American Mineralogist, Volume 58, pages I0I6-1022, 1973

Gibbs Free Energiesof FormationGalculated from Dissolution Data Using Specific 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, , ,labrador- ite, , and 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 . 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; , 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- (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: 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. 31 8 8 0.31 0.69 1.54 0.t5 2.31 3.08 -942,7 -49.69 Anortlrite

Speciflc, AbI241860.2 0.12 0.85 0.02 2.07 L,97 8 7.96 0.12 0.85 0.02 r.16 0.31 -9s9,4 -s3.27 Ideal, Ab12An88 0.12 0.88 1.88 2.12 8 8 0.r2 0.88 1.60 o.28 2.r2 3,20 -9s7.7 -52.06 Righ-K plagloclase***

Specific, Ab440.56 o.42 0.53 I.LI 2.92 B 7,98 o.42 0.53 1.03 0.08 2.92 1.90 -896,4 -40.05 Idea1, Ab,,Or-_ o,44 0.56 I388 o.44 -896.9 -39,7r 4q )o 0.56 0.93 0.07 3 1.86

* Exanple: The subscripf/coefficienL numbers of line 1 refer to the reaction: (N.o.gtcoo.0tKo.o4)(A11.16si2.88)08+7.98H20=0.91r,tp++0.olc^2++0.04r*+1.13j\l(oH);+o.o3At(oH);+2.88H4siu4+2.o7oH-

**Exaopr" (Ab95An1or4) o'" o'ot of calculaEion: for albi.e K" = 1la+J Ia.t*] ["* ]o'oa 1or1or;l l1'13 tlt(on)i 1o'03 lnosiool2'88 1611-12.02 = -41.43 Then, 1og Ks Ac; (producrs) - IAc; (reactanEs)= -840.63 - AC; (albrre) AG"- -1.354 1os Ks Ac; (alblre, Abg5Anlor4)= -840.63 * 1.354 1og Ks = -897.I kcal/mole

***A sPecimenpurchased as and 1abel1ed "" proved to be a high-K vaaiety of plagioclase by bulk chehlcal analyses. Labotatory dissolutlon data (Euengand Kel1er, 1972) are ln accotd with this conposilion.

( 1) The differencein AGol for albite by the two significant in determining stabilities of minerals calculations (Table 3) is 2.4 kcal/mole. The in some geologic systems. AG"r (-894.7 kcal/mole) for albite (AbseAnl) (4) Our data on AGol for anorthite is lower than in terms of the ideal structural formula, however, the reported data of -955.6 kcal/mole for anor- is smaller than the value obtained by Waldbaum thite (An16e)by Barany (1.962). (1966) for low albite (Abroo) (aG", : -884.0 (5)The value for hieh-K plagioclase(-896.4 o'r kcal/mole). The presenceof one mole percent -896.9 kcal/mole) lies just between the value of CaAlzSizOsin our albite sample could signifi- for albite (Abe5An1Ora,or -887.3 kcal/mole, cantly affect the AGo1. this study) and that for microcline (Ab25Or6An7, (2) Our data o'n AG"1 for labradorite in terms -887.3 kcal/mole, or 01166,ideal, -892.6keal/ of the specific mineral formula or the ideal mole, Huang and Keller, 1,972). Our AGol for structural formula (Table 3) lie just between this "high-K plagioglase"specimen indicates that the values for oligoclase and the labradorite the mineral is not andesine;if the sample were (Aba6AnseO\= -932.4 kcal/mole,or Ab46An66 andesine,its AG"t should lie between -910.3 = -932.1 kcal/mole) reported by Huang and for oligoclase and -930.9 kcal/mole for labra- Keller (1972). This addsconfidence to the validity dorite. of the dissolutionmethod used for the calculation of AG"r. (B) AG"r basedon equilibrium with secondaryphase (3) The difterencein AGor for the two bytownite The results of analysesin Table 2 show that the calculationsis 5.8 kcal/mole, which might become concentrationof Al in the solution is less than that ^G.I CALCULATED FROM DISSOLUTION DATA: PLAGIOCLASES 1019

TlsLs 4. Summary of AGor Calculated on the Basis of Equilibrium with SecondaryPhase

Reac Eants Product s Ilineral Fornula Assuned for DlssoluEion

+ (wa K ) (A1 S.i) O+H2O -, Nr*+CoZ++r+ *nrrOHlj+AlroH);+H4sio4+oH A1(oH)3(kca1/iore)

Albi te Speclfic, Ab95Ar10.4 0.91 0.01 0.04 1.16 2.88 8 7.98 0.91 0.01 0.04 0.89 0.02 2.88 1.84 0.25 -897.0* Idea1, Ab99An1 0.99 0.01 1.01 2.99 88 0.99 0.01 0.91 0.03 2.99 r.89 0.07 -894.1

o1i goc1a se Specific, Ab75A"180.7 0.70 0.17 0.06 t,44 2.64 I 7.99 070 0.17 0.06 0.23 0.01 2.64 I.32 L.20 -909r Ideal, AbB0An2O 0.80 0.20 1.20 2.80 88 0.80 0.20 024 0.01 2.80 -1.4i 0.95 -905.9

Labradori te specific, nb5oA'46o.4 0.47 o.43 o 04 7 74 2.34 e l.gt I 0.47 0.43 0.04 0.72 0.02 2.11 \ 47 1.60 -928.9 Ideal, Ab52An48 0.52 0.48 1.48 2.52 8 8 i O.Sz o.4g 0.13 0.02 2.52 1.59 1.33 -926.8

Bycomi te Specific, ob3OA.67O.3 0,31 0.70 0.03 7 87 2.15 1.97 1 o.!- 0.70 0.03 009 0.01 2.r5 r.82 r.t7 -946.1 Idea1, Ab31An69 0.31 0.59 I-69 2.31 I + 0.31 0.69 0.10 0.01 :.]] r.78 L58 -940,o

Anorlhi re Specific, Ab12A"86Or2 0.12 0.85 0.02 2 01 1.97 I 7.96 a 0.12 0.85 o 02 0. 06 0.01 r.97 1.89 2.00 -956.Z Tdea1, lbt2An88 0.12 0.88 I.8a 2.12 88io.tzo.ae 0.07 0.01 2.r2 r.94 1.80 -956.6

High-K plagioclase Specific, Ab44nrS6 0.42 0.53 7.11 2 92 S Z,Sg ? 0.42 0.53 0,34 0.03 2.92 r.26 4.74 -895.6 -896 Idea1. Ab,,Or-- o44 0.56 I 3 B B ? o.44 0.56 0.35 0.03 3 r.32 0.62 .2

*Exampre 0a 89 88 84 of carculalion: to, (Ab95An1or4) r" = 1ll.+10'91 [a^2*]0'01 Io*10 ter(on)f10 llrlonyf;0'02 lrrosroo]2 tou-11 "1irte Then, los K. = -:e.Zt Ac; (products) - IAGi (reactants) = -844.84 -,4c; (albiEe) tc'= -1 354 log Ks Ac; (albite, Ab95Anlo!4) = -844.84 + 1.364 loe K" = -897.0 kcal/mo1e' *i\c; caLculated on Ehe basis of equilibrium with secondary amorphous aluminum hydroxide (Xc; = -271.3 kcal/no1e).

TesLB 5. Comparison of AG": Obtained from Different Calculations

Ac? based Aci based on equilibriun with secondary phase*

AI bi te Specific, Ab9SA"t0.4 -897 .l -897.0 -897.2 -897,6 -891,9

Ideal, AbggAnl -894.1 -894.7 -894 .7 -894.8 -894.9

Ollgoclase specitic, nb7SA"tgo.6 -910,3 -909.1 -910.3 -9r2.2 -913.9 tdedl, AbBOAn2O -906 .8 -905 . 9 -906 .8 -908 .3 -909 .7

Labradorite Specific, AbSOA"46o.4 -930 9 -928.9 -930.5 -931.0 -93s 3

tdeal, -4.b524n48 -928.5 -926.8 -928.2 -930.3 -932.r

Bytomi te specific, Ab30An670.3 -948.5 -946.4 -948.1 -9s1.0 -953.4

tdeal. Ab^.An-^ -942.7 - 940.8 -942.3 -944,9 -947.t JI bY

Specific, obt2A"86u.6 -959.4 -956.2 -958.2 -96r.4 -964.2 10 20 30 40 50 60 70 80 90 Ideal, AbI2AnSe -957,7 -956.6 -958.4 -961.3 -963.8 Mole% An

High-K plagioclase a = -8971;b = = -930 = Specific, Ab44or56 -896.4 -895.5 -896.4 -897.5 -898.6 910 3;c 9; d 9324 e = '948 5; f = -9594; s =-8a7 3; h ='896 4 IdeaI. Ab,,0r-. -896. 9 -896.Z -896,8 -897.8 -898.7 Frc. 1. Triangular diagram showingthe AG"r (kcal/mole) * A: equilibrium with aEorphous A1(OH)3 for the plagioclasesand K-. The value, -887.3 B; equilibrium with nicrocrysralline gibbslte (g) from Huang and C: equilibriuE with gibbslte (LGi =-273.9 kcal/rcle) kcal/mole, for microcline is obtained D: equilibriun with glbbsite (Lci --275 3 kcal/mole) Keller ( 1972). 1020 W. H, HUANG AND W. C. KIANG

Discussion and Conclusions 1) In Figure 1 are plotted the Gibbs free energies of formation for plagioclase minerals of specific mineral formulas (data taken from Table 3) in terms of Ab (albite), An (anorthite), and Or (microcline). Thero is a consistentdecrease of AG"r from Na-rich (albite) to Ca-rich (anorthite) plagio- clase minerals. Specificvalues in the trend are sub- ject to solid-solutionand other compositionaleffects. 2) The Gibbs free energiesof formation (AG"r) E of ideal mineral formulas (data taken from Table 3) = .930 are also plotted againstmole fraction of CaAlzSizOe (N",) in linear, quadratic, and cubic equations in Figures 2 (a), (b), and (c) respectively.Sta- tistical analysesof polynomial regressionof AGo1, Table 6, showsthat at the 1 percentlevel, the linear or quadratic relationship between AGot and Ne^ is highly significant.The cubic relationship,however, is not signifieant at the 1 percent level, but is sig- nificant at the 5 percent level. 3 ) The Gibbs free energy of fo,rmation for a

Motelracrion o[ CaAtZ Si2 0B (B) 0uadratic (NAn)

Frc. 2a. The best linear curve for five experimentally determined AG'r as a function of mole fraction (Nr.) of CaAl,Si"O". The linear equation is AG'r - -893,24 - 0.726 Ne".

of Si with respectto its mineral formula, suggesting € .930 that secondary Al-phase could be formed during the dissolution of plagioclasefeldspar. Thus, sec- ondary phase, such as amorphous aluminum hy- droxide (AGot = -271.3 kcal/mole, Feitknecht and Schindler, 1963), microcrystalline gibbsite (AG"t = -272.3 kcal/mole, Hem and Roberson, 1,967), or gibbsite (AGot = -273.9 kca/mole, Latimer, 1952; tG"t = -275.9 kcal/mole, Parks, 1972), may be assumedin the equilibrium equation from which AGol for plagioclaseis calculated.The results of AG"r frorn such calculations are shown 0.5 Ar in Table 4. Ab Molefraction ot CaAl2 Si208 As shown in Table 5, acor calculatedon the basis (Nnn) of equilibrium with secondary phase (arnorphous quadratic AI(OH)3, microcrystallinegibbsite, or gibbsite) are Ftc. 2b. The best curve for five experimentally determined AG'r as a function of mole fraction (Nr,) of somewhat different from AGo, calculated from CaALSiO'. The quadratic equation is AG"r - -893.70 aqueous solubility data. - 0.683 No" - 0.00048 (Nr")'. ^G.I CALCULATED FROM DISSOLUTION DATA: PLAGIOCLASES tozr

T^c.eI-r6. Polynomial Regression Analysis of Gibbs Free Energies of Formation (aG"r) for Plagioclase Feldspars

(C) Cubic Analysis of Variance Degree of freedon Sw of squares }lean square

The best LC"f= -893.24 - 0.726 NAn

Regress ion L 2632.27 2632.27

Residual 3 5.04 2.0r F = 1305.67(1,3) F1Z (1,3) = 34-r2 Fs7 (7,3) = 10.13 e .930

I The best quadratic equarion aG; = -893.i0 - 0.683NAn - o.ooo48(NAn)2

Regression 2 2636.64 1318.32

Kesadual z r.67 0.83 r = 1570.85(2,2) FrZ Q,2) = 99'00 rsy Q'2) = 19.00

The best cubic equation AG; = -893.88 - 0.640:tAn - 0.00179 (NAn)2+ o.0oool (NAn)3 Regression 3 2636'79 878.93 Resiclual 1 1.53 1.53 = (3.1) 0.5 | 572.04 Frt (3,1) = 5403 Molefraction of CaAl, Sit 0t = (Nnn) rr,, (3,1) 216

Frc. 2c. The best cubis curve for five experimentally determined AG't as a function of mole fraction (Nn") of Tesre 7, Comparison of Gibbs Free Energies of Formation CaAI"SLO'. The cubic equation is AGor = -893.88 for Plagioclase Feldspars (kcal/mole) - 0.640 Nn" - 0.00179 (No")' + 0.00001(No")". Mineral* Exper inental Others '"f plagioclasemineral of specific mineral formula is always a smaller negativequantity of AGot than for Alb ite that of an ideal structural formula. as shown in a (AbnrArrOr') -897. I -884.0 CAb1Oo) Table 7. b (An99Anf) -894 .1 (waldbaun,1966) 4) The valuesof AGorcalculated from dissolutiott 0ligoclase a (AbrtAntuort) -910 , 3 data of specific mineral samples are subject to b (Ab8OAn20) -906.8 uncertaintiesand possible sources of error in (a) mineral sample from Labradorite bulk chemical analysisof the a (abroAnouoro) -930.9 -932.4 (AbOOAn59011)'r'r which the specific mineral formula is calculated; b (AbrrAn.r) -928.5 -931.1 (Ab4OAn6O)'\'! (b) the solutionanalysis; (c) the AGorof ions used By tovni t e in the calculation; (d) the computedspecific rnineral a (AbrOAnUr0ra) -948.5 formula used in calculationof AGot; and (e) the b (Ab3r^n69) establishmentof completeequilibrium in the labora- Anorthite tory dissolution of minerals (Huang and Keller, a (AbrrAnUU0rr) -959.4 -9ss.6 (AnrOO) 1.972\. The facts that our AGor calculatedfrom b (Ab12AnBS) -951.1 (Barany,1962) dissolution data lie betweenthe two end-membered lligh-K plagioclase (Abooorru) -896. values of albite and anorthite, and that there is a a 4 b (Ab440r56) -396.9 consistentdecrease in AGot from Na-rich to Ca-rich plagioclase,suggest that the possible errors tend to '!" -! --r compensateono another,and add confidenceto the J: .: sne.ific minernl lor-' formula ** (1972) validitv of our calculation. Huang and Keller to22 W. H. HUANG AND W, C. KIANG

Acknowledgmenfs LeNcIrrurn,D. (1968) Stability of based on aqueous This work was supported in part by the Faculty Research solubility measurements. Geochim. Cosmochim. Acta, ,32,835-851. Council Award, University of South Florida, and also by (1952) the Earth Science Section, National Science Foundation, Lerruan, W. M. Oxidation Potentials.2nd ed. New pp. NSF Grant GA-33558 to W. H. Huang. We benefited in York, Prentice-Hall, 392 (1972) preparation of this paper from conversations with Professors Pe,nxs, G. A. Free energies of formation and W. D. Keller and D. R. Waldbaum. The authors, however, aqueous solubilities of aluminum hydroxides and oxide take complete responsibility for the content of the pap€r. hydroxides at 25"C. Amer. Mineral. 57, 1165-1189. Rerslr.rN, A. L., eNo W, D. KErrnn (1965) Calculation References of apparent standard free energies of formation of six- BARANv,R. (1962) Heats and free energiesof formation rock forming silicate minerals from solubility data. Amer. of some hydrated and anhydrous - and - Mineral. 5n, 1729-1739. (1969) aluminum silicates. U. S. Bur. Mines Rep. Inoest. 5900, E. E. PIcrsrr, eNo W. D. Kprrrn Alumi- l7 pp. num ions in aqueoussolution. Amer. l. 9ci.,267,99-113. (1963) BERNER,R. A. (1971) Principles of Chemical Sedimentol- RAUrAcH,M. Solubility of simple aluminum com- ogy. McGraw Hill Book Company, N.Y., 240 pp. pounds expectedin soils: I. Hydroxides and oxyhydrox- BurLER, J. N. (1964) Ionic Equilibrium-A Mathematical ides.Austr. l. Soil Res.1,28-35. Approach. Reading, Massachusetts, Addison-Wesley, RossrNr, F. D., D. D. WecrvreN, W. H. EveNs, S. LsvrNe, 547 pp. rNn L Jerrn (1952) Selectedvalues of chemical thermo- properties. FrrrxNrcnr, W., eNo P. ScnrNnrrn (1963) Solubility dynamic U. S. Nat. Bur. Stand. Cir. 500. (1964) Constqnts of Metal Oxides, Metal Hydroxides, and Metal Srrr6N, L. G., eNo H. E. Menrstr Stability con- Hydroxide ,Salls. Butterworths Scientific Press. London. stants of metal-ion complexes. Chem. Soc. London, Spec. 17, pp. Heu, J. D., eNo C. E. RosnnsoN (1967) Form and sta- Pub. 754 (1966) bility of aluminum hydroxide complexes in dilute solution. Weroneurvr, D. R. Calorimetric inuestigation ol the U. S. Geol. Suro. Water-SupplyPa:p. 1827-A. 55 pp. alkali feldspars. Ph.D. Thesis, Harvard University, 247 pp. (1963) HueNc, W. H., aNo W. D. KELLER (1972) Standard free Wrcxs, C. E., eNo T. E. BLocK Thermodynamic properties elements-their oxides, energies of formation calculated from dissolution data of 65 halides, carbines, using specificmineral analyses.Amer. Mineral. 57, ll52- and nitrides. U. S. Bur. Mines Bull.605. 146. 1162. eNo W. C. KreNc (1972) Laboratory dissolution of plagioclase feldspars in water and organic acids at room Manuscript receiued, lanuary 29, 1973; temperature.Amer. Mineral. 57, 1849-1859, accepted for publication, Iuly 3, 1973.