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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
I MIN
Flgure 4. Pulsed flow current (represented by the difference between H and L current tracings)for 1 1 M K,Fe(CN),. Conditions: as in Figure
Flow rates, 4.72 (H) and 0.37 (L) rnL/rnin. The pulsed flow current for the blank solution is represented by the difference between the dotted line and the L current tracings
K,Fe(CN)6 solution and the background electrolyte solution, as predicted by theory (9). In the ferricyanide solution, current measured experimentally at the no-flow condition (see asterisk in Figure 3) is significantly greater than the value extrapolated from measurements a t finite flow rates. This deviation and the nonzero intercept have been observed previously (41, and have been explained as a consequence of axial diffusion. Figure 4 is a reproduction of a pulsed-flow chart record for 1 pM K3Fe(CN)G.A detection limit of 2 X M may be estimated from the figure, if it is defined as equal to the peak-to-peak noise level of the signal. The sensitivity of the cell is calculated to be 0.36 kA/pM cm2 a t a flow rate of 4.72 mL/min.
3.
(3):the formal electron exchange rate constant (h"')is 0.00274 f 0.00074 cm/s; the transfer coefficient (cy) is 0.56 f 0.08; and E"' is 0.14 V. These values, except for a , are comparable to values obtained previously with a rotating disk electrode (8) and with a turbulent tubular electrode ( 3 ) . The significant difference in cy (reported as 0.378 f 0.07 (8) and as 0.380 f: 0.03 ( 3 ) )were ascribed to differences in pre-treatment of the electrode. Diffusion limited currents of 1 pM K3Fe(CN), and of background electrolyte solution were measured at various flow rates a t an applied potential of -0.40 V. A cube root dependence on flow rate (Figure 3) was found for both the l 1M
LITERATURE CITED H.F. Osswald, P. C. Meier, and R . E. Dohner, "Advances in Automated Analysis", Technicon International Congress,
W. Simon, D. Ammann,
Vol. 1, 1976, pp 59-62. J. G. Schindler. Biomed. Tech.. 22. 235-244 (1977). W. J. Blaedel and G.W . Schieffer, J . Hectroanal. Chem., 80, 259-271 (1977). W. J. Blaedel and D.G. Iverson, Ana/. Chem. 49, 1563-1566 (1977). A . H. Brand and R. J. M. Rao, U. S. Patent 3,853,732 (1974). G. W. Schieffer and W . J. Blaedel, Anal. Chem., 49, 49-53 (1977). D. R. Sawyer and J. L. Roberts, "Experimental Electrochemistry for Chemists", Wiley, New York, N.Y., 1974. W. J. Blaedel and G.A. Mabbott, Anal. Chem., 50, 933 (1978). W. J. Blaedel and L. N. Klatt, Anal. Chem., 38, 879 (1966).
RECEIVED for review April 10, 1978. Accepted June 19, 1978. This work has been supported in part by a grant (No. C H E 76-15128) from the National Science Foundation.
Accuracy of the Hydrogen Ion Selective Glass Electrode E. P. Serjeant" and A. G. Warner Faculty of Military Studies, University of New South Wales, Duntroon, A.C.T. 2600, Australia
A glass electrode, selected on the basis of its ability to exhibit a consistent Nernstian response between the pH values for 0.05 m potassium hydrogen phthalate (pH 4.008) and the equimolal phosphate buffer 0.025 m potassium dihydrogen phosphate, 0.025 m disodium hydrogen phosphate (pH 6.858) a t 25 "C ( I ) , was used in the cell glass electrodelaqueous solution + chlorideJAgC1;Agin order to evaluate the accuracy t h a t can be expected when any correctly functioning glass electrode is used in such a cell and how this accuracy varies with concentration. For this purpose, solutions were chosen such that the acid ( 2 ) or sodium ion ( 3 ) errors of the glass electrode were not likely to be significant over the range of concentrations studied. This study seeks also to explain the observations of previous workers (4-6) using cells of this type who have reported a slight but linear drift of cell emf with time that cannot be associated with the initial equilibrium period which occurs immediately after an electrode transfer. This drift has been attributed to small changes in the asymmetry potential of the glass electrode. Measurements using the cell glass electrodelaqueous solution + chlorideJAgC1;Ag are closely analogous to p H measurements if the acidity function p(aHycl) is invoked. Effectively a two-cell system is used in which the electrodes are common to both cells. One cell contains a solution whose acidity function is known, p(aHyCl)s,and the other a solution whose acidity function value is to be measured, p(aHyCl),. If the chloride ion molalities in the two cells are respectively m, and m,, the change in cell emf, AE, on transferring the 0003-2700/78/0350-1724$01 .OO/O
electrodes between the two (7) is related to p(aHy& by
where k is the Nernst constant (0.06916 at 25 "C). The standard chosen for this work was 0.02 m hydrochloric acid (p(aHycl)= 1.815 a t 25 "C (8)) and therefore Equation 1 can be written as
EXPERIMENTAL Potassium chloride and sodium chloride were each purified according to the general method of Pinching and Bates (9),with the exception that the final fusion process was replaced by heating the salts at 225 "C under vacuum (0.1Torr) for 1 h. Potassium dihydrogen orthophosphate and disodium hydrogen orthophosphate were recrystallized twice from water and dried at 120 "C. Solutions of hydrochloric acid were prepared from the constant boiling acid (9). These were standardized by gravimetric analysis and their molal concentrations checked subsequently by potentiometric titration against purified ( I O ) 2-amino-2hydroxymethyl-l,3-propanediol(Tris). All solutions were prepared in ion-free water stored under nitrogen. The pH measurements used in the initial selection of the glass electrode were made on a Vibron Electrometer Model 33B in conjunction with a pH Measuring Unit Model C-33B (Electronic Industries Ltd., Richmond, Surrey, England). The output from the electrometer 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
1725
Table I. p(oH7cl) Values Derived from the Cell Glass ElectrodeIKH,PO,(m,),Na,HPO,(m,),NaCl or KCl(m,)IAgCl;Ag at 25 "C, Electrodes Standardized Using 0.02m HCI m a= 0.05 m, = 0.02 m3 = 0.01 rn, = 0.005 m, = 0.002 NaCl NaCl KCI KCl KCI NaCl NaCl KCI NaCl m, = m 2 KCl 6.992 6.991 6.989 6.989 6.940 0.02 6,951 6.974 6.968 6.983 6.983 spread (t0.002) ( t 0 . 0 0 2 ) ( i 0 . 0 0 3 ) (iO.001) (iO.001) (tO.OO1) (iO.001) 7.113 7.098 7.110 7.096 6.989 7.057 7.050 7.081 7.075 0.0025 7.007 spread ( i 0 . 0 0 2 ) (i0.002) (iO.001) (i0.002) ( i O . O O 1 ) ( i 0 . 0 0 3 ) (i0.003) (iO.001) 1(+0.002) (iO.001) 7.142 7.142 '7.125 7.113 7.000 7.070 7.070 7.102 7.107 0.001 7.011 spread (k0.003) ( t 0 . 0 0 3 ) (i0.002) (20.008) (-0.004) ( t 0 . 0 0 6 ) ( ~ 0 . 0 0 3 ) ( i 0 . 0 0 6 ) i(iO.006) ( i 0 . 0 0 6 ) 7.131 7.129 7.145 7.133 7.109 0.0005 6.996 6.991 7.066 7.068 7.117 was connected to a potentiometric recorder via a resistance network adjusted so that a change of 10 mV indicated by the electrometer was shown as an exact full scale deflection on the recorder when the latter was operating in the 1-V fsd mode. A change of 0.001 pH unit corresponded to a change of one scale division on the recorder chart. The same equipment was employed also for many of the acidity function measurements using the cell: glass electrodelaqueous solution + chloride(AgC1;Ag. For this purpose the term AE/ 0.05916 in Equation 2 was replaced by "SpH" which is the observed change indicated by the pH meter at 25 "C when the electrodes are removed from the standard acidity function solution and reimmersed in a solution whose p(aHy,-,) value is to be measured. These measurements were checked subsequently using a Model K5 Potentiometer (Leeds & Northrup 7555) connected to the Vibron Electrometer which was used as a null detector for this application. The recorder, connected as outlined above, continued to be employed to indicate a stable emf value. The usual precautions (6) concerning the screening of terminals and connections were observed. The discrimination of the apparatus was 0.04 mV. The type of glass electrode chosen was dictated by its compatibility with the pH measuring equipment used and, more importantly, by the requirements that when incorporated with a calomel reference electrode (Philips Type R l l ) , it should reproduce to within f0.002 pH unit the pH values obtained for the following solutions at 25 "C ( I ) with the cell Pt;H2Jaqueous solutionJJSCE: 0.05 rn potassium hydrogen phthalate pH 4.008 0.025 m KH,PO,, 0.025 rn Na2HP04 pH 6.858 A glass electrode (Type 33 1070-020, E.I.L.. Richmond, Surrey) fulfilled both conditions and was used with a silver-silver chloride
electrode of the thermal electrolytic type (11) for all the subsequent measurements of the function p(aHycJ. When not in use, both electrodes were stored in 0.02 m hydrochloric acid at 25.00 & 0.01 "C in a stoppered 150-mL tall-form beaker mounted in a thermostatically controlled bath which was filled with distilled water. The cells, also stoppered 150-mL tall form beakers, were supported by a grounded metal cover plate in the bath. The bath temperature was checked periodically using a platinum resistance thermometer. The solutions in the cells were purged of oxygen immediately before measurement of emf by bubbling oxygen-free nitrogen, pre-saturated with water vapor, through the solution. This flow of gas would be diverted across the surface of the solution while an actual measurement was in progress. Washing of the electrodes during their transfer between solutions was accomplished by the washing of each electrode three times with the solution into which they were to be immersed. No attempt was made to superficially dry the electrodes with tissue paper. RESULTS AND DISCUSSION In order to establish that the silver-silver chloride electrode was functioning correctly and as an additional confirmation that the response of the glass electrode was linear, the acidity function values for hydrochloric acid solutions within the concentration range 0.002-0.05 m were measured. The standardization of the electrodes was performed using the p(aHya) value of 1.815 for 0.02 m hydrochloric acid. The mean of three p ( u ~ ~ c values 1) for each of the following concentrations of hydrochloric acid solutions 0.05, 0.01, 0.005, and 0.002 m was found to he 1.462 (1.462), 2.087 f 0.001 (2.087),
2.366 f 0.001 (2.366), and 2.740 f 0.002 (2.741), respectively. The values given in parentheses are calculated from published data (12) obtained with the cell Pt;H2JHC11AgC1;Ag. An assessment of the accuracy of response of the glass electrode was made using the two cells glass electrodelHC1 (rn = 0.02)JAgCl;Ag (Cell
S)
glass electrodelKH2P04(ml),N a 2 H P 0 4 ( r n J , C1 ( m J IAgC1;Ag (Cell X) Cell S was used for standardization (p(aH c,) = 1.815)and Cell X contained the solution whose acidity function value. p( a ~ - y c Jwas ~ , to be measured. In the latter cell, m1 = m2 and
the cell emf was measured for the phosphate buffer concentrations of 0.02, 0.0025, 0.001, and 0.0005 mol kg-'. T h e concentration of chloride ion, m3, was varied within the concentration range 0.002-0.05 m a t concentrations identical to those studied for the hydrochloric acid solutions. Both sodium chloride and potassium chloride were used separately as a source for these chloride ion concentrations. During the series of measurements, a standardization would be performed using 0.02 m hydrochloric acid. T h e AE values a t the concentrations of chloride given for a particular concentration of phosphate buffer would be measured and the standardization checked a t the end of the series. The standardization was therefore checked about twice per day and no allowance was made for any deviation from the initial standardization in the calculation of the p(aHycl) values given in Table I. Where the spread is stated, the values are an average of a t least three series of measurements and the spread is the maximum deviation (f)from that average. T h e only value that can be compared directly to a previously published result is for the solution KH2P04(0.02 m ) , Na2HP04(0.02 rn), NaCl(0.02 m) whose p(aH~c,)value of 6.968 agrees exactly with the value calculated from the data of Bates and Acree (13). It is noteworthy that the values obtained for the same phosphate solution measured in potassium chloride and sodium chloride solutions differ in some instances. These differences are to be expected from the fact that the mean activity coefficients for hydrochloric acid solutions in the presence of potassium chloride differ from those obtained in the presence of sodium chloride. For the phosphate solutions these activity effects not only vary with ionic strength, but also with the ratio of chloride to phosphate. This confirms previous observations (13) that separate regression lines were necessary in order to obtain the thermodynamic p K for the dihydrogen phosphate ion from emf data in which this ratio was varied significantly. That the precision of the results for the 0.02 and 0.0025 rn phosphate solutions given in Table I is closely related to their accuracy could be checked directly by comparing values of the acidity functions a t zero chloride ion concentration (p(a~ycl)'values) with the published values for these solutions (14). For the 0.02 m phosphate buffer solutions, a linear relationship between the concentrations of chloride and their corresponding p(uHycl)values was obtained which allowed a direct graphical extrapolation to yield the p(aHycl)' value of
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
Table 11. Comparison between Published, Calculated, and Values of p(aHYc1)' for KH,PO,(m,),Na,HPO,(m,) Solutions Found in This Work (25 C) 0.0250 0.0200 0.0150 0.0125 0.0100 0.0075 0.0050 0.0025 0.001 0.0005 m, = m, 0.1 0.02 I 0.08 0.06 0.03 0.01 0.004 0.05 0.04 0.002 ~ ( u H Y c ~ publishedQ )' 6.974 6.992 7.013 7.026 7.040 7.058 7.080 7.111 P(aHYc1)' calcdb 6.974 6.992 7.013 7.025 7.040 7.058 7.080 7.112 7.143 7.160 P(QHYC1)' foundC 6.992 7.115 7.147 7.151 0.000 0.003 0.004 0,009 ErrorC Values from ( 1 4 ) . Calculated from p(QHYC1)' vs. JT(1 t 1.5Jq relation using published data only. This work. Table 111. Change in Cell emf Observed for a New Glass Electrode Conditioning in the Cell Glass Electrode IKH,PO,(O.O2 m),Na,HP0,(0.02 m),NaCl(O.O2 m)lAgCl;Ag at 25 "C Day emf (V) drift'
0
1
2
5
0.0737
0.07967
0.08371 0.17 0.003
0.09043 0.09 0.002
a P ( Q H Y c i )h" a
0.25
0.004
7 0.09237 0.03
14 0.09440 0.02
0.0005
0.0003
93 0.09478
Average change in emf in mV h-I.
6.992, given in Table 11, which agrees exactly u i t h the published value. Such a simple relation between the chloride ion concentration and the relevant P(aH7cl) values was not found in the case of the more dilute phosphate solutions for, as the ratios of chloride to phosphate became larger, increasing divergences from linearity were observed. T h e values of P(aHYcl)' for these solutions were obtained, therefore, from a regression analysis, performed by computer, whose results were obtained in a graphical form. In these instances. the deviation obtained from the graphical representation of each analysis was no greater than the spread associated with the mean of each experimental value. For example, the error of 0.004 between the ~ ( C L H ~ value ~ ~ ) ' of 7.115 for 0.0025 m phosphate solution obtained in this analysis and the published value of 7,111is within the maximum error of &0.003 given in Table I for this series of phosphate concentrations. Published data for the two more dilute solutions (0.001and 0.0005 mj are not available and, therefore, an estimate of the errors was made by submitting only the published P(aHYc1)' values (14) t o a linear regression analysis against the function v'?/(1+ 1.5, 7) and applying the resulting equation to the ionic strengths used in this work. The calculated values of Table I1 were obtained in this manner and yield estimated errors of 0.004 and 0.009 in the P(aHycl)' values for the 0.001 and 0.0005 m phosphate solutions, respectively. R i t h i n the equimolal phosphate concentration range 0.001-0.002 m,the errors in the p(aHycl)' values given in Table I1 are equal to or less than the maximum spread of the experimental values of p(aHYcl)given in Table I. It would be a conservative estimate of the error of the glass electrode, therefore, to use the maximum spread observed for each of these concentrations as an indication of the accuracy of the electrode. We feel that quoting these maximum errors is justified as reflecting the order of accuracy which can be expected when using a correctly functioning glass electrode to record a single measurement on a given solution. Using this criterion, the errors are f0.003. f0.003, and ~k0.008for the respective phosphate buffer concentrations 0.02, 0.0025, and 0.001 m , indicating that a t concentrations greater than 0.0025 m the accuracy approaches that of the hydrogen electrode. These errors are somewhat smaller than those obtained in a previous study (15) in which 0.1 m hydrochloric acid was the standardizing solution and, among other solutions, equimolal phosphate buffer solutions prepared in 0.1 m potassium chloride were used in assessing the magnitude of the errors for 15 glass electrodes when they were transferred between the acid and the buffer solutions. The only results available for direct comparison, both in terms of buffer concentration and of the previous histories of the
electrodes examined, are those for the most dilute (0.0025 m) phosphate solution studied and three new glass electrodes whose errors were found to be 0.012, 0.022, and 0.010. In magnitude, these errors approach the error estimated for the most dilute solution studied in our work (0.0005 m ) . This is likely to exceed the value of 0.009, given in Table 11, and, from the deviation of the p ( a ~ y c Jvs. molality of chloride ion relation, is about 0.015. An attempt was made also to determine the error at a phosphate buffer concentration of 0.0001 m but this had to be abandoned because a stable value of the cell emf could not be obtained. Stability of cell emf was regained, however, when the electrodes were returned to the standardizing solution and their subsequent performance was not impaired. The response of the glass electrode in the p(aH*,(-,) range intermediate between the values for the hydrochloric acid and the phosphate buffer solution was checked by measuring the thermodynamic pK, value for benzoic acid over the concentration range 0.00254.01 m. For this purpose, the standard method for cells without liquid junction (16)was used. The value obtained a t 25 "C, 4.208 f 0.002, is in agreement with the value 4.205 i 0.002 and the more recent value 4.204 f 0.005 (17) within the experimental errors quoted. Throughout the whole series of measurements reported here, the drift hitherto associated with slight changes in asymmetry potential was not observed. On transferring the electrodes from the standardizing hydrochloric acid solution to the phosphate buffers, a smooth curve in the values of the emf with time was observed culminating in a stable value after about 10-15 min. This equilibration time varied slightly with the concentration of phosphate buffer, being of shorter duration a t the higher concentrations. On returning the electrodes from the phosphate to an acid solution containing the same chloride ion concentration, it was noted that in some instances the pre-equilibration curve exhibited a maximum in emf which was attained within the first 2-3 min. Thereafter, the emf changed in a smooth fashion to an equilibrium value which was reached about 10 min after the immersion of the electrodes. This "peak phenomenon". in a much more exaggerated form, has been observed (18) when a glass electrode was transferred from 0.01 M potassium hydroxide to 0.1 M hydrochloric acid and was interpreted in terms of a reduction in the thickness of the gel layer associated with the electroactive portion of the electrode in the alkaline solution. Regardless of the direction of transfer, whether from acid to phosphate or vice versa, the value of the cell emf was stable for periods of 3 h after the equilibrium value had been reached.
ANALYTICAL CHEMISTRY, VOL. 50, NO. 12, OCTOBER 1978
This was the maximum period over which the cell was tested using the recorder. However, the emf value for 0.02 m hydrochloric acid varied little over a 24-h period and agreement to within 0.1 mV (
