Constant Current Potentiometric Acid-Base Titrations with Lanthanum Hexaboride Indicator Electrode D. J. Curran and K. S. Fletcher 111’ Department of Chemistry, Uniuersity of Massachusetts, Amherst, Mass. 01002 Lanthanum hexaboride has been used as an indicator electrode for acid-base titrations in aqueous solutions using constant current potentiometry. Titrations of hydrochloric acid with potassium hydroxide and the reverse titration have demonstrated a precision and accuracy of a few parts per thousand. The pH region corresponding to the potential break of the electrode is such that the titration of weak bases is particularly appropriate, and this is illustrated by titrations of THAM and of sodium carbonate with sulfuric acid. An accuracy of a part per thousand has been demonstrated for the titration of approximately 0.2-gram samples of sodium carbonate.
INA PREVIOUS study it was shown that linear sweep voltammetry at the lanthanum hexaboride electrode in aqueous solutions produced well defined peak polarograms for the reduction of hydrogen ion ( I ) . Plots of peak currents 0s. hydrogen ion concentration were linear, and the current-time behavior at constant potential in quiet solution obeyed the equation for linear diffusion to a plane electrode. The foot of the current-voltage curve for the hydrogen reduction occurred in the region -0.8 to -0.9 V us. SCE. In alkaline solution, the reduction of water limited the potential span of the electrode, At pH 9, for example, measurable current for this reduction began to appear in the vicinity of -1.4 V us. SCE. These facts suggested that the La& electrode would be a useful indicator electrode for acid-base titrations using constant current potentiometry. Depending on pH, polarization of the electrode using a small constant cathodic current will force the LaB6 electrode to indicate the potential of one of the following half-reactions:
Here, the potential of the electrode when operated under an impressed constant current will shift cathodically as the concentration of hydroxyl ion increases. Similarly, the electrode potential will shift in the anodic direction as acid is added to a basic solution. Should the change in pH of the solution which produces the abrupt shift in electrode potential correspond to the region of the equivalence point pH for a titration, the electrode could be used to follow acid-base titrations. On the basis of the peak polarograms obtained for the reduction of hydrogen ion in quiet solutions, application of a constant cathodic current of a few microamperes would result in a shift in the potential of the LaB, electrode from approximately -0.9 V us. SCE at pH 5 to approximately - 1.4 V us. SCE at pH 9. Although exact description of this potential shift is not possible in the absence of a series of currentvoltage curves obtained in stirred solution, this 0.5 V change is more than twice the potential change expected for any reversible hydrogen ion indicator electrode which has a Nernst factor of 59.2 mV at 25 “C. Application of constant current potentiometry to acidbase titrations has not been previously reported. Other applications have been reviewed by Kolthoff (3) and have been discussed in textbooks (4-6). In this work the La& electrode has been used to follow the course of the following titrations: hydrochloric acid with potassium hydroxide and the reverse titration, tris(hydroxymethyl)aminomethane(THAM) with sulfuric acid, potassium hydrogen phthalate with potassium hydroxide, and sodium carbonate with sulfuric acid. End point detection is precise and accurate in all cases except in the titration of the weak acid. EXPERIMENTAL
2 HzO
+ 2 e-+
HZ+ 2 OH-
(2)
In stirred acidic solutions, the limiting current, il, would be directly proportional to the bulk concentration of hydrogen ion. The equation for the current-voltage curve may be written as ( 2 ) :
E
=
Eliz
+ (RT/an,F)ln(ii - i)”i
(3)
where LY is the transfer coefficient, n, is the number of electrons involved in the rate determining step, and the rest of the symbols have their usual meaning. As the solution is made less acidic, the limiting current decreases, the contribution to the potential by the logarithmic term becomes less positive, and the potential will shift in the cathodic direction. When il becomes equal to the applied current, there will be an abrupt shift in potential to a new value governed by Equation 2. 1 Present address, Research Center, The Foxboro Company, Foxboro, Mass. 02035
(1) D. J. Curran and K. S. Fletcher 111, ANAL.CHEM., 40, 78 (1968). (2) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience, New York, 1954, pp 222-6,
1804
ANALYTICAL CHEMISTRY
Reagents and Solutions. All chemicals were reagent grade
unless otherwise stated. Solutions were prepared from water redistilled from alkaline permanganate. Hydrochloric and sulfuric acid solutions were prepared in supporting electrolytes of KC1 or K2S04, respectively, and were standardized against weighed samples of Na2C03 (previously ignited at 300 “C for 4 hours) to the color change of bromcresol green. Potassium hydroxide solutions were prepared in supporting electrolytes of K2SO4 and were standardized against dried and weighed samples of primary standard potassium hydrogen phthalate to the color change of phenolphthalein. These solutions were protected from atmospheric COz in storage. The titers of acids and bases were verified, within 0 . 2 z , by titrations against each other to the color change of phenolphthalein. Solutions of THAM[tris(hydroxymethyl)aminomethane] were prepared determinately from weighed quantities of undried standard material and were verified, (3) I. M. Kolthoff, ANAL.CHEM., 26, 1685 (1954). (4) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience, New York, 1954, pp 251-4. (5) G . Charlot, J. Badoz-Lambling, and B. Tremillon, “Electrochemical Reactions-The Electrochemical Methods of Analysis,” Elsevier, New York, 1962, pp 173-87. (6) J. J. Lingane, “Electroanalytical Chemistry,” 2nd ed., Interscience, New York, 1958, pp 153-7.
I " " ' " " ' '
Table I. Titrations Involving Strong Acids and Strong Bases Polarizing current = 10.00 pA Titrations of 40.00 ml of 0.1017N HCI (4.068 meq) with 0.0906N KOH End point Acid Relative volume, ml found, meq error, 44.70 4.050 -0.4 44.70 4.050 -0.4 44.82 4.061 -0.2 44.78 4.057 -0.3 44.80 4.059 -0.2 Av. 4.055 + 0.005 -0.3 Titrations of 50.02 ml of 0.0906N KOH (4.532 meq) with 0.1017N HCI
End point volume, ml 44.73 44.76 44.71
0.20
0.40 0.60 0.80 FRACTION T I T R A T E D
Base found, meq 4.549 4.552 4.547 Av. 4.549 10.003
Relative error, $0.4 $0.4
$0.3 +0.4
I,OO
Figure 1. Constant current voltammetric titrations at the polarized lanthanum hexaboride electrode 0 40.00 ml of 0.1017N HCl with 0.0906N KOH 0 50.02 ml of 0.0906N KOH with 0.1017N HCl
within 0.2%, by titration against standardized sulfuric acid to the color change of methyl orange. Solutions of potassium hydrogen phthalate were prepared determinately from weighed samples of the primary standard salt which had been dried at 110 "C for 1 hour. Apparatus. All potentials were measured with a Corning Model 12 pH Meter (Corning Co., Medfield, Mass.). The constant current source consisted of a module, described by Brubaker (7), which plugged into a Heath Model EUW-19A Operational Amplifier System (Heath Co., Benton Harbor, Mich.). A frequent check on the magnitude of the current was obtained by measuring the IR drop across a standard resistor in series with the cell. The potential of the lanthanum hexaboride cathode was measured us. a Corning Model 47600 SCE. The procedure for mounting the LaB6 rod has been described ( I ) . The end of the rod (geometric area = 0.179 cm2)was exposed to the solution. A platinum wire electrode served as the counter electrode. Titrations were performed in a 200-ml electrolysis beaker fitted with a Lucite top which had holes drilled in it to accommodate the counter, working, and reference electrodes plus a Corning model 476020 pHglass electrode, the buret tip, and nitrogen inlet system. Prepurified nitrogen was used to purge oxygen from the solutions. The solutions were stirred with a Fisher magnetic stirrer (catalog no. 14-511-1V2) using a 1-inch Teflon-coated stirring bar. Stirring rates were sufficient to produce moderate cavitation and while sensibly constant during the course of a single titration, were not necessarily reproduced from one titration to the next. RESULTS AND DISCUSSION
Titrations Involving Strong Acids and Strong Bases. Titrations of 40.00 ml of 0.1017M HC1 with 0.0906M KOH and of 50.02 ml of the base solution with the acid solution (7) R. Brubaker, Ph.D. Thesis, Department of Chemistry, Princeton University, Princeton, N. J., 1966.
were performed using a constant current of 10.00 FA. All solutions were 1.OM in KCl. The potential of the LaBBSCE electrode pair was measured at intervals during the course of the titration, and typical titration curves, plotted in terms of fraction titrated, are shown in Figure 1. A large potential break occurred in the vicinity of the equivalence point. The rate of potential change near the equivalence point is approximately 35 mV per 0.1 titrated, and the midpoints of the potential breaks are within 40 to 50 mV of the equivalence point. A small error is involved in taking the midpoint as the end point because the former occurs before the equivalence point in the titration of acid with base and occurs beyond the equivalence point for the reverse titration. Results for a series of titrations are shown in Table I, which demonstrates that the error is consistently negative for titrations of the acid and consistently positive for titrations of the base when the midpoint is taken as the end point. The average relative error shown in Table I is -0.3% for the titration of HCl and +0.4% for the titration of KOH. If results accurate to 1 0 . 1 are required, the best procedure would be to establish the end point potential with known solutions whose concentrations are as close as possible to the concentrations of the unknowns. It will be pointed out later that it is also possible to adjust the position of the midpoint relative to the volume axis by adjusting the magnitude of the polarizing current. The precision of the results shown in Table I is *O.l% relative. To support the polarizing current, reduction of hydrogen ion or water occurs at the cathode and oxidation of water or some other component of the supporting electrolyte occurs at the anode in the absence of any other anodic depolarizer. To ensure that no pH change occurs in solution as a result of the electrode reactions, the hydrogen ion consumed or the base produced at the cathode must be equivalent to the acid produced at the anode according to Equation 4. When titrating 2 H 2 0 + O2
+ 4 H+ + 4 e-
(4)
tenth normal solutions, the magnitude of the polarizing current is sufficiently small that the amounts of acid or base produced by electrolysis would not affect the analysis, should they not be exactly equivalent. For the purposes of this study, it was felt that any possibility of nonequivalency should be VOL. 40, NO. 12, OCTOBER 1968
1805
-1330
-1250
w 0 -1200 v)
$-I050
vj
>
-
-1150
s
P
$000 -I
m“
-
-I
-1100
L
IA
0
0
-I
-I
4 -950-
5-1050
Iz w
z
0
IO
I-
w
c
-
n
-900
-850
-1000
-
-950
-
-900
-800
39.5 7.5
8.0 8.5 VOLUME OF HSO,,
9.0
9.5
Figure 2. Constant current voltammetric titrations of 9.97 ml of 0.0994M THAM in 50 ml of 0.500N K2SOIwith 0.1106N H2S04in 0.400N Polarizing current = 19.80 p A 0 Polarizing current = 10.00 p A 0 Polarizing current = 5.0 p A V Titration curve obtained with pH-glass electrode avoided. Since the production of acid at platinum anodes in chloride media can proceed at less than 100% current efficiency (8), all further titrations were performed using a KzS04 supporting electrolyte. Titration of Weak Acids and Bases. Titrations of THAM were performed using polarizing currents of 19.80, 10.00, and 5.00 PA. A volume of 9.97 ml of 0.0994N THAM and 50 ml of 0.500N K2S04 were placed in the cell and titrated with 0.1106N in 0.400N K2S04. A pHglass electrode was introduced to allow observation of the potential change of both the LaBo electrode and the glass electrode during the titration. The titration curves are shown in Figure 2. The theoretical equivalence point occurred at a volume of 8.96 ml of HzS04and is indicated in the figure by the dashed line. For unsymmetrical titration curves of this type, the inflection point of the titration curve theoretically precedes the equivalence point. This is noted in the titration curve for the glass electrode where the inflection point occurred at 8.92 ml. The potential scale for the glass electrode is arbitrary since the electrode was not standardized with buffer solutions of known pH. For the titration of a weak base with a strong acid, the concentration of hydrogen ion at the equivalence point is given by the approximate expression: (5)
(8) P. Delahay, “New Instrumental Methods in Electrochemistry,” Interscience, New York, 1954, p 270.
1806
ANALYTICAL CHEMISTRY
40.5
41.0
41.5
VOLUME OF K O H , M L .
ML.
[H+l = d ( K w / K X
40.0
Figure 3. Constant current voltammetric titrations of 9.97 ml of 0.4418N potassium hydrogen phthalate in 50 ml of 0.500N K 2 S 0 4with 0.1077N KOH in 0.500N K 2 S 0 4 o Polarizing current = 19.8 pA 0 Polarizing current = 10.0 /LA 0 Polarizing current = 5.0 p A V Titration curve obtained with pH-glass electrode where K, is the ion product of water, Kb is the ionization constant of the base, and C is the total concentration of the salt formed at the equivalence point. Using K, = 1 X lO-I4, KO= 1.2 X 10-6 (9), and C = 1.4 X M , the concentration of hydrogen ion at the equivalence point is calculated as 1.1 X IOd5M,corresponding to a pH of 4.96. With the lanthanum hexaboride electrode, the titration curves show a shift in inflection point with the magnitude of the polarizing current. At the lowest current used, the equivalence point occurred after the inflection point. With the intermediate current, the inflection and equivalence points nearly coincided, and with the highest current, the equivalence point preceded the inflection point. The source of this effect is clear from consideration of the current-voltage curves described by Equation 3. With the larger polarizing current, the entire titration curve is shifted in the cathodic direction, and a larger concentration of hydrogen ion is necessary to produce the shift in potential in the vicinity of the equivalence point. The best procedure for locating an end point would be to adjust the magnitude of the current until the inflection point and the equivalence point of a known solution coincide. The concentration of the known solution should be as close as possible to that of the unknown. These results show that the reduction of hydrogen ion becomes potential determining in the vicinity of pH = 5 , and the titration of THAM is particularly well-suited to end point detection with the La% (9) J. H. Fossum, P. C . Markunas, and J. A. Riddick, ANAL.CHEM., 23, 491 (1951).
5
IO
15
20 2 5
VOLUME OF
30 H,SO,,
35
40 4 5
ML.
Figure 4. Titration of 0.2477 gram of Na2C03in 50 ml of 0.500N K 2 S 0 4with 0.1173N H2S04 Constant current voltammetric titration using lanthanum hexaboride electrode polarized with a constant current of 19.83 p A 0 Titration curve obtained with pH-glass electrode
electrode as would be the titration of any weak base with a similar ionization constant. The potential break with the La& electrode is larger than that for the glass electrode as is the slope in the vicinity of the equivalence point. Smaller errors are then expected when using the La& electrode. A similar series of constant current voltammetric titrations of potassium hydrogen phthalate was studied. For these titrations 9.97 ml of 0.4418N potassium hydrogen phthalate and 50 ml of 0.500N KzS04 were placed in the titration beaker and titrated with 0.1077N KOH in 0.500N KZSO4. The titration curves are shown in Figure 3, where the dashed line indicates the equivalence point volume (40.90 ml). The inflection points preceded the equivalence point in all cases. Using K, = 3.9 X (IO), the equivalence point pH is calculated as 9.14. The titration curves are shifted cathodically, and the difference between the points of inflection and the equivalence point increases as the current is increased. Also, the potential changes in the vicinity of the equivalence point with the La& electrode are somewhat smaller than that obtained with the glass electrode. The cathodic shift in the titration curves with increasing current was explained above. In this titration, the solution has an initial pH of about 4 and at the larger polarizing current, il becomes smaller than the applied current at an earlier point in the titration, producing the potential break which precedes the equivalence point and increasing the difference between the equivalence point and the inflection point. Since the (10) H. H. Willard, N. H. Furman, and C . E. Bricker, “Elements of Quantitative Analysis,” 4th ed., D. Van Nostrand, Princeton, N. J., 1956, p 522.
theoretical equivalence point pH is 9.14 and the solution of potassium hydrogen phthalate was in its buffer region when pH 5 was traversed, the slopes of the titration curves obtained with the La& electrode are more drawn out than that of the glass electrode and the potential breaks smaller. The LaB6 electrode thus presents no significant advantage over other hydrogen ion indicator electrodes for the titration of weak acids. Titration of Sodium Carbonate. Similar procedures were followed for titrations of sodium carbonate samples in 0.5N K2SO4. The curves for the titration of 0.2477 gram of sodium carbonate dissolved in 50 ml of 0.500N potassium sulfate are shown in Figure 4. The upper curve shows the data obtained with the La& electrode while the lower curve is that for the glass electrode. The titrant was 0.1173N sulfuric acid and the current was constant at 19.83 PA. Both curves show two potential breaks, the first due to the formation of bicarbonate and the second due to the formation of carbon dioxide and water. The theoretical volumes of sulfuric acid required to reach each equivalence point are 19.92 and 39.84 ml. The potential break with the LaB, electrode at the bicarbonate end point is too small to be useful, but the second break is much larger than that observed with the glass electrode. The pH at the C 0 2 end point is approximately 4 (11). This lies reasonably close to pH 5 where the abrupt shift in electrode potential occurs. The magnitude of the potential break at the second equivalence point can be increased if COZis removed from the solution prior to reaching the equivalence point. This is probably due to the following equilibrium (12): HC03-
$ COz
+ OH-
(6)
where removal of COZ results in replacement of the weak base, HC03-, by the strong base, OH-. To take advantage of this situation, a titration was performed in which sulfuric acid was added to within 2 ml of the second equivalence point, the titration was stopped, and the stirred solution was purged with nitrogen until the increase in pH due to formation of hydroxyl ion ceased. A period of about 10 minutes was required. The titration was then continued with slow additions of acid and continued purging with nitrogen until the potential break was passed. Typical curves using both the glass and La& electrodes are shown in Figure 5. These particular data are for the titration of 0.2320 gram of sodium carbonate dissolved in 50 ml of 0.500N potassium sulfate with 0.1106N sulfuric acid in 0.400NK2S04. The dashed line indicates the calculated equivalence point volume of 39.58 ml. The La& potential break is very large compared to the glass electrode. The inflection point could be taken as the end point with an error of only a few parts per thousand. The intersection of the dashed line with the La& titration curve occurred at a potential of -0.950 V us. SCE. To illustrate the effect of the magnitude of the potential break, a number of titrations were performed by titrating to this potential using sample sizes of sodium carbonate which differed from the above sample size by only a few per cent at most. Table 11 presents the results of these experiments. While this procedure cannot be recommended in general for titration of weak bases, under the conditions of these experiments the results are very good. As expected, the sample size which deviated the most from the reference sample size showed the largest error, but even here the result (11) Ibid., p 188. (12) D. M. Kern, J. Chem. Educ., 37,14 (1960). VOL. 40, NO. 12, OCTOBER 1968
1807
~
~~~
~
~~~~
Table 11. Titrations of N a ~ C 0 3with 0.1106N H a 0 4 Polarizing current = 19.83pA; preset end point potential = -0.950 V US. SCE Na2C03 End point NanC03 Re1ative taken, gram volume, ml found, gram error, 0.2332 39.81 0.2333 Ito.0 39.52 0.2316 0.2314 $0.1 39.95 0.2341 0.2339 fO. 1 39.97 0.2343 0.2343 fO.0 0.2354 -0.5 0.2366 40.17
0
- I 150
00
Ij
0
50
; > s'
r O w '
a
0 K I-
50
kj W In
is acceptable. In general, results with a precision and accuracy of j=O.lzcan be achieved in this titration by empirical calibration of the electrode.
100
2 U
0
I50 $
F
CONCLUSIONS
End point detection with the LaBs electrode in acid-base titrations is necessarily empirical, but excellent results have been achieved in certain cases. As mentioned earlier, the slopes of the titration curves shown in Figure 1 are approximately 35 mV per 0.1 titrated in the vicinity of the equivalence point. Titrations of 50 ml of 0.1N solutions of strong acids or bases accurate to are easily achieved. Although the slope of the titration curve as determined with the glass electrode would be steeper than that shown by LaBs for this case, the slopes shown by the latter are sufficiently steep to produce very acceptable results. Figure 2 shows that the slope of the titration curve for the titration of THAM is greater with the LaBBelectrode than with the glass electrode. If the equivalence point potential is measured with the same degree of carefulness with either electrode, better accuracy is to be expected using the L a b electrode. No particular advantage can be gained, however, in the titration of weak acids. The electrode is, therefore, particularly applicable to the titration of weak bases. Further evidence for this is obtained from the titrations of sodium carbonate. Here, the electrode is uniquely able to take advantage of the equilibrium expressed by Equation 6, and very large potential breaks are observed in the vicinity of the second equivalence point. Interferences have not been examined but oxidizing agents should be avoided. Cerium (IV) and warm 8N nitric acid will oxidize the electrode ( I ) . Moderately strong oxidizing agents which may not attack the electrode may yield a reduction wave and interfere by polarizing the electrode at a potential
z
IW
200g
2 50
z
*O.lz
1808
ANALYTICAL CHEMISTRY
385
39.0
39.5
VOLUME OF H2SO,,
40.0
40.5
ML
Figure 5. Titration of 0.2320 gram of NazC03in 50 ml of 0.500N KzS04with 0.1106N in 0.400N KSOa 0 Constant current voltammetric titration using lanthanum hexaboride electrode polarized with a constant current of 19.83 ,uA 0 Titration curve obtained with pH-glass electrode
anodic to that for the hydrogen wave. In general, any oxidant which has a current-potential curve anodic to that of hydrogen ion will interfere. Work in our laboratories has shown that this includes the species: Cd2+, Eu3+,Fe(G04)33-,Cr042-, IO3-, and 02. Finally, it should be mentioned that the use of a high input impedance pH meter to measure the potential of the LaBe electrode is not necessary since previous work has shown that this is a low impedance electrode ( I ) .
RECEIVED for review May 20, 1968. Accepted July 3, 1968. Taken in part from the Ph.D. thesis of K.S.F. 111.
