1138
Anal. Chem. 1984, 56, 1138-1142
Temperature Dependence and Measurement of Resistivity of Pure Water Truman S . Light Corporate Research Center, The Foxboro Company, Foxboro, Massachusetts 02035
Hlgh-purlty water wAh Ionic lmpurltles of less than 0.1 pg/kg Is commerclally avallable. Its quality may be monltored by reslstlvHy measurement corrected for temperature and trace Impurltles. Thls paper calculates Improved theoretical reslsthmy, conductivity, temperature coefflclent, and pH values for water from 0 to 100 OC. These values are reported for the first time from 100 to 300 O C . The detectlon of trace Ionic lmpurltles as low as 0.1 pg/kg Is discussed, as Is the maxlmum reslstlvlty of water occurring at pH 7.04 at 25 O C and sodlum hydroxlde concentratlon of 0.8 pg/kg.
High-purity water and its measurement have become an important topic in several advanced technology fields including the production pf semiconductors for solid-state electronic devices ( I ) , the coolant water for nuclear reactors in the power industry ( 2 ) ,and ultratrace analysis. A recent symposium, and publication, devotes itself extensively to this topic (3). The American National Standards Institute (ANSI) and The American Society for Testing and Materials (ASTM) have promulgated a "Standard Specification for Reagent Water" in which four classes of water are defined (4). These types of water, which are shown in Table I, are essentially described by their conductivity at 25 "C. This ASTM table reflects the jargon of the industry in that conductivity is defined in units of pmhos/cm rather than the preferred SI system units of identical value, pS/cm. For very low values of conductivity, the reciprocal term resistivity, in units of Mi2 cm, is preferred industry terminology. Type I water, with a resistivity of 16.67 MQ cm or higher at 25 "C, is produced by ppification in mixed bed (cation and anion) exchange resins and may be done on a large scale with commercially available systems. This water is frequently used as a solvent in semiconductor wafer processing (1). Type I1 water, with a resistivity greater than 1 Mi2 cm at 25 "C,is considered to be very good quality laboratory distilled water. Types I11 and IV, with still greater quantities of permissible impurities, are also acceptable quality water for many purposes. Types I1 and I11 water, which have the same conductivity/resistivity specification, are distinguished from each other by additional requirements. Type 11, with a maximum total matter content of 0.1 mg/L and no deteceble soluble silica, must be prepared by final distillation. Type I11 water, with a paximum total matter content of 1 mg/L and maximum soluble silica of 10 pg/L, may be prepared by distillation, ion exchange, reverse osmosis, or a combination thereof followed by polishing with a 0.45-pm membrane filter. This paper is primarily concerned with type I water resistivity-the theoretical values for pure water over a wide range of temperatures, the measurement of pure water, and the calibration of measurement equipment. The purity requirements of type I water are indeed extraordinarily high compared with the requirements of earlier technology, Glasstone (5) has discussed the purity of water in some detail noting that water distilled several times with a tinned condenser gives water in equilibrium with the carbon dioxide of air that has a conductivity of approximately 1.3 Mi2 0003-2700/84/0356-1138$01.50/0
~
Table I. Partial List of ASTM Requirements for Reagent Water ( 4 ) type I electrical conductivity, max 0.06 [pmho/cm at 298 K (25 "C)l electrical resistivity, min. 16.67 [ M a cm at 298 K (25 "C)]
type type type I1 I11 IV 1.0
1.0
5.0
1.0
1.0
0.2
cm (0.8 pS/cm). This is considered the highest resistivity attainable for water in equilibrium with the carbon dioxide in air. He also discusses the "purest water hitherto obtained by Kohlrausch and Heydweiller (6) in 1894 who distilled it 42 times under reduced pressure. This water had a specific conductance of 0.043 X lo4 0-l cm-' at 18 "C. This calculates to a resistivity of 16 MQ cm at 25 "C and today would not be quite acceptable as type I water. The theoretical resistivity of water due to self-ionization into hydrogen and hydroxide ions has been calculated again by Light and Sawyer (7) to be 18.2 MQ cm at 25 "C. This value is dependent upon other physical constants, namely, the water dissociation constant (K,) and the limitin equivalent conductances of hydrogen and hydroxyl ions (AoJ and XooH-). These are temperature-dependent terms; therefore the resistivity of water is temperature dependent. Reference 7 reported an apparent anomaly indicating that the maximum resistivity of water, at 18.3 MQ cm and at pH 7.04 at 25 "C, occurred not for pure water but for water containing 0.8 pg/ kg (parts per billion, ppb) of sodium hydroxide. The present paper, using more accurate data at elevated temperatures, has calculated improved values for the resistivity of pure water and its temperature coefficient over the temperature range 0 to 100 O C and extends these values to 300 "C. The sensitivity of the resistivity measurement to the parts per billion range of impurities is calculated, and some measurement techniques, including calibration of the conductivity cells, are discussed.
THEORY The theoretical resistivity, due to the self-ionization of pure water HzO + H+ OH(1)
+
may be obtained from the equations (7,8)
+ X"oH-)(Kw)1/2
= i0-3dt(X0H+
(2) Pt = 1/Kt (3) where the symbols are as follows: K~ is the conductivity in siemens (S)/cm at t "C; pt is the resistivity of pure water in Q cm at t OC; t is the temperature in O C ; T i s the temperature in Kelvin (T = t + 273.15); A" is the limiting equivalent conductance of ions at t "C; dt is the density of water, in g/mL, at t "C; qt is the viscosity of water in centipoises at t "C; K , is the ionization constant of water at temperature t O C (molal units). Table I1 is a collection of the physical chemical data utilized to calculate the resistivity of water. Over the range of 0-60 O C , and especially at the reference temperature 25 O C , Kt
0 1084 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
Table 11. Data Used for Calculation of pH, Conductivity, and Resistivity of Pure Water (8)
0 14.944 1 0 14.535 18 14.236 20 14.167 25 13.997 30 13.833 40 13.535 50 13.262 60 13.017 70 12.813b 75 12.712b 80 12.613b 90 12.431 100 12.265 200 11.289 300 11.406b a Reference 13. calculation ( I I ).
127.8 156.2 178.8 184.4 197.8 211.6 237.2 261.4 284.2 324.2' 344.1 ' 364.8' 405.9' 447d 701 821
224.2 275.5 315.6 325.5 349.8 373.7 419.5 462.6 502.5 545.8' 565.2' 582.8' 612.5' 634d 824d 894
Reference 10. Reference 12.
0.99987 0.99973 0.99859 0.99823 0.9 970 7 0.99567 0.99224 0.98807 0.98324 0.97781 0.4061 0.97489 0.3799 0.97183 0.3565 0.96534 0.3165 0.95838 0.865d 0.712d
7.472 7.268 7.118 7.084 6.999 6.917 6.768 6.631 6.509 6.407 6.356 6.307 6.216 6.133 5.645 5.703
0.0119 0.0233 0.0376 0.0420 0.05479 0.0706 0.111 0.167 0.240 0.334 0.391 0.455 0.599 0.764 2.99 2.42
Walden product
84.2 42.9 26.6 23.8 18.25 14.1 8.98 5.98 4.17 3.00 2.56 2.20 1.67 1.31 0.334 0.413
-7.21 -6.30 -5.67 -5.52 -5.18 -4.86 -4.30 -3.81 -3.47 -3.14 -3.00 -2.87 -2.63 -2.43 -0.7ab t0.38'
where A, B , C, and D are constants. By use of a computer program, the constants of eq 5 have been evaluated from the data in Table I11 for four temperature ranges corresponding to four levels of accuracy and are given in Table IV. Over the temperature range 0-60 "C, where the data are most accurate, the set of constants for the equation describe the function with a standard deviation of 0.2%; over the range 0-100 "C,where the limiting equivalent conductance of the hydroxide ion was deduced from the Walden equation, the standard deviation is 0.4%;over the range 0-200 "C, where the uncertainties of the limiting equivalent conductances and of the water ionization constant are greater, the standard deviation is 0.5%;and as this temperature limit goes to 300 "C, the standard deviation increases to 3%. Once the equation for the resistivity is defined, the temperature coefficient of the resistivity, at in units of percent change per degree Celsius, may also be defined (7)
and from eq 5 this becomes at =
( B / P+ 2 C / P
+ 3D/T4)(-100)
EXPERIMENTAL SECTION
Harned and Owen (9) appear to have selected the best data. Above this temperature, and up to 300 "C (the critical temperature of water is 374 "C), the water ionization constant data of Marshall and Franck (IO) were used. Since the limiting equivalent conductance of the hydroxide ion has been difficult to obtain over the intermediate temperature of 60-90 "C from earlier papers, interpolation of the Walden constant calculation was used involving the viscosity of water as shown by Pebler (11) from the relation (4)
Apparatus. The resistivity measurements of pure water over the temperature range 0-70 "C and the calibration of conductivity cells may be accomplished with the apparatus shown in Figures 1and 2. A Foxboro Model 921D digital resistivity monitor, which employs a microprocessor to relate all measurements to a standard temperature of 25 "C, not only corrects for pure water temperature but also for water containing traces of impurities calculated as sodium chloride. The sensors were Foxboro resistivity cells, Model 921-EE2, with a cell constant of 0.100cm-', which have contacting electrodes made of titanium and self-contained temperature sensors. The heart of the pure water system is the "nuclear grade" mixed bed ion-exchange resin cartridge MRN-1 provided by Vaponics, Inc., Plymouth, MA. Several research grade mixed bed resins, purchased from scientific laboratory supply houses, were found to be inadequate, making water in the 12-17 MQ cm range at 25 "C. Fluorocarbon tubing and flow-through vessels were
Table IV. Equations for Resistivity and Temperature Coefficient of Pure Water over Various Temperature Ranges resistivity (
~ cm): 0
temp coeff (%/"C): temp range, "C
A
B
0-60 0-100 0-200 0-300
-1.7756 -10.858 1.5035 14.010
-903.75 7215.8 -4490.4 -17650
(7)
The values for the temperature coefficient, over the range from 0 to 300 "C as computed from eq 7 are included in Table 111.
Using eq 7 Using eq 7 for 0-100 "C; cf. Table IV. Using eq 7 for 0-300 "C; for 0-200 "C; cf. Table IV. cf. Table IV.
VthooH- = constant
I n the range 100-300 "C, elevated temperature data for the limiting equivalent conductance of hydrogen, hydroxide, and several other common ions have been reported by Quist and Marshall (12). Water density and viscosity data have been taken from a handbook (13). From eq 2 and 3 and the data of Table 11,the pH, conductivity, and resistivity of pure water over the range 0-300 "C have been calculated and are given in Table 111. For many purposes, including recalculation of measured resistivity to standard temperature and for instrument design and construction, it is useful to have the relationship between resistivity of pure water and temperature expressed by an equation. The resistivity function may be described by the equation
(5)
Table 111. Theoretical pH, Conductivity, Resistivity, and Temperature Coefficient of Pure Water as a Function of Temperature conductemp tivity, resistivity, coeff: pS/cm M a cm %/"C temp, "C pH 0 10 18 20 25 30 40 50 60 70 75 80 90 100 200 300
1139
pt = ,(A+B/T+C/T*+D/~) cut =
(B/T2 + 2C/T3 t 3D/T4)(-100) C
0.41340 -0.20004 0.16752 0.62158
X X X X
lo6 10' lo' lo'
D
std dev, %
0.81046 X los 0.31968 X lo9 -0.630539 X 10' -0.57764 X lo9
0.19 0.36 0.52 2.75
1140
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* ANALYTICAL CHEMISTRY, VOL. 56. NO.
7.
JUNE
1984
H
Table V. Comparison of Cell Constants Determined in Pure Water and in ASTM Standard Potassium Chloride cell no.
+ 0.1
1 2 3
0.0993 0.1009
0.0994
0.1006
0.1008
4
0.1005 0.1005
+ 0.2
0.1007 0.1008
+0.2
5
I
cell constant cell constant in pure in 10.' N % water: cm-' KCl,b c m ~ ' difference 0.1005
-0.4
+0.3
Using Foxhoro Model 921D resistivity monitor in pure water. Using Radiometer Model CDM 83 conductivity meter in lO~' N KCI. ASTM D1125-77. by ASTM procedures (14), were measured with a Radiometer Model CDM-83 conductivity meter, calibrated against resistors traceable to the National Bureau of Standards.
Figure 1. Apparatus for calibration of conductivity cells used for highpurity water measurements: A, 4-L water storage vessel (polyethylene); E. pump, 200-1200 mL/min: C. nuclear grade, mixed bed (cation and anion) ion exchange resin: D and E. Conductivity celis. 0.1 Cm-' cell constant. wim SeWantained temperature senws: F, Foxboro Model 921D resistivity monitor; G. flowmeter.
Flgure 2.
Photograph of apparatus for high-purity water measure-
ments. found to be desirable between the ion-exchange cartridge and the conductivity cells. It was necessary to maintain flow above 200 mL/min or trace impurities dissolving from the components were detectable. Cleanup of a new system to make "18.25 MR cm" water might take up to 2 days, but the system will produce pure water for 2 years if only distilled water is used as the starting water. Filters and organic and oxygen removal cartridges were not deemed necessary for preparation of totally ion-free water and were not included in this system, thus reducing maintenance requirements. For elevated temperature experiments, up to IO "C, electrical heating tape was used around the water storage vessel. Softening of this plastic container and fittings determined the upper temperature limit of the experiments. For primary cell constant determination, standard potassium chloride solution of nominal value of 0.001 N KCI, as detailed
RESULTS AND DISCUSSION The apparatus of Figure 1 was used for measuring the resistivity of pure water over the range 10-67 O C . Over this range, the theoretical values of Table 111were measured within *l%. The upper measurement temperature limit of67 " C was determined by failure of the plastic components of the measuring system. The upper temperature limit of the mixed bed resins is not known. Since the water must he kept circulating a t a relatively high rate of 201F1200 mL/min, thermostating to constant temperature is not feasible. The validity of the temperature coefficients of Table I11 was also proved by this experiment over the temperature range covered, since the correction to the standard temperature of 25 "C involved the observed resistance and temperature as well as the temperature coefficient. Very few experimental values for the resistivity of pure water are reported in the literature, especially as a function of temperature. As mentioned above, Kohlraush had prepared 16 MR cm water by distillation (6); Iverson, using mixed bed ion-exchange resins, had prepared and measured pure water over the range 5-55 O C obtaining results similar to those reported here (16). Cell Calibration. The calibration or verification of conductivity cell constants for pure water has been carried out traditionally by ASTM methods using standard potassium chloride solutions (14). The conductivity cells used for pure water determinations have had cell constants of 0.01 cm-' because of the high resistance being measured. The Foxhoro Model 921D instrument, with circuitry designed to minimize many of the documented pitfalls of tweelectrode alternating current measurements (151,uses a cell with a constant of 0.100 cm-'. In connection with demanding applications to certify "18.25" MR cm water, there had been speculation that the constants obtained by calibration with standard potassium chloride solutions were different when the cells were used in the range of pure water resistivity. This has been shown not to be true, not only by the data presented below but also by a Literature discussion in 1923 of the 'Parker" effect (17). This effect was an apparent decrease in cell constant with increasing resistance. Jones and Bollinger (18)showed that there was a design problem in the conductivity cell whereby electrical capacity between the electrolyte in the cells and parallel columns of mercury used for making electrical contact were causing alternating current measurement errors. Table V presents a comparison of cell constants determined in standard N potassium chloride solution with those determined in pure water with a demonstrated resistivity of 18.25 Ma cm a t 25 O C . The average difference between the two sets of measurements, approximately 0.3%, is within the experimental error of the measurements. The apparatus of Figure 1 may also be utilized for cell calibration by two possible methods. The first method does
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
1141
I""
Table VI. Resistivity of Water with 2 &/kg (ppb) of Various Salts over a Moderate Temperature Range resistivity, Ma cm at 0 "C at 25 "C at 75 "C water, pure water + NaCl(2 ppb) water t KCl (2 ppb) water t CaCl, (2ppb)
84.2 70.5 70.5 69.0
18.25 16.9 16.9 16.7
2.56 2.50 2.50 2.49
where Rs and Rx are observed resistivities, in MQ cm, of the two cells. The temperature of the test solution is not important as long as the temperature of the two cells is the same. The second cell calibration method requires that the water be known to be 18.25 MQ cm f 0.570at 25 "C. This is usually accomplished with a conductivity cell that has been standardized with potassium chloride and the ASTM method. Then the resistance, R, in megohms, of the cell under test is observed along with the temperature ( t )to within f O . l "C, and the cell constant (L,) may be computed from (Cm-1) where R h is the resistivity of pure water in MQ cm a t the temperature ( t )obtained from Table 111, and interpolated to f 0 . 1 "C. If an instrument, such as the Model 921D, is used, with built-in temperature compensation, then the temperature sensor must be previously verified to be accurate to f O . l "C. Impurities. The resistivity measurement of pure water is sensitive enough to detect ionic impurities in the microgram per kilogram (pg/kg, parts per billion, ppb) range. When corrected for temperature, this measurement furnishes much useful information about the ultimate ionic purity of water and, in comparison with most other instrument methods, is more reliable and maintenance free. Because the equivalent conductance of many salts have roughly the same numerical values, it is convenient to treat the typical impurity as sodium chloride. In this case the equation for the conductivity of water, by extension from eq 2 becomes = 10-3d,[(X0H+ XooH-)Kw1/2(AoNa+[Na+]
+
+
+
x
*e-
0
%?..-
I@
not require a high degree of certainty that water being circulated is of "18.25" MQ cm quality or that there be certainty that the mixed bed ion-exchange resin be of nuclear grade quality. It does require that there be available a second "primary standard" cell which has had its cell constant determined by another apparatus using the ASTM potassium chloride method (14). This cell is then used in series with the same water loop as the cell under test and the cell constant, Lx,of the cell under test is obtained by ratioing to the cell constant of the primary standard cell, Ls, by the equation
Kt
A PURE WAIER
[Cl-lll (10)
where the brackets denote molal concentrations of the ions. If the impurities are salts other than sodium chloride, con-
1
I
0 l0
10
20
30
10
50
TEMPERATURE
60 (OC)
70
30
ductivity may be calculated by an equation analogous to eq 10. In Table VI, the resistivities of water, with 2 pg/kg (Le., 2 ppb) of the salts sodium chloride, potassium chloride, and calcium chloride, have been listed for temperatures of 0, 25, and 75 "C and compared with that of pure water. This table shows that at 25 "C, 2 pg/kg produced a change in resistivity from 18.25 to 16.9 MQ cm. If it is assumed that a 170decrease in resistivity, from 18.2 to 18.0 MQ cm can be detected, then the ultimate sensitivity at 25 "C may be estimated a t approximately 0.3 pg/kg. It should be noted that at this trace level of concentration, the sensitivity does not differ significantly among the three salts. I t also may be seen in Table VI, that this sensitivity decreases as the temperature increases, due to the greater ionization of water. At 75 "C, 2 gg/kg is scarcely distinguishable from pure water. Conversely, as the temperature decreases to 0 "C, the sensitivity increases, and a change of 1% in the resistivity value results in an increased impurity sensitivity to 0.1 gg/kg. Table VI1 shows the resistivity of water with trace amounts of sodium chloride over a wider range of temperatures and concentrations. This table covers the temperature and concentration ranges of 0-100 "C and 0-lo00 pg/kg and has been calculated from eq 10 and data for the equivalent conductances of sodium and chloride from various sources (7,9,12). The data of Table VI1 enables the plotting of a family of curves, shown in Figure 3, which show the effect of salt impurities on the resistivity of water from 0 to 100 "C. Figure 3 indicates the greater sensitivity to impurities at lower temperatures. This figure also illustrates the principle of the temperature correction applied to water resistivity measurement when trace impurities, assumed to be sodium chloride, are present. If pure water were measured at ca. 50 "C, then the observed resistivity of 5.98 MQ cm could readily be back-calculated to the standard value of 18.25 MQ cm at 25 "C from Table 111. However, if the observed resistivity were less, ca. 4.98 MQ cm, then this would indicate the presence
resistivity at NaCl concna 84.2 18.25 5.98 2.56 1.31 1 ppb is equivalent to 1 pg/kg. 0 25 50 75 100
a
0 PPb
100
Flgure 3. Resistivity of water with NaCl impurity in parts-per-billion range.
Table VII. Resistivity of Water (in M a cm) witn Trace Sodium Chloriae Impurity at Various Temperatures temp, "C
90
1 PPb
2 ppb
10 ppb
76.7 17.6 5.87 2.53 1.30
70.5 16.9 5.76 2.50 1.29
42.8 13.1 4.98 2.28 1.21
50 ppb 14.5 6.14 2.97 1.59 0.931
100 ppb
1000 ppb
7.90 3.69 1.98 1.15 0.723
0.863 0.451 0.282 0.194 0.144
1142
ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984
where [OH-l,i,, is the hydroxide ion concentration at which the minimum conductivity occurs. At 25 "C the concentration of sodium hydroxide corresponding to the maximum resistivity of water is shown to be 0.76 pg/kg (aproximately 0.8 ppb) and the pH to be slightly alkaline at 7.04. The conductivity may be calculated from the concentration of the hydrogen, hydroxide, and sodium ions present. The maximum resistivity is recalculated in the present paper to 18.33 MQ cm and is to be compared with 18.25 MQ cm for pure water. Figure 4 illustrates this concept by plotting resistivity vs. p H in the vicinity of the neutral point. The maximum resistivity point, differing by less than 0.1 MQ cm from the resistivity of pure water, is probably not within the limits of detection by experimental means.
5
ACKNOWLEDGMENT The experimental assistance of W. Vallett and the computer calculations and data reduction of M. P. Olmstead are gratefully acknowledged. Registry No. Water, 7732-18-5. LITERATURE CITED
L 6,O
6,4
6,87.07,2
7.6
8.0
PH
Flgure 4. Maximum resistivity of water and variation of resistivity with pH around neutral point by addition of small amounts of HCI and NaOH at 25 O C .
of 10 pg/kg of sodium chloride or its equivalent, and backcalculation to 25 "C would have to be made from eq 10 and the known temperature coefficient values for both water and sodium chloride resistivity. An instrument with a microprocessor memory and calculating ability, such as the Foxboro Model 921D used in this study, has this capability. Maximum Resistivity. Normally, when a slight amount of ionic impurity is added to pure water, the conductivity would be expected to increase and the resistivity to decrease. However, because the equivalent conductance of the hydrogen ion is nearly twice that of the hydroxide ion as shown in Table 11, the addition of a small amount of hydroxide ion depresses the hydrogen ion concentration causing an initial net decrease in the conductivity. This anomaly has been discussed by Light and Sawyer (7) and the minimum conductivity of water may be derived from the equation
(1) Hango, R. A. So/idState Techno/. 1983, (July), 107-111. (2) Hlckam, W. M.; Peterson S. H.; Pensenstadler, D. F.; Bellows, J. C. Instrum. Techno/. 1982, (May), 59-61 (3) Lane, R. W., Otten, G., Eds. "Power Plant Instrumentation for Measurement of High-Purity Water Quality"; American Soclety for Testing and Materlals: Philadelphia, PA, 1981; ASTM STP 742. (4) "American Soclety for Testing and Materials Annual Book of Standards"; ASTM: Philadelphia, PA, 1981; Part 31, ANSI/ASTM D1193-77. (5) Glasstone, S. "An Introduction to Electrochemistry"; D. Van Nostrand: New York, 1942; pp 44 and 340. (6) Kohlrausch, F.; Heydweiiler, A. 2.Phys. Chem. 1894, 74, 317. (7) Light, T. S.;Sawyer, P. 8. I n "Power Plant Instrumentation for Measurement of High-Purity Water Quality", Lane, R. W., Otten, G., Eds.; American Society for Testlng and Materials: Philadelphia, PA, 1981; ASTM STP 742, pp 175-184. (8) "International Critical Tables"; McGraw-Hill: New York, 1929; Vol. VI, pp 152, 259. (9) Harned, H. S.;Owen, 8. B. "The Physical Chemistry of Electrolytic Solutions", 3rd ed.; Reinhold: New York, 1958; pp 231, 233, 638, 645. (10) Marshall, W. L.; Franck, E. U. J . Phys. Chem. Ref. Data 1981, 70, 295-304 (11) Pebler, A. Anal. Chem. 1981, 53, 1134-1136. (12) Quist, A. J.; Marshall, W. L. J . Phys. Chem. 1965, 6 9 , 2984-2987. (13) Dean, J. A., Ed. "Lange's Handbook of Chemistry", 11th ed.; McGrawHIII: New York, 1973; pp 10-125 to 10-126, 10-288. (14) "American Society for Testing and Materials Annual Book of Standards"; ASTM: Phliadelphla, PA, 1961; Pari 31, ASTM D l 125-77. (15) Janz, G. J.; Tomklns, R. P. T. J . Electrochem. SOC. 1977, 724, 55C. (16) Iverson, A. J . Phys. Chem. 1964, 68, 515-521. (17) Parker, H. C. J . Am. Chem. SOC. 1923, 4 5 , 1366, 2017. (18) Jones, G.; Bollinger, G. M. J. Am. Chem. SOC. 1931, 53, 411.
RECEIVED for review November 22,1983. Accepted February 6, 1984. This paper was presented a t the 186th National Meeting of the American Chemical Society at Washington, DC, August 1983.
