Pitzer Ion Activities in Mixed Electrolytes for Calibration of Ion Selective Electrodes

Pitzer ion activities in mixed electrolytes for calibration of ion selective electrodes used in clinical chemistry

Frank Bastkowskia)*, Petra Spitzera), Ralf Eberhardta), Beatrice Adela), Samuel Wunderlib), Daniel Berdatb), Hanspeter Andresb), Olivier Brunschwigb), Michal Máriássyc), Roger Fehérd), Caspar Demuthd), FabianoBarbieri Gonzagae), Paulo Paschoal Borgese), Wiler Batista da Silva Juniore), AlenaVospělováf), Martina Vičarováf), Sirinapha Srithongtimg)

a)Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany,

e-mail: , phone: +495315923323, fax: +49531592693323

b)Federal Institute of Metrology (METAS), Lindenweg 50, 3003 Bern-Wabern, Switzerland

e-mail: , phone: +41583870383, fax: +41583870210

c)Slovak Institute of Metrology (SMU), Karloveská 63, 842 55 Bratislava 4, Slovakia

e-mail: , phone:+420260294522, fax: +420260294561

d)Zurich University of Applied Sciences (ZHAW), Campus Grüental, 8820 Wädenswil, Switzerland

e-mail:, phone: +41589345763, fax: +41 58 934 50 01

e)National Institute of Metrology, Quality and Technology (INMETRO),Santa Alexandrina St, 416 Rio Comprido, 20261-232 Rio de Janeiro, Brazil

e-mail: , phone:+552126799134, fax: +552126799069

f) Ceský metrologický institut (CMI), Okružní 31, Brno 638 00, Czech Republic

e-mail: , phone: +420 545 555 322, fax: +420 545 555183

g)National Institute of Metrology (Thailand) (NIMT), 3/4-5 Moo 3 Tambol Klonghar Amphur Klong Luang Pathumthani, 12120 Thailand

Environmental Research Training Center (ERTC),Technopolis. Klong 5, Klong Luang Pathumthani, 12120 Thailand

e-mail: , phone: +66025774197, fax: +66025774197

In the following, Pitzer´s equations for an aqueous electrolyte solution containing calcium-, magnesium-, sodium-, potassium- and chloride ions, are shown. Moreover, all functions and parameters are given, which are included in these equations[1]. Figure 7 gives an impression of the number of influences contributing to the overall uncertainty of the ion activity coefficient of a cation, which is determined by the Pitzer equation.

Cations: Na+, K+, Mg2+, Ca2+

Anion:

Hückel-Term for electrostatic long-range interaction between solution species:

C-Term independent of ionic strength

from Pitzer-Tables

ionic strength

Hückel-Parameter is one third the debye-Hückel limiting slope:

Hückel-Parameter

Density of water

(cf. literature [2])

Relative permittivity of water (cf. literature [3])

t: absolute temperature in °C

B-functions (depending on ionic strength):

For 1:1, 1:2 or 2:1 electrolytes, respectively: ()

For 2:2 electrolytes: ()

argument for g- and g'-functions

for pairs in which cation or anion is univalent,

for higher valence pairs,

from Pitzer-Tables (cf literature [4]),

mostly is zero for pairs with one univalent ion

Temperature dependence of b-parameters used:

q1 q2 q3 q4 q5

Na+Clˉ 0.0765 -777.03 -4.4706 0.008946 -3.3158E-6

K+Clˉ 0.04835 0 0 5.794E-4 0

Mg2+Clˉ 0.35235 0 0 -1.943E-4 0

Ca2+Clˉ 0.3159 0 0 -1.725E-4 0

q6 q7 q8 q9 q10

Na+Clˉ 0.2664 0 0 6.1608E-5 1.0715E-6

K+Clˉ 0.2122 0 0 10.71E-4 0

Mg2+Clˉ 1.6815 0 0 3.6525E-3 0

Ca2+Clˉ 1.614 0 0 3.9E-3 0

T0=298.15 K

is considered to be zero in case of 1:1, 1:2 ions

Temperature dependence of C-parameters:

q16 q17 q18 q19

Na+Clˉ 0.00127 33.317 0.09421 -4.655E-5

K+Clˉ -0.00084 0 0 -5.095E-5

Mg2+Clˉ 0.00519 0 0 -1.649333E-4

Ca2+Clˉ -0.00034 0 0 6.213E-5

from Pitzer-Tables (cf. above)

Ion interaction approach: Theory and data correlation, Chapter 3, K.S. Pitzer, p.75-129

Activity coefficients in electrolyte solutions 2nd ed. (cf. literature [5])

Second virial coefficients , , are dependent mainly of ionic strength:

Theta parameter values for cation-cation´ respectively anion-anion´ interactions

from Pitzer-Tables

-values (cation-cation´ respectively anion-anion´):

Na+K+ -0.012

Na+ Mg2+ 0.07

Na+Ca2+ 0.07

K+Mg2+ 0.0

K+Ca2+ 0.032

Mg2+Ca2+ 0.007

arguments for J-functions (Integrals)

is a function of the ionic strength and electrolyte pair type and is nonzero only for non-symmetric electrolytes (e.g.1-2 types).

is the derivative of the function with respect to

J-integrals for

Fig. 5 / Cause and effect diagram for the Pitzer single ion activities g of a cation in a complex electrolyte mixture (cf. Appendix). For each influence parameter a standard uncertainty is attributed to the value. The uncertainties of the Pitzer parameters were estimated type B uncertainties. All coefficients of the model equations (water density, water relative permittivity with its temperature dependence, temperature dependence of the Pitzer parameters including constants such as the Avogadro and Boltzmann constant, etc.) were included with their uncertainties.

References

1. Harvie CE, Møller N, Weare JH (1984) The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-CI-SO4-OH-HCO3-CO3-CO2-H2O system to high ionic strengths at 25°C Geochimica et Cosmochimica Acta 48:723-751

2. M. Tanaka, G. Girard, R. Davis, A. Peuto, Bignell N (2001) Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia 38:301-309

3. D.R. Lide (1995) CRC Handbook of Chemistry and Physics. 76th edn. CRC Press, Boca Raton, FL

4. Pitzer KS, Mayorga G (1973) Thermodynamics of Electrolytes. I I. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent. J Phys Chem 77:2300-2308

5. Pitzer KS (1974) Thermodynamics of Electrolytes. III. Activity and Osmotic Coefficients for 2-2 Electrolytes. Journal of Solution Chemistry 3:539-546

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