The fundamental conductivity and resistivity of water

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Pure water has a very low. but not quite zero, electrical conductivity. This conductivity provides a probe into fundamental properties of water, including the electrochemical mobility of the hydrogen and hydroxide ions. Deviation from this value is a measure of trace ionic impurities. Ultrapure water (UPW). with impurities at or below the sub-parts-per-billion range, is used extensively in many critical applications. Applications include chip fabrication for semiconductors, intravenous solutions for pharmaceuticals, and in high-pressure boilers for power generation.

We report here correction to a considerable error in the values for water conductivity and hydroxide mobility. In 1987. data was collected to establish the conductivity of pure water over a wide temperature range.1 In 1989. Thornton and Light measured the intrinsic resistivity of ultrapure water from 0 to 100CC.2 The results exhibited agreement within 0.25% to other values below 30CC. but showed the uncertainty rose to almost 3% at temperatures approaching 100CC. This discrepancy implied that at elevated temperatures, the resistivity change for impurity levels below about 1 jig/L (or part-per-billion. ppb) could not be calculated. This is an unacceptable limitation for modem conductivity instrumentation, necessitating a new study with detailed attention to the known issues that affect conductivity measurement and calculation accuracy.

The theoretical conductivity of pure water, k. and its reciprocal, resistivity, p. are related to its basic physical chemical properties according to

K(S/cm) = 1/p = 10'3rf(CiJXiJ + CqhXot)            [1]

where d is the water density (g/cm3). X^ and X0H are the specific conductances of H+ and OH' (S-cm2/mol), and C^ and CqH are the respective concentrations of these ions (mol/kg water), hi pure water, the only source of ions is due to auto-dissociation, which, are determined from the H20 dissociation constant Kw and from Eq. 1

K(S/cm) = p-1 = 10'3rfK^(XiJ + XSH)              [2]

The 1980 measurements of Strong provide a reproducible source of specific conductance of the hydrogen ion.3 We estimate that the accuracy of this data is —0.25% at 25°C. but the accuracy is less at higher and lower temperatures. Uncertainties of the specific conductance of the hydroxide ion are much larger. The density of water is known to relatively high accuracy, hi particular, the data prepared by Schmidt.4 given for 1°C intervals over the 0 to 374°C range, is sufficiently accurate as to not cause even a 0.1% error in the resistivity calculation. For the water dissociation constant, recent researchers have used data from a 1974 paper by Sweeton. Mesmer. and Baes. which agree with other studies to within about ±0.004 pK units.5 hence conductivity errors introduced from this source are less than 0.5%. At 25°C the accepted values with then uncertainties for conductivity- k and its reciprocal, resistivity, p. are2

k = 0.05501 ± 0.0001  fiS/cm   at 25.00°C
p = 18.18 ± 0.03 Mil-cm   at 25.00°C               [3]

Ill this study, accurate values are determined through 100°C for water conductivity, and used to build a fundamental water coefficient table including hydroxide and hydrogen ion mobilities, ionization constant, density, conductivity, and resistivity.

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