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Gibbs Free Energies of Formation Galculated from Dissolution Data

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Gibbs Free Energies of Formation Galculated from Dissolution Data American Mineralogist, Volume 58, pages I0I6-1022, 1973 Gibbs Free Energiesof FormationGalculated from Dissolution Data Using Specific Mineral Analyses.ll. PlagioclaseFeldspars WnN H. HUANG,nNo WsN C. KreNc Department of Geology, Uniuersity ol South Florida, TamW, Florida 33620 Abstract Gibbs free energiesof formation (AG"r) for plagioclasefeldspars, albite, oligoclase,labrador- ite, bytownite, and anorthite were calculated from the dissolution in aqueous solutions, using (a) the actual mineral formulas derived from the chemical analyses of the specific mineral samples,and (b) the ideal structural formulas of the minerals. Results with AG'r in kcal/mole were: albite, AbnuAn'Or+ -897.1; albite, AboAn,, -894.7; oligoclase, AbrAn:aOrz, -910.3; oligoclase, AbpAn-, -906.8; labradorite, AbmAnrOr,, -930.9; labradorite, Abs,An.e, -928,5: bytownite, Ab*An.Or", -948.5; bytownite, Abr.An., -942.7; anorthite, Ab'rAnmOr,, -959.4, and anorthite, Ab',An"r, -957.7. The Gibbs free energy of formation for a high K-plagioclase (AbuOro) was also calculated to be -896.4 kcal/mole. fntroduction Methods of Calculation Supplernentingthe calculation of Gibbs free en- The detailedsteps and assumptionsfor the cal- ergiesof formation (aGor) for primary rock-forming culation of AGot from the laboratory dissolution silicate minerals (Huang and Keller, 1972\, this data were given in a paper by Huang and Keller paperpresents the calculationof AGol for a seriesof (1972). These include the following: plagioclaseminerals from aqueousdissolution data. (l) Species in the Equilibrium Soltttion. It is possibleto calculate,if chemicalequilibrium is as- Laboratory Work sumed,the proportion of each dissolvedspecies of a Three grams (3.00 gm) eachof freshlyfractured specificelement in the system,where certain species albite, oligoclase,labradorite, bytownite, anorthite, are assumedmore likely to be presentin the system. and a high-K variety of plagioclasein particle size The equilibrium concentration (Huang and Keller, between44 p,m and 150 /rm were equilibratedat 1972) of each speciesin the systemswas calculated room temperaturein deionizedwater for periods (l) from the pH of the solution;(2) from the con- np to 24 days,The detailedexperimental procedure centrationof each cation in the solution in which and analyticalresults have beenpublished in a paper Si, Al, Fe, Mg, Ca, K, and Na were deterrnined by Huang and Kiang (1972). The results of the and reported as moles/liter as in an earlier paper laboratory dissolution show that the dissolution of (Huang and Kiang, 1972); and (3) usingthe con- major cations(Si, Al, Ca, and Na) from the plagio- stants of hydrolysis and dissociationobtained from claseminerals increased very rapidly within the first Sill6nand Martell (1964). The validity of the calcu- 24 hours, sloweddown betweenthe period of one lation is based on the law of mass action (Butler, day and six days, and then reachednear saturation 1964). The results of the calculationof eachAl, Fe, after 24 days. Although complete equilibrium can- Mg, Ca speciesfrom the dissolution of plagioclase not be established,the cation concentrationsat 24 are shownin Table 2. days dissolutionmay be taken as "apparently" equi- (2) Actioities.Using the Debye-Htickelmethod, librated concentrations,and the solubilities (K) ions in the solutionwere computed on an IBM360/65 calculatedfrom theseconcentrations then represent electroniccomputer. "apparent"solubilities. (3) Mineral formulas. The actual mineral for- r0r6 ^G", CALCULATED FROM DISSOLUTION DATA: PLAGIOCLASES 1,0r7 mulas, as determined for each plagioclasefeldspar Trnr-e 2. Analytical Data and Activities of Dissolved from bulk analyses published earlier (Table I, Speciesin the Dissolution of PlagioclaseMinerals Huang and Kiang, 1972), were used in calculation of ,AGor.For comparison,ideal structural formulas Species Moles / Ii ler Act iviEy were also used in calculationof AGot. (I) ALBITE (4) Solubility constants(K')'qnd Gibbs lree ener- pH = 5.81.; ionic stref,gEh = f.Z5 x 10-4 + gies of lormation (AG"). Assuming "apparent" Na 0.231 x 1o-4 0.228 x 1o-4 -4.64 + -a -6- equilibrium in the systems,the solubility constants K 0.332 x 10 " 0.328 x 10 -6.48 ,+ plagioclase 0.548 x 1o-4 0.521 x 1o-4 -4 .24 (K") from aqueousdissolution of min- + A1(0H) ^ 0,518 x ro-5 0.511 x 1o-5 -5.29 erals could be calculated from the most probable -a- -6- A1(oH); 0.121 x 10 0.119 x 10 -6.92 chemical reactions of the minerals in water. Then, H,SiO, 0.156 x to-4 0.166 x 1o-4 -4,78 Gibbs free energiesof formation for the minerals 0H- l0-8,19 -8.19 (aG'r) can be calculatedfrom the following two (II) OLIGOCLASE relationships: (1) AG'" (Gibbs free energiesof pH = 5.83; ionic strength = I.73 x I0-4 + reaction) : -L364log K. (Nernst equation),and Na 0.199x10-4 o196x1o-4 + - - -5.16 - K 0.703 x 10 0,693 x l0 (2) aco" = IAGot (products) IAG"I (react- - 0.758 x 10 0.714 x 10 -4.15 ants), using known Gibbs free energiesof formation A1 (oH) 0.385 x to-5 0.379 x ro-5 -5 .42 2 - - -6.91 for other speciesin equation (2) (Table 1). Al (oil ); 0.126 x 10 0.124 x 10 H,Si0, 0.436 x 1o-4 0.436 x lo-4 -4.36 I 7 -8.17 Results 0H- to-8. (III) (A) data IABRMORI1D LG't based on aqueous solubility pH = 6.05; ionlc strength = 2.86 x 10-5 The analytical data and calculated activities for --+ 0.892 x 1o-5 0.886 x 1o-5 -5.05 the dissolution of the plagioclaseminerals are listed _.+ 0.271 x 1o-5 0.269 x l.o-5 -5.57 )+ in Table 2. Table 3 summarizesthe reactants and 0.103 x 1o-4 o.ro1 x 1o-4 -4 .99 for mloHlj 0.116 x 1o-5 0.115 x 1o-5 the assumedproducts of dissolution calculated -6.68 A1 (0H); 0.208 x ro-6 0.207 x 1o-6 ideal mineral formulas. Points -4.64 both specific and H, SiO, 0.229 x l-o-4 0.229 x 7o-4 7.95 worthy of note are as follows: 0H- 10- (IV) BYTOI,INITT TAsre 1. Gibbs Free Energies of Formation Used in pH = 5.95; ionic strength = 5,74 x 10-5 -L -L Calculation of AG'r Na- 0.153 x I0 0.161 x l0 -4.19 + - - 0.332 x 10 0.330 x 10 -6.48 0.169 x l0 0.163 x 10 -4 .19 - - Species Gi kcal/mo1e Source Ar(on) i 0.158 x 10 0.167 x 10 - ^1 (0H); 0.153 x 10 " 0.162 x 10 -6.79 H,Sio, 0.393 x 10 0.393 x 10 -4.4r Fl,si0, -3t2.8 I{eesnan and Ke11er (1965) '1+ 011- , ^-8.05 -8.05 I1-' -115.0 Rossini et al (1952) - (V) ANORTHITE (0u) -L64.9 Raupach (1963) A1 pH = 5.91; iotric strength = 3.71 x 10-5 A1(0H)l -zro. r Reesman et al (1969) + - - ' 'z Na 0,196 x 10 0.194 x 10 -5.77 -311.3 - - A1(0H);' '4 Reesnan et al (1952) d 0.102 x 10 0.102 x 10 1+ 2+ o.I15 x 10 0.162 x t0 -4.79 Fe-' -20.30 Rossini et al (1952) + - - A1 (0H) ^ 0.885 x l0 0,887 x 10 -6.06 - Fc (01{)+ -52. 58 lluang and Ke11er (1972) (0H) " 0.148 x 10 A1 4 0,149 x 10 t+' ' Fe (Otl)'- -55.9r Rossini ct al (1952) H,Si0. 0,280 x 10 0.280 x 10 -4.55 , ^-8.09 + 0H- -8.09 ." \"../, -106.2 Rossini et al (1952) )-t' (VI) RIGH_KPLAGIOCLASE Ifc- -108.76 Langrnuir (1968) pH = 5.97; ionic strength = 1.05 x 10-5 -t49 Berner (1971) + -L Ilg(0ll)' .76 Na 0-124 x 10 0.121 x 10 UA -132.35 Langnuir (1968) (* 0-187 x 10 0.186 x I0 + ^2+ ' - -5.34 lla -62.59 iiossini et al (1952) 0.474 x L0 0,462 x I0 - A1(0n) i 0.229 x 10 O-21t+x 70' -5.67 K. -67.47 Rossini ct al (1952) - - At (0H); 0.171 x 10 0.170 x 10 0li- -31.63 Iteesnan and Ke1ler (1965) H,Si0, 0.180 x 10 0.180 x 10 -4.14 .^-8.0J -8.03 ilro -56.7 2 Wiclcs and Blocr,: (1963) 0R- l0l8 W. H, HUANG AND W, C. KIANG Tnsl-s 3. The Subscripts* (and/or Coefficients)and Calculated AGor and log K" Values for Laboratory Dissolutions of Several Plagioclase Minerals Reac tants Produc !s Mineral ** Fornula Assuned for Dissolutlon ""t loe K (kca1/no1e) 6 (Na Ca K) (Ar sl)o+H2o ? N.++c.2*+K* *m1on;j +erton[+H4sio4+oH Albtte Speclfic, Ab95A.tOr4 0.91 0.01 0.04 1.16 2.88 8 7.98 0.91 0.01 0.04 1.13 0.03 2.88 2.O7 -897.1 -41.43 Ideal, Ab99An1 0.99 0.01 1.01 2.99 8 8 0.99 0. 0r 0.98 0.03 2.99 r.96 -894.7 -40.36 01lgocIa6e Specific, Ab75Ant80t7 0.70 0.17 0.05 ).,44 2.64 a 7.99 0.70 0.17 0 06 1.39 0.05 2.64 2,44 -910.3 -43.64 Ideal, Ab80An20 0.80 0.20 1.20 2.80 8 8 0.80 0.20 1.15 0.05 2.a0 2,30 -906.8 -42.t8 Labradorite Specific, AbSOh460.4 0.47 0,43 0.04 1-.74 2.34 8 7.97 o.47 0,43 0.O4 7.48 0.26 2.34 2.59 -930.9 -46.72 Ideal, Ab52An4B 0.52 0.48 r.48 2.52 8 I 0,52 0.48 L.26 0.22 -928.5 -4s,70 Bytomlte Specific, Ab304.67o.3 0.31 0.70 0.03 I.87 2,I5 a 7,97 0.31 0.70 0.03 t-.70 0.17 2,t5 3,27 -948.5 -5I.80 Idealr Ab3IAn69 0.31 0.69 1.69 2.
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