CO2在Na2Cr2O7溶液中的平衡溶解度模型

周恩年 余志辉 曲景奎 齐 涛 韩晓英 张国庆

(1中国科学院过程工程研究所,湿法冶金国家重点实验室,北京100190;2中国科学院过程工程研究所,绿色过程与工程院重点实验室,北京100190;3中国科学院研究生院,北京100049;4四川安县银河建化(集团)有限公司,四川安县622656)

1 Introduction

With the growing demand for cleaner production processes, the manufacture of sodium chromate according to the sulfuric acid method is being gradually phased out and replaced with a process involving the carbonation of aqueous sodium chromate.1-3Very little,however,is known about the fundamental thermodynamic properties of this new processing technology. The process itself involves the absorption of carbon dioxide into an aqueous sodium chromate solution.4,5To investigate the influence of the known by-product NaHCO3on the absorption of CO2,Han et al.6investigated the solubility of CO2in aqueous NaHCO3solutions.To the best of our knowledge,prior to the current study,no research had been conducted to evaluate the influence of the concentration of Na2Cr2O7in the aqueous solution on the solubility of CO2.In the carbonation process for the manufacture of sodium chromate,however,sodium dichromate is generated in significant quantities and could inhibit the carbonation process by decreasing the solubility of CO2. The purpose of this work,therefore,was to investigate the CO2-H2O-Na2Cr2O7vapor-liquid equilibrium system and collect fundamental data pertaining to the manufacture of aqueous sodium chromate according to the carbonation process.To acquire an adequate volume of experimental data to describe the thermodynamic process,the decision was taken to measure the solubility of CO2in aqueous solutions of Na2Cr2O7at several different concentrations(0,0.361,0.650,and 0.901 mol·kg-1) at temperatures and pressures in the ranges of 313.2 to 333.2 K and 0.1 to 1.9 MPa,respectively.The temperature and pressure ranges were chosen to closely reflect the conditions used in the current industrial manufacturing process.2

There have been a large number of experimental studies focused on the solubility of CO2in pure water and salt solutions. Maurer et al.7evaluated the solubility of CO2in aqueous N-methyldiethanolamine and used the Pitzer equation to correlate their data.Feyzi et al.8investigated the solubility of CO2in a 30%(w)aqueous solution of 2-((2-aminoethyl)amino)ethanol and used a thermodynamic model based on the Deshmukh-Mather method to represent their solubility data.Rebolledo-Morales et al.9measured the solubility of CO2in aqueous 1-amino-2-propanol and applied the Kent-Eisenberg model to correlate their solubility data.Ferrentino et al.10measured the solubility of CO2in aqueous NaH2PO4solution using three different thermodynamic models,including the UNIFAC(universal functional activity coefficient)with Peng-Robinson(PR) equation,the Chen-NRTL(non-random two-liquid)model with a Redlich-Kwong equation,and the predictive Soave-Redlich-Kwong equation.Kamps et al.11determined the solubility of CO2in aqueous KCl and K2CO3solutions and the vapor-liquid equilibria of the CO2-KCl-H2O and CO2-K2CO3-H2O systems were described by the Pitzer equation.Gao et al.12determined the solubility of CO2in aqueous NaHCO3and applied the modified Patel-Teja equation of state to describe the system.Wong et al.13determined the solubility of CO2in aqueous HCl and NaHCO3solutions and used the Pitzer equation to correlate their solubility data.Han et al.6measured the solubility of CO2in aqueous NaHCO3solutions and applied the modified Setschenow and PR-Duan equations to correlate their solubility data.There have also been other reports in the literature from Han et al.6providing data for the solubility of CO2in a variety of other salt solutions.To study the influence of Na2Cr2O7on the solubility of CO2,the solubility of CO2in Na2Cr2O7solutions of different concentrations was measured and two thermodynamic models were applied to correlate the experimental data.

2 Experimental

2.1 Materials

All materials are listed in Table 1.

2.2 Apparatus

The solubility was measured according to the static approach that has been reported previously in the literature.9,10,14,15The apparatus used to determine the solubility of CO2is shown in Fig.1.

The experimental setup(model GCF2,Dalianzikong Co., China)consisted of a 1000-mL stainless steel cylindrical tank equipped with a magnetically coupled stirrer attached to its top.The tank could tolerate a maximum pressure of 30 MPa and was attached to a 2XZ-4 vacuum pump,which had a pressure limit of 6×10-2Pa.An electronic balance(Mettler Toledo AL104)with an accuracy of 0.0001 g was used together with aCH2015 thermostatic bath,which had an accuracy of±0.05 K. A gas mass-flow controller(SevenStar CS200)with an uncertainty of±1 mL·min-1was also used as well as a pressure transducer(Rosemount 3051T)with an accuracy of±0.075% of scale(0 to 2.1 MPa).

Table 1 Experiment materials

Fig.1 Schematic representation of the experimental equipment1:magnetic stir;2:equilibrium caldron;3:water bath;4:heating jacket; 5:vacuum pump;6:gas mass-flow controller;7:computer; V1,V2,V3:valves;P:pressure transducer

2.3 Procedure

The aqueous Na2Cr2O7solutions were prepared and their concentrations were determined using a conventional titration method.

All of the air was removed from the equilibrium cell(the whole volume of the equilibrium cell is Vt)using a vacuum pump.Aqueous Na2Cr2O7solutions of known volume(Vsol(the volume of the aqueous Na2Cr2O7solution),500 mL)and concentration were injected into the equilibrium cell.The aqueous Na2Cr2O7solutions were all degassed prior to use.The temperature of the vapor-liquid equilibrium cell was controlled by the thermostatic water bath to within±0.1 K of the desired temperature.The gas volume(V0)was controlled using a gas flow meter that was operated and read from a computer.The gas-liquid equilibrium pressure(peq)was obtained from a pressure transducer when the equilibrium was reached.

The solubility(unit in mol)of CO2in the aqueous Na2Cr2O7solutions was determined from the difference between the amount of CO2(n0),where n0represented the molarity(unit in mol)of CO2initially injected into the equilibrium cell,and the amount of CO2(neq),where neqrepresented the molarity(unit in mol)of CO2remaining in the gas phase when the equilibrium was achieved.The n0value was calculated using equation(1).

where,ρ(CO2)and M(CO2)are the density and molar mass of CO2,respectively.

The neqvalues were determined using the PR equation16,17in concordance with equations(2)to(6),where the pCO2,pH2O,and T represented the CO2partial pressure,water partial pressure, and temperature,respectively,when the equilibrium was achieved,and the symbols Vgand Vmrepresented the volume of gas phase in the equilibrium cell and the molar volume of CO2, respectively.The pCO2value in this instance was computed using Daltonʹs law,and the partial pressure of water(pH2O)in the vapor mixture was the same as the saturation pressure of pure water.18Thus,pH2Ovalues were 0.00737,0.01228,and 0.01988 MPa at 313.2,323.2,and 333.2 K,respectively.

The solubility of CO2in the aqueous Na2Cr2O7solutions was given by mCO2(mol CO2per kg H2O)according to equation(6) as follows: where,msolis the mass of the water(kg)present in the fresh aqueous Na2Cr2O7sample.

Table 2 Comparison of the data for the solubility of CO2in pure water from this work and literature at 303.2 K

The mexvalue was estimated with an uncertainty of 4%.This uncertainty value was determined from the uncertainty values in temperature,pressure,and volume,which were±0.1%, ±0.075%,and±1%,respectively.

2.4 Experimental method validation

To establish the accuracy of the experimental equipment and method used in the current study,we measured the solubility data for CO2in pure water at a temperature of 303.2 K and pressures of 0.1 and 1.5 MPa,and compared the data obtained to those reported by Lide et al.19for the solubility of CO2in pure water.A comparison of these data sets is shown in Table 2.From these data,it was clear that the experiment values differed from the literature values20by 1.6%and-2.0%at 0.1 and 1.5 MPa,respectively,indicating that this equipment was capable of producing accurate solubility results that were in good agreement with the experimental values previously reported in the literature.

3 Experimental results

The solubility of CO2in aqueous Na2Cr2O7solutions was measured at different concentrations(0,0.361,0.650,and 0.901 mol·kg-1)as well as temperatures and pressures in the ranges of 313.2 to 333.2 K and 0.1 to 1.9 MPa,respectively. The experimental results are shown in Table 3.It is clear from these data that the solubility of CO2in aqueous Na2Cr2O7decreased as the concentration of the Na2Cr2O7solution increased at a given temperature and pressure.

4 Thermodynamic models

4.1 Modified Setschenow equation

It is well known that a linear relationship is obeyed between the dissolved CO2concentration and the equilibrium CO2partial pressure in the gas phase of the low pressure region,which can be described as follows according to Henryʹs law.

where H represents the Henry constant.

The modified Setschenow equation20was derived using the concentration of the salt solutions(ms)and T,according to equation(8).

where,ksand k0represent the salting-out effect constants.In this instance,the non-idealities of both the gas and liquid phases were neglected.A combination of equations(7)and(8)pro-vides equation(9).

Table 3 Solubility of CO2in aqueous Na2Cr2O7solutions

In accordance with the work of Li and Mather,the ksand k0parameters,which were dependent upon T,were selected as in equation(10).

The objective function for regression was defined according to equation(11).

where,mcarepresents the correlated solubility of CO2derived from equation(9).

The fitted parameters have been presented in Table 4,whereas the correlation results are shown in Figs.2-4.The average relative deviation in the solubility of CO2in pure water was 3.61%,whereas the value was 4.24%for all of the experimental data.

4.2 PR-Pitzer equation

According to a report in the literature,22the chemical potential of CO2in the liquid phase(μlCO2(T,m))can be related to the temperature(T)and the concentration(m)of physically dissolved CO2as follows:

Table 4 Fitted values for the Henry constants of the CO2-Na2Cr2O7-H2O system derived from the modified Setschenow equation

Furthermore,the chemical potential of CO2in the gas phase ((T,p))can be related to the temperature(T)and the CO2partial pressure(p)as follows:22

From the equality of the chemical potentials of CO2in the liquid and the vapor phases,we obtain equation(14).

Fig.2 Solubility of CO2in the aqueous Na2Cr2O7solutions as a function of pCO2at 313.2 KThe points represent the experimental data.The dotted lines represent the correlated values derived from the modified Setschenow equation. mNa2Cr2O7/(mol·kg-1):■0;▼0.361;■0.650;▼0.901

Fig.3 Solubility of CO2in aqueous Na2Cr2O7solutions as a function of pCO2 at 323.2 KThe points represent the experimental data.The dotted lines represent the correlated values derived from the modified Setschenow equation. mNa2Cr2O7/(mol·kg-1):■0;▲0.361;■0.650;▼0.901

Fig.4 Solubility of CO2in aqueous Na2Cr2O7solutions as a function of pCO2at 333.2 KThe points represent the experimental data.The dotted lines represent the correlated values derived from the modified Setschenow equation. mNa2Cr2O7/(mol·kg-1):■0;▲0.361;■0.650;▼0.901

where,αCO2,fCO2,and φCO2are the activity coefficient,fugacity, and fugacity coefficient of CO2,respectively.and(T,p)represent the standard chemical potentials of CO2in the ideal liquid phase(mCO2=1 mol·kg-1)and in the ideal gas phase (pCO2=1 MPa),respectively.The difference betweenandcan be defined as ΔGm0,CO2.

The fugacity coefficient of CO2(φCO2)can be expressed as follows:

In the current work,the fugacity coefficient of CO2in the pure CO2phase was used as opposed to that of the coefficient from the gas phase of CO2-H2O.In accordance with the work reported by Peng and Robison,23lnφCO2was derived from the following equation.

whereA,B,Z are defined as follows:

lnγCO2was derived from equation(17),which was obtained from Pitzer et al.24-26

where mcand marepresent the concentrations of cations and anions in the liquid phase,respectively,and the parameters λ and ζ are the second-and third-order interaction parameters,respectively.By substituting equation(17)into(14),equation(18)is obtained:

5 Discussion

From the data presented in Tables 2-5 and Figs.2-7,it isclear that the amount of CO2dissolved in the aqueous solutions studied was proportional to the partial CO2pressure and decreased with the increase in the salt concentration.The CO2-H2O-Na2Cr2O7system therefore obeyed Henryʹs law,and the phenomenon can be interpreted according to the“salting-out effect”.The deviations of the two thermodynamics models,including the modified Setschenow and PR-Pitzer equations,were 4.24%and 3.32%,respectively.

Table 5 Temperature dependence of several parameters for the PR-Pitzer equation

Fig.5 Solubility of CO2in aqueous Na2Cr2O7solutions as a function of pCO2at 313.2 KThe points represent the experimental data.The dotted lines represent the correlated values derived from the PR-Pitzer equation. mNa2Cr2O7/(mol·kg-1):■0;▲0.361;■0.650;▼0.901

Fig.6 Solubility of CO2in aqueous Na2Cr2O7solutions as a function of pCO2at 323.2 KThe points represent the experimental data.The dotted lines represent the correlated values derived from the PR-Pitzer equation. mNa2Cr2O7/(mol·kg-1):■0;▲0.361;■0.650;▼0.901

Fig.7 Solubility of CO2in aqueous Na2Cr2O7solutions as a function of pCO2at 333.2 KThe points represent the experimental data.The dotted lines represent the correlated values derived from the PR-Pitzer equation. mNa2Cr2O7/(mol·kg-1):■0;▲0.361;■0.650;▼0.901

To allow for a quantitative study of the influence of Na2Cr2O7on the solubility of CO2,the modified Setschenow equation was applied to calculate the reduction amplitude of the CO2solubility in pure water relative to that of the solubility in an aqueous Na2Cr2O7solution at different concentrations and temperatures.The reduction amplitude(ηCO2)can be defined as follows:

where,mCO2-pureand mCO2-solrepresent the CO2solubility in pure water and in aqueous Na2Cr2O7solutions,respectively.

According to the modified Setschenow equation(9),equation(20)can now be calculated as follows:

Table 6 Reduction amplitude(ηCO2)at Na2Cr2O7concentrations of 0.1,0.5,and 1.0 mol·kg-1and temperatures in the range from 313.2 to 333.2 K

It was clear that at certain temperatures the reduction amplitude was only a function of the concentration of Na2Cr2O7.The reduction amplitude at concentrations of 0.1,0.5,and 1.0 mol· kg-1was calculated at temperatures in the range of 313.2 to 333.2 K.The results are shown in Table 6.

It is clear from Table 6 that the solubility of CO2in the aqueous Na2Cr2O7solutions decreased significantly with increasing Na2Cr2O7concentration.With this in mind,it is therefore necessary to consider the influence of Na2Cr2O7on the absorption of CO2in the carbonization process.

6 Conclusions

The solubility of CO2in aqueous Na2Cr2O7solutions was measured in a stirred vapor-liquid equilibrium cell at temperatures and pressures in the ranges from 313.2 to 333.2 K and 0.1 to 1.9 MPa,respectively.Based on the results,three conclusions were made as follows.

(1)The solubility of CO2in aqueous Na2Cr2O7solutions obeys Henryʹs law and the phenomenon can be interpreted according to the“salting-out effect”.

(2)The modified Setschenow and PR-Pitzer equations provided data that were in good agreement with the experimental data with deviations of 4.24%and 3.32%,respectively.

(3)The Na2Cr2O7concentration had a significant influence on the absorption of CO2and should be taken into consideration during the carbonization process for the manufacture of sodium chromate.

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