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The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutralization of Na2SiO3
@X6-7037/83/l
Gtwhrmrcu PI Cawnwkimica Am Vol. 47, pp. 1931-1936 Q Pergamon Press Ltd. 1983. Printed in U.S.A.
I1931-06$03.00/0
The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutrali~tion of Na$3i03 J. PETER HERSHEY Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33 149 and IVER W. DUEDALL Department of Oceanography and Ocean Engineering, Florida Institute of Technology, Melbourne, Florida 32901 (Received April 28, 1981; accepted in revisedform August 4, 1983)
Abstract-The partial modal volume of silicic acid f ~(Si(OH).+))in 0.725 M NaCl at 1“C was calculated from the measured volume change (Ap,) due to the neu~i~tion of anhydrous sodium met&l&ate with HCl and the p(HCl) and P(NaCI) obtained from the literature. p(Si(OH),) = 59.0 cm3 moi-‘, determined under experimental conditions of pH = 2.2, compares favorably with V(Si(OH),) = 58.9 cm3 mol-’ calculated from the measured volume change due to the hydrolysis of the meta-silicate salt at pH = 11 and from the partial molal volume due to electrostriction (PC,) of water by charged Si species present in the solution at the high PH. This agreement lends support to a semiempirical model for calculating G;bndeveloped by MILLERO (1969). GINaOH) = -5.45 cm3 mol-’ in 0.725 M NaCl needed for this calculation was also uterine in this work. The rate of ~~~e~tion of Si(OH), at 1“C was monitored to insure that the monomer SifOH), was the main Si species present during the determination of VC5i(OH)4)by neuWalization of the alkali silicate. flSi(OH),) determined in this study compares favorably with the value calculated from high pressure solubility measurements. (a In K,‘dP), = -Ap/‘IRT
!Nl-RODUCMON
SILICA IS one of the most abundant compounds found in continental and oceanic crusts and forms the skeletons of many marine organisms. Hence the physical chemistry and cycles of silica are of great interest to marine geochemistry and to chemical and biological oceanography. Monomeric silicic acid (Si(UH)4), the dissolved form of silica found in natural waters, takes part in many reactions in natural systems. It is known, for example, that terrestrial clays (MACKENZIE et al., 1967; SIEVER, 1968) and marine sediments (WILLEY, 1978) react with Si(OH)h, releasing and taking up SifOH)., in waters that are poor and rich, respectively, in dissolved silica. Although there is general agreement that the relatively low concentrations of Si(OH)4 in the open ocean are biologically controlled, the usually high concentrations of Si@H), found in interstitial waters are determined, in large part, by the competing equilibria of the dissolution of dctrital amorphous silica and of diagenetic silicic acid/clay systems. Additionally, kinetic factors (HURD, 1972, 1973; DAYAL, 1977; LUCE et al., 1972; LAWSON et ai., 1978) are superimposed on these equilibria. Of prime importance in understanding reactions involving Si(OH)4 are its physical solution properties and, in particular, the partial molal volume, J?Si(OH),), at temperatures and solution composition approximating those found near the ocean floor. A knowledge of Isis) permits the calculation of the pressure dependence of reactions involving Si(OH), from
(1)
where AF is the change in partial molal volume of any reaction having, for example, Si(OH)., as a reactant or product; K is the thermodynamic equilibrium constant; P is the pressure in bars; T is the temperature in “K; and R is the universal gas constant. The ~(Si(OH)~) has been determined indirectly (JONES and PYTK~WICZ, 1973; WILLEY, 1974,198O; GRIFFIN, 1980) by measuring the pressure dependence of the solubility of amorphous silica. DUEDALL et al. ( i 976) have determined v(Si(OH),) directly by measuring the partial molal volume change of the hydrolysis of NazSiO, at 20°C. However, their data were for systems of pH = f I and a semiempirical approximation was necessary to correct for electrostriction of solvent by ionized species of silicic acid and its dimers calculated to be present at the high PH. Here we present new experimental results at 1 “C for (1) the partial molal volume change associated with the neutralization (Avn) of Na2SiOs with HCl in 0.725 M (M = molar) NaCl solution, (2) the partial molal volume change due to hydrolysis of the salt (Ar,,) in 0.725 M NaCI, and (3) a new value for V(NaOH) at I “C in 0.725 M NaCl which is necessary for the calculation of r(Si(OH)h) from the hydrolysis reaction. In a separate experiment we examined the rate of polymerization of Si(OH), in 0.725 M NaCl at I “C to insure that monome~c Si(OH)4 was the main Si species present during the experiment to determine A F,, . 1931
1932
J. P. Hershey and I. W. DuedaJJ EXPERIMENTAL
Dilatometer Our approach for determining J$Si(OHh) was the dilatometricmethodpmviowJy&acriborJbyDuuD~and WEYL (1%5).BriefJy,tJremetJmdconsistedofmeasur@ the voJume change resrdtingfrom the disuohrtion OfincmmentaJ additions of a salt into the desired solution. @aJt) (or A.ii, or Av-. the partiaJ moJaJvotume a rest&g from the hydroJ& and neutrahxation, nspectively, of the meta-skate salt) is determined by extrapolating the ratio of cumulative volume change to cumulative mass of salt added (C AV/Z Aw) versus mass of salt added (Z Aw) to Z Aw = 0. In a modification of the diJatometer used by DUEDALL and WEYL(I %5), a SensomxcombinationpH/rekenceeJecuak(Moddf.s~, c.aJibratedusing skndard bulkrs (ROWN and SXXES, J965), was incorporated into the dUometer JhtsJtaJJowing simultaneous monitoring of the pH during a run with an Orion 701 pH-mV meter. TJre measured pH in the test solution (0.725 M N&I) is not a Nation& Bureau ofStanda& scale pH due to the liquid junction potentird ark&g from the transfer of UteeJectm& from the stand& bufk soJution to test soJution. Never&&a, rektive pH values am of sufficient accuracy and pm&Jon (PmroowRz er al., 1966) to insure that the pH values for A?” de&m&ion described below coincide witJ~the pH measumme nts obtained in the exJXrimemtodeteRðemteof~tionofSi(DH)4 (see beknw Rate of Polymerization). All dilabxnetcx expuiments were carried out in a btth maintained at 1.000 +-0.002’C using a Y.S.I. Model 72 pmportktud temperature controJJer.llu temperatum was monitored with a BecJtmann thermometer previousiy caJJbrated with a TJrermometrics Model S JOthermistor and Wheatstone bridge.
Sir& = 0.080 M. A smaJJexcess of HCJ was addeeJ to the HCJ-NaCJ mixture to insure that the pH wouJd remain at 2.2. The soJution was immed&eJy tmn&raJ to a poJyethylene bottle. Solution pmpamtionwas mermostated at I .OO f 0.05”C. The rate of addition oftJreNp2sios sohrtion was adjusted to maintain its pH at 2.2, the estimated isoelectric point of Si(OH), beinS pH = 2.0 (I= 1979). The total time for addition of the NaaSiO, sdution to the HCJ solution was approximateJy 10 minutes. Spectrophotometric measurement of the concentration of monomeric sikic acid wasstarted immediately using the motybdate yebow method described by ILER (1979). Matrix A 0.725 M NaCJ matrix instead of seawater was chosen for the partiaJ moJaJ volume determinations to avoid the precipitation ofinsoh&e sikates. The ionic stren@h of this solution was considered to be similar to seawater of salinity 35%~. Reagents N&Cland NaOH were anaJytiarJ lfede used without fur&r puriktiot Na$K+ was *w Be&s 2048 providedbythePtr&d&&QuattzCompany.ThesaJtwas am@oussodJummet&ks@intbefannofstuaUbeads which facJJitamd d&pent&g into the diJatometer. TJte Na$JO~wasdriedunderJGghvacuumforatlcast J2hours immediateJy pior to use. A purity conection factor for NaaSiOaof98.018, detesmined by potenliometric titration, was used in aU caktdations. RESULTS AND DESCUSSIOJ’J
ofpolymerization of Si(OHj4
Partial molal volume measurements
Rate
AVmof NafiiOs with HCI in 0.725 M NaCl at IT. A volume of 3.65 ml of 4.295 M HCJ was added to the diJatometer, which was then 6JJed with 0.725 NaCJ; the final moJarity was m-ad&&d to 0.725 M (in N&J) by adding an appropriate amount of NaCJ. The diJatometer was thermostated at J.OOO f O.O02*C.Five or six ahquots @groximateJy O.ISgeach)ofanhydrousN~O,wcnaddedinapaiod of six hours, aJJowingabout 40 min between selt additions and the voJume change meaaumments to insure disolution
The extent of polymerixation over time of monomeric Si(OH), in 0.725 M NaCJ was determined to insure that only monomeric siJicic acid was present and that condensation of the monomer to oligomers and higher polymers did not occur during the determination of Av,,. Fiiure J shows a plot of the concentration ver%r time of monomerk sikic acid of a 0.080 M NasSiOs solution acid&d to pH i= 2.2. Prior totbefitutspectmphatomctricm eaatnument$therewas an initial 13% loss of monomer presumably due to polymerization. These rest& am in agreement with ALEXANDER(1954). This initial monomer loss was followed by ~3% polymer formation over a period of et of. (1977) using 29Si about JOhours. ENGELHARDT NMR reported a slow decrease over time of monomer in concentrated silicic acid sohrtions at 0% and pH = 2; they aJso noted a slow increase of various chain and cyclic low molecular we@ht oligomers. The relatively minimaJ polymer formationofthe present study is due to the absence of OH- ion neuxsary to catalyze the condensation reaction @RR, 1979) and the JcineticaJJy uufavornbk! temperature. Furthermore, low pH e@ctiveJy eliminates iouixatioa produds such as Si(OH)sO- and SiOdOH)22- (BUSEY and MESMER, J977). The final concentration of Si(OH), in the dilatometer after a run to determine AT, was roughJy 0.026 M, this Si(OH), concentration is leas than the Si,, = 0.08 M used in the Jcineticz3experiment. Thus monomeric silicic acid should have been the main species present in the Av” runs.
and subsequent tbumal quiiiium.
AT, ojNasSiOs in 0.725 M NaCl41I”C. The diktometer was6JJedwitba0.725MNaCJsoJutionand&emmsm& at J”C.TheadditionsofN~~tothcdilPtometaintbis expetiment were ementiaJJy identical to the measurement of Ap, dmcrJbed above. V(Na0M) in 0.725 M NaCI 111PC. The determination of the RN&H) in 0.725 M NaCJ m&red snecird care due to the hygrosc&c nature of the saJt -kd surkce carbonate formation from atmospheric Co2 uptaJce. NaOH peJkts were ground to a powder and pked into salt disposers underadry,ni~atmoap&m.Thedkpememwere quicJdytrsmsfbrredtoahighvacuumsystemwberethey remainedatJeast4houm.We@iugandadditionofthe s contents were comp@ted quickJy in order to minimize contact with atmospberk H@ and Co,. Rate of polymerization A soJutioo of monomeric siJicic acid was pmpared by a mod&mtionof ALExINDw’s (1954) imn&ure. An amount of2.~gof~y~us~~Iml4~ofN~wasdis~~in85EnlHtOinaTeflcm~hlllIld;the contentsoftJ3efuuneJwaethenaddedwithv&omusatirring to another solution in a 250 mJ voJumetric flask containing __ -_ an equivaJent amount of HCJ and an amount of NaCJ to give a final solution of 0.725 M NaCJ and
J. P. Hershey and I. W. Due&h
1934
The calculation of ~(Si(OH)~) from Aph requires the value of p(NaOH) and RHrO). The P(Na0t-l) in 0.725 M NaCl at 1“C has not been previously reported and was therefore determined as a part of this study. A plot of Z AV/E Aw versus C Aw for NaOH in 0.725 M NaCl is given in Fig. 5. A linear least squares fit of the data gives an intercept of @NaOH) = -5.45 + 0.07 cm3 mol-‘. Substituting r(H,O) (in 0.725 M NaCl) = 18.01 cm3 mol-* and the values for @NaOH) and Ap;, given above into Eqn. (8), a preliminary value (not accounting for electrostriction) for @Si(OH)s) = 54.46 + 0.25 cm3 mol-‘.
Comparison of ~(Si(oH))3 from neutralization and ~~r~~~sis exper~~ts The extrapolation procedure for calculating {AT* + F’NasSiOa)), however, involved Sir& concentrations weil above those in which there was a dramatic drop in pH as C Aw - 0. That is, the hydrolysis of the met@licate salt results in a pH = 11 and the value of @Si(OH),) determined from A& includes the partial molal volume due to soiveat electrostriction, P,, in the 6rst hydration sphere of the charged Si species present, for example, dissociated monomers and dimem and possible d&anions. MUKERJEE (I 96 1) proposed a theoretical model that divides the partial molal volume of an ion, Pk,, , into Pin<, the intrinsic partial molal vokune which is ~0~~0~ to the cube of the crystal radius of the ion, and l?&+ Using ‘this model MILLERO (I 969) derived the following semiempirical equation for calculating Uti from P& data: ~,cci = -7.W/r
(9)
where z is the ionic charge and r is the ionic radius in A. DUEDALL et al. (I 976) considered the pH and total Si concentration dependence of the dimerixation and dkociation equilibria of monomer and dimer. Using constants (BIL~N~KIand INGw, f967) for various dissolved silica species equilibria in 0.5 m NaCl at 25°C and assuming a iiT,1 concentration corresponding to the first wtion in a ~iatometer run, DuEnALL et a!. (1976) determined the monoanion to be the predominant species and calculated (Eqn. 9) t7,k, = -4.4 cm3 mol-‘. Using this value to correct lQi(OHk) obtained from the A p&measurement at 1“C, ~Si(OHh) = 58.9 em3 mol-*. This value is in excellent agreement with P(Si(OH),) = 59.0 cm3 mol” obtained from Ap, measurements. Discrepancy between the two values of p(Si(OHh) may arise from the use of 2YC thermodynamic data to calculate Si speciation for the VW calculation. This agreement lends strong support for the model of MILLER0 (1969) for estimating the partial molal volume due to solvent eimn by an ion and further suppot?s the @Si(OH),) results of DUEDALLet al. ( 1976) determined from Av’ at 20°C.
FIG. 5. Volume change fur the addition of NaOH to a 0.725 M N&l soiution at l°C.
@3i(OH),) directly measured in the present study can be compared with the value of Y(Si(OH)4) calcuIated from the pressure dependence of the equilibrium constant for the dissolution of amorphous silica. The dissolution of amorphous silica is given by SiO, (s) + 2HrO (1) = Si(OHh (aq)
iw
Assuming that AP is a function of pressure, integration of Eqn. (1) and applying it to Eqn. (10) gives RTln KP/P’ = -AL?rt;i(P- 1) t OSAr,(P
- l)* (1 1)
where the equilibrium constants Kp and K” are at pressures P and 1 bar (zero applied), respectively, and can be equated, as a first approximation, to the solubility of silica. APi is the change in partial molal volume for Eqn. (10) and is given by A t’l = ~(Si(OH)~} - 2 V(H*O) - V(Si02, amorph)
(12)
whem Y(Sic)2, amorph) is the molar volume of the solid. AK, is the change in partial molal compressibility for Eqn. (IO). Values of A pi in artificial seawater and in media of similar ionic stren@h obtained (Eqn. 11) from amo~hous silica soiubility measurements by various investigators are given in Table I. Substituting these values and the values of P(HsO) and r/i(SiOz, amorph) into Eqn. (IZ) gives the values of ~Si(OHh~ which are also given in Table I. There is considerable scatter in these data. WILLEY (1980, 1982) noted that AL\picalculated from Eqn. (11) is highiy dependent upon the 1 bar solubility of amorphous silica for which there is also considerabie disagreement. W~LLEY (1982) has suggested that this variability is the result, in part, of the aging of the
1935
Pax&d molal volume of siticic acid Table
I.
ii(SilOHl,) ,calculated from as a function of pressure AV'vl -1 C.3lIWl
Jones and Pytkowiez (1973) willey f1975) Griffin (1980) Hilley 11980) This
Temp.
-5.3 -11.6 -9.0 -11
the
not
astifrcial seLIwster 0.6m N&l 0.7m N&l 0.96 NaCl+ 0.11 NaHCO 0.7251 NaCjf ceport@d,
present
The partial molal volume of silicic acid in 0.725 M NaC1 at i”C was calculated from the volume change due to the neutralization of NazSiOj by HCl and was found to be 59.0 cm3 mol-‘. This value compares favorably with @%(OH).+) = 58.9 cm3 mol-’ calculated from the partial molal volume change for the hydrolysis of NazSi03 in 0.725 M NaCi at 1°C when adjusted for the partial molai volume due to ehxtrostriction of water by ionic species using the semiempirical model by MILLERO (1969). The @Si(OH)J (derived from Ap,,) was successfully determined by the dilatometer method because of the favorably slow kinetics for the condensation of monomeric Si(OH), to higher polymers at the low temperature and PH. The directly measured ~(Si(OH)~) is within experimental error of the value calculated from the results of solubility measurements as a function of pressure. Acknuwledgemenfs-We thank David Hurd, Frank Miller0 on the
manuscript. We also thank the Marine Chemistry Division (Grant No. OCE7621504) in the Oceanographic Section of the National Science Foundation for its support of this work. RBFFXENCXS ALEXANDER G. B. (1954) The preparation of monosili~c acid. J. Amer. Chem. Sot. 75, 2887-2888.
57.9 52.3 54.2 52.7
27.9
59.0b value
~a9
used
(Iler,
work.
CONCLJJSIONS
comments
-1 C13lUOl
27.P 27.9 27.2 27.9
Pn average
silica
V1Si(OH)4)
-1 c103UlCll
silica surface in the ionic medium and reported (WILLEY, 1980) a decrease in surface area, mean pore volume and solubility wiih time. This suggests a change in phase of the silica surface with aging. Averaging five data sets WILLEY (1982) calculated a I bar silica solubiity of 880 t 38 PM. Using this one bar solubihty she then averaged three data sets for aged (over 60 days) silica solubility as a function of pressure and obtained a value of At’, = 55 + 5 cm3 mol-*. The large uncertainty reflects the uncertainty in the 1 bar solubility of amorphous silica. The p(Si(OH)J = 59.0 cm3 mol-r from the present work compares favorably with this value. v(Si(OH),) from the present work is also in good agreement with ~(Si(OH)~) = 56 cm3 mol-’ calculated from the theoretical equations of WALTHER and HELGBsON ( 1977).
and Joan Willey for their constructive
of amorphous
VtSi02,amorph)
Matrix
1.0 was
solubility
OC
2 a 2 2.3
work
a. Since V(SiO2,amorph) 1979). b. Measured value from
the
BILINSKI H.
and INGR! N. (1967) A determination of the formation constant of SiO(OH)s. Acta Chem. &and. 21, 2503-25 10.
BUSEY
R. I-l. and MEsMERR. E. (1977) ionization ~uilib~a ofsihcic acid and polysihcateformation in aqueous sodium
chloride solutions to 300°C. Inorg. C/tern. l&2444-2450.
DAYALR. (1977)Kinetics of silica sorption and clay dissolution reactions at l°C and 670 atm. Geochim. Cosmcxhim. Acta 41, 135-141. DUEDALLI. W. and WEYLP. K. (1965) Apparatus for determining the partial equivalent volume of salts in aqueous solutions. Rev. Sci. Ins@. 36, 528-53 1. DUEDALLI. W., DAYAL R. and WILLEY 3. D. (1976) The partial modal volume of sihcic acid in 0.725 M NaCI. Geochim. Cosmochim. Acta 40, I 183-l 189. ENGELHARDTVON G., ALTENBURG W., HOEBBELD. UND
WIEKERW. (1977) 29-Si-NMR-Spektroskopie an silicatlosungen. IV: Unte~uchu~en zur kondensation der monokieselsaure. Z. Anorg. AIlg. Chem. 428,43-52. GRIFFIN J. W. (1980) The effect of pressure on the soiubi~i~
of I1 silicates in 2*C, pH 8 seawater. M. S. Thesis, University of Hawaii. HARNEDH. S. and OWEN B. B. (1958) The Physical Chemistry ofEteczrolyre ~oiu~io~s, 3rd ed. Van Nostrand, Reinhold, New York. HERSHEYJ. P. (1982) The physical chemistry of aqueous silicic acid: Partial molal vofume and partial moIaf cornpressibility in NaCi solution at 1%. Ph.D. dissertation, State Univ. New York, Stony Brook. HURD D. C. (1972) Factors affecting solution rate of biogenie opai in seawater. Earth Planet. Sci. Left. 15, 41 k-417. HURD D. C. (19‘73) Interactions of bio8enic opal, sediment and seawater in the Central Equatoriai Pacific. Geochim. Cosmochim. Acia 37, 2257-2282. ILERR. K. (1979) The Chemistry of Silica. Wiley-lntersciencc, New York. JONES M. M. and PYTKOWKZ R. M. (1973) Soiubihty of sitica in seawater at high pressures. Bull, Sot. Roy. Sci. 42, 118-120. LAWSOND. S., HURD D. C. and PANWTZ H. S. (1978) Silica dissolution rates of decomposing phytoplankton assemblages at various temperatures. Amer. J. Sci. 278, 1373-1393. LOSJRIXI A., ALZOLAE. M. and MILLEROF. J. (1982) The (P, V, I) properties of concentrated aqueous electrolytes. 1.Densities and apparent molar volumes ofNaC1, NazSO,, MgCi2 and MgSO, solutions from 0.1 mol kg to saturation and from 273: 15 to 323.15’K. J, Chem. Thermodynamics 14,649-662. LUCE R. W., BARTLETTR. W. and PARKS G. A. (1972) Dissolution kinetics of m~esium silicates. Geochim. Cosmochim. Acta 35, 3560.
MACKENZIEF. T., GARREL~R. M., BRICKER0. P. and BICKLEYF. (1967) Silica in seawater: Control by silica minerals. Science 155, 1404-1405.
1936
J. P. Hemhey and I. W. Due&U
MELEROF. J. ( 1969) The partial molal vohunes of ions in
seawater. Limnol. Oceamp. 14, 376-385. MILLEROF. J., LAFERRIERE A. L. and CHETIRKINP. V. (1977) The partial molal volumes of eiectrolytes in 0.725 m sodium chloride at 25’C. J. Bp.s. Chem. 81, 17371745. MUKEiUEEP. (196 1) On ion-solvent interactions. Part 1. Rwtid molal volume of ions in aqueous solution. J. Phys. Chem. 65,740-7&I. I’YTK~WI~ R. M., KBTER ID. R. and BURGENERB. C. ( 1966) R~~u~~ty of pH measurements in seawater. Limnol. Oceanogr.. fl, 417419. ROEIN~~NR. A. and S’IXXESR. H. (1965) Electrolyte Sulutions, 2nd Edition. Buttenvorths, London. SEVER R. (1968) Fstabhshment of equilibrium between clays and seawater. Earth Planet. Sci. Lett. 5, 106-I 10. WALTHERJ. V. and HELGESEIN H. C. (1977) Calculation of the thermodynamic prop&es of aqueous silica and
the solubihty of quartz and its polymorphs at high pressures and temperatures. Amer. J. Sci. 277, 1315- 1351. WSLLEY J. D. (1974) The effectof pressure on the solubihty of amorphous silica in seawater at OOC.Mar. Chem. 2, 239-250. WILLEYJ. D. (1978) Release and uptake of dissolved silica in seawater by marine sediments. ,4&r. Chem.7, 53-65. WILLEYJ. D. (1980) Eikcts of aging on sihca solubihty: A laboratory study. G~him. Cosmochim. Acta 44, 573-538. WILLEYJ. D. (1982) PartiaI moial volume calculations for the dissolution of aged amorphous silica in a&t water and seawater at 0-2°C. Gecchim. Cosmorhim. Acta 46, 13071310. YOUNGT. F. and SMITHhf. B. (1954) Thermodynamics ~~70~~lytm in aqueous sohttion. J. Phys. Chem. 9 *
Gtwhrmrcu PI Cawnwkimica Am Vol. 47, pp. 1931-1936 Q Pergamon Press Ltd. 1983. Printed in U.S.A.
I1931-06$03.00/0
The partial molal volume of silicic acid in 0.725 M NaCl at 1°C determined by the neutrali~tion of Na$3i03 J. PETER HERSHEY Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33 149 and IVER W. DUEDALL Department of Oceanography and Ocean Engineering, Florida Institute of Technology, Melbourne, Florida 32901 (Received April 28, 1981; accepted in revisedform August 4, 1983)
Abstract-The partial modal volume of silicic acid f ~(Si(OH).+))in 0.725 M NaCl at 1“C was calculated from the measured volume change (Ap,) due to the neu~i~tion of anhydrous sodium met&l&ate with HCl and the p(HCl) and P(NaCI) obtained from the literature. p(Si(OH),) = 59.0 cm3 moi-‘, determined under experimental conditions of pH = 2.2, compares favorably with V(Si(OH),) = 58.9 cm3 mol-’ calculated from the measured volume change due to the hydrolysis of the meta-silicate salt at pH = 11 and from the partial molal volume due to electrostriction (PC,) of water by charged Si species present in the solution at the high PH. This agreement lends support to a semiempirical model for calculating G;bndeveloped by MILLERO (1969). GINaOH) = -5.45 cm3 mol-’ in 0.725 M NaCl needed for this calculation was also uterine in this work. The rate of ~~~e~tion of Si(OH), at 1“C was monitored to insure that the monomer SifOH), was the main Si species present during the determination of VC5i(OH)4)by neuWalization of the alkali silicate. flSi(OH),) determined in this study compares favorably with the value calculated from high pressure solubility measurements. (a In K,‘dP), = -Ap/‘IRT
!Nl-RODUCMON
SILICA IS one of the most abundant compounds found in continental and oceanic crusts and forms the skeletons of many marine organisms. Hence the physical chemistry and cycles of silica are of great interest to marine geochemistry and to chemical and biological oceanography. Monomeric silicic acid (Si(UH)4), the dissolved form of silica found in natural waters, takes part in many reactions in natural systems. It is known, for example, that terrestrial clays (MACKENZIE et al., 1967; SIEVER, 1968) and marine sediments (WILLEY, 1978) react with Si(OH)h, releasing and taking up SifOH)., in waters that are poor and rich, respectively, in dissolved silica. Although there is general agreement that the relatively low concentrations of Si(OH)4 in the open ocean are biologically controlled, the usually high concentrations of Si@H), found in interstitial waters are determined, in large part, by the competing equilibria of the dissolution of dctrital amorphous silica and of diagenetic silicic acid/clay systems. Additionally, kinetic factors (HURD, 1972, 1973; DAYAL, 1977; LUCE et al., 1972; LAWSON et ai., 1978) are superimposed on these equilibria. Of prime importance in understanding reactions involving Si(OH)4 are its physical solution properties and, in particular, the partial molal volume, J?Si(OH),), at temperatures and solution composition approximating those found near the ocean floor. A knowledge of Isis) permits the calculation of the pressure dependence of reactions involving Si(OH), from
(1)
where AF is the change in partial molal volume of any reaction having, for example, Si(OH)., as a reactant or product; K is the thermodynamic equilibrium constant; P is the pressure in bars; T is the temperature in “K; and R is the universal gas constant. The ~(Si(OH)~) has been determined indirectly (JONES and PYTK~WICZ, 1973; WILLEY, 1974,198O; GRIFFIN, 1980) by measuring the pressure dependence of the solubility of amorphous silica. DUEDALL et al. ( i 976) have determined v(Si(OH),) directly by measuring the partial molal volume change of the hydrolysis of NazSiO, at 20°C. However, their data were for systems of pH = f I and a semiempirical approximation was necessary to correct for electrostriction of solvent by ionized species of silicic acid and its dimers calculated to be present at the high PH. Here we present new experimental results at 1 “C for (1) the partial molal volume change associated with the neutralization (Avn) of Na2SiOs with HCl in 0.725 M (M = molar) NaCl solution, (2) the partial molal volume change due to hydrolysis of the salt (Ar,,) in 0.725 M NaCI, and (3) a new value for V(NaOH) at I “C in 0.725 M NaCl which is necessary for the calculation of r(Si(OH)h) from the hydrolysis reaction. In a separate experiment we examined the rate of polymerization of Si(OH), in 0.725 M NaCl at I “C to insure that monome~c Si(OH)4 was the main Si species present during the experiment to determine A F,, . 1931
1932
J. P. Hershey and I. W. DuedaJJ EXPERIMENTAL
Dilatometer Our approach for determining J$Si(OHh) was the dilatometricmethodpmviowJy&acriborJbyDuuD~and WEYL (1%5).BriefJy,tJremetJmdconsistedofmeasur@ the voJume change resrdtingfrom the disuohrtion OfincmmentaJ additions of a salt into the desired solution. @aJt) (or A.ii, or Av-. the partiaJ moJaJvotume a rest&g from the hydroJ& and neutrahxation, nspectively, of the meta-skate salt) is determined by extrapolating the ratio of cumulative volume change to cumulative mass of salt added (C AV/Z Aw) versus mass of salt added (Z Aw) to Z Aw = 0. In a modification of the diJatometer used by DUEDALL and WEYL(I %5), a SensomxcombinationpH/rekenceeJecuak(Moddf.s~, c.aJibratedusing skndard bulkrs (ROWN and SXXES, J965), was incorporated into the dUometer JhtsJtaJJowing simultaneous monitoring of the pH during a run with an Orion 701 pH-mV meter. TJre measured pH in the test solution (0.725 M N&I) is not a Nation& Bureau ofStanda& scale pH due to the liquid junction potentird ark&g from the transfer of UteeJectm& from the stand& bufk soJution to test soJution. Never&&a, rektive pH values am of sufficient accuracy and pm&Jon (PmroowRz er al., 1966) to insure that the pH values for A?” de&m&ion described below coincide witJ~the pH measumme nts obtained in the exJXrimemtodeteRðemteof~tionofSi(DH)4 (see beknw Rate of Polymerization). All dilabxnetcx expuiments were carried out in a btth maintained at 1.000 +-0.002’C using a Y.S.I. Model 72 pmportktud temperature controJJer.llu temperatum was monitored with a BecJtmann thermometer previousiy caJJbrated with a TJrermometrics Model S JOthermistor and Wheatstone bridge.
Sir& = 0.080 M. A smaJJexcess of HCJ was addeeJ to the HCJ-NaCJ mixture to insure that the pH wouJd remain at 2.2. The soJution was immed&eJy tmn&raJ to a poJyethylene bottle. Solution pmpamtionwas mermostated at I .OO f 0.05”C. The rate of addition oftJreNp2sios sohrtion was adjusted to maintain its pH at 2.2, the estimated isoelectric point of Si(OH), beinS pH = 2.0 (I= 1979). The total time for addition of the NaaSiO, sdution to the HCJ solution was approximateJy 10 minutes. Spectrophotometric measurement of the concentration of monomeric sikic acid wasstarted immediately using the motybdate yebow method described by ILER (1979). Matrix A 0.725 M NaCJ matrix instead of seawater was chosen for the partiaJ moJaJ volume determinations to avoid the precipitation ofinsoh&e sikates. The ionic stren@h of this solution was considered to be similar to seawater of salinity 35%~. Reagents N&Cland NaOH were anaJytiarJ lfede used without fur&r puriktiot Na$K+ was *w Be&s 2048 providedbythePtr&d&&QuattzCompany.ThesaJtwas am@oussodJummet&ks@intbefannofstuaUbeads which facJJitamd d&pent&g into the diJatometer. TJte Na$JO~wasdriedunderJGghvacuumforatlcast J2hours immediateJy pior to use. A purity conection factor for NaaSiOaof98.018, detesmined by potenliometric titration, was used in aU caktdations. RESULTS AND DESCUSSIOJ’J
ofpolymerization of Si(OHj4
Partial molal volume measurements
Rate
AVmof NafiiOs with HCI in 0.725 M NaCl at IT. A volume of 3.65 ml of 4.295 M HCJ was added to the diJatometer, which was then 6JJed with 0.725 NaCJ; the final moJarity was m-ad&&d to 0.725 M (in N&J) by adding an appropriate amount of NaCJ. The diJatometer was thermostated at J.OOO f O.O02*C.Five or six ahquots @groximateJy O.ISgeach)ofanhydrousN~O,wcnaddedinapaiod of six hours, aJJowingabout 40 min between selt additions and the voJume change meaaumments to insure disolution
The extent of polymerixation over time of monomeric Si(OH), in 0.725 M NaCJ was determined to insure that only monomeric siJicic acid was present and that condensation of the monomer to oligomers and higher polymers did not occur during the determination of Av,,. Fiiure J shows a plot of the concentration ver%r time of monomerk sikic acid of a 0.080 M NasSiOs solution acid&d to pH i= 2.2. Prior totbefitutspectmphatomctricm eaatnument$therewas an initial 13% loss of monomer presumably due to polymerization. These rest& am in agreement with ALEXANDER(1954). This initial monomer loss was followed by ~3% polymer formation over a period of et of. (1977) using 29Si about JOhours. ENGELHARDT NMR reported a slow decrease over time of monomer in concentrated silicic acid sohrtions at 0% and pH = 2; they aJso noted a slow increase of various chain and cyclic low molecular we@ht oligomers. The relatively minimaJ polymer formationofthe present study is due to the absence of OH- ion neuxsary to catalyze the condensation reaction @RR, 1979) and the JcineticaJJy uufavornbk! temperature. Furthermore, low pH e@ctiveJy eliminates iouixatioa produds such as Si(OH)sO- and SiOdOH)22- (BUSEY and MESMER, J977). The final concentration of Si(OH), in the dilatometer after a run to determine AT, was roughJy 0.026 M, this Si(OH), concentration is leas than the Si,, = 0.08 M used in the Jcineticz3experiment. Thus monomeric silicic acid should have been the main species present in the Av” runs.
and subsequent tbumal quiiiium.
AT, ojNasSiOs in 0.725 M NaCl41I”C. The diktometer was6JJedwitba0.725MNaCJsoJutionand&emmsm& at J”C.TheadditionsofN~~tothcdilPtometaintbis expetiment were ementiaJJy identical to the measurement of Ap, dmcrJbed above. V(Na0M) in 0.725 M NaCI 111PC. The determination of the RN&H) in 0.725 M NaCJ m&red snecird care due to the hygrosc&c nature of the saJt -kd surkce carbonate formation from atmospheric Co2 uptaJce. NaOH peJkts were ground to a powder and pked into salt disposers underadry,ni~atmoap&m.Thedkpememwere quicJdytrsmsfbrredtoahighvacuumsystemwberethey remainedatJeast4houm.We@iugandadditionofthe s contents were comp@ted quickJy in order to minimize contact with atmospberk H@ and Co,. Rate of polymerization A soJutioo of monomeric siJicic acid was pmpared by a mod&mtionof ALExINDw’s (1954) imn&ure. An amount of2.~gof~y~us~~Iml4~ofN~wasdis~~in85EnlHtOinaTeflcm~hlllIld;the contentsoftJ3efuuneJwaethenaddedwithv&omusatirring to another solution in a 250 mJ voJumetric flask containing __ -_ an equivaJent amount of HCJ and an amount of NaCJ to give a final solution of 0.725 M NaCJ and
J. P. Hershey and I. W. Due&h
1934
The calculation of ~(Si(OH)~) from Aph requires the value of p(NaOH) and RHrO). The P(Na0t-l) in 0.725 M NaCl at 1“C has not been previously reported and was therefore determined as a part of this study. A plot of Z AV/E Aw versus C Aw for NaOH in 0.725 M NaCl is given in Fig. 5. A linear least squares fit of the data gives an intercept of @NaOH) = -5.45 + 0.07 cm3 mol-‘. Substituting r(H,O) (in 0.725 M NaCl) = 18.01 cm3 mol-* and the values for @NaOH) and Ap;, given above into Eqn. (8), a preliminary value (not accounting for electrostriction) for @Si(OH)s) = 54.46 + 0.25 cm3 mol-‘.
Comparison of ~(Si(oH))3 from neutralization and ~~r~~~sis exper~~ts The extrapolation procedure for calculating {AT* + F’NasSiOa)), however, involved Sir& concentrations weil above those in which there was a dramatic drop in pH as C Aw - 0. That is, the hydrolysis of the met@licate salt results in a pH = 11 and the value of @Si(OH),) determined from A& includes the partial molal volume due to soiveat electrostriction, P,, in the 6rst hydration sphere of the charged Si species present, for example, dissociated monomers and dimem and possible d&anions. MUKERJEE (I 96 1) proposed a theoretical model that divides the partial molal volume of an ion, Pk,, , into Pin<, the intrinsic partial molal vokune which is ~0~~0~ to the cube of the crystal radius of the ion, and l?&+ Using ‘this model MILLERO (I 969) derived the following semiempirical equation for calculating Uti from P& data: ~,cci = -7.W/r
(9)
where z is the ionic charge and r is the ionic radius in A. DUEDALL et al. (I 976) considered the pH and total Si concentration dependence of the dimerixation and dkociation equilibria of monomer and dimer. Using constants (BIL~N~KIand INGw, f967) for various dissolved silica species equilibria in 0.5 m NaCl at 25°C and assuming a iiT,1 concentration corresponding to the first wtion in a ~iatometer run, DuEnALL et a!. (1976) determined the monoanion to be the predominant species and calculated (Eqn. 9) t7,k, = -4.4 cm3 mol-‘. Using this value to correct lQi(OHk) obtained from the A p&measurement at 1“C, ~Si(OHh) = 58.9 em3 mol-*. This value is in excellent agreement with P(Si(OH),) = 59.0 cm3 mol” obtained from Ap, measurements. Discrepancy between the two values of p(Si(OHh) may arise from the use of 2YC thermodynamic data to calculate Si speciation for the VW calculation. This agreement lends strong support for the model of MILLER0 (1969) for estimating the partial molal volume due to solvent eimn by an ion and further suppot?s the @Si(OH),) results of DUEDALLet al. ( 1976) determined from Av’ at 20°C.
FIG. 5. Volume change fur the addition of NaOH to a 0.725 M N&l soiution at l°C.
@3i(OH),) directly measured in the present study can be compared with the value of Y(Si(OH)4) calcuIated from the pressure dependence of the equilibrium constant for the dissolution of amorphous silica. The dissolution of amorphous silica is given by SiO, (s) + 2HrO (1) = Si(OHh (aq)
iw
Assuming that AP is a function of pressure, integration of Eqn. (1) and applying it to Eqn. (10) gives RTln KP/P’ = -AL?rt;i(P- 1) t OSAr,(P
- l)* (1 1)
where the equilibrium constants Kp and K” are at pressures P and 1 bar (zero applied), respectively, and can be equated, as a first approximation, to the solubility of silica. APi is the change in partial molal volume for Eqn. (10) and is given by A t’l = ~(Si(OH)~} - 2 V(H*O) - V(Si02, amorph)
(12)
whem Y(Sic)2, amorph) is the molar volume of the solid. AK, is the change in partial molal compressibility for Eqn. (IO). Values of A pi in artificial seawater and in media of similar ionic stren@h obtained (Eqn. 11) from amo~hous silica soiubility measurements by various investigators are given in Table I. Substituting these values and the values of P(HsO) and r/i(SiOz, amorph) into Eqn. (IZ) gives the values of ~Si(OHh~ which are also given in Table I. There is considerable scatter in these data. WILLEY (1980, 1982) noted that AL\picalculated from Eqn. (11) is highiy dependent upon the 1 bar solubility of amorphous silica for which there is also considerabie disagreement. W~LLEY (1982) has suggested that this variability is the result, in part, of the aging of the
1935
Pax&d molal volume of siticic acid Table
I.
ii(SilOHl,) ,calculated from as a function of pressure AV'vl -1 C.3lIWl
Jones and Pytkowiez (1973) willey f1975) Griffin (1980) Hilley 11980) This
Temp.
-5.3 -11.6 -9.0 -11
the
not
astifrcial seLIwster 0.6m N&l 0.7m N&l 0.96 NaCl+ 0.11 NaHCO 0.7251 NaCjf ceport@d,
present
The partial molal volume of silicic acid in 0.725 M NaC1 at i”C was calculated from the volume change due to the neutralization of NazSiOj by HCl and was found to be 59.0 cm3 mol-‘. This value compares favorably with @%(OH).+) = 58.9 cm3 mol-’ calculated from the partial molal volume change for the hydrolysis of NazSi03 in 0.725 M NaCi at 1°C when adjusted for the partial molai volume due to ehxtrostriction of water by ionic species using the semiempirical model by MILLERO (1969). The @Si(OH)J (derived from Ap,,) was successfully determined by the dilatometer method because of the favorably slow kinetics for the condensation of monomeric Si(OH), to higher polymers at the low temperature and PH. The directly measured ~(Si(OH)~) is within experimental error of the value calculated from the results of solubility measurements as a function of pressure. Acknuwledgemenfs-We thank David Hurd, Frank Miller0 on the
manuscript. We also thank the Marine Chemistry Division (Grant No. OCE7621504) in the Oceanographic Section of the National Science Foundation for its support of this work. RBFFXENCXS ALEXANDER G. B. (1954) The preparation of monosili~c acid. J. Amer. Chem. Sot. 75, 2887-2888.
57.9 52.3 54.2 52.7
27.9
59.0b value
~a9
used
(Iler,
work.
CONCLJJSIONS
comments
-1 C13lUOl
27.P 27.9 27.2 27.9
Pn average
silica
V1Si(OH)4)
-1 c103UlCll
silica surface in the ionic medium and reported (WILLEY, 1980) a decrease in surface area, mean pore volume and solubility wiih time. This suggests a change in phase of the silica surface with aging. Averaging five data sets WILLEY (1982) calculated a I bar silica solubiity of 880 t 38 PM. Using this one bar solubihty she then averaged three data sets for aged (over 60 days) silica solubility as a function of pressure and obtained a value of At’, = 55 + 5 cm3 mol-*. The large uncertainty reflects the uncertainty in the 1 bar solubility of amorphous silica. The p(Si(OH)J = 59.0 cm3 mol-r from the present work compares favorably with this value. v(Si(OH),) from the present work is also in good agreement with ~(Si(OH)~) = 56 cm3 mol-’ calculated from the theoretical equations of WALTHER and HELGBsON ( 1977).
and Joan Willey for their constructive
of amorphous
VtSi02,amorph)
Matrix
1.0 was
solubility
OC
2 a 2 2.3
work
a. Since V(SiO2,amorph) 1979). b. Measured value from
the
BILINSKI H.
and INGR! N. (1967) A determination of the formation constant of SiO(OH)s. Acta Chem. &and. 21, 2503-25 10.
BUSEY
R. I-l. and MEsMERR. E. (1977) ionization ~uilib~a ofsihcic acid and polysihcateformation in aqueous sodium
chloride solutions to 300°C. Inorg. C/tern. l&2444-2450.
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WIEKERW. (1977) 29-Si-NMR-Spektroskopie an silicatlosungen. IV: Unte~uchu~en zur kondensation der monokieselsaure. Z. Anorg. AIlg. Chem. 428,43-52. GRIFFIN J. W. (1980) The effect of pressure on the soiubi~i~
of I1 silicates in 2*C, pH 8 seawater. M. S. Thesis, University of Hawaii. HARNEDH. S. and OWEN B. B. (1958) The Physical Chemistry ofEteczrolyre ~oiu~io~s, 3rd ed. Van Nostrand, Reinhold, New York. HERSHEYJ. P. (1982) The physical chemistry of aqueous silicic acid: Partial molal vofume and partial moIaf cornpressibility in NaCi solution at 1%. Ph.D. dissertation, State Univ. New York, Stony Brook. HURD D. C. (1972) Factors affecting solution rate of biogenie opai in seawater. Earth Planet. Sci. Left. 15, 41 k-417. HURD D. C. (19‘73) Interactions of bio8enic opal, sediment and seawater in the Central Equatoriai Pacific. Geochim. Cosmochim. Acia 37, 2257-2282. ILERR. K. (1979) The Chemistry of Silica. Wiley-lntersciencc, New York. JONES M. M. and PYTKOWKZ R. M. (1973) Soiubihty of sitica in seawater at high pressures. Bull, Sot. Roy. Sci. 42, 118-120. LAWSOND. S., HURD D. C. and PANWTZ H. S. (1978) Silica dissolution rates of decomposing phytoplankton assemblages at various temperatures. Amer. J. Sci. 278, 1373-1393. LOSJRIXI A., ALZOLAE. M. and MILLEROF. J. (1982) The (P, V, I) properties of concentrated aqueous electrolytes. 1.Densities and apparent molar volumes ofNaC1, NazSO,, MgCi2 and MgSO, solutions from 0.1 mol kg to saturation and from 273: 15 to 323.15’K. J, Chem. Thermodynamics 14,649-662. LUCE R. W., BARTLETTR. W. and PARKS G. A. (1972) Dissolution kinetics of m~esium silicates. Geochim. Cosmochim. Acta 35, 3560.
MACKENZIEF. T., GARREL~R. M., BRICKER0. P. and BICKLEYF. (1967) Silica in seawater: Control by silica minerals. Science 155, 1404-1405.
1936
J. P. Hemhey and I. W. Due&U
MELEROF. J. ( 1969) The partial molal vohunes of ions in
seawater. Limnol. Oceamp. 14, 376-385. MILLEROF. J., LAFERRIERE A. L. and CHETIRKINP. V. (1977) The partial molal volumes of eiectrolytes in 0.725 m sodium chloride at 25’C. J. Bp.s. Chem. 81, 17371745. MUKEiUEEP. (196 1) On ion-solvent interactions. Part 1. Rwtid molal volume of ions in aqueous solution. J. Phys. Chem. 65,740-7&I. I’YTK~WI~ R. M., KBTER ID. R. and BURGENERB. C. ( 1966) R~~u~~ty of pH measurements in seawater. Limnol. Oceanogr.. fl, 417419. ROEIN~~NR. A. and S’IXXESR. H. (1965) Electrolyte Sulutions, 2nd Edition. Buttenvorths, London. SEVER R. (1968) Fstabhshment of equilibrium between clays and seawater. Earth Planet. Sci. Lett. 5, 106-I 10. WALTHERJ. V. and HELGESEIN H. C. (1977) Calculation of the thermodynamic prop&es of aqueous silica and
the solubihty of quartz and its polymorphs at high pressures and temperatures. Amer. J. Sci. 277, 1315- 1351. WSLLEY J. D. (1974) The effectof pressure on the solubihty of amorphous silica in seawater at OOC.Mar. Chem. 2, 239-250. WILLEYJ. D. (1978) Release and uptake of dissolved silica in seawater by marine sediments. ,4&r. Chem.7, 53-65. WILLEYJ. D. (1980) Eikcts of aging on sihca solubihty: A laboratory study. G~him. Cosmochim. Acta 44, 573-538. WILLEYJ. D. (1982) PartiaI moial volume calculations for the dissolution of aged amorphous silica in a&t water and seawater at 0-2°C. Gecchim. Cosmorhim. Acta 46, 13071310. YOUNGT. F. and SMITHhf. B. (1954) Thermodynamics ~~70~~lytm in aqueous sohttion. J. Phys. Chem. 9 *