstract: This paper reviews the last two decades the development of calculation methods of the electrolyte solution activity coefficients. Electrolyte solution thermodynamic study of the activity is an important parameter, which has focused on the specified solvent and between the particles and solvent-ion interaction. Of ion solvation, ion association and solution structure of the theoretical study of great significance 【1】.Therefore, to understand the activity coefficients of electrolyte solution methods of calculating has special significance. Key words: activity coefficient ；electrolyte solution ；Calculation 1.引言 近年来电解质溶液理论的发展较快，其研究已逐渐从经典理论和半经验模型向统计力学理论发展，电解质溶液活度计算理论也逐渐成为近期研究的热点。在涉及电解质溶液中的反应，以及和溶液有关的性质，都直接地和溶液的浓度有关。而对电解质溶液，由于和理想溶液有偏差，所以在讨论电解质性质时，就不能用浓度这一概念，对于活度，关键在于活度的计算。 2.电解质溶液活度系数的计算方法 2.1德拜--休格尔理论--非缔合式电解质离子互吸理论 德拜-休格尔提出物理模型：一个阳离子(中心离子)的周围有较多的阴离子形成一种阴离子氛。同样，一个阴离子周围有较多的阳离子．形成一种阳离子氛。中心离子和离子氛之间阴阳离子的分布是不均匀的，因而产生电位，计算不均匀的分布用波尔兹曼公式，计算电位用泊松公式。德拜一休格尔把两者结合起来，并加以简化，得到可用于稀释电解质溶液的泊松——波尔兹曼公式。他们进一步假设中心离子和离子氛之间的电位只起静电吸引作用，然后用简化的泊松—— 渡尔兹曼公式算出了电解质溶液的活度系数。 公式为：I 1z z lg B a I A i +- =- +±γ 式中：±γ--水溶液中电解质的平均活度系数； i a --与离子有效直径有关的常数； +z 、-z -- 正、负离子电荷数； ∑= 2i i Z m 2 1 I 为水溶液的离子强度； 由于该理论不够用于较浓的电解质溶液，半个多世纪来许多化学家都力图改善这个公

活度系数

活度系数 百科名片 活度系数是指活度与浓度的比例系数。在电解质溶液中由于离子之间的相互作用,使电解质的总浓度不能代表其有效浓度,需要引进一个经验校正系数fi(活度系数),以表示实际溶液与理想溶液的偏差。 活度 物理化学中，活度（Activity）即某物质的“有效浓度”，或称为物质的“有效摩尔分数”。此概念由吉尔伯特·牛顿·路易斯首先提出。 将理想混合物中组分i的化学势表示式中的摩尔分数（xi）替换为活度（ai），便可得到真实混合物中组分i的化学势，见下： 理想情况下xi与ai相等。 活度系数（γi，或称“活度因子”）则按下式定义，相当于真实混合物中i偏离理想情况的程度。 电解质的活度系数通常可由测定电动势、溶解度和凝固点等求得。活度系数的大小受温度、水的介电常数、离子的浓度和价数等影响。为使理想溶液（或极稀溶液）的热力学公式适用于真实溶液，用来代替浓度的一种物理量。 溶液 绝大多数的冶金反应都有溶液（固溶体、冶金熔体及水溶液）参加，而这些溶液经常都不是理想溶液。要进行定量的热力学计算和分析，溶液中各组分的浓度必须代以活度。活度是组分的有效浓度（或称热力学浓度）。组分的浓度必须用一系数校正，方能符合于若干物理化学定律（例如质量作用定律、拉乌尔定律、亨利定律、分配定律等等），此校正系数称为活度系数。 ai＝γiNi (1) 式中,ai为溶液中组分i的活度；Ni为溶液中组分i的摩尔分数；γi为溶液中组分i的活度系数。 计算 由拉乌尔定律及亨利定律计算活度溶液是由两种或两种以上的物质（称为组分）组成的均一相。如果异种质点（原子、分子或离子）间的作用力和同种质点间的作用力相同，则此溶液称为理想溶液，而服从拉乌尔定律,也即溶液中组分i的蒸气压pi与其以摩尔分数表示的浓度Ni成正比，比例常数是纯组分i的蒸气： 真实溶液中各组分的质点有的相互吸引，有的有排斥倾向，导致质点间的作用力不同。只有对组分的浓度加以校正，表示蒸气压关系的拉乌尔定律才能适用， pi=p孂(γiNi)