翦立新，吳曉婭，譚雨齊，陳子芳，尹 霞

(湖南大學(xué) 化學(xué)傳感與計(jì)量學(xué)國(guó)家重點(diǎn)實(shí)驗(yàn)室， 湖南 長(zhǎng)沙 410082)

1 模型方法

為準(zhǔn)確描述電解質(zhì)溶液的熱力學(xué)性質(zhì)，Clegg和Pitzer等人[3]提出了一個(gè)用于計(jì)算任意多元電解質(zhì)溶液由稀到濃的熱力學(xué)性質(zhì)的模型(簡(jiǎn)稱PSC模型)，該模型關(guān)于體系中各物種活度系數(shù)的計(jì)算公式較為復(fù)雜，基本形式如下：

A=a+bT,(A=Bca,WW,ca,UW,ca,VW,ca,Wijk,

QW,ijk,Uijk)

在計(jì)算三元體系及多元體系相圖之前，需要知道體系中各固相的平衡常數(shù).對(duì)任何給定的鹽Mv+Xv-·nH2O，其溶解平衡可表示為：

Mv+Xv-·nH2O=v+M++v-X-+nH2O

達(dá)到平衡時(shí)，平衡常數(shù)K的表達(dá)式為：

lnK=v+lnaM++v-lnaX-+nlnaH2O

aM+,aX-和aH2O分別為M+，X-和水的活度.利用二元模型參數(shù)和二元體系的溶解度數(shù)據(jù)可計(jì)算出不同溫度下的平衡常數(shù)K，并將其與溫度關(guān)聯(lián)成以下形式：

lnK=A+B/T+CT+DlnT

結(jié)合所獲得的二元及三元模型參數(shù)以及不同溫度下的平衡常數(shù)K，就可以計(jì)算三元和四元體系的溶解度.本文在模型計(jì)算中所用的程序均為作者用C語言自行編寫.

2 三元體系溶解度的計(jì)算

2.1 三元體系溶解度的計(jì)算

KCl-H2O體系的PSC模型參數(shù)采用Holmes等人[4]所提供的298.15 K和423.15 K時(shí)的滲透系數(shù)，KNO3-H2O體系的模型參數(shù)擬合于Zeng等人[5]及Barry[6]所給的298.15 K和425.5 K的水活度數(shù)據(jù).對(duì)于MgCl2-H2O體系，本文用Rard等人[7]提供的298.15 K的水活度和Fangh?nel等人[8]所給的373.45 K的水活度擬合二元參數(shù)，Mg(NO3)2-H2O體系的二元參數(shù)擬合于298.15 K[9]和333.15 K[10]的水活度數(shù)據(jù)，NaCl-H2O體系的二元參數(shù)擬合于文獻(xiàn)[11]所提供的298.15 K和348.15 K的水活度，NaNO3-H2O體系的二元參數(shù)采用Pearce等人[12]提供的298.15 K的水活度和Bobmann等人[13]提供的424.96 K的數(shù)據(jù).所有二元參數(shù)與溫度的關(guān)系式列于表1.

表1 二元PSC模型參數(shù)

表2 四元體系中固相的ln K與溫度T (K)的關(guān)系

100 w

100 w

2.2 三元鹽水體系的熱力學(xué)計(jì)算

根據(jù)本組前期研究[2]可知，僅用PSC模型的二元參數(shù)難以準(zhǔn)確計(jì)算三元體系的相圖.為獲得三元鹽水體系的準(zhǔn)確信息，用相關(guān)體系的溶解度數(shù)據(jù)分別擬合三元相互作用參數(shù)，所用實(shí)驗(yàn)數(shù)據(jù)來源及參數(shù)與溫度的關(guān)系式見表3.結(jié)合表1～3中的二元及三元模型參數(shù)分別計(jì)算KCl-MgCl2-H2O,KNO3-Mg(NO3)2-H2O,KCl-KNO3-H2O,MgCl2-Mg(NO3)2-H2O,KNO3-NaNO3-H2O,MgCl2-NaCl-H2O,Mg(NO3)2-NaNO3-H2O,KCl-NaCl-H2O和NaCl-NaNO3-H2O體系的相圖，并與實(shí)驗(yàn)值對(duì)比，結(jié)果見圖2～10.

對(duì)于KCl-KNO3-H2O體系，預(yù)測(cè)了溫度范圍在273.15 K～364.15 K的共飽和線(圖4(a)中的點(diǎn)劃線)，并與文獻(xiàn)值[17](圖4(a)中的符號(hào))進(jìn)行比較，發(fā)現(xiàn)二者完全吻合.同時(shí)計(jì)算了不同溫度下共飽和點(diǎn)組成所對(duì)應(yīng)的飽和溶液的水活度，并按式(4)換算成飽和蒸汽壓，與實(shí)驗(yàn)值[17]進(jìn)行對(duì)比(見圖4(b))，結(jié)果發(fā)現(xiàn)計(jì)算值與實(shí)驗(yàn)值基本一致.

aw(T)=p(T)/p*(T)

式中p(T)和p*(T)分別為溫度T時(shí)鹽溶液和純水的飽和蒸汽壓.

另外將預(yù)測(cè)的KNO3-NaNO3-H2O和NaCl-NaNO3-H2O體系在363.15 K時(shí)飽和溶液的水活度與實(shí)驗(yàn)值[18]對(duì)比，結(jié)果分別見圖6(b)和圖10(b))，預(yù)測(cè)值與實(shí)驗(yàn)值基本吻合，且誤差在實(shí)驗(yàn)值所給誤差范圍內(nèi).

圖3 KNO3-Mg(NO3)2-H2O體系溶解度計(jì)算值與實(shí)驗(yàn)值[14]比較

圖4 KCl-KNO3-H2O體系熱力學(xué)計(jì)算值與實(shí)驗(yàn)值[14, 17, 18]比較

圖5 MgCl2-Mg(NO3)2-H2O體系溶解度的計(jì)算值與實(shí)驗(yàn)值[16]比較

3 四元鹽水體系溶解度的預(yù)測(cè)

圖6 KNO3-NaNO3-H2O體系熱力學(xué)計(jì)算值與實(shí)驗(yàn)值[14, 19]比較

圖7 MgCl2-NaCl-H2O體系溶解度的計(jì)算值與實(shí)驗(yàn)值[14]比較

圖8 Mg(NO3)2-NaNO3-H2O體系溶解度的計(jì)算值與實(shí)驗(yàn)值[16]比較

圖9 KCl-NaCl-H2O體系溶解度的計(jì)算值與實(shí)驗(yàn)值[14]比較

NaNO3 mole fraction (free water)

表3 三元PSC模型參數(shù)

J(Mg2+)

圖12 K+，Na+∥體系干鹽圖的預(yù)測(cè)值與實(shí)驗(yàn)值[22]比較

圖13 Mg2+，Na+∥體系干鹽圖的預(yù)測(cè)值與實(shí)驗(yàn)值[16]比較

圖14 298.15 K時(shí)K+，Mg2+，Na+∥體系干鹽圖的預(yù)測(cè)值與實(shí)驗(yàn)值[25]比較

4 結(jié) 論

表4 K+，Na+∥體系的飽和蒸汽壓預(yù)測(cè)值與實(shí)驗(yàn)值[23]比較

所用的二元模型參數(shù)擬合于水活度或滲透系數(shù)實(shí)驗(yàn)值，三元模型參數(shù)通過擬合三元體系的溶解度實(shí)驗(yàn)數(shù)據(jù)得到.

計(jì)算結(jié)果充分說明應(yīng)用PSC模型，借助有限的二元及三元鹽水體系的實(shí)驗(yàn)數(shù)據(jù)，可較為準(zhǔn)確地預(yù)測(cè)復(fù)雜鹽水體系的熱力學(xué)性質(zhì)，為工程應(yīng)用提供可靠的理論指導(dǎo).

[1]WANG W L, ZENG D W, YIN X,etal． Prediction and measurement of gypsum solubility in the systems CaSO4+ HMSO4+ H2SO4+ H2O (HM = Cu, Zn, Ni, Mn) at 298.15 K[J]. Industrial and Engineering Chemistry Research, 2012, 51: 5124-5134.

[2]YIN X, CHEN Q Y, ZENG D W,etal. Phase diagram of the system KNO3+ LiNO3+ Mg(NO3)2+ H2O[J]. Calphad, 2011, 35: 463-472.

[3]CLEGG S L, PITZER K S, BRIMBLECOMBE P. Thermodynamics of multicomponent, miscible, ionic solutions. Mixtures including unsymmetrical electrolytes[J]. J Phys Chem, 1992, 96(23): 9470-9479.

[4]HOLMES H F, MESME R E. Thermodynamic properties of aqueous solutions of the alkall metal chlorides to 250 ℃[J]. J Phys Chem, 1983, 87: 1242-1255.

[5]ZENG D W, WU Z D, YAO Y,etal. Isopiestic determination of water activity on the system LiNO3+ KNO3+ H2O[J]. J Sol Chem, 2010, 39: 1360-1376.

[6]BARRY J C, RICHTER J, STICH E. Vapour pressures and ionic activity coefficients in the system KNO3+ H2O from dilute solutions to fused salts at 425 K, 452 K and 492 K[J]. Ber Bunsenges Phys Chem, 1988, 92: 1118-1122.

[7]RARD J A, MILLER D G. Isopiestic determination of the osmotic and activity coefficients of aqueous magnesium chloride solutions at 25 ℃[J]. J Chem Eng Data, 1981, 26(1): 38-43.

[8]FANGHANEL T, GRJOTHEIM K. Thermodynamics of aqueous reciprocal salt systems. Ⅲ. Isopiestic determination of osmotic and activity coefficients of aqueous MgCl2, MgBr2, KCl and KBr at 100.3 ℃[J]. Acta Chemica Scandinavica, 1990, 44: 892-895.

[9]RARD J A, WIJESINGHE A M, WOLERY T J. Review of the thermodynamic properties of Mg(NO3)2(aq) and their representation with standard and extended ion-interaction (Pitzer) models at 298.15 K[J]. J Chem Eng Data, 2004, 49: 1127-1140.

[10]EWING W W, KLINGER E, BRANDNER J D. Studies on the vapor pressure-temperature relations and on the heats of hydration, solution and dilution of the binary system magnesium nitrate-water[J]. J Am Chem Soc, 1934, 56: 1053-1057.

[11]GIBBARD JR H F, SCATCHARD G, ROUSSEAU R A,etal. Liquid-vapor equilibrium of aqueous sodium chloride, from 298 to 373 K and from 1 to 6 mol·kg-1, and related properties[J]. J Chem Eng Data, 1974, 19: 281-288.

[12]PEARCE J N, HOPSON H. The vapor pressures of aqueous solutions of sodium nitrate and potassium thiocyanate[J]. J Phys Chem, 1937, 41: 535-538.

[13]BOBMANN E, RICHTER J, STARK A. experimental results and aspects of analytical treatment of vapour pressure measurements in hydrated melts at elevated temperature[J]. Ber Bunsenges Phys Chem, 1993, 97: 240-245.

[14]LINKE W F, SEIDELL A. Solubilities: inorganic and metal-organic compounds[M]． 4th Ed. Washington DC: American Chemical Society, 1965.

[15]FANGHANEL T H, KRAVCHUK K, VOIGT W,etal. Solid-liquid-phase equilibria in the system KCl-MgCl2-H2O at elevated temperatures. Ⅰ. The binary system MgCl2-H2O at 130-250 ℃[J]. Allg Chem, 1987, 547: 21-26.

[16]SIEVERTS A, MULLER H Z. Reciprocal system MgCl2, Na2(NO3)2, H2O[J]. Anorg Allg Chem, 1930, 189: 241-257.

[18]APELBLAT A , KORIN E. Temperature dependence of vapor pressures over saturated aqueous solutions at invariant of the NaCl + KCl + H2O, NaCl + NaNO3+ H2O, KCl + KBr + H2O, KCl + KI + H2O, KCl + KNO3+ H2O, and KCl + K2SO4+ H2O systems[J]. J Chem Eng Data, 2009, 54(5): 1619-1624.

[19]CARROLL S, CRAIG L, WOLERY T. Deliquescence of NaCl-NaNO3, KNO3- NaNO3, and NaCl-KNO3salt mixtures from 90 to 120 ℃[J]. J Geochim Trans, 2005, 6(2): 19-30.

[21]宋彭生, 羅志農(nóng). 三元水鹽體系25 ℃溶解度的預(yù)測(cè)[J]. 化學(xué)通報(bào), 1983, 12: 13-19.

SONG Peng-sheng, LUO Zhi-nong. Prediction of solubiltiy of the ternary salt-water system at 25 ℃[J]. Chemistry(Huaxue Tongbao), 1983, 12: 13-19. (In Chinese)

[22]REINDERS W Z. The reciprocal system KCl + NaNO3= KNO3+ NaCl and the preparation of nitrate[J]. Anorg Allgem Chem, 1915, 93: 202-212.

[23]APELBLAT A, KORIN E. Temperature dependence of vapor pressures over saturated aqueous solutions at invariant points of the NaCl + KNO3+ H2O, NaCl + Na2CO3+ H2O, and NaCl + Na2SO4+ H2O systems[J]. J Chem Eng Data, 2011, 56: 988-994.

[24]黃雪莉, 朱麗娟, 梁濤, 等. 298.16 K Na+, K+, Mg2+//Cl-, NO3--H2O五元體系的相平衡研究[J]. 化學(xué)學(xué)報(bào), 2007, 65: 798-802．