楊 俊，肖劉萍, 滿雪玉，劉士軍

(中南大學(xué)化學(xué)化工學(xué)院，中南大學(xué)有色金屬資源化學(xué)教育部重點(diǎn)實(shí)驗(yàn)室，中國(guó) 長(zhǎng)沙 410083)

硅和鋁分別是地殼中第二及第三豐富的元素，也是地球生態(tài)最重要的元素．許多自然界過(guò)程如礦物形成、巖漿沉積、地下水循環(huán)、及植物生長(zhǎng)等都與硅酸鹽及鋁酸鹽溶液有關(guān)；而鋁冶金、分子篩及各種材料制備、造紙、采油等眾多工業(yè)領(lǐng)域與硅酸鈉溶液及鋁酸鈉溶液更是密切相關(guān)[1-6]．在鋁冶金中，硅酸鈉溶液與鋁酸鈉溶液反應(yīng)生成鈉硅渣而達(dá)到除硅的目的，但同時(shí)易在換熱器及管道內(nèi)結(jié)垢；硅鋁分子篩的結(jié)構(gòu)在很大程度上取決于硅酸鈉溶液的性質(zhì)．因此硅酸鈉溶液的熱力學(xué)性質(zhì)對(duì)地球化學(xué)的研究及相關(guān)生產(chǎn)工藝的設(shè)計(jì)與優(yōu)化具有重要的理論意義．

在硅酸鈉溶液體系中，存在硅酸根離子的質(zhì)子化及聚合等復(fù)雜的相互作用，其溶液結(jié)構(gòu)與濃度、pH值、溫度等因素密切相關(guān)，但在高堿性條件下，一般都認(rèn)為單硅酸根是主要組分[7-11]．這些復(fù)雜的相互作用使得硅酸鈉溶液的熱力學(xué)性質(zhì)具有異于普通電解質(zhì)溶液的規(guī)律，其相關(guān)的研究雖比較困難，但也得到人們的重視[9-14 ]．這些研究主要集中在溶解度、溶液中各組分的活度、及相關(guān)熱力學(xué)模型等方面，而關(guān)于硅酸鈉溶液熱容的研究還未見(jiàn)文獻(xiàn)報(bào)道．

本文用C80微熱量計(jì)步進(jìn)升溫的方法測(cè)定了一系列不同模數(shù)及不同濃度的堿性硅酸鈉溶液(NaOH-Na2SiO3-H2O)在298 K～363 K范圍內(nèi)的恒壓熱容，并建立了該溶液體系恒壓熱容隨總濃度、模數(shù)及溫度變化的模型方程，可為相關(guān)工藝設(shè)計(jì)及優(yōu)化提供基礎(chǔ)數(shù)據(jù)．

1 實(shí)驗(yàn)部分

1.1 試劑和量熱儀器

NaOH(s)(天津試劑三廠)，偏硅酸鈉Na2SiO3·9H2O(s)(天津市光復(fù)精細(xì)化工研究所)均為優(yōu)級(jí)純?cè)噭甆aOH(aq)儲(chǔ)備液根據(jù)文獻(xiàn)[15]配制，其質(zhì)量分?jǐn)?shù)根據(jù)GB629-81(84)由標(biāo)準(zhǔn)鹽酸滴定，3次平行滴定的相對(duì)偏差小于0.1%，碳酸鈉的含量低于總堿度的0.1%．Na2SiO3(aq)儲(chǔ)備液濃度根據(jù)GB/T 4209-2008由標(biāo)準(zhǔn)鹽酸滴定，3次平行滴定的相對(duì)偏差小于0.3%．待測(cè)樣品溶液由已知濃度的Na2SiO3(aq)儲(chǔ)備液、NaOH (aq) 儲(chǔ)備液和高純水三者按確定的比例混合而成．實(shí)驗(yàn)用水皆為超純水系統(tǒng)Synergy UV純化所得的高純水(電導(dǎo)率小于1×10-4S/m)．

熱容測(cè)定采用C80微量熱量計(jì)(Setaram，法國(guó))．該熱量計(jì)恒溫穩(wěn)定性為±0.001 K；分辨率為0.1 μW．測(cè)定前用焦耳校正法對(duì)儀器進(jìn)行校正．采用步進(jìn)升溫模式[16]測(cè)量樣品溶液的升溫焓變，每次升溫5 K，升溫速率0.25 K·min-1，基線維持1 h后繼續(xù)升溫．為避免強(qiáng)堿性待測(cè)溶液對(duì)樣品池的腐蝕，加入一個(gè)與池內(nèi)壁緊密貼在一起聚乙烯塑料內(nèi)襯保護(hù)管．測(cè)量過(guò)程中的參比池為空白，樣品池中裝入5～6 g的樣品溶液，壓強(qiáng)為大氣壓．

1.2 實(shí)驗(yàn)原理和方法

(1)

(2)

(3)

式中Ai(i=1,2,3,4)是方程的回歸系數(shù)．則對(duì)式(3)求導(dǎo)，即得到樣品的恒壓熱容方程；

(4)

2 結(jié)果與討論

2.1 恒壓熱容測(cè)量的可靠性檢驗(yàn)

表1 水的恒壓熱容實(shí)驗(yàn)值Cp和文獻(xiàn)

從表1的結(jié)果可見(jiàn)，測(cè)量結(jié)果與文獻(xiàn)值的相對(duì)偏差小于0.6%，表明本文所采用的實(shí)驗(yàn)方法及儀器可靠．

2.2 堿性硅酸鈉溶液體系的恒壓熱容

表2 樣品溶液的組成*(1 kg溶劑)

*根據(jù)簡(jiǎn)化的NaOH-Na2SiO3-H2O三元溶液體系確定的組成．

No.T/KΔTT0H2/(J·g-1)No.T/KΔTT0H2/(J·g-1)No.T/KΔTT0H2/(J·g-1)302.7018.790302.7518.111307.7517.433307.6637.685307.7136.266312.7135.079312.6156.593312.6654.482317.6652.807317.5675.564317.6372.853322.6170.632322.5494.724322.5991.254327.5788.568327.51113.921327.55109.710332.51106.4911332.46133.1134332.50128.1747337.46124.495337.39152.293337.47146.751342.42142.567342.33171.564342.40165.214347.37160.624347.28190.906347.37183.859352.32178.697352.24210.297352.32202.462357.28196.816357.22229.745357.30221.217362.24214.942362.19249.099362.25239.901302.7518.806302.7617.602302.7418.468307.7137.701307.7135.249307.737.087312.6756.647312.6753.110312.6655.852317.6375.648317.6471.136317.6374.771322.5894.667322.5989.175322.693.782327.53113.744327.55107.306327.55112.7892332.5132.9545332.51125.4728332.51131.888337.46152.182337.46143.627337.46150.991342.42171.463342.43161.882342.42170.167347.37190.756347.41180.213347.37189.332352.33210.132352.36198.495352.33208.563357.27229.470357.32216.908357.29227.826362.25248.997362.26235.384362.25247.126302.7518.149302.7520.352307.7719.521307.7136.250307.7139.695312.7339.227312.6654.412312.6759.138317.6859.005317.6272.692317.6478.708322.6478.908322.5791.002322.6198.350327.698.876327.53109.405327.57118.012332.55118.8513332.51127.9296332.52137.6839337.52138.940337.46146.381337.47157.393342.47158.971342.42164.908342.43177.173347.43179.059347.39183.509347.38196.936352.38199.122352.34202.073352.34216.757357.33219.200357.3220.719357.31236.630362.29239.341362.25239.378362.28256.512

注：1.T0=297.77 K,k=0.350 6，I=1.996 8 mol·kg-1；2.T0=297.79 K,k=0.093 4，I=2.009 1 mol·kg-1；3.T0=297.80 K,k=0.156 9，I=4.013 8 mol·kg-1；4.T0=297.78 K,k=0.079 01，I=3.962 7 mol·kg-1；5.T0=297.78 K,k=0.183 9，I=6.016 5 mol·kg-1；6.T0=297.72 K,k=0.178 3，I=1.239 3 mol·kg-1；7.T0=302.80 K,k=0.410 9，I=5.730 4 mol·kg-1；8.T0=297.78 K,k=0.420 0，I=2.364 3 mol·kg-1；9.T0=302.81 K,k=0.425 0，I=0.879 0 mol·kg-1.

表4 樣品溶液熱容方程(4)的系數(shù)

各樣品溶液的熱容隨溫度的變化關(guān)系如圖2所示．從圖2可見(jiàn)，各樣品溶液的熱容隨溫度的升高而增加，但部分樣品的熱容在較高溫度下有下降的趨勢(shì)．

圖1 樣品溶液的關(guān)系

圖2 各樣品溶液的熱容曲線Fig.2 Curves of Cp～T

2.3 溶質(zhì)的總量對(duì)溶液熱容的影響

在確定溫度下(如308 K及358 K)，堿性硅酸鈉溶液的恒壓熱容隨溶質(zhì)總質(zhì)量分?jǐn)?shù)(wT)的變化關(guān)系如圖3所示，其它溫度時(shí)的變化趨勢(shì)大致相同．

圖3 熱容與溶質(zhì)總量(wT)的關(guān)系 Fig.3 Relationship between heat capacities and mass fraction of the solutes

2.4 溶液的恒壓熱容與溫度及組分含量的關(guān)系

為了確定堿性硅酸鈉溶液的恒壓熱容與NaOH的質(zhì)量分?jǐn)?shù)(wa)、Na2SiO3的質(zhì)量分?jǐn)?shù)(wSi)、及溫度的定量關(guān)系，作者進(jìn)行了模型研究，即將各樣品溶液在不同溫度點(diǎn)的熱容值對(duì)相應(yīng)溶液的wa、wSi及溫度按不同的模型函數(shù)進(jìn)行回歸．計(jì)算發(fā)現(xiàn)，以下模型方程能較好表達(dá)實(shí)驗(yàn)結(jié)果，

(5)

式中k0，ki和pj為相應(yīng)的回歸系數(shù)，其結(jié)果列于表5．

表5 模型方程(5)的系數(shù)

式(5)的計(jì)算值(Cp,mod)與相應(yīng)條件下的測(cè)量值(Cp,exp)比較，其相對(duì)偏差都在1.5%以內(nèi)，表明方程(5)能較好地表達(dá)堿性硅酸鈉溶液的恒壓熱容與NaOH的質(zhì)量分?jǐn)?shù)、Na2SiO3的質(zhì)量分?jǐn)?shù)及溫度的定量關(guān)系．

圖4 確定離子強(qiáng)度和模數(shù)時(shí)堿性硅酸鈉溶液的Cp～T曲線(k=0為NaOH溶液，其值取自文獻(xiàn)[18])Fig.4 Cp～T curves of sodium silicate solutions at determinated modules (when k=0, the solutions are NaOH(aq.), and the Cp is from Ref[18])

在確定的離子強(qiáng)度和模數(shù)時(shí)，溶液的恒壓熱容隨溫度的變化關(guān)系如圖4所示，其中模數(shù)k=0所對(duì)應(yīng)的為NaOH溶液，其值取自文獻(xiàn)[18]．從圖4中可見(jiàn)，確定溫度下堿性硅酸鈉溶液的恒壓熱容隨離子強(qiáng)度的增大而減??；離子強(qiáng)度相同時(shí)，熱容隨模數(shù)的增加而減?。?/p>

3 結(jié)論

實(shí)驗(yàn)測(cè)定了常壓及298～362 K溫度范圍內(nèi)不同濃度下的堿性硅酸鈉溶液(NaOH-Na2SiO3-H2O)的恒壓熱容，建立了堿性硅酸鈉溶液的恒壓熱容隨溫度及溶質(zhì)總量變化的模型方程． 溶液體系的恒壓熱容隨溶質(zhì)總量或離子強(qiáng)度的增大而減小，并呈負(fù)指數(shù)的關(guān)系；而在溫度及離子強(qiáng)度相同時(shí)，溶液的模數(shù)越大，熱容越?。?/p>

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