RESISTIVITY OF PURE WATER
havior properly. However, they do show that the relaxation processes are much faster for both a t a given temperature than in N-methylformamide. The temperature dependence of relaxation times is described in all cases by an Arrhenius rate expression r0 = A exp(AH*/RT), as shown by the plots of log r0 us. 1/T in Fig. 5 , and the values of A and AH* fitting the data are given in Table IV. From these, a regular progression is evident : that both the times at a given temperature and the activation energies are least for dimethylformamide, larger for formamide, and con-
515
siderably larger for the E-methyl amides. The order indicates that hydrogen bonding limits the rate of molecular orientations very considerably, particularly when it produces chainwise association. The activation energies are of magnitudes commonly found for polar liquids, and for the methyl amides are comparable with various estimates of NH..O hydrogen bond energies.21 Acknowledgment. Much of the work reported here was supported by the U. S. Air Force Office of Scientific Research.
The Measured Resistivity of Pure Water and Determination of the Limiting Mobility of OH- from 5 to 55"
by A. Iverson Electroglas Incorporated, M e d o Park, California
(Received September 17, 1969)
By the use of new materials and fabrication techniques, a self-contained recirculating water system has been designed and built to provide water, the resistivity of which corresponds to that calculated over the temperature range 5' (60 megohms) to 55' (5 megohms). Resistivity measurements made using a certified cell, Wheatstone bridge, and accurately calibrated thermometers gave resistivity values greater than those calculated, increasing linearly with temperature (5% a t 55'). Using the K w values of Hamer, the work of Owen and Sweeton giving values for the limiting mobility of Hf and its nonlinear temperature coefficient, and using assumptions provided by Hamer for the temperature coefficient for the limiting mobility of OH-, new values are calculated for the resistivity of pure water. The measured values and the calculated values corresponded to within 1.4% from 5 to 55', thc experimental error being 3=0.5%. From this, new values for the limiting mobility of OH- are determined froni 5 to 55".
The need for high-purity water has increased considerably in recent years. Improvements in various technologies and the creation of entirely new fields have steadily advanced the art of water purification. Various types of analyses which utilize water as a solvent require water of a higher degree of purity as instrumentation and techniques improve in chemistry, biology, the food industry, etc. Additionally, areas in atomic energy require very pure water as, for ex-
ample, in use in reactor coolers' and in radiation chemistry. The need for clean surfaces in solid state devices such as transistors and for vacuum tube parts is fulfilled by a final wash in ultra-pure water.2 There are two basic limitations on the degree of (1) F. Alquist, "The Preparation and iMaintenance of High Purity Water." and H. Huntley and S. Untermeyer, "The Use of Water in Atomic Reactors," Symposium on' High Purity Water Corrosion, Am. SOC.for Testing LMaterials, STP 179.
Volume 68, Number 9 March, 1964
A. IVEMON
516
purity which may be obtained in water. First is the ability of the various agents used, such as ion-exchange resins, carbon, filters, etc., to remove various contaminants contained in water. The other is determined by the contaminants introduced by the water-purification system itself. The state of the art in water purifying agents is of a very high order already. It was felt that the next order of improvement could be obtained by providing a system which introduced little or no contamination. An investigation of the properties of various materials of construction indicated that there were relatively few classes of material which showed reasonable promise as noncontaminating construction materials. Integrated pure-water systems, ie., systems which remove all contaminant sources (particulate, ionizable, organic, inorganic, and organisms) are generally constructed of metal. I n a metal system, the principal mechanism of system contamination arises from corrosion, the prime source being galvanic. Galvanic corrosion is generally caused by the presence of two or more metals, with different electromotive forces in an aqueous system. Even in single metal systems, corrosion takes place due to stress c o r r ~ s i o n ,intergranular ~~~ corrosion, crevice corro~ion,~,‘ cavitation corrosion (pump impeller),8*9moto-electric currents,lo and impingement attack.i1B12 Thus, it is seen that it is impossible to design an all-metal or partial-metal system for production of ultra-pure water which does not contribute corrosion contaminants to the system. By use of good engineering practice, effects of various corrosion mechanisms can be minimized ; however, they cannot be eliminated. Thus, the resolution of the problem is one of degree, not of kind, as is required to provide water of near ultimate purity. Another class of construction material is plastics, which have the advantage of being easily shaped to any specific need. M o s t plastics contain plasticizers, which are gross sources of coritamiriation. Furthermore, the temperature characteristics of plastics in general are such that the rate of contaminant transfer increases rapidly with temperature. One exception to the above has been found in the plastic Teflon. Contaminant transfer tests to a sensitivity of 0.2 x lo-’ g./cm.2 (one-tenth of a molecular layer) have shown no detectable contamination transfer.I3 This material also possesses excellent temperature characteristics. The construction materials containing metal oxides, generally glass and ceramic, also possess the desired characteristics. Being dielectric, they do not suffer from galvanic corrosion. They are generally The Journal of Physical Chemistry
quite stable; only under circumstances of unusual environment and temperature does chemical corrosion occur. With few exceptions, metal oxides (of which glass and ceramic are composed) are virtually insoluble in water. Furthermore, decomposition does not occur until extremely elevated temperatures are reached. Thus, it is seen that ceramics and glass (except soft glasses) tend to meet the criteria for noncontaminating construction material. The design of the system was then resolved about an all-glass-Teflon structure. The system was built incorporating the following contaminant removal means : nuclear grade, mono-bed ion-exchange resins for ion contaminants; a high grade of activated carbon, further treated, for organic materials; an ultraviolet light for organisms, and a specially developed inert volumetric filtering system for particulate matter which is effective into the submicron region. To provide flexible, noncontaminating joints between the various members, the previously mentioned Teflon plastic appeared to be the only suitable material. A novel Teflon bellows was developed (Fig. I) to give flexibility to otherwise stiff Teflon tubing. To meet the necessary requirements, a centrifugal pump was designed with Teflon on all wetted parts. The system provides a flow rate of about 1 gal./min. and a cycle time of about 4 min. During initial experiments, it was found that the glass required special treatment before it could be used effectively. After fabrication of several units (Fig. a), the following experiment was carried out to measure the resistivity of the water in the system. Experimental Equipment and Technique Temperature Measurement. Temperature measurements were made using four thermometers, described Tab’e I. ~
(2) D. Koontz and J. Sullivan, “Preparation and Use of High Purity Intrinsic Water for Electron Device I’ro[:esning,” Bell Telephone System Monograph 3143. (3) U. R. Evans, “The Corrosion and Oxidation of Metals,” St. ?dartins Press, 1960, pp. 389. 666, (4) H. Uhlig. “The Corrosion Handbook,” John Wiley and Sons, Inc., New York, N.Y.. 1948, pp. 13, 569. (5) H. Uhlig, ibid., pp. 161, 191. (6) U. R. Evans, ibid., pp. 207, 214. (7) H. Uhlig, ibid., pp. 155, 172, 550. (8) H. Uhlig, ibid., p. 597. (9) U. R. Evans, ibid.,pp. 733, 751. (10) U. R. Evans, ibid., pp. 130, 753. (11) H. Uhlig, ibid., p. 76. (12) U. R. Evans, ibid., pp. 476, 769. (13) D. 0. Feder and D. Koontz, “Detection, Removal and Control of Organic Contaminants in the Production of Electron Devices,”
Bell Telephone System Monograph 3143.
RESISTIVITY OF
517
h R E \V.ATER
The calorimetric thermometer was factory calihrated and certified to 0.01'. The two titer test units and the 100' unit were checked at three points as shown in Table 11.
Table 11 Tiler
Temp.. 'C.
0 18
26.6
Fiatare 2.
Apparatus riaed in resistivity meiuurements
I t is to I,c notrd that tlir titrr tcst thermomet,ers could be rrad rasily to 0.lo and extrapolated to 0.05'.
- 1 to
+0.05"
+O. ino
+n.11.5*
-n.nr,o
-0.05"
-0.0.5~
+0.05"
+n.05°
fn.02'
Method
no. I
(Distilled water-ice
bath (Calorimetric therrnorneter) (Calorimetric ther"mnrter)
Titer test 2
teat
00.
1W*
A t the temperatures where the t,wo titer test and 100' thermometers were used, the individnal thermometer readings were within 0.05'of each other. The accnracy of the thermometers is purported to be 0.1"; thns at the temperature readings of 35' and above, the accuracy is O.RO/, or better; however, a t the 10 and 15" points, the error could be 1 and 0.7%, respectively. This then throws doubts on the validity of these readings. It is hoped that since the thermometers checked qnite accurately at the calibration points and tracked qnite closely, the error will he much smaller than appears to he possible. The readings at 18, 20, and 25" were taken with the calorimetric thermometer. Ren'stance Measuremenl. A precision ax. resistauee bridge (Fig. 3) was constructed to facilitate precise resistance measurements over the specific range of interest, which was approximately 6 to f4 megohms. The water conductivity cells used have a constant of 0.1, making the bridge resistance range from 0.6 to 6 megohms. A Hewlett I'ackard Model 200 CD audio oscillator was used as the a.c. signal soiirce and a Tektronix oscilloscope, Model 531 A with Type CA plug-in unit (with 50-mv. sensitivity) was ufed as a null indicator. The Bridge. The bridge circuit utilizes a G.R. shielded transformer Type 578 to isolate the bridge circnitry from the ax. generator, minimizing the effect, of capacitance to ground from changes in the electrostatic potential in the generator. The bridge resistors used are G.R. Type 500V with an accuracy each of *O.O.i%. The movable or readmit arm of the bridge nses a cninbination of the G.R. Type 5OOV resistors with switch and a G . R . Type 1432-1' resistance decade box.
5 18
A. IVERSON
Table 111 Temp.,
G R . T Y P E 5 7 8I,
! II
I
-
OC.
Resistivity, megohms
5f0.1 10 f 0 . 1 15f0.1 18 i 0 . 0 1 20 i0 . 0 1 25 f 0 . 0 1 35hO.l 40fO.l 45i0.1 5OiO.l 55fO.l 65fO.l
59.76f0.03 42.82 f 0 . 0 3 31.67 1 0 . 0 3 26.66i0.03 23.86 & 0 . 0 3 18.36f0.02 11.33i0.02 9 . 0 9 ri: 0 . 0 2 7.36f0.015 6.00 f 0.015 4.98f0.010 3.30 f0,010
puted for pure water, calculations were made using the equation for the variation of the conductance of pure water with temperature. l 4
log k
[log ( A d )
- 3 - ’/~Pw]
(1)
+
Figure 3.
Diagram of the resistance bridge,
The a x . signal used was BO-, keeping the inductive and capacitive effects of the bridge resistors to a minimum. Read-out accuracy or null sharpness was kept to an absolute maximum by the proper reactance network used to balance out the shunt lead and cell capacitance and the series inductance of the leads and bridge circuitry. This network is adjustable to compensate for changes in the dielectric constant of water with temperature, which changes the effective cell capacitance. Read-out reproductibility was generally in the order of f0.02%. The complete bridge circuitry then was calibrated against G.R. Type 5OOV 0.05% resistors installed a t the cell position. Range accuracy varied then from *0.1 to 0.2% over the range measured, 0.5 to 4 megohms, becoming 0.30Q/,a t 6 megohms (5’ reading). D i p Cell. The data were taken on a sealed Pyrex, platinized-platinum dip cell, certified to *l% by the manufacturer. The measurements were conducted and the results are shown in Table 111.
Calculations I n order to determine how closely the measured values of the resistivity corresponded to those comThe Journal of Phvsical Chemistru
where Pw = -log K w , A = A H i AOH-, and d = density of water. Values for -log Kw14 and the limiting mobility of H + and OH- l5 were also obtained from the International Critical Tables. Values for the density (d) of water were obtained from the “Handbook of Physics and Chemistry.” Table IV shows the values available for -log Kw, Hf, OH-, and d, and gives the corresponding calculated conductivities. Since resistivity readings are more generally used to describe water of high purity, conductivity calculations will be converted to corresponding resistivity values; graphs will also be in terms of resistivity.
Table 1V
OC.
H-
10 15 18 25 35 40 50
275.6 300.4 315.2 350 399.6 421.4 464.3
- 10
R X
R X
log
106, ohms
43.36 31.85 26.68 18.16 10.97 8.72 5.83
OH-
d
Kw
10 -6, mho
149 164.5 174 196 228 244 276
0.9997 ,9990 ,9986 ,997 ,994 ,992 ,988
14.53 14,34 14.23 13.99 13.67 13.52 13.26
0,02306 ,03140 ,03748 05507 ,09121 ,1147 ,1715
Temp
(14) International Critical Tables, Vol. VI, p. 152. (15) International Critical Tables. Vol. VI, p. 259.
RESISTIVITY OF PUREWATER
519
It is to be noted that there is fairly close agreement between the measured (Table 111) and calculated (Table IV) values of resistivity. It is also interesting to note that the measured values, a t the low temperature end, are slightly lower than those calculated. However, for increasing temperature, the difference becomes less and above 18’ the measured values become increasingly greater than those calculated. The small differences between the measured and calculated values and the large range to be covered would not render a plot of the two curves very meaningful. Therefore, to better illustrate how the measured and calculated values deviate from each other, they will be shown as a percentage difference. That is, the percentage difference of the measured resistivity, as compared to the calculated, will be plotted.
% difference
=
meas. (ohms) - calcd. (ohms) calcd. (ohms)
These percentage values are calculated from Tables
I11 and IV and are plotted in Fig. 4. It is to be noted that the variation is close to being linear and considerably exceeds the experimental error of *0.5%. Since it is obviously impossible for the measured “purity” to be greater than the calculated, the measurement equipment was checked for calibration. Both the bridge and thermometers were within the limits previously mentioned. The change in the platinum dip cell dimensions due to thermal expansion is negligible over the 60’ temperature range measured. The cell constant changes 0.0540/, from 5 to 65’ and also is such as to cause lower resistivity readings with increasing temperature. Since it was not immediately apparent where the discrepancy stemmed from, assistance was sought’6 in an effort to track it down. The first efforts involved recalculating the resistivity of water using recent data. The values of K w were taken from Harned and Hamer” and the values for H f and OH- are given by the equations’* H+ht.,
= hgs[l
- 0.014(t
- 25)]
A~:,= 349.82 OH-Ato
= A25[1
A25 =
198
(2)
- 0.016(t - 2 5 ) ] (3)
The density values were again taken from the “Handbook of Physics and Chemistry.” Table V gives the values of resistivity as calculated from the above data arid using eq. 1 , Figure 5 shows the percentage difference vs. temperature of the measured resistivity (Table 111) as
Figure 4. Plot of per cent difference of measured resistivity of pure water as compared to calculated value us. temperature.
Table Y Kcalcd-
Temp., OC.
H+
5 10 15 20 25 35 40 45 50 55
251.87 276.36 300.84 325.33 349.82 398.80 423.28 447.77 472.26 496.74
-log
OH-
d
Kw
mhos X 10-0
Rcslcdv
ohms
x
10‘
134.64 0.999965 14.73049 0.01667 59.99 150.48 ,9997 14.53313 ,02310 43.29 166.32 .999 14.34486 ,03138 31.87 182.16 .998 14.16685 ,04180 23.92 198.00 ,997 13.99654 ,05483 18.24 229.88 13.68027 ,09027 11.08 994 ,1133 245.52 13.53521 ,992 8.83 261.36 .990 13.39621 ,1407 7.11 277.20 13.26154 ,1733 988 ij.77 293 04 13.13686 ,2103 ,9857 4.75 I
compared to calculated (Table V), plotted as before, It is noted that there is now closer agreement between the measured and calculated values. However, the increasing difference in the measured values, as compared to calculated, still exists. It was pointed out1*that the temperature coefficients describing the variation of the limiting ionic mobility of H + and OH- with temperature were not well known. A literature search disclosed the work of (18) Dr. Walter Hamer, Chief, Electrochemistry Section, National Bureau of Standards, Washington, D. C. (17) H. S.Harned and W. J. Hamer, J . A m . Chem. Soc., 5 5 , 2194 (1933). (18) W. J. Hamer. private correspondence.
Volume 68, Number 3 March, 1964
vided in the literature, the difference increasing with increasing temperature. Applying these values to eq. 1 for the resistivity of water brings the experimental and calculated values into closer agreement. A further search of the literature was not fruitful in yielding data on empirical values for the limiting mobility of OH- a t various temperatures. The work of Owen and Sweeton also indicated that the limiting conductance of OH- varies in a similar fashion.19 To test this,I8 the sum of H + and OHwas determined from the experimental measurements, using Harned and Hamer's Kw values and eq. 1. Table VI1 Ohms X 108
Temp., OC.
-log Kw
d
AOH-
59.76 31.67 18.30 11.33 7.36 4.98
14.73049 14 34486 13.99654 13.68027 13.39621 13.13686
0.999965 ,999 ,997 I994 ,990 .9857
387.9 470 542.8 613.8 684.9 754
5 Figure 5. Plot of per cent difference of measured resistivity of pure water as compared to calculated value us. temperature.
Owen and Sweetonle where, as part of the measurements on the conductance of HC1 solutions, the limiting ionic mobility of H + from 5 to 65' is given. Using these empirically determined values Of Hf and Solving eq. 2 for the temperature Coefficient, Values for the temperature coefficient are determined from 5 to 65".
+
(mesrrd.)
15 25 35 a5 55
I
AHt
Using eq. 3 for the temperature variation of OH+, and assuming that the nonlinear temperature coefficients derived from the H + values of owen and Sweeton (Table VI) applied also to OH-, values for OH- are then calculated.
Table VU1 Table VI
Temp..
T , "C.
1%
k
5
250 6
15
300.9 349.82 396.7 440.8 482.1 520.8
0 01418 0 Oi398 ... 0.01341 0.01301 0,01261 0.01222
25 35 45 55 65
+
I
Table VI shows these values. It is seen that the temperature coefficient decreases rapidly with temperature. This then gives lower values of H + than proThe Journal of Phyeical Chemistry
'C.
K
Aor
5 15
0.01418 0 01398
25 35 45 55
0.01341 0.01301 0.01261
141 8 170.3 198 224.5 249.5 272.9
I
..
I
The calculated H+ values are then compared to Owen and Sweeton's H+. It is seen that the two sets of H + are within 2%. Using Owen and Sweeton's H+ values, the OH- values calculated from Owen and Sweeton's temperature (19) B. B. Owen and F. H . Sweeton, J . Am. Chem. Soc.. 63, 2811 (1941).
RESISTIVITY OF PUREWATER
521
Table I X
5 15 25 35 45 55
+
AOH (Table VII)
AOH-
H+
(Table VIII)
H+
(Owen and Sweeton)
387.9 470 542.8 613.8 684.9 754
141.8 170.3 198 224:5 249.5 272.9
241.6 299.7 344.8 398.3 435.4 481.1
250.6 300.9 349.9 396.7 440.8 482.1
AH+
Temp., 'C.
Table X Temp., OC.
5 15 25 35 45 55
-log
H+
OH-
250.6 300.9 349.9 396.7 440.8 482.1
141.8 170.3 198 224.5 249.5 272.9
Kw
d
K,
R,
mho
ohms x 10'
x
10-
14.73049 0.999965 0.01697 58.91 ,999 ,03148 31.77 14.34486 ,997 ,05482 18.24 13.99654 ,994 ,0893 11.20 13.68027 7.29 ,990 ,1372 13.39621 4.97 ,9857 ,2012 13.13686
coefficient (Table VIII), eq. 1, and Harned'and Hamer's K w values, the resistivity of water is calculated. The percentage difference of the measured resistivity (Table 111),as compared to the calculated (Table X), is plotted as before, in Fig. 6. It is seen that the maximum deviation from the calculated is 1.4Oj,, and the total spread 1.7% This compares favorably with the &0.50/, experimental error. The mean of the experimental variation is about +0.6%. This mean line also passes through the measured value at 25'. The measured resistivity at 25' is a point of maximum accuracy because of the hO.01 ' thermometer calibration; moreover, the calculated resistivity a t 25' is also a most accurate point because the values of H + and OHhave been empirically determined to a high degree of accuracy. Thus, this also tends to indicate that a mean value at +0.6% is probably a reasonable assumption, the +0.6% being accounted for by cell constant error (cell constant is certified to 3=1%). From the foregoing, the values of the limiting mobility of OHas given in Table VI11 are assumed to provide a higher degree of accuracy than heretofore.
Figure 6. Plot of per cent difference of measured resistivity of pure water as compared to calculated value vs. temperature.
Future Work Additional work is to be done to measure the resistivity of water more accurately over a broader temperature range. Temperature will be determined more accurately with the use of a calibrated platinum resistance thermometer. The cell constant would be determined accurately with standard KC1 solutions. The temperature range over which measurements were made would be extended as close to the freezing and boiling points as feasible. From these data, empirical values for the sum of the limiting conductance of H + and OH-, not presently available, could be obtained.
Acknowledgments. The writer wishes to acknowledge the assistance of Dr. Walter Hamer of the National Bureau of Standards, whose suggestions and direction have been instrumental in the preparation of this paper. Thanks go to Larry Davis for the design and fabrication of the electronic measuring equipment, and to Robert Berggrenn for the fabrication and assembly of the water system.
Volume 68,Number S March, 1964
