Alternating current polarographic method of analysis in the presence

The influence of irreversible alternating current elec- trode processes on the analytical applications of ac polarography to the determination of reve...
0 downloads 0 Views 606KB Size
Alternating Current Polarographic Method of Analysis in the Presence of Oxygen and Other Irreversibly Reduced Species A. M. Bond and J. H. Canterfordl Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia The influence of irreversible alternating current electrode processes on the analytical applications of ac polarography to the determination of reversibly reduced/oxidized electroactive species has been shown to be extremely important. In particular, the influence of oxygen with respect to the frequently reported advantage that ac polarography can be carried out without degassing to remove irreversibly reduced oxygen has been examined in detail to find conditions in which to best utilize this advantage in a general manner with comparable results to degassed solutions. The presence of oxygen is shown to interfere in two ways. (a) The product of the electrode process, hydroxide ion, can interact with electroactive species reduced at more negative potentials. (b) The presence of the ac oxygen wave itself is important and decreases the limit of detection. From this investigation, it was shown that a highly acidic medium such as 5M HCI is the most satisfactory medium to use in ac polarography if degassing i s to be eliminated. Interference (a) is virtually eliminated in this medium and with only interference (b) present, the method can be used reliably down to concentrations of about 10-SM with comparable precision to degassed solutions. The effect of irreversibly reduced iron on the determination of tin and other elements is also reported; unlike oxygen, interference i s not readily removed. INTHE INITIAL STAGES of the development of ac polarography, it was believed that no ac waves occurred for irreversible dectrode processes ( I ) . However, later theoretical studies ( 2 , 3 )have shown that ac waves are in fact expected, although the sensitivity is low. In view of the low sensitivity to irreversible electrode reactions, the ac method should, in principle, be applicable to the determination of reversibly oxidized o r reduced species with limited interference from irreversibly reduced/oxidized electroactive species present. An extremely important consequence of this insensitivity toward irreversible electrode processes results in the possibility of carrying out ac polarographic analysis without the time-consuming degassing step to remove oxygen, as is required with dc polarography. As reduction of oxygen is irreversible in many media, the ac method is therefore fairly insensitive toward oxygen. Hence, in principle, the ac method can be used without degassing, but other considerations might also apply. In practice, any irreversible electrode process must occur a t the dropping mercury electrode (DME), even if it is not detected by ac polarography. If this reaction proceeds prior to the reduction o r oxidation of the species being determined, then it can have a marked effect o n the observed behavior of the species being examined.

Present address, Division of Mineral Chemistry, CSIRO, P.O. Box 124, Port Melbourne, Victoria 3207, Australia. (1) B. Breyer and H. H. Bauer, “Alternating Current Polarography and Tensammetry,” Interscience, New York/London, 1963. (2) B. Timmer, M. Sluyters-Rehbach, and J. H. Sluyters, J . Elecrroanal. Chem., 14, 169, 181 (1967). ( 3 ) D. E. Smith and T. G . McCord, ANAL.CHEM., 40,474 (1968).

228

F o r instance, the dc polarographic reduction of oxygen produces two waves in the usable potential range and these steps interfere with the dc measurement of other electroactive species. Although the reduction of oxygen is irreversible and it might be expected that oxygen would not interfere with the ac method of analysis, the reduction of oxygen leads to the formation of hydrogen peroxide and hydroxide ions. Thus, if other electroactive species can interact with hydroxide o r hydrogen peroxide o r both, then interference can occur even with ac polarography ( I ) . It is well known from dc polarography that in the presence of oxygen the solution near the electrode is extremely alkaline relative to the bulk of the solution, and in some cases precipitation of hydroxy species can occur at o r near the electrode when they are readily soluble in the bulk of the solution. The same consideration must also apply with ac polarography and precipitation interference could also be encountered. The interference of irreversibly reduced oxygen has previously been reported by various workers (4-6) and a number of forms of interference as described above have been encountered. The general reliability of the ac method without removal of oxygen is therefore questionable. The present work was undertaken t o show that if an irreversible ac wave is observed, it will necessarily decrease the sensitivity of the method (compared with its removal) and that the possibility that the product of the electrode process can cause interference by interacting with other species always exists. In particular, we have set out to investigate the extent of interference of oxygen, if and how it can be removed, and to compare the results obtained with deoxygenated solutions to establish rigorously the conditions under which the important advantage of ac polarography can be used without removal of oxygen. Some of the previously studied systems have been reexamined in considerable detail to critically assess the degree of interference and as a means to ways of overcoming it. The influence of irreversibly reduced iron o n the determination of tin has also been examined. EXPERIMENTAL

Reagents. The solutions used in the present study o n the effects of oxygen were made up from reagent grade cadmium (11), lead(II), and thallium(1) nitrates and indium(II1) sulfate. The supporting electrolyte was 1M NaCl o r 5M HCI. All stock solutions were prepared at p H ( 5 + 0.3), except for indium(III), which was maintained at approximately p H 3 with hydrochloric acid. Where degassing was carried out, argon was passed through the solution for a standard time interval. While polarograms of degassed solutions were being recorded, a flow of argon was maintained over the solution. (4) Reference ( I ) , pp 147, 165, 167,173-175, 181, 183,187, 191. ( 5 ) K. Itsuki and F. Suzuki, Jap. Analyst, 8, 89 (1959). (6) W. F. Head, Anal. Chim. Acta, 23, 297 (1960).

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971

I

I 0

1 - 2.0

- 1.2 volt

VI.

-0.4

A O / A ~ CI

Figure 1. Dc polarogram in 1M NaCl A . In the presence of oxygen B. After removal of oxygen

/

V o l t vs. A g A g CI

Figure 2. Ac polarogram of oxygen in 1M NaCl

For the work o n the interference caused by iron on the determination of tin, ammonium hexachlorostannate(1V) and iron(II1) chloride were used in a supportigg electrolyte of 5M HC1. Apparatus. Polarograms were obtained using the Metrohm Polarecord E 261. Ac polarography was carried out using the Metrohm ac Modulator E 393 with an ac voltage of 10 mV, rms at 50 Hz. To minimize cell impedance, the modulated ac voltage was applied through an auxiliary tungsten electrode. A constant head of mercury was maintained throughout. All solutions were thermostated at 25 + 0.1 “C. All polarograms were recorded by scanning in the negative direction at a rate of 1 voltil2 minutes. All potentials reported in this work are measured relative to a silver/silver chloride reference electrode (5M NaCI). RESULTS AND DISCUSSION

Ac Polarography in the Presence of Oxygen in Moderately Acid Solutions. Figure 1 shows the dc electrode process of oxygen in a “neutral” (pH 5) 1M NaCl solution which has not been degassed, and the corresponding scan for the degassed solution. Two distinct waves are observed, with halfwave potentials, Eliz, of approximately -0.1 and -0.9 volt cs. AgiAgCl. Thus, reduction of oxygen is occurring over virtually the whole of the usable voltage range of mercury in sodium chloride. Any species which can interact with oxygen or the reduction products of hydroxide or peroxide could be affected. Figure 2 shows the ac electrode process of oxygen in a “neutral” 1M NaCl solution which has not been degassed. Despite the fact that the sensitivity is extremely low relative to the dc polarogram (compare Figures 1 and 2), two oxygen waves with summit or peak potentials, E,, of -0.22 and - 1.1 volts us. Ag/AgCl were observed. This is contrary to earlier reports ( I ) but in agreement with theory (2, 3). The differences between Elii and E, values and the broadness of the second wave show the irreversible nature of both oxygen waves in “neutral” chloride media. Figurz 3 shows the ac polarogram of a degassed “neutral” 1M NaCl solution. The residual wave due to the adsorption e desorption equilibrium of chloride, or other electrode pro-

- 0.0

-1.6

V o l t vs. A q h q CI

Figure 3. Ac polarogram of degassed 1M NaCl solution

cesses, can be seen clearly. The oxygen waves, however, have been completely removed. CADMIUM(II).In the absence of oxygen, the ac cadmium(I1) electrode reaction in 1 M NaCl Cd(I1)

+ 2e

Cd(0)

was observed to be reversible. The half-width was 50 i 2 mV and the E, value of -0.601 volt cs. Ag/AgCl was independent of concentration up to 4 x 10-4M cadmium(I1). The calibration curve was very close to linear up to 1 X 10-4M cadmium(I1) (Figure 4). At higher concentrations, curvature was observed. This is believed to be due to the increasing

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2 , FEBRUARY 1971

229

81

lo

X

1

x /,

0 -

6

x

6 -

/i'

4 4

4 . 2

I

0

I/

IO

/.'

q

2.

/

X

/ ; I I I

I

0

OY

I :o

2:o

3!0

M x IO4 Figure 4. Ac calibration curves for Cd(I1) in 1M NaCl Figure 5. Ac calibration curves for In(II1) in lMNaCl

0 In the presence of oxygen

x Oxygen removed

0 In the presence of oxygen

importance of the ohmic ZR drop at the higher currents produced with higher concentrations. In the presence of oxygen, the electrode reaction was still reversible but the E, value had shifted approximately 20 mV more negative t o -0.620 volt cs. Ag/AgCl, and the ac wave height ( i d - ) decreased for the same concentration of cadmium(II), as shown in Figure 4. The negative shift in E, can be attributed to the formation of cadmium(I1) hydroxy complexes a t the electrode. The stability constants of the cadmium(I1) hydroxy species have been reported by Dyrssen and Lumme (7) to be pK1 = 4.3, pK2 = 3.4, pK3 = 2.6, and pKc = 1.7 for sodium perchlorate solutions, a t a n ionic strength of 3, and a t 25 "C. At the pH of the present study, negligible amounts of complexation could occur in solution, so that formation of the cadmium(I1) hydroxy species must occur a t the electrode. As the electrode reaction retains its reversibility, the complexation reactions at the electrode must be very rapid. The decrease in id- does not appear to be attributable to kinetic changes in the electrode process and presumably it changes because of differences in diffusion coefficients. The results obtained in the present work are similar to those reported by Breyer et al. (@,although the interpretation o n the decrease in id- is different. INDIUM(III). In a 1M degassed sodium chloride solution the indium(II1) electrode reaction is In(II1)

+ 3e S In(0)

for which E, is -0.557 volt DS. Ag/AgCl. The id- varies linearly with concentrations up to 2.5 X 10-4M indium(II1). The electrode reaction possesses a high degree of reversibility (7) D. Dyrssen and P. Lurnme, Acta Chem. Scarzd., 16, 1785 (1962). (8) B. Breyer, F. Gutmann, and S . Hacobian, Aust. J . Sci. Res., A3, 567 (1950).

230

x Oxygen removed

as E, is independent of concentration and the half-width is 38 i 2 mV. The behavior of indium(II1) in nondegassed solutions is unusual. No wave was observed at concentrations lower than 1 X 10-4M indium(II1). Above this concentration, a linear plot of id- us. concentration, lying just below that for the degassed system, was obtained, as shown in Figure 5. The Es value in the presence of oxygen is -0.576 volt rs. Ag/AgCI, that is, approximately 20 mV more negative than the E, value of the degassed solution. The electrode reaction retains its reversibility in the presence of oxygen and the negative shift in Es is again consistent with hydroxy complexation, similar to the cadmium(I1) case. The absence of a wave a t low concentrations suggests that precipitation occurs near the electrode. The solubility products (log K,) of In(OH), and InyO3are reported (9) to b- 36.9 and - 35.9, respectively, and the increase in the p H a t the electrode would be sufficient to cause precipitation. The much higher solubility of cadmium hydroxide (log K , = - 14.4) (9) shows why cadmium(I1) does not precipitate at the electrode. These results are slightly different from those of Breyer et al. (8) but are in agreement with the work of Takahashi er al. (IO) The importance of p H was noted as the absence of the indium (111) wave in the presence of oxygen occurred only for solutions of p H greater than about 4. LEAD(II). F o r a degassed lead(I1) solution in 1M NaCl, the ac electrode process possesses a high degree of reversibility, (9) W. Feitknecht and P. Schindler, Pure Appl. Chem., 6 , 130 (1963). (10) T. Takahashi, H. Shirai, and E. Niki, Rep. Inst. Ind. Sci. Unil;. Tokyo, 59 (3), 8 (1959).

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971

8 -

6 -

Q

4 4 -

2-

0

u 4.0

2-0

[Pb]

M

.-_-

_.. ....- J I

1

-0.55 -0.45 Volt vs. Ag/Ag CI Figure 7b. Ac polarogram of 4 X 10-4MPb(I1) in l M N a C l in the presence of oxygen

x 1 0

Figure 6. Ac calibration curves for Pb(I1) in 1M NaCl 0 In the presence of oxyren X Oxygen removed

t a

i

a

Ln

I

Figure 7a. Ac polarogram of 4 X 10-5MPb(II) in 1M NaCl in the presence of oxygen

I

l i v

I

-015

-0.3 Volt vs. Ag / A 9 CI

Figure 7c. Ac polarogram of 4 X lO-‘M Pb(I1) in l M N a C l in the absence of oxygen

- 0855

-0.45

Volt vs. Ag/Ag CI the E, value of - 0.392 volt US. Ag/AgCI being independent of concentration up to 4 x 10-4M lead(I1). The half-width of 53 + 2 mV is slightly higher than that for cadmium(I1) and suggests that the reaction is quasi-reversible, rather than completely reversible. The calibration curve is close to linear up to 1 X 10-4M lead(II), with curvature at higher concentrations, as shown in Figure 6. In the presence of oxygen, the electrode process undergoes

a remarkable change. At low concentrations of lead(II), the ac peak is very narrow and has an unusual nonsymmetrical shape (Figure 7n). As the concentration of lead(I1) increases the wave becomes more symmetrical and broader (Figure 76). However, it does not have the characteristics of the wave in the absence of oxygen (Figure 7c). Table I summarizes the characteristics of the lead(I1) wave in the presence of oxygen at various metal ion concentrations. The Es value in the presence of oxygen appears to be dependent o n metal ion concentration, but it is of the order of -0.50 volt us. Ag/AgCl.

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971

0

231

4 Table 11. Influence of Oxygen Concentration on the Height of the Ac Wave of 4 x 10-jM Lead(I1) in 1M NaCl

Time, min 0 13 20 35 m

6 2 =L

0

2.0 [TI]

1

4.0

Mx104

PA 0.25

idN,

0.40

0.64 0.87

0.98

volt us. Ag/AgCl and the electrode process is highly reversible. In the presence of oxygen, the wave has very similar characteristics, the E, value being shifted by only 10 mV t o -0.460 volt os. AgiAgCl. Again the electrode reaction has a high degree of reversibility. Comparison of the id- values (Figure 8) shows that complexation in the presence of oxygen is probably very small as only a slight lowering of idoccurs. The small negative shift in E, is also consistent with a small amount of hydroxy complex formation. Bell and Panckhurst (13) report log Kstab = 0.85 for the hydroxy complex. Thus, little interference due to hydroxy species would be expected. The results of the present study are to be contrasted with those of Breyer et ai. (8) who reported that the thallium(1) wave was not affected by oxygen.

Figure 8. Ac calibration curves for TI(1) in 1M NaCl DEPENDESCE OF \t'A\'E HEIGHT O S OXYGEN CONCESTR.ATION

0 In the presence of oxygen X Oxygen removed

Comparison of E, values in the presence and absence of oxygen indicates a large negative shift of greater than 100 mV due t o the presence of oxygen. Part of the negative shift may be attributed to complex formation, but because of the unusual shape of the wave in the presence of oxygen, kinetic effects must play a n important part in the electrode process. The complexity of the electrode reaction in the presence of oxygen can be appreciated by the very different behavior of lead(I1) in noncomplexing perchlorate media (ZI) where a two-peaked wave is observed. Presumably the difference in behavior in chloride media results from complexation of chloride ions. Chloride is strongly adsorbed at the mercury electrode at the potential a t which lead(I1) is reduced and interaction of lead(I1) hydroxy, chlorohydroxy complexes, etc., with adsorbed chloride at the double layer may lead t o the peculiar phenomenon observed. The observations are essentially the same as those reported by Breyer et al. (8) and by Grahame (12). THALLIUM(I).I n the absence of oxygen, the thallium(1) ac wave for a 1M NaCl solution has an E, value of -0.450

From the work above, it appears likely that the height of a n ac wave could be proportional to oxygen concentration as the concentration of hydroxide at the electrode is proportional to this parameter. This would be a n undesirable effect in the analytical sense. The proportionality of wave height with oxygen concentration was confirmed for lead(I1) in 1M NaCI. Argon was passed over the solution and the wave was recorded as a function of time. In this manner the oxygen content of the solution was gradually decreased. Table I1 gives the lead(I1) peak height as a function of time of passage ofargonover 4 X 10-5Mlead(II)in 1MNaCI. Ac Polarography in the Presence of Oxygen in Highly Acidic Media. The work described above for slightly acidic solutions suggests that such media are not suitable for quantitative analysis without removal of oxygen. Results are proportional to oxygen concentration and are markedly pH dependent. Neither effect is encountered after removal of oxygen. In all cases, in the presence of oxygen there is reduced sensitivity and precision, in some cases because of kinetic effects (cf. lead) and in others precipitation (CJ indium). Thus the ac method of analysis without degassing in neutral o r moderately acid media is not comparable with that for degassed solutions. The discrepancies however decrease with decreasing pH, as was shown by addition of hydrochloric acid to the sodium chloride electrolyte. To utilize the very important advantage of ac polarography effectively it is desirable to have a general method which gives results comparable with degassed systems. Buffering would be one possibility but the most convenient would probably be t o use a highly acidic supporting electrolyte. This highly acidic medium would remove interference presumably because of its ability t o instantaneously neutralize any hydroxide formed at the electrode before it can interact with the species being determined. Furthermore, peroxide rather than hy-

(11) A. M. Bond, Anal. Chim. Acra, in press. 30, 1736 (1958). (12) D. C . Grahame, ANAL.CHEM.,

(13) R. P. Bell and M. A. Panckhurst, J. Chem. Soc., 1956,2836.

Table I. Ac Polarographic Data for Non-Degassed Lead(I1) Solutions Concn - E , (volt cs. Ac half-width, M Ag/AgCl) mV 4.0 X 0.486 16 8.0 X 0.495 23 1 . 5 x 10-4 0.506 33 2.0 x 10-4 0.510 38 3 . 0 x 10-4 0.505 42 4 . 0 x 10-4 0.502 48

232

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971

I

I

1 I

1

0.41

Y U J ,

1

-1 0

-0.6 v o i t VS. ACJ/ACJCI

- 0-8

-092

Figure 11. A . Ac background; B. Ac polarogram of 5 x 10-3MFe(III) in 5MHCl

Figure 9. Ac polarogram of 5MHCI in the presence and absence of oxygen

Volt

VS.

Ag/Ag

CI

Figure 10. A . Dc polarogram of 5 X in 5M HCI ; B . Dc background ~

~

~

M Fe(II1)

~

Table 111. Summit Potentials for Various Metal Ions in 5M HCl in the Presence and Absence of Oxygen -E,? (volt L.S. Ag/AgCl) Metal ion Not degassed Degassed Cadmium(I1) Indium(111)

Lead(I1) Thallium(1)

-0 4 Volt %Ag/Ag CI

0.690 0.656 0.491 0.540

0.692 0.653 0.494 0.540

I

I

I

-0.8

-0.4

-0.6

Volt vs. Ag /Ag

CI

Figure 12. Ac polarogram of Sn(I1)-Sn(0) wave from 5 X 10-4MSn(IV) in 5MHCI

droxide is the major product in acid media, and this is a potentially less interfering species. Figure 9 shows that a n oxygen wave is observable in 5M HCI and so the electrode process still occurs, Table 111 gives the E8 values for the previously studied systems in 5M HCI in the presence and absence of oxygen. These results clearly indicate that oxygen has virtually n o effect when the supporting electrolyte is highly acidic. However the influence of oxygen is still important at low metal ion concentrations because the oxygen wave itself reduces the detection limit compared with degassing (Figure 9), and the current produced at each drop is significantly higher. The oxygen wave means that irregular base lines are incurred for low concentrations of other depolarizers and the ease of measurement

and therefore reproduciblity are slightly decreased compared with degassing. F o r concentrations above about 10-5M in 5M HCI the ac method in the presence of oxygen however, is quite acceptable and is comparable with degassed solutions. The limit of detection of about lO-5M can be compared with 5 X 1 0 P to 10-6Mafter removal of oxygen. Ac Polarography in the Presence of Iron. In hydrochloric acid media, iron(II1) is irreversibly reduced to iron(I1) at potentials more negative than the mercury-mercury chloride couple; that is, over the entire usable potential range for analytical purposes. The dc electrode process is shown in Figure 10; from Figure 11, it can be seen that no interference from the ac iron(II1) electrode process would be anticipated

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971

233

process for tin. Similar effects were observed in the present study with other elements. This type of interference has not been sufficiently studied in the past and obviously needs to be considered. After the failure of the iron crucibles, the method for the determination of tin was then achieved satisfactorily with nickel crucibles. The nickel ac wave which is irreversible but occurs subsequent to the analytical tin wave does not cause any interference and shows that interference from preceding waves is likely t o be a n important one.

r. \

/

I

CONCLUSIONS

._...

as the ac current produced by iron(II1) is extremely low over the usable potential range and certainly no interference from an overlapping iron wave will occur. In the ac polarographic methods of analysis for tin in geological samples described by Bond et a / . (Id), platinum crucibles were used for the fusion process. Since the report of this work, for reasons of economy, it was thought that iron crucibles would be suitable as a n alternative to platinum. However, it has now been found that iron introduced into the tin samples from the iron crucibles rendered the results invalid. Figure 12 shows a n ac tin polarogram normally used for analytical purposes. Figure 13 shows the ac polarogram for the same solution in the presence of a high concentration of iron. With increasingly higher iron concentrations, the wave becomes broader, more irreversible, shifts to more negative potentials and id- decreases. The tin(I1) e tin(0) wave obviously becomes profoundly influenced by the preceeding ac electrode process of iron(II1) for concentrations in excess of about 10-*M. Little interference is observed below this concentration. It is clear that although iron does not interfere by a n overlapping ac wave, the electrode process still occurs and the environment near the electrode substantially alters the electrode

Irreversible ac electrode processes, as theoretically expected, have been found to be not analytically themselves very sensitive and normally d o not cause substantial interference, by an overlapping ac wave? t o the determination of another species which exhibits a reversible ac electrode process. However, the irreversible electrode processes still occur and can cause interference if electroactive at potentials prior to the reduction of the species being determined. This interference arises from alterations occurring to the D M E itself o r to the solution near the DME. In a changed electrode environment, the reduction process of the species being analyzed for, compared with the calibration curve, can be quite different and so interference is observed. The best known example of this is with the ac polarographic determination of a species in the presence of oxygen. Oxygen produces two irreversible ac waves in most media and interference is not superficially expected. This work shows clearly that if a calibration curve was established for a particular species in the normal manner (degassed and no oxygen present) in alkaline, neutral, or slightly acidic solutions, then determination of the species in the presence of oxygen and referring to the calibration curve would frequently suffer severe interference. To overcome this problem, a calibration curve needs to be prepared in the presence of the interfering species o r the latter be removed. F o r oxygen, in highly acidic o r buffered media, the first approach can be attained by preparing a calibration curve without degassing and using this as the reference. Alternatively, oxygen can simply be eliminated by degassing. Oxygen is undoubtedly a particular case for what is a generally unrecognized form of interference. Other irreversibly reduced species could easily interfere in a similar manner t o oxygen and the interfering species will always need t o be either removed o r added in the calibration procedure. Removal, of course, will not usually be as simple as for oxygen (degassing), and adding to the calibration solution will cause a loss in sensitivity and possible reproducibility.

(14) A. M. Bond, T. A. O’Donnell, A. B. Waugh, and R. J. W. McLaughlin, ANAL.CHEM., 42, 1168 (1970).

RECEIVED for review July 6, 1970. Accepted October 12, 1970.

-08

- 0.0

-0*6 volt

VS.

-0.6

~ 9 / ~CI g

Figure 13. Ac polarogram of Sn(I1)-Sn(0) wave from 5 x 10-4MSn(IV) in 5MHCI A . In the presence of 5 X 10-3M Fe(II1) B. In the presence of 5 X 10-ZMFe(II1)

234

ANALYTICAL CHEMISTRY, VOL. 43, NO. 2, FEBRUARY 1971