γ Radiolysis of Liquids at High Pressures. III. Aqueous Solutions of SodiumBicarbonateRobert R. Hentz, Farhataziz, David J. Milner, and Milton Burton Citation: The Journal of Chemical Physics 47, 374 (1967); doi: 10.1063/1.1711902 View online: http://dx.doi.org/10.1063/1.1711902 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/47/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in γ Radiolysis of Liquids at High Pressures. VII. Oxidation of Iodide Ion by Hydrogen Atoms in AqueousSolutions J. Chem. Phys. 51, 1236 (1969); 10.1063/1.1672128 γ Radiolysis of Liquids at High Pressures. V. Reaction of the Hydrated Electron with Water J. Chem. Phys. 47, 5381 (1967); 10.1063/1.1701806 γ Radiolysis of Liquids at High Pressures. IV. Primary Yields in Neutral Aqueous Solutions J. Chem. Phys. 47, 4865 (1967); 10.1063/1.1701724 γ Radiolysis of Liquids at High Pressures. II. Aqueous Solutions of Ceric Sulfate J. Chem. Phys. 46, 4154 (1967); 10.1063/1.1840503 γRadiolysis of Liquids at High Pressures. I. Aqueous Solutions of Ferrous Sulfate J. Chem. Phys. 46, 2995 (1967); 10.1063/1.1841168

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 47, NUMBER 2 15 JULY 1967

'Y Radiolysis of Liquids at High Pressures. III. Aqueous Solutions of Sodium Bicarbonate

ROBERT R. HENTZ, FARIIATAZIZ,* DAVID J. MILNER, AND MILTON BURTON

Department of Chemistry and the Radiation Laboratory, t University of Notre Dame, Notre Dame, Indiana

(Received 28 March 1967)

The 'Y radiolysis of deaerated aqueous solutions containing sodium bicarbonate and either glucose or isopropanol has been studied at ",200 in the applied pressure range 0 to 7 kbar. For O.OSM bicarbonate and 0.036M isopropanol, G(H2) increases from 0.89 to 2.43 as applied pressure increases from 0 to 6.9 kbar. A 100-fold change (O.OOS-O.SM) in bicarbonate concentration has little or no effect on the pressure de­pendence of G(H2). Because primary yields are invariant over the pressure range studied, the results are interpreted in terms of an effect of pressure on the competition between Reactions [2J and [3J

e.Q - +COr>C02-,

eaq-+HC03--.H+ C032-,

with Reaction [3J followed by Reaction [4J

[2J

[3J

H+RH-.R+H2• [4J

Such an interpretation gives a difference in activation volumes of Reactions [2J and [3J as Ll V2t-Ll V3t ",. 18.4 ml mole-I and a specific rate k30",.6X 1Q6M-I. sec-I at atmospheric pressure. Assumption that Reaction [2J is diffusion controlled rermits estimation of Ll V2t ",.1.6 ml mole-I, from the pressure depend~nce of water viscosity. Thus, Ll V3 '" -16.8 ml mole-I. The latter value, in turn, yields an estimate of V (eaq-) in the range -10.9 to -6.S ml mole-I relative to V(H+) =0. Use of an absolute value of Vo(H+) = -S.4 ml mole-I gives an absolute value of Vo(eaq -) in the range -S.S to -1.1 ml mole-I. Approximate equality of the values for Vo of the electron and of the proton is consistent with their having a negligible intrinsic volume and approximately equal electrostriction volumes.

INTRODUCTION

This paper presents results of a study of the radiolysis over a large pressure range ('" 1 to 7000 bar) of aqueous solutions containing sodium bicarbonate and an appropriate scavenger for conversion of hydrogen atoms to molecular hydrogen. This system was chosen for study with the idea that hydrogen yields would serve as an indicator of an effect of pressure on the fate of electrons produced in the radiolysis of water. Such information should provide a basis for estimation of the partial molal volume of the hydrated electron.

EXPERIMENTAL

The purification of water, cleaning of glassware, analytical techniques, and the syringe technique for study of the radiolysis of aqueous solutions have been described.! Nitrogen was used to force deaerated solu­tion into the 10-ml syringes, and argon was used as flow gas in chromatographic analyses. The high-pressure system and irradiation techniques were described in the initial paper of this series.2 All solutions were deaerated and irradiated at ",200 in the Notre Dame lO-kCi GOCo facility; the dose rate was ",1.6Xl016 eV g-l·min-l based on G(Fe3+) = 15.6 for the Fricke dosimeter and a molar extinction coefficient at 304 m,u of 2240M-l·cm-l

at 25 0 (with 0.7% increase per degree). Sodium

,. On leave from the Pakistan Atomic Energy Commission. t The Radiation Laboratory of the University of Notre Dame

is operated under contract with the U.S. Atomic Energy Com­mission. This is AEC Document No. COO-38-S2S.

1 Farhataziz, J. Phys. Chern. 71, S98 (1967).

bicarbonate and glucose were Baker-Analyzed reagents; isopropanol was a Fisher-Certified reagent. Because isopropanol was partially removed by the degassing procedures, its concentration in the solutions was determined by gas chromatography.

RESULTS

Solutions of O.OlM glucose or 0.036M isopropanol in O.SN H2S04 were irradiated over a pressure range from atmospheric to 6.4 kbar. At a dose of 4Xl017 eV g-l, G(H2) =4.1±0.1 over the entire pressure range. For unbuffered solutions (pH",S.5) containing three different concentrations of NaHCOa and either O.OlM glucose or 0.036M isopropanol, Fig. 1 presents the dependence of hydrogen yields on pressure for a dose of 1018 eV g-l. Each point represents the average of at least two determinations. For the glucose-NaHCOa solutions, G(H2) was shown to be independent of dose up to 1018 eV g-l at both atmospheric pressure and 6.34 kbar.

DISCUSSION

Bicarbonate-Free Solutions

In a previous study of the radiolysis of O.SN H2S04

solutions,2 it was shown that primary radical and molecular yields are invariant as pressure varies from atmospheric to 6.34 kbar. The concentrations of glucose and isopropanol used in the present work are sufficient to convert all H atoms into H2.a Consequently, in the

2 R. R. Hentz, Farhataziz, D. J. Milner, and M. Burton, J. 3 J. T. Allan and G. Scholes, Nature 187, 218 (1960); J. Rabani, Chem. Phys.46, 299S (1967). J. Am. Chern. Soc. 84,868 (1962).

374

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'Y RADIOLYSIS OF LIQUIDS AT HIGH PRESSURES. III 375

0.8N H2S04 solutions containing only these solutes

(1)

where g denotes primary yields. The observed con­stancy of G(H2) = 4.1±0.1 for such solutions, over the applied pressure range 0-6.4 kbar, is consistent (a) with the previous conclusion that primary yields are pressure independent in 0.8N H2S04 2 and (b) with values of g(H) = 3.65 and g(H2) = 0.45.4 Presently unpublished work in this Laboratory (on solutions containing glucose and an electron scavenger such as N20) indicates that primary yields in near-neutral solutions are similarly invariant over the applied pressure range from 0 to 7 kbar.

Bicarbonate Solutions

Because of the pressure independence of primary yields, the observed increase in G(H2) with increased pressure in bicarbonate solutions (d. Fig. 1) must be related to some pressure-dependent secondary reaction whereby the hydrated electron eaq - is converted to H. A significant contribution of the reaction

eaq-+H2~H+OH-,

in competition with the reaction

eaq -+COrC02-,

[lJ

[2J

is precluded by the observation that a l00-fold change in bicarbonate concentration has little or no effect on the pressure dependence of G(H2)' Thus, the results suggest a competition between Reactions [2J and [3J,

eaq-+HCOa-~H+COa2-. [3J

Gordon and co-workers6 have given the specific rate of Reaction [2J in neutral solution at atmospheric pres­sure as k2o= 7.7Xl09M-l·sec1; Kevan, Moorthv, and Weiss6 have presented evidence for occurence of Re­action [3J in 'Y-irradiated ice solutions at 77°K.

Kinetic analysis of the proposed mechanism for hydrogen formation gives

G(H2) =GO(H2) + {g(eaq-)ka[HCOa-J/(ka[HCOs-J

+k2[C02J) }. (2)

GO(H2) represents the yield at atmospheric pressure,7 to which Reaction [3J makes a negligible contribution. From the relation

4 A. O. Allen, The Radiation Chemistry of Water and Aqueous Solutions (D. Van Nostrand Co., Inc., Princeton, N.J., 1961), p.41.

5 S. Gordon, E. J. Hart, M. S. Matheson, J. Rabani, and J. K. Thomas, Discussions Faraday Soc. 36, 193 (1963).

6 L. Kevan, P. N. Moorthy, and J. J. Weiss, J. Am. Chern. Soc. 86, 771 (1964).

7 The decrease in CO(H2) with increase in bicarbonate concen­tration (d. Fig. 1) is attributed to scavenging of certain pre­cumors of HI within the spurs.

2.6

2.2

(.) +

il.a ~

1.0

c=o 6

FIG. 1. G(H2) vs ap'p'lied pressure: ~, [HCOs-]=O.5M and [glucose]=O.01M; e, LHCOa-]=O.05M and [glucose]=O.01M; 0, [HCOa-]= O.05M and [i-CaH 70H]=O.036M; e, [HCO.-]= O.OO5M and [glucose]=O.01M.

(where Ka and Kb are the first and second dissociation constants, respectively, of carbonic acid) it follows that, very closely,

{g(eaq-) /[G(H2) -GO(H2) Jl-l

= (kdka) (Kb/Ka)1/2=K. (4)

The pressure dependence of K is given by

(0 10gK/oP)r= -~V/2.3RT, (5) in which

~V=~V2L~Va~+H~Vb-~Va). (6)

The value g(eaq -) = 2.858 and the data of Fig. 1 are used to give the plot of 10gK vs P in Fig. 2. The points for all three bicarbonate concentrations are seen to fall on the same reasonably good straight line. A rough estimate indicates that ionic strength effects would be obscured by the scatter in values of 10gK. Thus, over at least a pressure range of 2.5 to 7 kbar, ~V of Eq. (5) is essentially independent of pressure, and the integrated form of Eq. (5) becomes

logK= logK-(P~V/2.3RT), (7)

where K denotes the value of K obtained by extrapolation to atmospheric pressure (P~O). From Eq. (7) for T=293°K and from Eq. (6), the slope of the least­squares line in Fig. 2 gives

~V=~V2L~Va~+H~Vb-~Va) = 19 ml mole-1 (8)

over the pressure range 2.5 to 7 kbar.

8 A. O. Allen, Radiation Res. Suppl. 4, 54 (1964).

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376 HEN T Z, FAR HAT A Z I Z, ~I I L ~ E R, .\ N D BUR TON

2.2

\ \

\ \

1.8 \

\ \

\ \ \

\ 1.4 \

\

• e 1.0

I..!.

'" 0 ...J 0.6

0.2

-0.20 2 4 6

Pressure. kbar

FIG. 2. Plot of log" vs applied pressure; symbols correspond with those in Fig. 1.

Partial Molal Volume of the Electron

Although the individual values of ~V2t, ~V3t, ~Va, and ~ Vb are probably pressure dependent,9b.Io the linearity evident in Fig. 2 indicates an approximate cancellation of any such effects in the over-all ~ V of Eq. (6) over the pressure range 2.5 to 7 kbar. The increase in G(H2) is not sufficient below 2.5 kbar for calculation of meaningful values of K. Agreement of the intercept in Fig. 2, 10gK, with an independent value of 10gKo would lend support to a linear extrapolation below 2.5 kbar (as was the case with aerated O.8N H2S04 solutions of ferrous sulfate2). Unfortunately, a value for kao is not available. Consequently, validity of the extrapolation to atmospheric pressure is noted as an assumption, i.e., K= KO, the significant consequences of which may be conveniently developed.

The intercept in Fig. 2, see Eqs. (4) and (7), yields a value of KO= (k20jkaO) (KbOj KaO) 1/2 from which kaO~6XI05M-I'secI is estimated by use of k2°= 7.7XI09M-I· sec I, Kao=4.2XIQ-7, and KbO=4.7XIQ-ll [dissociation constants given in Ref. 9(a)]. Use of the a tmospheric pressure valuesll of ~ V n = - 29 ml mole-I and AVb= -27.8 ml mole-l in Eq. (8) gives, for atmospheric pressure,

~V2L~Vat~18.4 ml mole-I, (9)

Reaction [2J is probably diffusion controlled; therefore, an estimate of ~ V2 t~1.6 ml mole-l may be obtained

9 S. D. Hamann, High Pressure Physics and Chemistry, R. S. Bradley, Ed. (Academic Press Inc., New York, 1963), Vol. 2, (a) p. 150; (b) pp. 150, 152, 186, and 188; (c) pp. 168-171, 182-184, and 200-203; (d) p. 148.

1O,H. S. Golinkin, W. G. Laidlaw, and J. B. Hyne, Can. J. Chern. 44, 2193 (1966).

II B. B. Owen and S. R. Brinkley, Chern. Rev. 29, 461 (1941).

from the pressure dependence of water viscosity.2 Then,

~V3t=V(HCOa2-) t_ V(eaq-)- V(HCOa-)

= -16.8 ml mole-I, (10)

where, as in Reactions [IJ-[3J, hydration of each species is understood .

Reaction [3J is formally a bimolecular exchange reaction. For such reactions,9c formation of the transi­tion state appears to involve only a slight stretching of the bond being broken, O-H in this case, with approach of the incoming group, eaq- in this case, to near the covalent-bond distance; i.e., a considerable decrease in volume usually occurs with formation of an activated complex that resembles rather closely a condensation product of the reactants. Strong attention should be addressed to the fact that the last statement represents a basic assumption of the subsequent analysis. Such an assumption also can be looked at from the opposite direction. In the reverse of Reaction [3J, formation of the activated complex should approximate formation of a covalent bond between Hand COa2- with con­comitant adjustment of the hydration sphere, resultant in part from a slight displacement of an electron. There­fore, the van der Waals volume of H plus V(COa2-) should give a number close to the upper limit of V(HCOa2-) t. The volume of H, based on a van der Waals radius of 1.2 1,12 is 4.4 ml mole-I; consequently, a reasonable range of values for V(HCOl-) t is given by

V(COa2-);;:;; V (HCOa2-) t;;:;; V(COa2-) +4.4 ml mole-I.

(11)

From Eqs. (lO) and (11), with the valuesll of V(COa2-) = -3.7 ml mole-l and V(HCOa-) = 24 ml mole-l relative to V(H+) =0,

-lO.9;;:;;V(eaq-)~-6.5mlmole-l. (12)

Zana and Yeagerla give 'Vo(H+) = -5.4 ml mole-l as the absolute partial molal volume of H+ (based on ionic vibration potential measurements), which is in good agreement with a number of theoretical estimates.14 Thus, an absolute value of fTo(eaq-) is estimated as

-5.5;;:;; f-o(eaq-) ~ -1.1 ml mole-I. (13)

Comparison with Ammonia and Theory

An absolute value of Vo(eaq-) in the range -1.1 to - 5.5 ml mole-l is not necessarily inconsistent with the corresponding value in liquid ammonia Vo(e8-). From their results for partial molal volumes of several alkali halides in liquid ammonia at 0°, Gunn and GreenI5

arrive at an equation for representation of absolute

12 L. Pauling, The Nature of the Chemical Bond (Cornell Uni-versity Press, Ithaca, N.Y., 1945), p. 189.

13 R. Zana and E. Yeager, J. Phys. Chern. 71, 521 (1967). 14 P. Mukerjee, J. Phys. Chern. 70, 2708 (1966). 16 S. R. Gunn and L. G. Green, J. Chern. Phys. 36, 363 (1962).

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'Y RADIOLYSIS OF LIQUIDS AT HIGH PRESSURES. III 377

partial molal volumes of the individual ions at infinite dilution. That equation, in a modified form (for liquid ammonia at 0°) , is

l;'o= 2.52(1.2r)L (51.6/1.2r) ml mole-I, (14)

where r is the crystal ionic radius in angstroms and 1.2r may be considered a cavity radius.16 Use of Eq. (14) gives Vo(Na+) = -42 ml mole-l in ammonia; this value, when combined with V(Na) = 57 ml mole-lls at 0°, yields Vo(e.-) =99 ml mole-I.

For the solvated electron in ammonia, Eq. (14) may be modified as follows:

Vo(e.-)=2.52RL(51.6/f) mlmole-l (15)

in which R is the cavity radius in angstroms and l' is the mean radius of the bound electron in angstroms. Use of Vo(e.-) =99 ml mole-l and R=f in Eq. (15) gives R= 3.56 A in good agreement with Jortner's theoretical estimatel6 of 3.2-3.45 A. Conversely, use of the values R=3.5 A and 1'=4.6 A (obtained from Jortner's theoretical calculationsl6) gives Vo(e.-) = 108-11 = 97 ml mole-I, in which 108 ml mole-l is the cavity volume and 11 ml mole-l is the electrostriction volume.

A treatment similar to that of Gunn and Green for the solvated electron in liquid ammonia may be applied to the hydrated electron. For aqueous solutions, relative partial molal volumes at 25° and infinite dilution9d of Na+, K+, Rb+, Cl-, Be, and 1- were used to obtain partial molal volumes of the nine possible salts. From the latter, Eq. (16) is obtained for repre­sentation of the absolute partial molal volumes of the individual ions at infinite dilution in aqueous solution,

Vo= 2.52(1.2r)3- (8.64/1.2r) ml mole-I. (16)

For the nine saIts used in derivation of Eq. (16), the maximum deviation of partial molal volumes calculated by use of Eq. (16) is 1.7 ml mole-I; the average devia­tion is 0.8 ml mole-I. Partial molal volumes of HCl, HBr, and HPd can be combined with absolute values for the halide ions, calculated from Eq. (16), to obtain

J6]. Jortner, ]. Chern. Phys. 30, 839 (1959).

Vo(H+) = -3.6±0.07 ml mole-I; such a value IS ill

reasonable agreement with the value of - 5.4 ml mole-l

obtained from the experimental results of Zana and Yeager.IS

For aqueous solutions, the analog of Eq. (15) is

Vo(eaq-) = 2.52R3- (8.64/1') ml mole-I. (17)

By use of Jortner's theoretical estimate17 that R=O and 1'=2.6 A, Vo(eaq-) =-3.3 ml mole-l (i.e., an electro­striction volume) is obtained from Eq. (17). Such a value lies within the range given by Eq. (13). Thus, the present results and analysis support Jortner's conclusion that the electron cavity size in water is much smaller than in liquid ammonia.

An estimate of Vo(H+) can also be obtained by adaptation of Eq. (17). For this purpose R=O, i.e., the intrinsic volume of a proton is taken as zero. Assumption that the proton is bound to a water mole­cule, with its unit charge spread over a volume of ",,18 ml mole-I, gives a value of f~1.9 A for use in Eq. (17). Then, from Eq. (17), Vo(H+) =-4.5 ml mole-l

is obtained. Thus, approximate equality of the electron and proton absolute partial molal volumes is consistent with their attribution to the effect of electrostriction alone.

Comment

The estimate obtained for the absolute partial molal volume of an electron is presented and should be accepted with caution. It is conditional based on the validity of a postulated mechanism for interpretation of the dependence of G(H2) on pressure in radiolysis of a particular aqueous system; in addition, a number of other explicit assumptions and approximations are involved. Obviously, it is essential to confirm the present estimate by study of other selected aqueous systems. Such studies are in progress. On the other hand, it is worthy of comment that the present experi­ments and interpretation are consistent with the notion that (unlike the case in ammonia) electrostriction is the dominant physical process in the solution of an electron by water.

17]. Jortner, Radiation Res. Supp!. 4, 24 (1964).

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