Use of the Glass Electrode in Deuterium Oxide and the Relation between the Standardized pD (pa,) Scale and the Operational pH in Heavy Water A. K. Covington,' M a y a Paabo, R. A. Robinson, and Roger G . Bates National Bureau of Standards, Washington, D . C. 20234
Commercial glass electrodes have been compared both directly and indirectly with the deuterium gas electrode at 2 5 O C in buffered solutions of pD from 1 to 13. It i s confirmed that the glass electrode functions as well in heavy water as in ordinary water. The relation between the operational pH of a buffer solution in heavy water (obtained with a glass electrode stanardized in an ordinary water buffer solution) and its pD or pad value obtained from measurements on cells without liquid junction has been examined and correction factors determined for both glass and gas electrodes. The operational pH of buffer solutions in heavy water at 2 5 O C, measured with the glass electrode, can be converted into a pD value by adding 0.41 (molar scale) or 0.45 (molal scale) for 2 < pD < 9.
Pt; Dz (g), or glass
ALTHOUGHthere are indications (1-10) that the glass electrode functions as well in heavy water as it does in ordinary water, no tests have previously been made directly against the deuterium gas electrode. A number of workers (2-9) have reported that a n empirical correction of about 0.4 must be added to the observed meter reading when a glass electrode standardized with a buffer solution in ordinary water is used to measure acidity in heavy water. This correction converts the operational p H to a value on a p D scale. This p D scale was established using a strong acid of known concentration or weak acid buffer systems of known pK in heavy water. Recently, however, a p D (or paD) scale has been set up (11, 12) on the basis of emf measurements of cells without liquid junction: Pt; Dz (9, 1 atm), Buffer soln, C1-, AgCl; Ag
(1)
utilizing the deuterium gas electrode in acetate and phosphate buffer solutions. With the twofold object of checking the validity of the empirically determined correction factor and of establishing the deuterium response of the glass electrode, measurements have now been made at 25" C on the following cells: Pt; Dz (g), or glass
Buffer s o h in D20
I
buffer in H 2 0
,
Pt;Hz (g>,
(lIsgas) or (IIag')
KCI (sat),
Hg2C12;Hg
(IIbgaS) or (IIbg')
These two cells, when combined, give Cell 111, which was also
Buffer soln or glass ( I I I ~ ~ Sor )
1 On leave from the Department of Physical Chemistry, School of Chemistry, University of Newcastle upon Tyne, England.
ANALYTICAL CHEMISTRY
or glass
(1) P. R. Hamrnond, Chem. and Ind. (London), 7, 311 (1962). (2) R. B. Fischer and R. A. Potter, Ar. Energy Comm. Doc. MDDC, Washington, 715 (1945). (3) R. G . Hart, Nat. Res. Council Can. Doc. CRE 423, Chalk River, Ontario, June 1949. (4) R. Lumry, E. L. Smith, and R. R. Glantz, J. Am. Chem. Soc., 73, 4330 (1951). (5) E. Mikkelsen and S.0. Nielsen, J . Phys. Chem., 64, 632 (1960). (6) P. K. Glasoe and F. A. Long, Ibid., p 188. (7) H. H. Hyman, A. Kaganove, and J. J. Katz, Ibid., p 1653. (8) N. C. Li, P. Tang, and R. Mathur, J . Phys. Chem., 65, 1074 (1961). 19) - . and F. A. Long, - . J . Am. Chem. Soc., ~, P. Salomaa. L. Schalener. 86, 1 (1964). (10) V. Gold and B. M. Lowe. Proc. Chem. Soc.. 1963. 140. i i l j R. Gary, R. G. Bates, and R. A. Robinson, J . Phys. Chem., 69, 2750 (1965). (12) Ibid., 68, 3806 (1964).
HgZCl2;Hg
i a
in DzO
EXPERIMENTAL
or glass
700
Buffer soln, Dz (g); Pt
The heavy water used to prepare the solutions had an isotopic purity of 99.7 mol or better, except where otherwise noted in the tables and for the solutions in Cell V, where
KC1 (sat), in HzO
in which the vertical lines mark a liquid junction. measured directly pt; D2 (g),
~
Stan- KCl (sat) dard buffer in DzO
(111~')
it was 99.4 mol %. The preparation of solutions containing deuterium chloride ( I S ) , NaOD ( 1 4 , acetate buffers ( I ] ) , and phosphate buffers (12) has been described previously. Other solutions were prepared by dissolving the purest available protium-containing reagents in heavy water. The phosphate, phthalate, borax, and tetroxalate salts were National Bureau of Standards (NBS) reference materials. The cell vessels for the measurements on Cells I1 and 1V were H-shaped, with central tap and standard taper fittings to accommodate the electrodes. For measurements on Cell I11 and Cell V, a cell vessel with provision for forming two liquid junctions was used (15). The liquid junctions were formed in the capillary tubes below the bulbs (e,e' in Figure 1 of reference 15). The preparation and use of deuterium gas electrodes and silver-silver chloride electrodes were in accord with previous practice (13, 14). Commercial calomel electrodes, Beckman Type 39170 and Corning Type 476002, were used. These differed slightly in their potentials from time to time during the investigation, and measurements were therefore repeated in light water standard buffer solutions (against a hydrogen electrode) at the same time as the measurements in the heavy water solutions were made. In some of the measurements, a commercial silver-silver chloride electrode with liquid junction (saturated KCl, AgCl; Ag in ordinary water) was also used; emf differences between pairs of solutions were in good agreement with those found using saturated calomel electrodes. For Cell 111, calomel electrodes were prepared as described earlier (15). The glass electrodes studied were Sargent-Jena Types HTA 530056-10 and U 530050-15c, Beckman Type 41263, and Radiometer Type 202B. They were mounted in male standard-taper joints with paraffin wax. Measurements of cells involving glass electrodes were made using the Radiometer Type 4d pH meter, which has discrimination to 0.1 mV. Comparison with other potentiometric equipment showed that this electrometer was reliable to 0.1 mV (including measurements involving polarity change). All other cell measurements were made with potentiometric equipment currently in use in this laboratory. All of the cells were maintained at a temperature of 25 a C within 0.1 a C. RESULTS
Comparison of the Glass Electrodes with the Deuterium Electrode. Before undertaking a comparison of glass elec-
trodes and deuterium gas electrodes (Cell IV), the glass electrodes were conditioned for five days in heavy water. According to the manufacturers, all Radiometer and SargentJena electrodes are tested in standard buffer solutions prior to shipment. This was therefore not the first contact of the electrodes with water. The Beckman electrode was not used in these tests. Six solutions were used. Solutions IC, 5a, 7a, and 12a of Table I, for which paD values were known from previous work, were chosen and were supplemented by 0.05m potassium tetroxalate and a mixture of borax (0.01m) and sodium chloride (0.01m). Deuterium gas electrodes were allowed two hours to reach equilibrium. The glass electrodes were then transferred between cells with prior washing with solution of the same composition as that into which the electrode was about to be placed (16). The glass electrodes were then (13) R. Gary, R. G. Bates, and R. A. Robinson, J. Phys. Chem., 68, p 1186 (1964). (14) A. K. Covington, R. A. Robinson, and R. G. Bates, Ibid., 70, 3820 (1966). (15) R. G. Bates, G. D. Pinching, and E. R. Smith, J . Res. Nutl. Bur. Sld., 45, 418 (1950). ( 1 6 ) A. K. Covington and J. E. Prue, J . Chern. SOC.,1955, 3696.
I " " " " " " ' 1
656
:I
Ii
E- 596
5921
I-
X
,,+
I
P
i
i
Figure 1. Comparison of four glass electrodes with the deuterium gas electrode at various paD values From top to bottom, the plots refer to the glass electrodes in the order mentioned in the experimental section
+
Direct comparison. Glass electrodes exposed only to heavy water; data normalized to 0.05m DCI (Cell IV) X Direct comparison. Data normalized to first measurement of Cell II@ 0 Indirect comparison using emf of Cells II& and I I p S ; data normalized to first measurement of Cell IIbg'
conditioned in ordinary water for two days and the experiment repeated. The electrodes behaved more regularly in the first experiment when they had been conditioned in heavy water and used only in that medium. Drifts on transfer to a different solvent were, however, fairly small in the second experiment. A change of 3.0 0.4 mV toward a more positive value was noted for each electrode in Cell IV from the first experiment to the second. This change in asymmetry potential is presumably associated with the change from heavy water equilibration of the electrode surface to equilibration with ordinary water. Subsequently, the electrodes were compared directly against the deuterium gas electrode (Cell 1V) in four other solutions, and indirectly using Cells IIagasand IIagl. To take into account long-term variations in the asymmetry potentials, each glass electrode was measured in Cell IIbg*as well. Shortterm drifts were allowed for by extrapolation to the time of transfer between cells (16, 17). An initial rapid change of potential over the first few minutes (described in ref (17) as feature A) was ignored. For purposes of presentation in Figure 1, the results have been normalized to the first measured value obtained with Cell IIbg'. Results are also shown in Figure 1 for the first experiment, using six solutions. These have been normalized to the measurements in 0.05m deuterium chloride, since no measurements were made in light water solutions.
*
(17) W. H. Beck, J. Caudle, A. K. Covington, and W. F. K. Wynne-Jones, Proc. Cliem. SOC.,1963, 110. VOL 40, NO. 4, APRIL 1968
701
Table I. Emf ( E I )of Cell I: Pt; DZ,Buffer Containing CI-, AgCl; Ag (in mV) and Reference Values of par, Solution no. la
Solution ml a DCI 0.1730 DC1 lb 0.09969 DCI IC 0.05417 DC1 0.05004 Id DC1 0.04984 le DCIe If 0.009997 DCI 0.009952 Ig DCI 0.001003 lh D3POa KDzPOa 2 0.06544 Citric acid 0.01ooo 3a Citric acid 0.01ooo 3b D2Suc NaDSucf 0.03689 4a DtSuc + NaDSuceJ 0.03689 4b DAc NaAco 5a 0.10425 DAc NaAcs 0.09956 5b 0.05ooO DAc NaAcp 5c NaDSuc NazSucf 6 0,02007 0.02502 7a KDzP04 NatDPO4 KDzPOa NaZDPOaa 0.025OO 7b 0.02500 7c KD2POa NazDFQ 8 Borax 0,05005 NaDC03 NazC03 9 0.02500 Na2C03 0,02500 10 Na2DPO4 Na2C03 0 . Olooo 11 0.01090 NaOD 12a 0.01ooo NaODh 12b 0.04435 NaODh 12c Refers to molality of first mentioned component. b Refers to molality of second component mentioned. Refers to molality of added sodium chloride. Calculated value interpolated from previous data. e 98.77z DzO. SUC= succinate. Ac = acetate.
+
+ + + +
+ + + + + +
mzb
mac
...
... ... ... ... ...
... ... ...
... ...
I 0.1730 0.09969
EI 316.18 343.14
...
...
...
P(aDYcl) 0.988 1.204
...
... ...
0.04984 0.009997 0.009952
376.78 454.68 455.05
1.472 2.091 2.096
... ...
... ...
0.01579
0.06544 0.01500 0.1ooo 0.08609 0.01500 0.10425 0.09956
0.1000 0.0164 0.1014 0.09839 0.02830
407.40 492.82 446.85 527.23 572.68
2.107 2.912 2.959 4.253 4.262
0.1992
585.82
5.306
0.02007 0.02502 0,02500
0.1004
...
...
0.01230 0.01230 0.10425 0.09956 0.05ooO 0,02007 0.02502 0,02500 0.02500
... 0.02500
... 0.00500
... ...
...
...
...
...
...
...
...
...
...
...
...
670.58
6.043
0.1250
751.48
7.506
0.1502 0.1250 0.1000 0.1000
873.78 948.15 1020.62 974.65
9.875 10.831 12.056 11.483
0.02000 0.08035
l&5:72 1101.64
12.928 13.584
...
... ...
0.05005 0.02500 0,02500 0.04ooo 0.005807 0.01ooo 0.03600
...
...
...
...
...
...
PaD 0.852 1,090 1.343d 1 . 380d 1.383 2.044 2.049 3.018d 1.993 2.854 2.844 4.139 4.190 5 . 174d 5.164 5.230d 5.929 7.3864 7.384 7.428d 9.745 10.708 11.942 11.369 12,936 12.865 13.478
0
f
@
' 98.22z D20.
Values of paD were calculated from measurements on Cell
I using the equation paD
=
(EI - E")/k
+ log mcl- + log
YCI-
(1)
pHgasD
pH(S)
+
(E1lagas
- E1,,'"7/k
(2)
where pH(S) is the assigned value of the particular light-water buffer solution used, in this case either 0.05m potassium hydrogen phthalate, pH(S) = 4.008, or the equimolal (0.025m) phosphate mixture, pH(S) = 6.865. Together with pan from Cell I (see Table I), values of 6,,, may be calculated by the equation
were k = (RT In 1O)/F. The standard electromotive force E" is known (13); for yCl-the Bates-Guggenheim convention (18), adjusted for dielectric constant and density differences between ordinary water and heavy water, was used (11, 12). 6,,, = paD pHgaaD (3) Other values of paD were interpolated from previous work (11-14). Values of paD were not known for either the potasThe quantity is the correction to be added to the opersium tetroxalate solution or the mixture of borax and sodium ationally determined pHD to obtain a value on the standard chloride. They have been calculated using the correction paD scale for heavy water solutions. Values of 6,,, are given determined as described below. The pan values are sumin Table I1 together with the emf data from which they were marized in Table I. derived. Measurements were also made on Cell IIIgas directly. As shown in Figure 1, the results of the direct and indirect The two liquid junctions of this cell were prepared anew for comparison are in good agreement. Within the accuracy of each determination. They had cylindrical symmetry ( I @ , the measurements, the glass electrode follows the potential in contrast to the liquid junctions of the commercial calomel of the deuterium gas electrode in the paD range 1 to 10. Deelectrodes which were of indefinite type (19). viations occur above paD = 10 for three electrodes and to a The values of 6,, have been plotted against paD in Figure lesser extent for the fourth. This is the alkaline error or 2. Apart from the points for three buffer solutions with high sodium error. From the nomographs furnished by the manuchloride content, is effectively constant at a mean value facturers, which are only a rough guide to the behavior of any of 0.072 in the paD range 2 to 12. The value is less, and even individual electrode, it would appear that errors are slightly negative, for values of paD below 2 and higher at paD above greater in heavy water at a given paD than in light water at 12. Except in these extreme regions, the results obtained the same value of pH. Further work will be necessary to with the two forms of liquid junction are in good agreement. confirm this suggestion. A small acid error is apparent for In acid solutions, the double liquid-junction cell did not give the one solution of paD less than 1 . Relation between the paD and the Operational pH in Deuterium Oxide. DEUTERIUM AND HYDROGEN GASELECTRODES. (18) R. G. Bates and E. A. Guggenheim, Pure Appl. Chern., 1, Measurements of the emf of Cells IIagas and IIbgasfurnish 163 (1960). values of pHD given by (19) E. A. Guggenheim, J . Am. Chem. Soc., 52, 1315 (1930).
-
702
ANALYTICAL CHEMISTRY
l
0.15
l
l
l
l
l
l
l
l
I
l
very reproducible results. It may also be seen from the two points at pan = 5.929 in Figure 2 that is unaffected by replacing the saturated solution of potassium chloride in light water with a saturated solution of this salt in heavy water in Cell IIIgas. In one of these determinations the buffer in light water was the equimolal phosphate solution, and in the other it was an equimolal (0.025m) solution of sodium hydrogen succinate and sodium succinate (pH 5.401). The sigmoid form of the curve in Figure 2 is the same as that for the corresponding quantity paH - pH for light water (see Figure 6 of reference 15) and for paD - pD (see below and Figure 3), except that the origin is displaced downwards. The deviations from a constant value at high acidity and high alkalinity are attributable to the fact that the residual liquidjunction potential is not negligible when appreciable concentrations of ions of abnormally high mobility are present. These deviations are in accord with predictions based on the Henderson equation. Values of pD for nine solutions were determined from measurements of Cell V in which the standard buffer solution was the equimolal (0.025m) phosphate (12) in deuterium
I XI
1
0 10
l
8
8
i'-
0
ol * /
- 0.05
0
1
1
2
1
1
1
4
l
6
1
8
l
I
I
IO
I
12
I
14
POD
Figure 2. Variation of,,a, X
0 0
+
with paD Commercial calomel electrode (phthalate reference buffer) Commercial calomel electrode Double liquid-junction cell (111) Double liquid-junction cell (111) with saturated calomel electrode in DzO
Table 11.
Emf of Cell IIa ( E I I p )and Cell 111 ( E I I p )in mV and Values of the Correction ,a, 6g.s
Solution no.
EIIsgaa
- EIIbgaa
la lb IC Id
292. 38a 307. 57b 322.3"
le
322. 90b
If 1g lh Ih 2 3a 3b 4a
4b 5a 5b 5c 6 7a 7b 7b 7c 7c 7c 8 8 8 9 10 11 12a 12b 12c
... ...
363. 77b
... ... ... ...
pHD (gas) 0.819 1.072 1.321 ... 1.331
...
2.022 ...
...
... ...
406.61a 483. 355
2.750 4.047
545.4" 544.99
5.100 5.085 ... ... 7.316 7.316
...
... ... 671.W
676. 95b
...
... ... 814.64b 814. 16e 815. l l f 872.76a
...
... 1001.5c
...
...
... ... ... ...
9.644 9.643 9.662 10.629
...
... 12.802
... ...
P H D (gas)
Emgaa
-354.01 ...
0.881 ...
-322.90 ... -285.49
1.407
...
...
... ...
2.039
...
-220.85 -222.37 -292.56 -241.23 -243.37 -166.97 -162.28 ...
3.133 3.106 1.920 2.787 2.751 4.043 4.122
- 101.30
5.153 5.865
...
...
...
-59.47
...
...
26.86 26.52 29.21 29.38 29.68 165.98 166.08 165.48
7.319 7.313 7.359 7.361 7.367 9.671 9.673 9.662
295.64 262.04 ... 349.49 384.06
11'.863 11.295 ... 12.865 13.478
...
With 0.025m equimolal phosphate buffer; E I I b = 650.07 mV. With 0.025m equimolal phosphate buffer; E I I =~ 650.25 mV. c With O.05m potassium hydrogen phthalate buffer in Cell IIb; E I I b d Omitted in taking average. e With 0.025m equimolal phosphate buffer: E I I b = 649.81 mV. 1 With 0.025m equimolal phosphate buffer; E I I b = 649.63 mV.
(commercial calomel electrode) 0.033 0.018 0.022 0: 052
... 0.027
... ... ...
0:094d 0. 092d
... 0.074 0.079
...
... 0.070 0.068
...
... ... ... 0 . lOld 0.102d 0.083 0.079
6gaB
(double liquidjunction cell) -0.029
... ... -0.027 ... 0.005 ...
-0.115 -0.088 0.073 0.067 0.093d 0.096d 0.068
... ...
0.077 0.064
...
0.065 0.071 0.069 0.067 0.061 0.074 0.072 0.083
...
...
0.079 0.074
... ...
0.092 0.121
... 0.134
...
a
b
=
481.4 mV.
VOL. 40, NO. 4, APRIL 1968
e
703
Table 111.
Emf Values for Cell Vasa in mV and Values of paD
Solution no. Ib If 3a 4b
5c 6 8 9 12b
PD 1.104 2.076 2.851 4.191 5.225 5.930 9.729 10.701 12.840
E -374.13 -316.68 -270.81 -191.55 -130.40 -88.67 136.06 193.49 320.11
0.08
- pD
paD - PD -0.012 -0.032 +0.003 -0.001 +0.005
1
X
0.04
X
-0.001
+0.016 +0.007 +0.025
1
I
0
2
4
8
6
IO
12
14
paD
Figure 3.
oxide (solution 7c, pD(S) by the equation
=
7.428), and pD was computed
PD = pD(S)
+ Ev/k
paD
- pHD (glass)
0
(5)
have been calculated and are given in Table IV. The form of the plot of &lasa against paD is the same as that shown in Figure 2, but with an origin further displaced by 6 g ~ a s s 6,, = 0.381 i 0,011, where the second number is the standard deviation of the results for the four electrodes in 12 solutions (omitting two high values). 8gless, like bgaB, is unaffected by a change from KCl(H20) to a KCl(D,O) bridge solution, as was found by Glasoe and Long (6), who concluded that the correction term arose solely from a change in potential of the glass electrode in deuterium oxide compared with ordinary water. In actuality, the experiment indicates only that the residual liquid-junction potential for the combination: buffer in H20/KC1(sat in H20)1buffer in D 2 0 is almost if not exactly the same as for: buffer in H 2 0 / K C I(sat in D20)1buffer in D20. The correction Gelass is the value that must be added to the observed pH meter readings for solutions in heavy water (obtained with the meter and glass electrode calibrated in light water) in order to obtain values on the standardized pD scale. It is thus to be compared with the correction factors for the glass electrode determined in previous work which will now be reviewed. Fischer and Potter (2), using the Cohn method (20) of standardization for acetate buffer solutions in heavy water, established a correction factor of 0.25 for the glass electrode and also 0.42 for the quinhydrone electrode. Their work was criticized by Hart, who repeated the extrapolation of the Cohn method and found it to be nonlinear for buffers in heavy water (3). He calculated log a m for hydrochloric acid and phosphate buffer solutions in deuterium oxide from the known deuterium ion concentration determined by titration or, in the case of the phosphate buffer, from an estimated pK 704
ANALYTICAL CHEMISTRY
X
+
Variation of paD-pD as a function of paD
From the emf of Cell Vgas From the emf of Cell Vgl (Beckman electrode) From the emf of Cell Vgl (Radiometer electrode) Reference point (phosphate buffer in D20)
(4)
Data for the emf of Cell VKasare given in Table 111 and are plotted in Figure 3. Just as for (paH - pH) (13, the values of (paD - pD) are zero over the range 3 to 8, within experimental error. The data for the corresponding cell with glass electrodes (Vg')are included in Figure 3. The deviations from zero are enhanced at high paD when glass electrodes are used; the alkaline errors of the two glass electrodes employed are very different. GLASSELECTRODES. The emf measurements of Cells 1Lg' and IIbg' furnish values of pHD (glass) by an equation similar to 2. These values (Table IV) differ from those of pHD(gas). From the measured paD(Table I), values of &lass, Bglass =
0
and estimated activity coefficients. He found the required correction factor to be 0.4. Lumry, Smith, and Glantz (4) used a similar procedure with stoichiometrically identical buffer solutions in light and heavy water. From the known pK difference in light and heavy water and the measured pH difference, they also found a correction factor of 0.4. A slightly more elaborate procedure was used by Mikkelsen and Nielsen (5) for mixtures of HCI(DC1) with KCI and mixtures of acetic acid, potassium acetate, and sodium chloride. A correction of 0.44 was found at 22" C, or 0.43 if a calomel electrode prepared with a saturated solution of potassium chloride in heavy water was employed. Later investigations have all used dilute acid solutions of known concentration, together with estimates of activity coefficients. Glasoe and Long (6) found 0.39 to 0.40. Their investigations were extended to H 2 0 - D 2 0mixtures by Salomaa, Schaleger, and Long ( 9 ) who found 0.408 for acid solutions in pure deuterium oxide. Glasoe and Long's data for bases require the assumption of the ionic product of DzO; the value taken we now believe to be too high (14, 21). Salomaa, Schaleger, and Long reversed the procedure. Using 0.40, they obtained a value for the ionic product consistent with that accepted at the time. Fife and Bruice (22) studied the temperature variation of the correction factor and found, at 25" C, a value in agreement with that of Glasoe and Long. All the above-mentioned values of the correction factor are based on the molarity scale. The difference between values on this and the molality scale is log door 0.043, where do is the density of heavy water. Taking this difference into account, and allowing for the inaccuracy of previous measurements, it is found that all of the results for buffer solutions except those of Fischer and Potter (2)are in good accord with the mean value of Bglass = 0.45 i 0.03, reported here (Table IV). Gary, Robinson, and Bates (12) found a correction of 0.467 for the phosphate buffer. The value of 6glaas in acid solutions is lower than that for the intermediate region of pD by as much as 0.03. Furthermore, the results scatter in the low pD region, probably because of liquid-junction potential variations. McDougall and Long (23),assumed that their value determined in solutions of strong (20) E. J. Cohn, F. F. Heyroth, and M. F. Menkin, J . Am. Chem. SOC.,50, 696 (1928). (21) V. Gold and B. M. Lowe, J. Chem. SOC.,A , 1967,936. (22) T.H. Fife and T.C. Bruice, J . Phys. Chem., 69, 1079 (1961). (23) A. C. McDougall and F. A. Long, Ibid.,66,429 (1962).
Table IV.
Emf of Cell IIP1 in mV and Values for d,lasa and,,a, [Efor Cell IIIgl =
Solution no. la
E
I
~
Ems'
E11.g'
- &laas
- EIIbg']
PHD 0.457 0.445 0.443 0.452 0.700 0.688 0.687 0.698 0.955 0.942 0.943 0.947 1.652 1.640 1.640 1.652 2.41 1 2.402 2.389 2.399 2.365 2.357 2.352 2.360 3.672 3.658 3.655 3.662 3.743 3.731 3.719 3.758 4.713 4.696 4.698 4.708 6.931 6.912 6.926 6.928 9.287 9.260 9.260 9.284 10.253 10.200 10.178 10.246
Glass electrode (6, lass) correction paD - pHD 0.395 0.407 0.409
6daaa
- 6gaB
0.362 0.374 0.376 0.367 0.400 0.392 0.374 lb 0.402 0.384 0.403 0.385 0.392 0.374 0.428 0.376 le 0.441 0.389 0.440 0.388 0.436 0.384 0.397 0.370 Ig 0.409 0.382 0.409 0.382 0.397 0.370 0.443 0.376 3a 0.452 0.385 0.465 0.398 0.455 0.388 0.479 0.384 3b 0.487 0.392 0.492 0.397 0.484 0.389 0.467 0.375 4a 0.491 0.399 0.484 0.392 0.477 0.385 0.447 0.379 4b 0.459 0.371 0.471 0.403 0.432 0.364 0.451 0.372 5b 0.468 0.389 0.466 0.387 0.456 0.377 0.453 0.384 7b 0.472 0.403 0.458 0.389 0.387 0.456 0.458 0.357 8 0.384 0.485 0.485 0.384 0.461 0.360 0.455 0.376 9 0.508 0.429 0.530 0.451 0.462 0.383 Averageb0.446 + 0.031 0.381 + 0.011 6 The four measurements listed for each solution refer to the electrodes in the order they are given in the experimental section, * The two high values for solution 9 were omitted in taking the average. -309.75 -360.35 -291 . g a -342. l a -296.9 -347.0 -278.8 - 330.3 -281.0 -331.2 -262.5 -312.8 -239.7 -290.0 -221.4 -272.2 -193.4 -243.9 -175.0 -225.3 -197.2 -247.2 -178.9 -229.4 -119.4 - 170.2 -101.8 - 152.2 -114.4 -165.3 -96.8 -147.2 -59.3 -109.4 -41.1 -93.3 71.4 21.0 89.4 37.6 211.9 160.9 229.2 178.6 269.2 217.2 283.7 236.7
69.4 19.5 88.1 37.3 67.8 18.4 86.7 34.5 68.6 19.2 87.8 37.3 68.7 19.1 87.7 36.2 70.1 20.1 89.8 38.9 69.0 19.5 88.1 37.1 69.5 19.5 88.1 37.3 70.3 20.1 89.3 36.6 68.0 18.9 87.1 34.3 67.5 18.2 85.8 33.9 68.6 19.2 87.5 35.5 68.8 19.9 87.7 36.7
acid was constant, independent of pD, and used it to obtain pK values for some acids in heavy water. Fortunately, this value (0.40 on the molar scale) is close to 0.41 which we now recommend for the intermediate range of pD. DISCUSSION
It may at this stage be helpful to clarify the nomenclature adopted here. Bates, Paabo, and Robinson (24) determined correction factors 6 to be added to the operationally determined pH values to obtain peaH(=paH*) values for water-
methanol and water-ethanol solvents. The nomenclature paH* or pH* was adopted to emphasize that the standard state was not pure water. The correction factors and &lass are analogous to, but differ in one important respect from, the correction factor for a mixed solvent such as methanolwater of a given composition. The difference lies in the fact that here we are concerned with two isotopically different, (24) R. G. Bates, M. Paabo, and R. A. Robinson, J. Phys. Chem., 67, 1833 (1963). VOL 40, NO. 4, APRIL 1968
705
pure solvents containing either H 3 0 +or D30+whereas Bates, Paabo, and Robinson were dealing with mixed solvents and solvated protons only. Hence, the correction factor is the same for both gas and glass electrodes. We retain here the symbols 6 with appropriate subscripts while recognizing that there is a difference in their origin for the unique case of isotopically different waters. As with mixed solvents, however, they are obtained on the basis of calibration measurements in light water standard buffer solutions. We have used the symbol pHD for the operationally determined quantity for deuterium oxide solutions based on a light water buffer standard. There is a n analogous quantity pDH for a light water buffer also determinable from Cell I11 by assuming the pD(S) value for the buffer solution in deuterium oxide. It is corrected to pH by the same correction factor 6.
The difference AE",,, - AEogImay be derived alternatively from measurements on two other cell combinations, VI and VII: glass, HC1 (O.Olm), AgCl; Ag-Ag;
AgCI, DC1 (O.Olm), glass (VI,)
and
Pt;Hz, HC1 (O.Olm), AgCl; Ag-Ag;
AgCI,
DC1 (0.01m), Dz, Pt (VIb) The emf of Cell VI, was found to be 33.2 mV, and the value for VIb, 464.1 - 454.7 = 9.4 mV, was derived from Table I and the results of Bates and Bower (25). Cell VI1 is a combination of
glass; HCI ( 0 .Olm)
DCI (0.01m); glass (VII,)
and Pt; Hz, HCI (0.01m) Either pDH or pHD values could be determined for buffers in Hz0-D20 mixtures using glass electrodes calibrated in heavy or light water buffers, respectively-cf. ref (9). It is reasonable to suppose that 6,, or 6 . 1 ~is~made ~ up of two contributions:
6 = AEj/k - AE"/k
(6)
where AEi is the residual liquid-junction potential (as in Cell 111) and AE" arises from a difference in standard potentials of the hydrogen and deuterium electrodes or the glass electrode in light and heavy water, respectively. There is no way of separating these contributions. However, 8.iass
- &,
= (A&,,
- AEgJ/k
(7)
because AE, is the same whether gas electrodes or glass electrodes are used. The reactions concerned are:
D+ (in DzO) UD+ = 1
+
'12
H&)
-,
H+ (in HzO) aH+= 1
+
'12
Ddg) AE",,,
(8)
KCI (sat) in H?O
~
DCI (O.Olm), Dz; Pt. (VIIb)
The emf of Cell VII, was found t o be 26.6 mV and that of Cell VIIb, 1.4 mV. The value of AE",,, - AEoEIderived from Cell VI is 23.8 mV, which lies almost within the range of 22.6 + 0.7 mV derived from Equation 7. The higher value derived from Cell VII, 25.2 mV, arises from 6,, being lower in acid solutions. An analogous quantity, AEoga8- AEoqb,can be derived for the gas and quinhydrone electrodes, The combination: Q, HzQ, HCI (O.Olm), AgCl; Ag-Ag; AgCI, DCl (O.Olrn), DzQ,Q, E
=
34.5 mV
was measured by Korman and LaMer (26). Hence AEogasAEoqh = 25.1 mV and 6qh = 0.49. Fischer and Potter (2) found 0.42 (molar scale) but the value of this comparison is doubtful, for their determination of the correction factor for the glass electrode was wrong. Until this quantity has been redetermined, the value of 0.49 (molal scale) could be used t o correct pHD,h measurements obtained from cells similar to 11, and IIb but with quinhydrone electrodes. ACKNOWLEDGMENT
and
D+ (in DzO) aw = 1
+ H+ (in glass) -, H+ (in HzO) aa+ = 1
+ D+ (in glass)
AE",I (9)
which, when combined, give Hz(g)
+ D+ (in glass)
+
H+ (in glass)
+
ANALYTICAL CHEMISTRY
A. K. C. wishes t o express his gratitude t o the University of Newcastle upon Tyne for granting study leave for the Epiphany Term, 1966, during which time the work reported here was initiated. RECEIVED for review October 12,1967. Accepted February 2,
Dz (g) (IO)
for which the numerical value of 22.6 f. 0.7 mV is obtained by substituting Bglaas - ,,a, = 0.381 + 0.011 in Equation 7. In itself, this does not appear to be a quantity of any great usefulness; it does, however, appear t o be independent of the nature of the glass.
706
1
I
1968.
(25) R. G . Bates and V. E. Bower, J . Res. Narl. Bur. Std., 53, 283 (1954). (26) S. Korrnan and V. K. LaMer, J . Am. Chem. SOC.,58, 1396 (1936).
