Catalytic effect of metal oxides on thermal-decomposition reactions. I

Potassium Chlorate in Mixtures with Potassium Chloride and Potassium Perchlorate ... The thermal decomposition of potassium chlorate was investigated ...
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1209

CATALYTIC EFFECT OF METALOXIDES

Acknowledgments. The authors express their appreciation to the National Science Foundation for support of this work by Grant No. GP-7012. Dr. Kenneth Conrow of this department graciously provided PL-1 computer programs for treatment of the data.

however, that these viscosity results, together with the conductance data, overwhelmingly support the dilution hypothesis to the virtual exclusion of any process involving gas molecules taking up existing liquid free volume (at least for Ar and Nz in NaN03).

The Catalytic Effect of Metal Oxides on Thermal-Decomposition Reactions. I. The Mechanism of the Molten-Phase Thermal Decomposition of Potassium Chlorate and of Potassium Chlorate in Mixtures with Potassium Chloride and Potassium Perchlorate by Winfried K. Rudloff and Eli S. Freeman I I T Research Institute, Chicago, Illinois

60616

(Received June 1 7 , 1 9 6 8 )

The thermal decomposition of potassium chlorate was investigated by means of differential thermal analysis (dta) , thermogravimetric analysis (tga) , and differential thermogravimetric analysis (dtga) . Nonisothermal decomposition to the final decomposition products occurred via an intermediate disproportionation reaction 2KC103--+ KC104 KC1 02. The reaction was verified by isothermal experiments at low temperatures and stepwise analysis of the thermogravimetric analysis residues. Addition of potassium chloride, one of the final reaction products, decelerated the reaction at low temperatures and high potassium chloride concentrations but accelerated the reaction at high temperatures and intermediate potassium chloride concentrations. Addition of potassium perchlorate did not catalyze the thermal decomposition. There is indication, however, that a eutectic is formed.

+

+

Introduction Solid-molten- and solid-solid-phase reactions are generally difficult to investigate and present problems in interpretation, particularly if they involve interaction between a solid catalyst surface and molten or solid reactants. Reasons for the problems are: contact surfaces between the catalyst and the reactant are difficult to define and evaluate, reaction products in the molten or solid phase are frequently complex, and models of solid-liquid or solid-solid interactions are more complex than those of solid-gas interactions. Work indicating that there is a relationship between electronic properties of metal oxides and their catalytic activity has been reported in the 1iterature.l Much of the work involves the decomposition of gases such as nitrous oxide? Experimental procedures and mechanistic interpretation of gaseous phases are, however, simpler than those of condensed phases. Several investigators have studied the catalyzed decomposition of chloratess-l1 and perchlorates.l*al However, no systematic investigation has clearly related defect structure of solid oxide catalysts t o their activity with respect to the thermal decomposition of solid and molten phases of chlorates and perchlorates.

This paper is the first in a series that is aimed a t elucidating the mechanisms of catalyzed decomposition (1) W. E. Garner, “Chemistry of the Solid State,” Butterworth and Co. Ltd., London, 1955. (2) K. Hauffe, Advan. Catal., 7, 213 (1956);9, 187 (1957),and references cited therein. (3) S. 8. Bhatnagar, P. Brahm, and J. Singh, J . Indian Chem. SOC., 17, 125 (1940). (4) F. E. Brown, J. A. Burrows, and H. M. McLaughlin, J. Amer. Chem. SOC.,45, 1343 (1923). See also references cited therein. ( 6 ) F. E. Brown and J. D. Woods, Proc. Iowa Acad. Sci., 6 3 , 410 (1956). (6) J. A. Burrows and F. E. Brown, J . Amer. Chem. SOC.,48, 1790 (1926). (7) J. M. Gaidis and E. G. Rochow, J . Chem. Educ., 40, 78 (1963). (8) H. M. McLaughlin and F. E. Brown, J . Amer. Chem. Soc., 5 0 , 782 (1928). (9) M. Meyer, J . Chem. Educ., 17, 494 (1940). (IO) H.A. Neville, J . Amer. Chem. SOC.,45, 2330 (1923). (11) F. Solymosi, and N. Krix, Acta Chim. Acad. Sci. Hung., 34, 241 (1962). (12) A. K. Galway and P. W. M . Jacobs, Trans. Faraday Soc., 55, 1165 (1959). (13) E. 9. Freeman and D. A. Anderson, Nature, 206, 378 (1965). (14) A. E . Harvey, Jr., M. T . Edmison, E. D. Jones, R. A. Seybert, and K. A. Catto, J . Amer. Chem. &c., 7 6 , 3270 (1954). (15) A. Hermoni and A. Salmon, Bull. Res. Council Israel, A , 9, 206 (1960). (16) 0.E. Otto and H. 8 . Fry, J . Amer. Chem. Soc., 4 5 , 1134 (1923). (17) M. M. Markowite and D. A. Boryta, J . Phys. Chem., 69, 1114 (1965). Volume 73,Number 6 May 196s

WINFRIEDK. RUDLOFFAND ELI S. FREEMAN

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in the solid or molten phase of potassium chlorate and its intermediate thermal-decomposition product, potassium perchlorate. Changes in the electrical conductivity properties which were induced by doping with altervalent cations and by y irradiation are correlated to the catalytic activity of metal oxides with respect to these specific thermal-decomposition reactions. The main concerns of this first paper are the mechanisms of thermal decomposition of pure potassium chlorate KC103 and its interaction with the intermediate and the final decomposition products, potassium perchlorate, and potassium chloride. Many investigat i o n ~ have ~ ~ - dealt ~ ~ with these problems without arriving a t satisfactory results. Farmer and Firth22as well as Glasner and Weidenfeld23found that KC1 accelerates the decomposition of Kclo,, while some of the data of Otto and Frey indicate deceleration of the reaction rate by KCl.z4 The catalytic activity of KC1 seems different when KC1 samples of different origins are At high temperatures KC1 partially dissolves in the molten phase of KClOa." KC104 also appears to accelerate the reaction.23 Unfortunately, the data of Glasner and Weidenfeld must be cautiously appraised, since bare chromel-alumel thermocouples were apparently used to measure temperatures inside the reaction vessel, and chromel-alumel thermocouples may oxidize and subsequently catalyze the decomposition of chloratesz6and perch1orates.l' The sequence of complex decomposition reactions and their reversibility are also subject to opposing interpretations. Otto and stated that two reactions occur simultaneously.

differential thermogravimetric analysis (dtga) were performed under various experimental conditions and were correlated to analytical findings,

Experimental Procedures Preparation and Standardization of Samples. The influence of recrystallization on the dta, tga, and dtga curves was given special attention, since the purity of the samples is of importance for reproducible results. Potassium chlorate (B & A reagent grade, ACS Code 2103, 99.5% minimum assay) was recrystallized from water and tested with dta and tga (Figures 1 and 2). The original KClOa was used without recrystallization for all subsequent experiments, since recrystallization apparently does not introduce significant differences into the thermal characteristics. II

I

0

I

I

I

200

400

I

I

600

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800

Temperature I O C . 1. Dta data for KClOs decomposition in air: 1, dashed, curve, recrystallized material; 2, solid curve, original material; heating rate, 10°/min. Figure

2KC103 -+ 2KC1+ 302 4KC103 3 3KC104 KCl

+

(1)

(2)

A third reaction ensues a t higher temperatures. KC104 4 KC1

+ 202

(3) Glasner and Weidenfeld23concluded that reaction 2 is not simultaneous but consecutive with respect to reaction 1. The hypothesis presented is that atomic oxygen is transferred to KC1 during decomposition of KC1o3. While Glasner and Weidenfeld indicated irreversibility of KC103 decomposition with respect to molecular oxygen, they speculated that the reaction may be reversible with respect t o atomic oxygen. On the other hand, Solymosi and Krix20still considered reactions 1 and 2 reversible reactions. This study was initiated to resolve some of the controversy about the chlorate-decomposition mechanism, since an investigation of catalytic effects on the thermal decomposition of KC103 is sensible only if the decomposition mechanism of the pure chlorate is understood. To achieve this understanding, dynamic and isothermal experiments using differential thermal analysis (dta) , thermogravimetric analysis (tga) , and The Journal of Physical Chemistry

Samples were standardized by crushing them in 8 mortar and sieving them. Sieve fractions with grain sizes of 53-63 p were used. The influence of crushing on the dta-tga curves was also probed. As expect.ed, crushing did not influence the curve shape, since the reactions primarily occurred in the molten phase. Samples were dried and stored in a desiccator prior t o the runs. XCl (B & A reagent grade) was sieved to a grain size of 53-63 p and dried prior to mixing with KClOa. (18) A. A. Shchidlovskii, L. V. Shagin, and B. B. Bulanova, T m . Vyssh. Ucheb. Zaved., Khim. Khim. Tekhnol., 8, 533 (1965). (19) F. Solymosi, Combust, Flame, 9, 141 (1965). (20) F. Solymosi and N . Krix, J. Catal., 1, 468 (1962). (21) F. Solymosi and L. RBvdsz, Kinet. Katal., 4, 88 (1963). (22) W. Farmer and J. B. Firth, J . Chem. Soc., 125, 82 (1924). (23) A. Glasner and L. Weidenfeld, J . Amer. Chem. Soc., 74, 2464 (1952). (24) C. A. Otto and H. S. Fry, {bid., 46, 269 (1924). (25) E. S. Freeman and W. K. Rudloff, Final Technical Report, U. 9. Army, Project IC! 5223018080, Contract NO. DA-18-035-AML341(A) (1967).

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CATALYTIC EFFECT OF METALOXIDES

147.6 mg Reagent

50

150.6 mg Recryetalllrrd

Results

KCIO,

Figures 1 and 2 show the dta and tga curves of reagent grade and recrystallized KC103. The curves do not differ appreciably, and a two-step decomposition is apparent. The influence of atmospheric conditions is shown in Figure 3. The peak positions of the data obtained in an oxygen or a nitrogen atmosphere did not differ significant1y . A comparison of pure KC103 and a KClOS--KCl mixture (molar ratio, 1:l) is pictured in Figure 4. The dtga curves had noise and the drawings were smoothed. Error limits at high temperature indicate the most severe noise levels. Pure E(c103appears more reactive a t lower temperatures, as evident in the earlier stages of the reaction of pure KCIOl and the

60

. I . . I

Time, sec,

70

Figure 2. Tga curves of reagent grade and recrystallized KClOs.

KClOr (B & A reagent) was similarly prepared after it was twice recrystallized from water. Wet analysis of the residues was performed according to Volhard's method. Tga and Dtga Isothermal Experiments. Dta was performed with a Stone apparatus. Tga and dtga were performed with a Stone-Cahn thermobalance that had a Cahn time derivative computer attached to obtain derivative weight-loss curves during nonisothermal (dynamic) decomposition. A Chevenard thermobalance measured isothermal decomposition rates. The furnace was brought to the desired temperature and placed over the sample, contained in a Vycor glass crucible. The crucible was

4 WPURlFlED

Oz PURIFIED OVER MOLECULAR SIEVE

t

Oe PURIFIED OVER MOLECULAR SIEVE THEN MOISTENED

Q IQ

I

N, UNPURlFlED

f

positioned on top of chromel-alumel thermocouples in capillaries located in the bottom of the crucible. The thermocouples led through a vertical, ceramic balance rod of the Chevenard thermobalance. Weight changes during decomposition were simultaneously recorded with temperature on a Bristol two-pen recorder.

Y

+lo

NaPURIFIED OVER MOLECULAR SIEVE

TEMPERATURE Ct2 -c

Figure 3. Dta data for KC108 decomposition in different atmospheres.

Table I: Isothermal Rates of Reaction as a Function of Extent of Reaction AV KC1:KClOa

ratio 0: 1 0: 1 0:l 0.1 0:l 0:l 0: 1 0:l

0:1 1:5 1:5 1:5 1:5 1:5 1:5 1:4 1:4 1:4 1:4 1:4 1:4 1:3 1:3 1:3 1:3 1:l 1:1 1:l 1:l 1:l 1:l 1:l

temp, 0 0

637 631 591 581 573 557 553 550 535 609 603 593 590 567 563 618 616 591 589 567 562 607 604 596 588 605 603 591 590 567 561 538

Slope, mg /min--------At 4 deAt 3 de+ decomposition composition composition At

16 13.3 5.25 3.8 3.55 0.94 0.98 0.93 0.52 20.25 16.1 8.8 9.7 3.08 2.63 26.0 20.5 7.5 5.85 3.0 2.44 18.2 18.8 9.8 8.13 15.8 15.7 8.65 9.5 2.92 2.1 0.7

17.3 15.5 6.0 3.8 4.1 0.97 1.1 1.05 0.47 24.75 14.5 7.0 7.45 2.55 2.16 59.0 34.5 7.5 5.9 2.23 2.1 17.0 18.3 9.7 7.8 11.5 10.5 6.0 6.27 2.1 1.6 0.55

10.5 9.0 3.05 1.85 2.4 0.47 0.5 0.65 9.25 10.1 4.55 4.68 1.75 1.42 13.8 8.4 4.2 3.7 1.40 1.22 7.9 9.4 5.1 4.0

6.7 5.4 2.98 3.17 1.2 1.o 0.36

Volume '73,Number 6 M a y iQ6Q

WINFRIEDK. RUDLOFF AND ELI S. FREEMAN

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50

-

1 T OJ

-

-I

DTGA t DIFFERENTIAL THERMOGRAVIMETRIC ANALYSIS (ARBITRARY SCALE 1

I 3b0

.I.

5dO

4b0

TEMPERATURE (%I

Figure 4. Decomposition of (1) KC108 and (2) a KC103-KCl mixture,

absence of an initial shoulder in the dtga curve of the KCIOs-KC1 mixture. At intermediate temperatures, the mixture appears more reactive than the pure KClOs as indicated by the crossing of the dtga curves. These well-pronounced dtga differences are quite reproducible. To investigate this strange observation in more detail, pure KCIOa and KC103-KC1 mixtures were decomposed isothermally. Figure 5 shows the comparison of isotherms of pure KCIOI to isotherms of various KC1KCIOa mixtures a t roughly comparable temperatures. Table I summarizes the isothermal-reaction rates as a function of the extent of reaction. The reaction proceeds faster above 500' if KC1 is present than if KClOa is pure. At temperatures below 500°, however, the

-

trend seems to be reversed (Figure 6). Isothermal decomposition within this lower temperature range appeared to stop after an approximately 33% oxygen weight loss (100% corresponds to the total theoretical loss of oxygen). The residue of one sample that was isothermally decomposed a t 480' was analyzed. The results are presented in Table 11. It is seen that equivalent amounts of KC1 and KC104 are formed during the low-temperature decomposition. Figure 7 represents the analysis of the residues after different tga runs were stopped a t various temperatures (nominal heating rate, 5'/min). Intermediate forma-

&o!

0

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10

20

30

40

---

Symbol

0

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10

I

to

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a0

40

7 M @IN)-

Figure 5. Comparison of isotherms of pure KClOa and KC1-KCIOs and KCl-KC103 mixtures. The Journal of Physical Chemistry

L

w

760

SdO

-0----I.

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I

50 60 70 Time, mln.

I

80

I

8

'

90 100 110

Mole ratio KCI / KClOs

I:[ 1:2 I:3 0:I

Figure 6. Isothermal decomposition of Kclo3 and KClOa and KCI-KClOd mixtures at 480'.

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CATALYTIC EFFECTOF METALOXIDES 400

~~

I

Table 11: Analysis of KC108 Reaction Products after

+ ClOac. c1- + ClOa- + c104-

Synthetic sample KClOa KC104

I

Mohr titration Reduction of ClOs- with Fez+, Mohr titration of total C1Reduction of ClOa- and Clopby ignition with NH4C1, Mohr titration of total C1-

3KclqnCClQ NR.-VI MR.=MOLE RATIO HEATING RATE=

I

Analysis A. C1B. C1c. c1-

+ clos+ ClOs- + ClOr

Theoret

Found

0 , 8 5 2 mequiv 0.967 mequiv 1.88 mequiv

0.850 mequiv 0.977 mequiv 1 . 8 4 mequiv

600

t--t

Isothermal Decomposition for Several Days a t 480' Method A. C1B. C1-

500

I I I

I I

I I

I

I II

Sample under investigation C10.748 mequiv/total sample = 55.8 mg of KCl CIOa0.071 mequiv/total sample = 8 . 7 mg of KC108 Clod0.760 mequiv/total sample = 105.4 mg of KC104

-

-

1.579 mequiv

169.9 mg

Sample w t given 172 7 mg 1.57 i0 005 mequiv I

Kf

I

~

~

~~

tion of KC104 apparently passes through a maximum (about 50% KC104 and 50% KCl), while at this point KCIOa goes through a minimum (about 0 mol %) with a small maximum at higher temperatures. At the maximum KC104 formation, the weight loss is 100

Weight loss (in % of total weight loss)

t

I

KClOs I I

+ E 0 0

Q

50

b,

a

P

0

550

600 Temperature,

-

TEMPERATURE [tl-

Figure 8. Decomposition of KClOa in mixtures with KClOI.

approximately one-third of the total. In view of the simultaneous KCI production by eq 5 , 8, and 9, the KC1 curve is probably more complex than is shown in Figure 7. This aspect has, however, not been pursued further, Mixtures of KCIOs and KC1O4 in molar ratios of 1:1 and 1:5 were subjected t o simultaneous tga and dta experiments in order to investigate the influence of KC104 on the decomposition. Weights of the pure KClOa samples of the comparative runs were adjusted to correspond approximately to the overall weight loss observed with the mixtures. Figure 8 shows the results. The addition of KC104 in a ratio of 1:5 does not significantly change the thermal characteristics of KClOs except for a small endotherm a t approximately 300' in the dta curve of the mixture. At a molar ratio of KC103 and KC104 of 1: 1, additional features occur in the thermal characteristics. (1) An endotherm again appears at approximately 300'. (2) The endotherm pertinent to KCIOa melting at approximately 360' is split into two bands with no weight loss visible. (3) Weight loss begins at higher temperatures than for pure KCIOs.

650

OC

Figure 7. Decomposition products and weight loss as a function of temperature during tga.

Discussion Two conclusions are drawn from the dta and tga results. (1) Molecular oxygen has no influence on the Volume 73,Number 6 May 1969

1214

WINFRIEDK. RUDLOFFAND ELI 8. FREEMAN

1 N

e Y

n

t. Figure 9. Second-order plot of isothermal decomposition of KCIOa at (480’): 0 , firstsrder plot; A, secondsrder plot; time factor, 1 unit = 16 min.

reaction (at least not at atmospheric pressure). This is supported by the observation that the dta peak locations of purified oxygen and purified nitrogen are similar (Figure 3 ) . Stern and BufaliniZ6also concluded that takeup of molecular oxygen by KCl is unlikely. (2) Decomposition occurs in two welldefined steps, as is evident from the dta and tga experiments (Figures 1 and 2). During the first step, approximately one-third of the total theoretical weight loss is indicated. Isotherms at lower temperatures suggest that this first step is apparently arrested after about 48 hr. If the isothermal data at these temperatures are analyzed according to a second-order reaction, a straight line is obtained (Figure 9 ) . This evidence and the analysis of the low-temperature residue (Table 11) is consistent with the following disproportionation reaction slow

+ (KC102) (KC10z) ---+ KC1 + 2KClO.g + KC104 + KC1 +

2KC103 -+ KClOi

(4)

fast

0 2

0 2

(5) (6)

Therefore an oxygen transfer appears to occur directly between two CIOa--anions

The resulting C104- anion is thermodynamically more stable than C10~-, while the hypothetical ClOzanion is very unstable at these temperatures and decomposes immediately to KC1 and oxygen. The Journal of Physical Chemistry

o! 0:I

I

I

I

I

1:s k3 I:2 kI I;4 KCI/KCIO~ ratio.

Figure 10. Isothermal decomposition rates as a funotion of KC1 :KClOa ratio at one-half decomposition.

The apparent deceleration of the Kc103 decomposition by KC1 at low temperatures can be explained by a dilution effect. Addition of KC1 reduces the probability that two c103-anions are close together since the most pronounced deceleration corresponds to the highest amount of KC1 (ratio, 1:1). On the other hand, for decomposition a t higher temperatures in which KC104 formed as an intermediate is further decomposing, KC1 seems to accelerate decomposition. Since KCl is most reactive as a catalyst in a KClKC103 mixture having an intermediate molar ratio of about 1:3 (Figures 5 and l o ) , two opposing factors influence the reaction at high temperatures. Within this context it is of interest to know the solubility of the reaction products, in particular, KC1 in the KC10, melt. KCIOs normally melts at about 355’ without apparent decomposition. Its reaction products, however, melt a t much higher temperatures. KC101 melts with decomposition at about 610’ (Figure 8) while KCl melts a t 7760e2’ Experiments were conducted in which it was found that KC1 is soluble to an appreciable extent in molten KCIOs at temperatures below 400’. Visual observation of KCI-KCIOI mixtures showed that KCl is soluble, up t o a mole ratio of approximately 1:2.5 KC1-KCIOa a t 400’. At higher temperatures, however, decomposition increases the amount of reaction products which eventually precipitate out. This rate coincides approximately with the maximum decomposition rates at 590 and 605’ (Figure 10). At (26) K. H. Stern and M. Bufalini, J. Phys. Chem.. 64, 1781 (1960). (27) “Handbook of Chemistry and Physics,” 46th ed, Chemical Rubber Publishing Co., Cleveland, Ohio, 1966, p B207.

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CATALYTIC EFFECTOF METALOXIDES lower mole ratios the catalytic efficiency is lower, while a t higher ratios the dilution effect of KC1 becomes more and more important. Between these extremes there is a maximum catalytic efficiency, where the apparent decomposition rate is accelerated most. An explanation of how KCl catalyzes the decomposition of the intermediate, KC104, or the KC103 formed from KClO4 after thermal bond breakage may be the formation of polarization centers within the melt with a maximum 1:3 molar ratio. Defects and/or impurities in the KC1 additives may act as polarization centers. This is brought out by the observation that KC1 additives of different history show different catalytic activity.23 The polarizing effect is counteracted if excessive KC1 additions dilute the melt and decelerate the decomposition. KC104 --$ I(C103 -k 0.502

(7)

+ 1.502 KC1 + 202

KC103 + KCl KC104 4

(8) (9)

Figure 7 gives proof of the existence of intermediate KC103 formed during decomposition of KC101 (eq 7 ) . The intermediate KClOs formation is indicated by a second, small maximum of KCIOa present in the tga residues.

KC1 polarization centers may influence the oxygen shell of the C1O4- anion, or even more feasible, the CIOa- anion and decomposition may be accelerated by KC1 a t high temperatures (Figure 7 ) . Another interpretation might be presented within the framework of the Arrhenius equation. Arrhenius plots of isothermal decomposition rates at different stages of decomposition are rather peculiar (Figure 11). All KC1-KC103 mixtures apparently follow Arrhenius.' law as is evident in straight lines of the semilogarithmic plot of the slope of the weight loss curve, dw/dt [mg/ min], vs. 1/T. Pure KC1o3, however, shows a t these stages a curvature indicating a more complex mechanism where the apparent activation energy decreases with increasing temperature. It is quite possible that nucleation of the product phases gives rise to an induction period in the pure melt, while such induction periods are virtually nonexistent in the mixtures. It may be speculated that early decomposition occurs a t interphases between the KC1o3 and KC1 phases even though both phases may be molten. Figure 8 indicates a small endotherm a t about 300' that is due to a phase transition of the added KC104.28 Regardless of the molar ratio of the mixtures, the acceleration of the KC103 decomposition that is claimed by some authors2a was not found. Apparent deceleration of the decomposition is due to the higher decomposition temperatures of the added KClOI. The strange phenomenon of a double band at about 360' without weight loss may indicate a complex formation between KC103 and KCI04 molecules within the melt (eutectic) creating a small exotherm between the two endotherm bands. This aspect has not been further pursued and is considered speculative.

Conclusions

0

0.11 1.10

I

I

1.12

75%

0:t I:I

0

I

I

1.14

75%

I

I

I

I

1.18 I / T x IO'(I/OK) 1.16

I

I

I

1.20

Figure 11. Isothermal decomposition rates at different stages of decomposition.

I

1.22

I

I

1.24

The experimental results presented lead to the following conclusions. (1) The decomposition reactions are irreversible with respect to molecular oxygen. (2) Kclo3 decomposes in a t least two steps. The first step involves disproportionation with an oxygen transfer from one C103- anion to a neighboring anion. The intermediate, KC104, is relatively stable, while a hypothetical intermediate, KC102, is very unstable and decomposes immediately after forming to KC1 and O2 (reactions 4 through 6 ) . At higher temperatures, the intermediate KC104 seems to decompose in two ways (reactions 7 through 9). (3) KC1 appears to influence decomposition in two opposite ways. At high temperatures and intermediate concentrations KC1 accelerates decomposition and a t low temperatures and high concentrations it decelerates decomposition. (28)

E.

8.

Freeman and D. Edelman, Anal. Chem., 31,

624 (1959).

Volume Y3, Number 6 M a y 1969