The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O

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1 IAPWS R-7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem Publiction in hole or in prt is lloed in ll countries provided tht ttribution is given to the Interntionl Assocition for the Properties of Wter nd Stem President: J.R. Cooper School of Engineering nd Mterils Science Queen Mry, University of London Mile End Rod London E 4NS, Englnd Executive Secretry: Dr. R.B. Dooley Structurl Integrity Assocites 94 South Sheridn Wy, Suite 33 Okville, Ontrio L6J 7L7, Cnd emil: bdooley@structint.com This relese contins 7 pges, including this cover pge. This relese hs been uthorized by the Interntionl Assocition for the Properties of Wter nd Stem (IAPWS) t its meeting in Lucerne, Sitzerlnd, 6-3 August, 7, for issue by its Secretrit. The members of IAPWS re: Argentin nd Brzil, Britin nd Irelnd, Cnd, the Czech Republic, Denmrk, Frnce, ermny, reece, Itly, Jpn, Russi, nd the United Sttes of Americ. In this relese, including the title, H O is used to refer to ordinry ter substnce. The eqution for the ioniztion constnt of ter, K, provided in this relese is semi-empiricl eqution for K s function of density nd temperture. Detils of the formultion cn be found in the rticle The Ioniztion Constnt of Wter over Wide Rnges of Temperture nd Density by A.V. Bndur nd S.N. Lvov []. This eqution represents vlues of pk log (K ) ithin experimentl uncertinties for temperture rnge from 5 to 8 C nd densities from to.5 g cm 3. This relese replces the relese Ion Product of Wter Substnce, issued in 98. Further informtion bout this relese nd other documents issued by IAPWS cn be obtined from the Executive Secretry of IAPWS or from

2 Contents Nomenclture Introductory Remrk 3 The Ioniztion Constnt Eqution 3 4 Rnge of Vlidity nd Estimtes of Uncertinty 5 5 References 6 Nomenclture Symbol Physicl quntity Unit ρ mss density g cm 3 ρ normlizing mss density = g cm 3 3 g cm g kg g kg K ioniztion constnt of ter t m = mol kg (moll stndrd dimensionless stte) K ioniztion constnt of ter t ρ = g cm 3 (idel-gs stndrd dimensionless stte) M molr mss of ter = g mol g mol m stndrd mollity = mol kg mol kg n ion coordintion number dimensionless p s vpor-liquid sturtion pressure MP t Celsius temperture C T bsolute temperture K Introductory Remrk This relese presents n nlyticl eqution for pk log (K ) over ide rnges of ter density from to.5 g cm 3 nd temperture from to 8 C. The eqution is bsed on comprehensive nlysis of the experimentl dt collected, nlyzed, nd presented in Ref. [].

3 3 3 The Ioniztion Constnt Eqution The ioniztion constnt of ter is ttributed to the folloing rection: H O H 3 O + + OH. Becuse the proton hydrtion is complete under ll conditions of prcticl interest, this rection my be used s representtive model for both liquid nd vpor phses to the zero-density limit. Here nd belo, the moll stndrd stte is used for the ionic species nd mole-frction stndrd stte for ter molecules. The ioniztion constnt eqution presented here is in form hich includes the equilibrium constnt of the ioniztion rection in the idel-gs stte,. The idel-gs ioniztion constnt of ter is clculted using the JANAF98 [] dt nd then pproximted by temperture function: p K = + T + T + 3 T here,,, 3 re empiricl coefficients given in Tble. 3 K, () Bsed on the results of Ref. [], the ioniztion constnt of ter, K, s function of temperture nd density cn be represented by the folloing eqution: p K = n log Q ( + Q) ρ( β + βt Q + Q = ( ρ / ρ )exp( α + α T + β ρ) + p K + α T ρ / 3 ), + log m M ;, () here M is the molr mss of ter nd α, α, α, β, β, β re empiricl prmeters. The lst term in Eq. () converts the ioniztion constnt of ter from the idel-gs stndrd stte (used for K ) to the moll stndrd stte (used for K ). In this formultion, K is defined s K + H3O OH =, (3) H O here i is the dimensionless ctivity of the species i. Also, in this formultion is ssumed tht the sum of the chemicl potentils of H + nd H 3 O + is formlly the sme s the tice of the chemicl potentil of H O t ny temperture nd density (pressure), so tht K is numericlly

4 4 equl to + H OH HO, thermodynmic constnt for the ioniztion rection of ter (H O H + + OH ), tht is most commonly used in the literture. In Figure, the experimentlly studied T-ρ regions re shon by both filled nd open symbols. The filled symbols represent the dt points used in the fit nd the open symbols re the dt hich ere not used in the fitting procedure due to lrger uncertinties of the experimentl studies crried out t very high pressure. The ion coordintion number n s fixed t 6. The vlues obtined for α, α, α, β, β, nd β re given in Tble. Tble. Empiricl coefficients of Eq. () Coefficient Vlue Units K K 3. 7 K ρ, g cm Figure. The temperture-density regions of the vilble experimentl K dt: - points used t, o C in the fitting procedure, - points tht ere not used for fitting.

5 5 Tble. Empiricl coefficients of Eq. () Coefficient Vlue Units n 6 α α K α 786. (g cm 3 ) /3 K β.6444 (g cm 3 ) β (g cm 3 ) K β (g cm 3 ) For the purpose of checking computer code, Tble 3 contins clculted vlues of pk t specified tempertures nd densities. Tble 3. Test vlues for clculting pk using Eqs. () nd () T, K ρ, g cm 3 pk Rnge of Vlidity nd Estimtes of Uncertinty This relese presents n nlyticl eqution to clculte pk over ide rnges of ter density from to.5 g cm 3 nd temperture from to 8 C. Vlues of pk clculted over rnge of temperture (-8 C) nd pressure (.- MP) using Eqs. () nd (), s ell s the IAPWS Formultion 995 for the Thermodynmic Properties of Ordinry Wter Substnce for enerl nd Scientific Use [3, 4], re presented in Tbles 4 nd 5. In the liquid-phse region nd t moderte temperture (less thn C) nd pressure (less thn MP), the devitions of the experimentl dt from the clculted vlues of pk do not generlly exceed.5. Most of the vilble experimentl dt do not differ from those clculted by Eqs. () nd () by more then the obtined stndrd devition of.6. Devitions up to.8 in the lo-density nd supercriticl regions re due to lrge experimentl uncertinties

6 6 t these stte prmeters. It is importnt to note tht, in spite of the fct tht the experimentl high-pressure (up to 3 MP) pk vlues (shon in Figure by open symbols) ere not used in the fitting procedure, Eq. () cn reproduce these dt up to pressure of 3 MP nd density of.7 g cm 3 ithin.5. Note tht the region of high temperture (bove the criticl point of ter) nd lo density (belo the criticl density of ter) hs not been experimentlly studied yet nd more experiments re needed in this region to precisely define the uncertinty of pk clculted in this region. The uncertinty of the clculted p K, the ioniztion constnt of ter t ρ = (idel-gs stte), is less thn.5 in the hole temperture rnge up to 8 C. For densities beteen the limit of experimentl dt (bout. g cm 3 ) nd the idel-gs limit, the physicl bsis for the interpoltion provided by Eq. () is not rigorous. Therefore, quntittive ccurcy cnnot be expected in this region. 5 References [] Bndur, A. V., nd S. N. Lvov, The Ioniztion Constnt of Wter over Wide Rnge of Tempertures nd Densities. J. Phys. Chem. Ref. Dt, Vol. 35, 6, pp [] Chse, M. W., JANAF Thermochemicl Tbles, 4th ed., J. Phys. Chem. Ref. Dt, Monogrph 9 (998). [3] Interntionl Assocition for the Properties of Wter nd Stem, Relese on the IAPWS Formultion 995 for the Thermodynmic Properties of Ordinry Wter Substnce for enerl nd Scientific Use, 995, vilble from: [4] Wgner, W., nd A. Pruß, The IAPWS Formultion 995 for the Thermodynmic Properties of Ordinry Wter Substnce for enerl nd Scientific Use, J. Phys. Chem. Ref. Dt, Vol. 3,, pp

7 7 Tble 4. Negtive logrithm (bse ) of the ioniztion constnt of ter, K, clculted t tempertures to 3 C nd pressures. to MP using Eqs. () nd (). Pressure, Temperture, C MP b MP t t < C nd t 4 C, or p s (sturted liquid) for C t 35 C b Metstble liquid stte Tble 5. Negtive logrithm (bse ) of the ioniztion constnt of ter, K, clculted t tempertures 35 to 8 C nd pressures to MP using Eqs. () nd (). Pressure, Temperture, C MP MP t t < C nd t 4 C, or p s (sturted liquid) for C t 35 C

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