陳 香,劉士軍,黃華強

(中南大學(xué)化學(xué)化工學(xué)院,中國 長沙 410083)

298.15 K時CuSO4-NiSO4-H2O三元溶液體系的活度

陳 香,劉士軍*,黃華強

(中南大學(xué)化學(xué)化工學(xué)院,中國 長沙 410083)

用等壓法測定了298.15 K時CuSO4-NiSO4-H2O溶液體系在離子強度范圍為0.387 7～5.798 6 mol·kg-1內(nèi)的滲透系數(shù),用Pitzer離子相互作用模型對實驗結(jié)果進行參數(shù)化研究,獲得了CuSO4和NiSO4純鹽參數(shù)以及混鹽參數(shù),滲透系數(shù)的模型計算值與實驗值的相對偏差為±0.03,表明Pitzer模型能較好描述298.15 K時該溶液體系的熱力學(xué)性質(zhì)；得到了該溶液體系中離子平均活度系數(shù)隨離子強度的變化規(guī)律.

CuSO4-NiSO4-H2O體系；等壓法；滲透系數(shù)；活度系數(shù)；Pitzer模型

電解質(zhì)中各組分的活度是溶液體系的基本性質(zhì),對了解各組分的相互作用及發(fā)展電解質(zhì)溶液理論都具有重要的作用[1-2].同時濕法冶金工藝的建立或優(yōu)化也需要相關(guān)混合電解質(zhì)溶液的活度性質(zhì)作理論指導(dǎo)[3-4].

關(guān)于CuSO4或NiSO4水溶液體系的活度研究已有較多文獻報道.Wetmore和Gordon[5]用電動勢法測定了298.15 K時硫酸銅溶液從0.02 mol·kg-1到飽和濃度的活度系數(shù)；Robinson和Jones[6]采用等壓法測定了硫酸銅(0.1 mol·kg-1～1.4 mol·kg-1)以及硫酸鎳(0.1 mol·kg-1～2.6 mol·kg-1)溶液的滲透系數(shù),并利用Randall-White[7]方程計算了其活度系數(shù)；Brown和Prue[8]采用凝固點降低法測定了稀濃度(<0.1 mol·kg-1)硫酸銅以及硫酸鎳溶液的滲透系數(shù), 討論了硫酸鹽在水溶液中的解離常數(shù)；Downes和Pitzer[9]采用等壓法測定了0.117 4 mol·kg-1～1.555 9 mol·kg-1硫酸銅溶液的滲透系數(shù),擬合獲得了Pitzer模型離子作用參數(shù).Malatesta等[10]用電動勢法測定了極稀濃度(2.969×10-5mol·kg-1)至0.998 mol·kg-1的硫酸鎳溶液298.15 K時的活度系數(shù)；Guendouzi等[11]采用濕度法測定了298.15 K時CuSO4及NiSO4水溶液從0.1 mol·kg-1到飽和濃度的滲透系數(shù)和離子平均活度系數(shù),并擬合得到了Pitzer模型離子相互作用參數(shù).其中,Robinson用等壓法測定的結(jié)果與電動勢法測定的結(jié)果基本一致[6],Miller[12]認為采用凝固點降低法測定的數(shù)據(jù)在低濃度時較等壓法準確,Pitzer[13]發(fā)現(xiàn)Robinson采用等壓法測定的數(shù)據(jù)較可靠,但在低濃度時存在一定的偏差.

在濕法冶金體系中,多元體系的熱力學(xué)性質(zhì)研究更為重要.與CuSO4或NiSO4相關(guān)的三元體系熱力學(xué)性質(zhì)研究已有文獻報道.Downes和Pitzer[9]采用等壓法測定了CuSO4-Na2SO4-H2O以及CuSO4-NaCl-H2O三元體系在298.15 K時的滲透系數(shù)和活度系數(shù),擬合得到了混鹽參數(shù),發(fā)現(xiàn)隨著混鹽參數(shù)的加入,能減小混合體系的滲透系數(shù)計算值與實驗值的偏差.Akilan[14]采用等壓法測定了298.15 K時CuSO4-Na2SO4-H2O和CuSO4-MgSO4-H2O三元體系的滲透系數(shù)以及活度系數(shù),發(fā)現(xiàn)CuSO4-MgSO4-H2O體系遵從Zdanovskii規(guī)則,而CuSO4-Na2SO4-H2O體系對Zdanovskii規(guī)則產(chǎn)生了正偏差,體系中陽離子之間存在較大的相互作用；Arvand等[15]采用電動勢法測定了298.15 K時NiCl2-NiSO4-H2O體系各組分的活度系數(shù),得到了Pitzer模型參數(shù)和Harned方程系數(shù),并計算了其超額吉布斯自由能；姚燕和Atkinson[16]用電動勢法研究CuSO4-Na2SO4-H2O體系的活度性質(zhì),得到了Pitzer模型參數(shù)和Harned方程系數(shù)；王琴萍等[17]用電動勢法測定了HCl-NiSO4-H2O溶液體系中HCl的活度系數(shù),研究表明其服從Harned規(guī)則.

本文用NaCl溶液為參比,采用等壓法測定了CuSO4-NiSO4-H2O體系的滲透系數(shù),并應(yīng)用Pitzer離子相互作用模型擬合滲透系數(shù),從而求得該溶液體系的Pitzer純鹽參數(shù)及混鹽參數(shù),獲得該溶液體系滲透系數(shù)以及離子平均活度系數(shù)隨離子強度的變化規(guī)律,以期為溶液熱力學(xué)提供基礎(chǔ)數(shù)據(jù),并為銅鎳濕法冶金提供指導(dǎo).

1 實驗部分

1.1 試劑及儲備液

NaCl儲備液由優(yōu)級純NaCl(Alfa Aesar化學(xué)有限公司)配制,其濃度由灼燒重量法標定, 3個平行樣的質(zhì)量摩爾濃度的相對偏差小于0.05%.CuSO4和NiSO4儲備液分別采用優(yōu)級純CuSO4·6H2O(Alfa Aesar化學(xué)有限公司)和NiSO4·6H2O(Alfa Aesar化學(xué)有限公司)配制.銅離子濃度由碘量法標定,鎳離子濃度采用EDTA溶液標定,3次平行測定結(jié)果相對誤差均小于0.05%.不同濃度的實驗溶液均采用質(zhì)量稀釋法準確稱重配制.所有溶液的配制均使用二次蒸餾水, 電導(dǎo)率小于1×10-5S/m.

1.2 儀器設(shè)備

本次實驗裝置在文獻[18]裝置的基礎(chǔ)上將箱體內(nèi)不銹鋼固定片換成紫銅固定底座,并增加了等壓杯數(shù),如圖1.所有稱重均采用AB265-s分析天平(Mettler Toledo儀器有限公司), 稱量精度±0.01 mg.

圖1 等壓箱和紫銅底座Fig.1 Diagram of the isopiestic apparatus and the under copper block

1.3 實驗方法

實驗時等壓箱中兩個等壓杯分別放置高低濃度的NaCl參比溶液,其他6個等壓杯放待測液(CuSO4和NiSO4的混合液),待測液中CuSO4的摩爾分數(shù)(YCu)為0～1之間均勻分布.等壓箱放入精確控溫為298.15±0.01 K恒溫水浴中,等壓平衡時間一般為5～12 d,兩參比溶液的濃度相對偏差小于0.2%即認為已達到平衡.

2 結(jié)果與討論

2.1 等壓平衡濃度以及體系水活度和滲透系數(shù)

等壓法的原理是等壓箱中的各溶液在恒溫及等壓的環(huán)境中將達到熱力學(xué)平衡,此時溶劑水具有相同的化學(xué)勢,即待測溶液與參比溶液具有相同的水活度.體系等壓平衡濃度列于表1, 體系水活度的計算公式為：

lnaw=Mwv*m*φ*/1 000.

(1)

式中:v*為參比溶液中1 mol溶質(zhì)在水中完全電離時產(chǎn)生陰陽離子的物質(zhì)的量之和；m*表示平衡時參比溶液溶質(zhì)的質(zhì)量摩爾濃度；MW為水的相對分子質(zhì)量；φ*表示參比溶液滲透系數(shù),其值根據(jù)文獻[19]提供的值擬合得到,偏差小于10-4.參比溶液NaCl的滲透系數(shù)以及CuSO4-NiSO4-H2O體系的水活度列于表1.

a) including the pure salt system only.

圖2 CuSO4-NiSO4-H2O體系等水活度圖Fig.2 Water iso-activity lines for the CuSO4-NiSO4-H2O system at 298.15 K

CuSO4-NiSO4-H2O體系的等水活度線如圖2.從圖2看出,CuSO4-NiSO4-H2O三元體系水活度符合Zdanovskii規(guī)則,表明具有相同的水蒸汽壓的CuSO4和NiSO4溶液形成的混合液也有相同的蒸汽壓.

當(dāng)待測溶液與參比溶液達到等壓平衡時,待測溶液的滲透系數(shù)可由式(2)計算得到:

φ=v*m*φ*/∑mi.

(2)

式中:φ表示待測溶液的滲透系數(shù),∑mi表示等壓平衡時溶液中各物種的總質(zhì)量摩爾濃度,其他物理量意義同上.

298.15 K時待測體系與參比溶液達到等壓平衡后,體系CuSO4-NiSO4-H2O中不同初始濃度的待測液的實驗滲透系數(shù)值列于表1,其中CuSO4以及NiSO4溶液由實驗測定結(jié)果擬合的滲透系數(shù)與文獻值[6, 9]有較好的一致性,結(jié)果如圖3所示,進一步驗證了本實驗裝置和方法的可靠性.

圖3 CuSO4-H2O, NiSO4-H2O體系滲透系數(shù)實驗值與文獻值比較圖Fig.3 Plots of experimental data of osmotic coefficients compared with the literature value for the pure salt at 298.15 K

2.2 溶液體系的Pitzer離子相互作用模型

對于CuSO4-H2O或NiSO4-H2O二元溶液體系, Pitzer滲透系數(shù)方程表達式為：

(3)

表2 298.15 K時CuSO4-H2O以及NiSO4-H2O體系的純鹽參數(shù)

對于CuSO4-NiSO4-H2O混合電解質(zhì)體系,Pitzer滲透系數(shù)方程表達式為：

φ=1+(2mCuSO4+2mNiSO4)-1{2Ifφ+2mCuSO4(mCuSO4+mNiSO4)[BCuSO4φ+

(mCuSO4+mNiSO4)CCuSO4φ]+2mNiSO4(mCuSO4+mNiSO4)[BNiSO4φ+(mCuSO4+

mNiSO4)CNiSO4φ]+mCuSO4mNiSO4[θCu2+Ni2++(mCuSO4+mNiSO4)ψCu2+Ni2+SO42-]}.

(4)

其中,

I=4(mCuSO4+mNiSO4),

fφ=-Aφ[I1/2/(1+1.2I1/2)],

根據(jù)方程(4),由表2中純鹽參數(shù)及表1中混鹽體系的滲透系數(shù)值,回歸擬合得到298.15 K時CuSO4-NiSO4-H2O體系的混鹽參數(shù)θCu2+Ni2+,ψCu2+Ni2+SO42-分別為0.019 63,0.000 46,擬合偏差0.004 4.

將表2中純鹽參數(shù)和混鹽參數(shù)θCu2+Ni2+,ψCu2+Ni2+SO42-代入方程(4)計算該混合體系的滲透系數(shù),所有滲透系數(shù)計算值與實驗值的相對偏差在±0.03以內(nèi),表明該Pitzer模型方程可以較好地描述298.15 K時CuSO4-NiSO4-H2O體系的熱力學(xué)性質(zhì).

2.3 三元溶液體系的離子平均活度系數(shù)

由Pitzer離子相互作用參數(shù)可計算單一電解質(zhì)溶液以及混合電解質(zhì)溶液的離子平均活度系數(shù),其計算公式見文獻[20, 22].

圖4 CuSO4-NiSO4-H2O體系298.15 K時CuSO4離子平均活度 圖5 CuSO4-NiSO4-H2O體系298.15 K NiSO4離子平均系數(shù)與I關(guān)系活度系數(shù)與I關(guān)系Fig.4 Plots of activity coefficients of CuSO4 vs. ionic strength at different YCu aqueous CuSO4-NiSO4-H2O at 298.15 K Fig.5 Plots of activity coefficients of NiSO4 vs. ionic strength at different YCu aqueous CuSO4-NiSO4-H2O at 298.15 K

圖4及圖5為三元體系中CuSO4及NiSO4的離子平均活度系數(shù)隨離子強度的變化關(guān)系.二者的離子平均活度系數(shù)均隨離子強度的增大而減小.相同離子強度下,兩者隨其摩爾分率的增大,離子平均活度系數(shù)均減小.說明在CuSO4-NiSO4-H2O體系中,隨離子強度增大陰陽離子的締合作用顯著,活度系數(shù)降低.混鹽體系的離子平均活度高于純鹽體系的離子平均活度,可能是混鹽體系形成了三離子物(Cu2+-SO42--Ni2+),三離子物的形成促使離子對離解成自由離子,即能削弱離子締合作用[23].對比圖4和圖5可見,在相同的離子強度時,NiSO4的離子平均活度系數(shù)比CuSO4的離子平均活度系數(shù)要大.由此說明,鎳離子結(jié)合水的能力比銅離子強,即水化作用強,自由水分子減少,溶質(zhì)的有效濃度增加,促進溶解,活度系數(shù)上升[24],硫酸鎳在水中的溶解度大于硫酸銅在水中的溶解度也可說明這一點[25].

3 結(jié)論

以NaCl溶液為參比,采用等壓法測定了CuSO4-H2O和NiSO4-H2O單體系的滲透系數(shù),所得數(shù)據(jù)與文獻值吻合較好,驗證了本實驗裝置和方法的可靠性；并測定了298.15K時CuSO4-NiSO4-H2O三元體系的等壓平衡濃度,水活度以及滲透系數(shù)；由單體系和三元體系的滲透系數(shù),獲得了以Pitzer方程為基礎(chǔ)的離子作用模型的純鹽參數(shù)和混鹽參數(shù),由擬合模型參數(shù)計算的滲透系數(shù)值與實驗值的偏差在±0.03以內(nèi)；三元體系CuSO4-NiSO4-H2O的滲透系數(shù)隨離子強度的增大呈先減小后增大的趨勢,二者的離子平均活度系數(shù)都隨離子強度的增大而減小.

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(編輯 楊春明)

Activity Coefficients of CuSO4-NiSO4-H2O System at 298.15 K

CHENXiang,LIUShi-jun*,HUANGHua-qiang

(College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China)

The osmotic coefficients of the CuSO4-NiSO4-H2O system at 298.15 K was determined by the isopiestic method in the ion strength range from 0.387 7～5.798 6 mol/kg. The experimental data were represented by the pitzer ion-interaction model, and the Pitzer ion interaction parameters were obtained from resulting osmotic coefficients by multiple linear regression. The osmotic coefficients values determined experimentally and those calculated by the model in reasonable agreement indicated that the Pitzer model can describle the system’s thermodynamics properties well at 298.15 K. The function between acitivity coefficients and the ionic strength was studied.

CuSO4-NiSO4-H2O system; isopiestic; osmotic coefficients; acitivity coefficients; Pitzer model

2014-05-12

國家973計劃資助項目(2014CB643401)；國家自然科學(xué)基金重點資助項目(51134007)

*

,E-mail：liushijun@hotmail.com/shujunliu@csu.edu.cn

O642

A

1000-2537(2014)05-0043-06