success implies the applicability of this algorithm in the field of chemistry where scientific information not yet fully analyzed abounds. The analysis and classification of industrial products will be greatly benefited by the pattern recognition technique (19, 20). The present algorithm makes it possible to apply this technique routinely in the chemical laboratory with a small calculator. ACKNOWLEDGMENT We are grateful to Min-Hon Rei of the National Science Council of the Republic of China for his interest and encouragement in this work. LITERATURE C I T E D (1) T. L. Isenhour and P. C. Jurs, Anal. Chem., 43 (IO),20A (1971) (2) B. R. Kowalski and C. F Bender, J . Am. Chem. Soc., 94,5632 (1972) (3) P. C. Jurs and T. L. Isenhour, “Chemical Application of Pattern Recognition”, Wiley-Interscience. New York, N.Y., 1975. (4) B. R.Kowalski, Anal. Chem., 47, 1152 (1975). (5) P. C Jurs, B. R. Kowalski, and T. L. Isenhour, Anal. Chem., 41, 1949 (1969).
(6) T. J. Stonham, I.Aleksander, M. Camp, W. T. Pike, and M. A. Shaw, Anal. Chem., 47, 1817 (1975). (7) B. R. Kowalski, P. C Jurs, and T.L. Isenhour, Anal. Chem., 41,1945 (1969). (8) T. R. Brunner, C. L. Wilkins, T F. Lam, L. J. Soitzberg, and S.L. Kaberline, Anal. Chem., 48, 1146 (1976). (9) L. B. Sybrandt and S. P. Perone, Anal. Chem., 43,382 (1971). IO) S.R. Heller, C. L. Chang, and K. C.Chu, Anal. Chem., 46,951 (1974). I 1) W. S.Melsel, “Computer-Orlented Approaches to Pattern Recognition”, Academic Press, New York, N.Y., 1972. 12) C. T. Zahn, I€€€ Trans. Comput., C-20,68 (1971). 13) B. R. Kowalski and C. F. Bender, J . Am. Chem. SOC.,95,686 (1973). 14) K. Fukunaga and W. L. G. Koontz, I€€€ Trans. Comput., ClQ, 31 1 (1970). 15) D.R. Olsen and K. Fukunaga, I€€€ Trans. Comput., C-22,915 (1973). 16) J. W. Sammon, Jr., I€€€ Trans. Compot., C-18,401 (1969). 17) K. Fukunaga and D. R. Olsen, I€€€ Trans. Comput., C-20,917 (1971). 18) R. W. Rozzett and E. M. Peterson, Anal. Chem., 47, 2377 (1975). 19) D. L. Duewer and B. R. Kowalski, Anal. Chem., 47, 526 (1975). 20) H A. Clark and P. C. Jurs, Anal. Chem., 47,374 (1975).
RECEIVED for review January 31,1977. Accepted May 2,1977. Financial support of the National Science Council of the Republic of China is gratefully acknowledged.
Buffer Solutions for Testing Glass Electrode Performance in Aqueous Solutions over the pH Range 0-14 at 25 “C Arthur K. Covlngton“ and M. Isabel A. Ferra Department of Physical Chemistry, University of Newcastie upon Tyne, NE1 7RU, England
The new method of testing glass electrodes has been extended to cover the whole pH range. It is based on indirect comparlson of potentials wlth those of hydrogen gas electrodes but uslng silver-silver chlorlde electrodes In cells wtthout llquld junction. Using specially developed chloride-contalnlng test buffers, it Is now possible to determine the errors of glass electrodes with an accuracy of f0.6 mV (fO.O1 pH) over the pH range 0-14 and to measure sodlum errors at up to 1 M Na’ at constant pH for pH > 6.5. The method Is Illustrated by results from testing commercial electrodes.
Departure from this behavior, or error, is indicated by the difference between emf values obtained with two different solutions. The following glass (G) and hydrogen (H) cells, which correspond to the invariant cell (I) if the solution used is identical, can be set up: glass electrodel s o l u t i o n I AgCl I Ag
Pt, H,lsolutionl AgClI Ag
(H) Denoting the emf of cell I when a reference solution R is employed by E?, then
EIR = EHR- E In this laboratory a new method of testing the performance of glass electrodes has been developed using buffer solutions containing no sodium ion in the pH range 6 to 1 2 (I). Sodium ion was then added to each of these solutions at three different Na’ concentrations to test the pH-response of glass electrodes in the presence of this cation. The method is based on indirect comparison of glass electrodes with the hydrogen gas electrode, using silver-silver chloride electrodes in cells without liquid-junction, and it was designed to be simple, accurate, and rapid so that it can be easily employed by manufacturers and users with the resources available in most analytical laboratories. The method has now been extended at both ends of the pH scale by devising suitable buffer solutions containing chloride ion. Results obtained with some commercial glass electrodes are given. METHOD The criterion of perfect behavior of a hydrogen-ion responsive glass electrode is that the emf of the cell
Pt, H 2 i s o l u t i o nI glass e l e c t r o d e
(1)
should be constant independent of solution composition.
(G)
G
(1)
where E H ~E , G are ~ the emfs of cells H and G, respectively, containing also a reference solution R. Replacing solution R in which the glass electrode is assumed to be error-free by another solution (T) of different pH, will give, in general new , E G so ~ that values E I ~EHT,
ElT = EHT- EGT
(2)
The error of the glass electrode AE is defined by (2)
AE=E?-ER I = (EHT- EGT)- (EHR- E G R ) = (EHT - EHR)- (EGT- E G )
(3)
Thus the error of a glass electrode, relative to a solution where it is assumed to be error-free, can be obtained by subtracting the difference between the two values obtained for cell G from the corresponding two values for cell H, which have been determined for specially devised buffer solutions in this work. The reference solution is chosen to be a neutral pH buffer (pH 6.58) for tests over the range 0-14. For direct measurement of the sodium ion error in the alkaline region the chosen reference solution has the same pH as the test solution but ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
1363
Table I. Substances Used in the Preparation of Buffer Solutions Substance Tetramethylammonium hydroxide (TMAH) (25% aq. s o h )
Supplier BDH
Glycine ( G )
BDH (AnalaR) BDH (AnalaR)
Succinic acid (H,Suc)
Mol wt 91.15
mp/bp, “C
NH,CH,COOH
75.07
...
CH,COOH CH,COOH NC(CH,OH),
118.09
186.5-188.5 (solid)
>99.5%
209.24
102-103 (solid)
> 98%
7510.21%
121.14
170-171 (solid) 169-173 (liquid) 105-108 (liquid) 801 (solid) 130 (solid)
>99.8%
110/0.019%
2,2-Bis(hydroxyethyl) imino-tris(hydroxymethyl) methane. “Bis-Tris” (BT)
AldrichU.S.A.
Tris(hydroxymethyl) methylamine. “Tris” (T) Ethanolamine (E)
BDH (AnalaR) BDH
NH,C(CH,OH), CH,( OH)CH,NH,
61.08
Piperidine (P)
BDH
C,H,o”
85.15
Sodium chloride
BDH ( AnalaR) BDH ( AnalaR)
NaCl
58.44
Sodium perchlorate
Drying temp (“C)/detected Stated purity water content > 24.5% Halide (as bromide) 99.0% 75/0.016%
I
(CH,CH,OH),
140.46
NaClO,,H,O
Table 11. Composition and Preparation of Buffer Solutionsa Soln no, Soln composition Acid component
...
11010.014%
...
> 99%
> 98% >99.9%
110
>99.0%
do not dry
Base component
Additive
A0 1MHCl 1000 mL 1M HCl 0.1 M HCI 100 mL 1 M HC1 A1 7.507 g glycine 50 mL 1 M HC1 A2 0.05 M GHCl t 0.05 M G 5.844 g NaCl 4.724 g H,SUCC 20 mL 1 M NaOH 0.02 M H, Succ + 0.02 M NaHSucc A4 5.844 g NaCl 4.724 g H,SUCC 60 mL 1 M NaOH 0.02 M NaHSucc + 0.02 M Na,Succ A5 50 mL 1 M HC1 20.924 g BT 0.05 M BTHCl + 0.05 M BT A6 18.171 g T 100 mL 1 M HC1 A7 0.10 M THCl + 0.05 M T 3.054 g E 30 mL 1 M HC1 A9 0.03 M EHCl + 0.02 M E 50 mL 1 M HCI 10.644 g P All 0.05 M PHCl + 0.075 M P 100 mL 1 M HCl 54.69 g TMAH (25% solnbb 0.05 M TMAH + 0.1 M TMACl A12 A14 0.80 M TMAH + 0.1 M TMACl 328.14 g TMAH (25% soln ) 100 mL 1M HC1 a The amounts given are those required to prepare 1 L of solution at 20 “C by addition of distilled water (except in case of If the concentration of the TMAH stock solution is x mol/kg solution, the required amount to prepare A12 is AO). (0415/x)X l o 3 g and t o prepare A14 is (0.9/x) X l o 3 g. Table 111. Preparation of Buffer Solutions Containing Sodium Ion Solution Components AiNa2 AiNal AiNaO A12Na2 A12Nal A12NaO A14Na2 A14Nal A14NaO
0.3511 g NaClO,.H,O + Ai ( i = 6, 7, 9, 11)to 3.511 g NaClO;H,O t Ai (i = 6, 7, 9, 11)to 35.115 g NaCIO,.H,O + Ai ( i = 6, 7 , 9, 11)to 25 mL 1 M HC1 t 13.67 g TMAH (25% soln) + 0.146 g NaCl + H,O to 4.56 g TMAH (25% s o h ) t 1.461 g NaCl + H,O to 20 mL 1M HC1+ 3 0 m L 1 M NaOH + 23.877 g NaClO,.H,O t o 25 mL 1 M HC1 + 82.03 g TMAH (25% soln) + 0.146 g NaCl + H,O to 72.92 g TMAH (25% s o h ) + 1.461 g NaCl t H,O to 50 mL 1 M HC1 + 125 mL 4 N NaOH + H,O to
the latter contains sodium ions a t 0.01, 0.1 or 1M. In the previous work, attention was concentrated on the alkaline region and the choice of amine buffer substances was made to avoid the complications of response of the glass electrode to small cations, that due t o sodium ion being the most important. Initially this principle was extended t o solutions in the range 3-5, but tests showed that no sodium ion errors were discernible in this pH range so the presence of sodium ions was permitted in these buffers making the solutions simpler and less costly t o prepare. Two changes have been made in the composition of the buffers devised earlier (1). T o avoid confusion, a new code 1364
Final volume/mL 250 250 250
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
250 250 200 250 250 500
for the buffer solutions has been introduced. Solutions are designated by Ai, indicating that the pH of a particular buffer solution lies between i and i 1. The composition of A12 differs from B6 used previously in order to keep the chloride concentration close to 0.1 M. The concentration of A6 (formerly B1) has been increased so that its buffer capacity is higher, and it is therefore less likely to contamination. This solution is particularly important since it is chosen as reference solution in which glass electrodes are assumed error-free and electrodes will be used more frequently in this solution than in others. Apart from these two differences, the following present and previous solutions are the same: A7 = B2, A9
+
Table IV. Observed emf Differences (mV) for a Perfect Glass Electrode Transferred between Buffer Solutions A6 From To A0 A1 A2 A4 A5 A6 A7 A9 All A12 640.0 743.2 802.6 120.2 219.9 294.7 374.5 461.8 523.3 A0 0 519.8 623.0 682.4 0 99.7 174.5 254.3 341.6 403.1 -1 20.9 A1 420.1 523.3 582.7 -99.7 0 74.8 154.6 241.9 -219.9 A2 303.4 448.5 345.3 507.9 167.1 -174.5 -74.8 0 79.8 -294.7 A4 228.6 265.5 428.1 -154.6 87.3 1.48.8 368.7 -79.8 0 -254.3 -374.5 A5 281.4 178.2 340.8 -241.9 -87.3 -167.1 -341.6 -461.8 A6 0 61.5 279.3 219.9 116.7 -303.4 -523.3 A7 -148.8 -61.5 0 -228.6 -403.1 162.6 0 103.2 -420.1 -640.0 -265.5 -345.3 -178.2 -519.8 A9 -116.7 -103.2 0 59.4 -523.3 A1 1 -743.2 -219.9 -368.7 -448.5 -281.4 -623.0 -162.6 -59.4 0 -682.4 -582.7 -279.3 -428.1 -507.9 A1 2 -802.6 -340.8 -256.3 -.153.1 -93.7 -521.8 -676.4 -373.0 -601.6 A14 -896.3 -434.5 -776.1 = B3, A l l = B4. The substances used for, and compositions of the buffers are given in Tables I, I1 and 111. Buffer solutions containing sodium ion are coded AiNaj 6 = 0, 1, 2) where j indicates pNa = -log (Na'). Thus A6Na2 means the p H of this solution lies between 6 and 7 and its sodium ion concentration is lo-* M. Solutions AiNaj for i = 6, 7, 9, 11 and j = 0, 1, 2; also for i = 12, j = 0 are obtained by adding sodium perchlorate monohydrate. In solutions containing tetramethylammonium ions, perchlorate precipitates and it is replaced by sodium chloride. Solutions A12Nal and A12Na2 are identical with B6Nal and B6Na2, respectively, but the higher sodium concentration A12NaO can now be prepared using sodium hydroxide which is less costly than tetramethylammonium hydroxide. A new A14 series of solutions has been devised thus extending the range to p H 14. In devising the testing procedure, the philosophy of keeping the solution preparation and testing procedure as simple as possible was adopted. Accordingly it is not intended that rigorous precautions to exclude carbon dioxide should be taken.
EXPERIMENTAL Solution Preparation. The substances used in the preparation of the buffer solutions are detailed in Table I and details of the solutions and their preparation in Tables I1 and 111. Solutions should be prepared with laboratory grade distilled water using Grade B volumetric glassware (20 "C). No special precautions to exclude carbon dioxide should be taken apart from keeping solutions stoppered. Hydrochloric Acid was provided in ampoules for the preparation of 1M HC1. They contain 0.001% w/v mercury(I1) chloride but no difference could be detected in the results for cell H between solutions prepared from this material and from constant boiling hydrochloric acid. Sodium Hydroxide was provided as carbonate-free 0.1, 1, and 4 M solution in polythene bottles. Preferably, solutions were prepared from freshly opened bottles which then were restoppered immediately. Tetramethylammonium Hydroxide (TMAH)was available in 100-mL quantities as approximately 25% w/w aqueous solution. Several samples were titrated and the concentration was found to vary by 1.5%; hence it is necessary to titrate the solution before the preparation of the buffer solutions. This may be done with 0.25 M HCl to a pH of 4 electrometrically or with a suitable indicator. The low pH is chosen because of the presence of carbonate detected by differential potentiometric titration and confirmed using a carbon dioxide electrode (Radiometer Type E5037) as 5 X lo-' M in a freshly opened bottle. Analysis also showed typically 10-'M Na', 4 X lo-" M K', 2 X M C1-, M Br-, M 504'- in the solution as supplied. M I-, and Ethanolamine should be used from a freshly opened bottle or for preference distilled (bp 171 "C) and a middle fraction collected. Piperidine should be used from a freshly opened bottle or for preference distilled (bp 106 "C) and a middle fraction collected. Yellowish colored samples should be rejected. Experimental details of how the tests should be carried out have been given previously (1). Tests should be made in a draft-free atmosphere, all solutions being at the same temperature 25 f 2 "C.
Ai A14 896.3 776.1 676.4 601.6 521.8 434.5 373.0 256.3 153.1 93.7 0
--*
Table V. Observed emf Differences (mV) for a Perfect Glass Electrode Transferred between Solutions of Increasing Na' Concentration at Approximately Constant pH From To AiNa2 Ai 1.1 A6 A7 0.3 A9 1.2 A1 1 0.7 A1 2 -2.5 A14 -3.7
AiNal
AiNaO
6.2 3.1 6.7 5.0 -0.5 -3.2
23.7 9.7 20.8 20.9 -3.0 -17.5
Assessment of Probable Errors Arising in Solution Preparation. All solutions were prepared by volume, in order to maintain the preparation process as simple as possible. The variation of emf due to changes in the concentration of buffer solutions can be evaluated as follows. The electromotive force, E , of cell H is given by
(4) where k = (RT In 10)/F, E" is the standard potential of silver-silver chloride electrode (E" = 222.5 mV). The uncertainty 6E in E , due to errors of the concentration is
-(-
6E = RT SmH +
2)
(5)
mH
obtained by differentiation of Equation 4 assuming YH and ycl are constant over small variations of the ionic strength. The difference between the molal or molar scales will be ignored. In preparing a solution by volume, three main sources of error arise: (1) Calibration of pipets and flasks, (2) Temperature variation, (3) Experimental technique. In the preparation of 1L of A1 from dilution of 100 mL of A0 with water, the probable error produced can be calculated as follows: The concentration of Al, (0.1 M), is given by couo c1=
u1
where u1 is the final volume of A1 (1000 mL), and cg and uo are the concentration (1M) and volume (100 mL) of AO, respectively. Differentiation of Equation 6 gives
(7) where 6c0 = 0.001 M, as stated on the ampoules supplied. The volume uo was dispensed by using a 50-mL pipet twice, and the tolerance on its capacity (3) is *0.08 mL (therefore, 6uo = 2 X 0.08 mL). The tolerance on the capacity of a 1-L flask (60,) is f0.80 mL ( 4 ) . Substituting these values in Equation 7 gives 6cl = 0.00034 M. For this solution, mH = mcl and 6mH = 6mc1, therefore, from Equation 5 6E1 = *0.17 mV, which is the error in the emf, assuming the solutions are prepared at 20 "C, since pipets and flasks are calibrated at 20 "C. If the solutions are prepared at 25 "C, the corresponding difference in the density of water is 0.00116 g Assuming ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
1365
Table VI. Manufacturers’ Information pn Glass Electrodes Tested Temperature Glass PH Additional information electrode range range, “C A 0-12 0-70 Combination electrode E ... 0-14 0-70 F 0-14 0-130 G 0-12 -20-70 ... K 10-100 Negligible sodium error 0-14 0-14 10-120 Negligible sodium error M N ... 0-12 10-70 20-70 High alkaline 0 0-14 P Low temperature 0-11 -10-70 0-60 S 0-12 0-14 10-140 No appreciable acid error T down to 0 pH. Alkaline error very small Very low electrical X 0-11 0-50 resistance 0-10 Corning 015 composition GG Table VII. Errors (mV) for Glass Electrodes Transferred between Buffer Solutions, at pH < 6 Glass electrodes A5 A1 A0 A4 A3 -0.3 t 0.2 AI -0.2 -0.1 -0.1 -0.2 -0.3 + 0.1 -0.3 -0.1 A2 -0.5 t 0.3 -0.2 -0.3 -0.2 El -0.1 -0.1 t 0.2 -0.2 0.0 E2 -0.1 -0.4 -0.2 -0.3 -0.4 Fl + 0.1 -0.1 -0.3 -0.4 -0.2 FZ -0.5 -0.9 -0.3 -0.2 -0.2 GI + 0.2 t 0.3 t 0.1 + 0.2 0.0 Kl 0.0 c0.1 K, +0.1 + 0.3 +0.3 -0.2 -0.2 0.0 -0.1 +0.1 MI -0.2 to.1 -0.2 -0.1 -0.3 M2 -0.5 -0.3 -0.1 0.0 -0.4 NI -0.3 -0.3 -0.2 -0.2 -0.2 N2 -0.5 -0.2 -0.3 0 1 -0.3 -0.1 -0.2 -0.4 -0.1 0 2 -0.2 -0.1 -1.8 -0.2 -0.2 -0.1 -0.5 PI -0.4 -5.5 -0.4 0.0 -0.1 p2 t0.1 -0.6 S 0.0 -0.3 -0.3 -0.6 -0.2 -0.1 T3 -0.7 +0.1 + 0.5 T5 + 0.4 + 0.8 +0.3 -0.3 -0.5 -0.6 -0.4 -0.3 -0.3 XI -0.4 -0.6 -0.4 -0.4 -0.3 XZ + 0.4 GG, -1.1 -0.2 +0.1 + 0.3 GG, -0.4 t 0.3 + 0.6 + 0.2 -25.4 paH 5.36 4.02 2.49 1.09 0.07
- .
the density of the solution is the same as that of water, and neglecting the expansion of the glass, Sco = 0.00116 M. 6vo = 0.1163 mL and 6ul = 1.163 mL. Substituting these values in Equation 7, 6cl = 0.000349 M and where 6E2 = hO.18 mV is the error due
to a change in temperature, from 20 to 25 “C. To estimate the possible error in the volumetric technique, it was assumed that one drop corresponds to 0.05 mL, and the effect was calculapd of a difference of two drops of water when preparing the two solutions (1M and 0.1 M HCl), and one drop in each use of the 50-mL pipet; these assumptions yield the results that 6co = 0.000099 M, 6uo = 0.10 mL and 6vl = 0.10 mL. Using Equation 7, as before, 6cl = 0.00012 M and 6E3 = h0.06 mV. The likely error produced by these three sources will be given by
6E = d 6 E I 2+ 6E:
+ 6E:
=
k0.25 mV
A similar error is likely to result in the preparation of the other buffers. It can be seen that the temperature variation is quite important as a source of error, In practice, if the ambient temperature does not change very much during the course of the experiments, the error would be smaller. In fact, the error found for A0 and A1 was hO.1 mV, from four measurements for A0 and 6 measurements for Al. The variation of pH of the buffers with dilution is very small as can be seen from the results of the following experiment: equimolar bis-tris buffer solutions (0.02 M) were prepared in 250-mL flasks, previously calibrated with water, in order to vary the final volume by fl mL; the emf readings of cell H were 713.3, 713.5, and 713.7 mV. Thus, the addition of 1mL of water to 250 mL solution altered the electromotive force only by 0.2 mV. However, solutions of strong acids and bases, although having higher buffer capacities than dilute weak acid systems, have much higher dilution values (e.g., for 0.1 M HC1, ApHllz = 0.28) (5). Calculation of pH Values of Buffers. From Equation 4 it follows that
(9) which is an experimental quantity. Using the Bates-Guggenheim convention (6) for ycl, paH = pH was calculated. Values can be found in Tables VII, VI11 and IX. These values are intended only as a guide to the pH of the solutions, because the Bates-Guggenheim convention has been applied above its intended limit of I , 0.1. An alternative procedure was used for buffers A0 and A1 where ycl was equated to Y H C ~and calculated directly using the equation and constants given by Pitzer (7) which relate to the molality scale. Correcting for concentration scale using density data indicates a difference in pH of no more than 0.01 at 1 M.
RESULTS Results f o r Hydrogen G a s Electrode Transfers. The emf differences for a perfect glass electrode (that is for a hydrogen gas electrode) when transferred between solution A6 and any other are given in Table IV. Assuming the glass electrode is error free in A6, the error in any other solution is obtained by subtracting the observed emf difference, E.4t(Lz6) from the corresponding difference for the hydrogen gas electrode, given in Table IV.
Table VIII. Errors (mV)for Glass Electrodes Transferred between Na*-free Buffer Solutions at pH > 6 Glass electrode A, El F, Gl Kl M, 0 1
p2 S
Xl GG 1 GG, paH
1386
A7 -0.1 + 0.3 -0.2 -0.2 + 0.3 + 0.3 + 0.4 + 0.3 +1.5 + 0.3 + 0.6 + 0.3 7.90
A9 t 0.5 + 0.3 +0.1 +0.5 +0.1 + 0.3 1.0.2 + 0.2 + 0.5 + 1.9 + 2.0 +2.1 9.38
A1 1 + 0.3 + 0.3 + 0.3 + 0.3 + 0.2 + 0.4 + 0.4 + 0.4 + 0.9 + 3.0 + 3.6
+ 2.6
11.34
ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
A1 2 + 1.5 + 1.2 t 1.1
+ 2.4
+1.1 t 0.5 + 0.9 + 8.3 + 2.8 + 18.1 + 10.8 + 7.4 12.60
A14 4.11.6 +3.7 + 4.9 t 20.8 + 5.2 t 3.5 t 3.2 + 55.1 + 19.6 t 59.7 + 58.4 ~42.4 14.1
c12 -0.1 -0.3 -0.1 0.0
-0.3 -0.3 -0.3 -0.2 -0.2 t 1.0 t 0.3 + 1.3 12.7
C12NaO + 23.8 + 2.4 + 2.2 t 59.6 + 5.8 + 1.9 + 0.4 t 98.2 +40.5 + 120.2 + 115.0 + 92.4 12.6
T o determine the sodium error, it is necessary to measure the difference between the electromotive forces of cells
Glass electrode I Ail AgClI Ag
(G') Glass electrode 1 AiNajl AgCll Ag (G") with i = 6, 7, 9, 11, 12, or 14 and j = 0, 1, 2; each value of i and j corresponds to a particular value of pH and pNa, respectively, as described previously. Since the solution in the first cell above contains no sodium, the error is obtained by subtracting the emf difference, between the two cells, E A I N a , - EA^, from the corresponding difference, when the hydrogen gas electrode replaces the glass electrode. These emf differences are given in Table V.
Results for Commercial Glass Electrodes. Acid Region
( p H < 6). Some commercial glass electrodes (Table VI) were tested, following the procedure described. The glass electrodes are represented by code letters and duplicates are indicated by subscripts. Some were new electrodes and some had been used in the previous work (1)(the same code letters have been retained for the same electrodes). Example: An emf difference of 339.7 mV was obtained for a glass electrode when transferred between A6 and A12. Subtracting this from the corresponding emf difference for the hydrogen gas electrode, 340.8 mV (Table IV), 6th row, 10th column), the error is 1.1 mV. The errors determined are given in Table VII. These were obtained using values for hydrogen electrodes determined at the same time. Use of the average values leads to values which may differ by up to A0.6 mV (0.01 pH) because of difficulties in reproducing solution preparation and solution contamination by carbon dioxide and solution carry over by the electrode transfer. A l k a l i n e Region ( p H > 6 ) . Twelve glass electrodes were also tested in the alkaline region (pH > 6), and the results obtained using hydrogen electrode values determined at the same time are given in Table VIII. S o d i u m Errors. Since the sodium error becomes important in the alkaline region, the glass electrodes were transferred from solutions without sodium to solutions containing sodium a t three different concentrations, at each pH value, from 6 to 14. The errors, given in Table IX, were calculated using the emf differences shown in Table V. Example: An emf difference of 4.9 mV was obtained for a glass electrode when transferred from A12 to A12NaO. Subtracting this value from -3.0 mV (Table V, 5th row, 3rd column), the error is +1.9 mV. Although addition of sodium ions alters the pH, it is constant within f0.2 pH, for each group of buffer solutions (Table IX). Thus the sodium error for each glass electrode has been determined a t approximately constant pH. Figure 1 shows the variation of the sodium error for glass electrode X I a t various pH values.
DISCUSSION The performance of glass electrodes over the whole pH range at 25 "C can now be tested simply, by preparing the appropriate buffer solutions and measuring the corresponding emfs, using the silver-silver chloride reference electrode. The method is more accurate than any involving the use of the calomel electrode, because of the irreproducibility of liquid junction potentials. Although electrode potentials vary with temperature, the testing temperature is not critical, since the method is based on comparison of differences between two emf readings; but it is important that the two readings are taken a t the same temperature. The measurements described were taken with temperature variation of no more than k0.50 "C; this could be responsible for some scatter found in the results, but better temperature control is not necessary, since a reproducibility ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
1367
PH 139
I2 6
II 4
9.4
79
0 4
66 3
2
I
0
P NO
Figure 1. Sodium errors of glass electrode XI
better than f0.6 mV is not achievable (by inspection of Tables VII-IX). The probable error in preparing a buffer solution was shown to be about f0.25mV; since the calibration of glass electrodes, at a particular pH, involves the preparation of four buffer solutions, the expected error would be f 4 X 0.25/& = f0.5 mV. Since the accuracy of most pH meters is fO.01 pH, which corresponds to f0.6 mV, solution preparation by volume is of adequate accuracy. Examining the results shown in Table VI1 it can be seen that, with the exception of electrodes G1, P1, Ps, and GGz in AO, all glass electrodes show no error in the acid region. The apparent errors observed are mainly caused by temperature variation, solution contamination, and uncertainties in the concentration of the solutions. In the alkaline region (Table VIII), for most glass electrodes the errors, up to pH 11, are very small and in good agreement with results for the same electrodes determined previously ( I ) . Electrode S in A7 (Table VIII) and electrode GG1 in A5 (Table VII) show errors which are out of line (+1.5 mV and -1.1 mV, respectively) with the results obtained in neighboring solutions for these same electrodes; this could be explained by a poor electrical connection on those occasions. It indicates that the performance of a glass electrode should not be judged on a single determination. In Table IX the errors observed in A7Nal are higher and of the opposite sign than expected, and of the same magnitude for all electrodes; this suggests that the solution has been contaminated. Electrode O1 seems to be the best electrode of the series; it shows no sodium error, even at pH 14, but the scatter in the results obtained with it is greater than for any other electrode. Generally, the errors observed at pH > 12 may be due either to the sodium ion impurity in tetramethylammonium hydroxide or to some response to tetramethylammonium ions themselves (8). No other explanation has ever been advanced of errors in alkaline solution except partial response to small cations. Light and Fletcher (9) have described a method for evaluating glass errors using silver-silver chloride electrodes. They employed three solutions: an acid solution (0.1 M HCl), an alkaline solution (0.05 M barium hydroxide), and an al-
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ANALYTICAL CHEMISTRY, VOL. 49, NO. 9, AUGUST 1977
kaline solution with added sodium ion (0.05 M barium hydroxide + 0.5 M NaN03). The ionic strength was kept high (2 M) by the addition of barium chloride to all solutions, thus providing chloride ions and permitting use of AglAgCl reference electrodes. It was thus possible to determine the electrode response between pH 1 and 1 2 approximately and the sodium ion error at p H 12. T o test the hypothesis of response t o tetramethylammonium ions, two barium-containing solutions C12 (0.1 M Ba(OH)2 0.1 M HC1) and C12NaO (+1 M NaC104) were prepared. The results of testing the same range of glass electrodes has been incorporated in Table VIII. All electrodes showed errors less than 1 mV in Cl2. In C12NaO the errors are comparable to those in A12NaO shown in Table IX. Preparation of C12Na3 and C12Na4 gave errors for electrode Pz of 2.3 mV and 0.8 mV, respectively, and for G1 of 1.9 mV and 0.4 mV, respectively. This suggests that if the errors found in A12 were due to sodium ions their concentration would have to be higher than M, which is not so according to flame M). Solutions with the same photometric analysis (4.3 X composition as A12 were prepared from tetraethyl- and tetrabutylammonium hydroxides. Electrode P2gave errors of 4.7, 13.3, and 10.5 mV and electrode G1, 0.8, 4.9, and 12.4 mV in TMAH, TEAH, and TBAH. The Na’ analysis were M (TEAH), and M (TMAH, new batch), 7.4 X 5.4 X M(TBAH). The new lower error in TMAH is 7.7 X consistent with the lower Na’ concentration but, on the other hand, it is known from previous work that the alkaline error depends on the immediate previous usage of the glass electrode. Although the matter is not resolved, response to low level Na’ concentration seems a more likely explanation than response to tetraalkylammonium ions. An attempt to remove Na’ ions from A12 by complexation with added benzo-15crown-5, 18-crown-6 (IO) or phenacyl kojate (11) gave no significant difference in the determined errors for the two crowns but an increased error in the presence of kojate. These findings are of considerable interest to the understanding of the origin of the errors of the glass electrode. It is hoped that the improved methods of testing glass electrodes described in this paper will lead to results which will stimulate manufacturers to make improvements in some of the glass electrodes now available, but will also lead to a better understanding of its mechanism of response.
+
ACKNOWLEDGMENT We thank various manufacturers for donating samples of their electrodes and members of British Standards Institution Technical Committee LBC/16 for their advice and encouragement.
LITERATURE CITED (1) M. F. G. F. C. Camoes and A. K. Covington, Anal. Chem., 46, 1547 (1974). (2) M. Dole, J. Am. Chem. SOC.,5 3 , 4260 (1931). (3) British Standard BS 1583 (1961). (4) British Standard BS 1792 (1960). (5) R. G. Bates, “Determination of pH-Theory and Practice”, 2nd. ed., Wiiey, New York, 1973, p 111. (6) R . G. Bates and E. A. Guggenheim, Pure Appl. Chem., 1, 163 (1960). (7) K . S. Pitzer and G. Mayorga, J . Phys. Chem., 7 7 , 2300 (1973). (8) G. Eisenman, in “The Glass Electrode”, Wiley, New York, 1965, p 289. (9) 5 . S. Light and K. S. Fletcher, Anal. Chem., 39, 70 (1967). (10) C. J. Pedersen and H. K. Frensdorff, Angew. Chem., Int. Ed. Engl., 11, 16 (1972). (1 1) Cambrian Chemicals Ltd. (Croydon, Surrey), News Bull., 1 (2), 1 (1975).
RECEIVED for review March 15, 1977. Accepted May 2 , 1977. Thanks are due to the Portugese Government for partial financial support of M.I.A.F.
