THE REDUCIXG ltADICALS PRODUCED I N WATER RADIOLYSIS: SOLUTIONS OF 0XYGE.K-HYDROGEK PEROXIDE-IIYDltOGEN ION‘ BY GIDEONCZAPSKIAND A. 0. ALLEN Department of Chemistry, Brookhaven National Laboratorg, Upton, Long Island, New York Ileceiued Julw 84, 19Gl
The reducing radical “II” or “HzO-” arising from the 7-radiolysis of water is shown to react compctitively with dissolved O2 and H202; the ratio of the respective rate constants is 2.0. It also reacts in a simple competitive bimolecular fashion with hydrogen ion, II+,t o givc an acid form of the radical which reacts several thousand times as fast with 02 as with H&. The rate constants for reaction of “H” with 0 2 and with Hfare equal. Thc yield of “H” deduced from the O2-H2Og competition in ncutral solution is 2.85, which is equal to the standard value of the total yield of reducing radicals. Thus esscntially none of the reducing radicals appear to be generated initially in the acid form, a conclusion which disagrees with recently proposed interpretations of some other radiolytic reactions.
Introduction
It hae been clear for some time that the reducing
free radicals, usually called H, formed in radiolysis of water, can exist in two different forms. Barr and Allen2 showed that the H atom formed by free radical oxidation of Hz reacts preferentially with oxygen rather t,hsn with hydrogen peroxide, whercas radicals produced in water radiolysis react with these solutes a t comparable rates. It was suggested that the product of I& oxidation was an acidic form of this radical, and that the radica.1produced in water radiolysis might in fact be a solvated electron. Hayon and Weiss3 showed that the acid form of H attacks chloroacetic acid to form mainly Hz, whereas the basic form originally produced from water gives mainly chloride ion in this solut,ion. Later Hayon and Allen4 showed that the reaction of the basic form with chloroacetic acid appeared to stand in simple competition with its rcaction with hydrogen ion to yield thc acid form, It seemed of interest to demonstrate the direct competition hetween hydrogcn pcroxidc and hydrogen ion for the radical, which could be shown by studying the variation of the yield of peroxide f o r m a t i o n or dest,ruction in systcms containing various concentrations of oxygen, peroxide and acid. This system also affords a mcans of determining the amount of the two diffcrent forms which may be produced in water radiolysis. Allan and Scholes6 have evidence from radiolysis of solutions of organic compounds that a yield G = 0.6 of the acid form is produced in water radiolysis, the balance G = 2.2 of the total production of reducing (1) Research pcrformed under t h e auspicea of t h e U. S. Atomic Energy Commission. (2) N. F. Barr and A. 0. Allen, J . P h w Chsm., 63,928 (1951)). (3) E. Hayon and .J. Wriss, Piwc. Second I n t r r n . Coni. I’enceful Uses Afomic Bnergu, 29, 80 (1058). (4) E. Hnyon and A . 0 . Allen, .I. Phiis. Ckem.. 66, 2181 (1961). ( 5 ) J . T. Allan and ‘2. Scholes, h’afure, 181, 218 (1060).
species being in a basic form, and Kelly and Smithe have quoted similar results. Experimental Materials and Methods.-The purification of water was as described by Allen and Holroyd,? except that after the distillation apparatus had been cleaned thoroughly it, was not found necessary to purify the water further by radiolysis and photolysis. Most of the solutions were air-satwatcd; oxygen concentration was varied in some cases by bubbling purified tank oxygen through the water in the irradiation tubes, or by using nitrogen-oxygen mixtures obtained from the Matheson Co., Inc. and stated to contain 50.6 and 5.16% oxygen. Acidities were determined with a Rcclrman pH meter. Peroxide was determined by thc Ghqrmlcy method. Treatment of the Data.-In solutions initially not containing any hydrogen peroxide, thc pcroxide concentration increased linearly with dosc and G-values werc obtained without difficulty. In some runs in which hydrogen peroxide was added initially, howovcr, thc yield of peroxide changed. so rapidly with increasing dose that an accurate determination of the initial yield was difficult. An example of high curvnture is shown in Fig. 1, To extrapolate to the initial yield In such eases an algebraic method of correction waR used. Thc ratc of change of peroxide concentration in these systcms is fixcd by the ratio of oxygen concentration to peroxide concentration present at any time in the solution. By material balance, the change in oxygen concentration must bo relatcd to the changes in hydrogen and hydrogcn pcroxidc conccntrations by the relation 2A02 = ATT2 - AH202, In solutions containing bromide, hydrogcn will bc produced with u Jrield G = 0.45, so that for AH2we may write simply 0.450, where D i s the dose given the solution (in units of e.v. I.-’ (6.02 X loz5)-’ if the concentrations are in moles per liter). For each cxpcrimental point the concentration of oxygen was calculated and it always was found that the ratio of oxygcn tjo peroxide could bc representcd within cxperimental error as a linear function of the dosc (Oz)/(HzO1) = (Oz)o/(,H20?)0 bD = PO bD According to the results of Allen and SchwarzRJconfirmedby the present work) the yield of peroxide then w ~ l bc l given by
+
(6) P. (7) A . (1 0 5 5 ) . (8) A . Peaceful
+
Kelly and M. Smith, .I. Chem. Soc., 1479 (1961). 0 . Allen and 11. A. IIolroyd, .I. A m . Chem. Soc.. 11, 6 8 5 2
0. Allen and IT. A. Schwars, I’roc. Second Intern. Con!. Uses Atomic Energy, 29, 30 (1958).
r , I he coefficient, of 1) iri the first term is the valuc of the initial yield heing sought,. The final tern1 shows the deviation of t,hc peroxide concentration from what it would be if the initial yield were maint~aincdthroughorit Lhe irradiation. The value of the final term was determind for each point,, using rcasonnblc values of IC and GH,and the resulting n u m t w s werc subtrwtcd from the observed concentrations. The corrccted vduos for the run of Fig. 1 are shown on the figure xnd were found to fall on a straight line. The diffirdty with this method was that the values of K and GH were precisely the quantities to be found. It was necessary, after this preliminary correction of all the runs had been made and better values of these constants dctermincd as describcd below! to repeat the entire proccdure on all t.he runs using the improved values of K and GE in order to obtain the final best valnes of these constants. Since the corrected initial yield values are not very sensitive to the assumed values of these constants, a third approximation was not necessary.
! 0
IO TIME
OF
I
20 IRRADIATION
(MINI
Fig. 1.-Peroxide destruction in a, solution containing initially 120 fiiM (11902) and 270 p.zI ( 0 2 ) . 1)ose rate (Fricke dosimetry) 99 w:U FcIII/min.: a, observed values; 0 , corrected values.
Results All solutions used contained l o - * M KRr tfoprotect) the hydrogen from radical attack. After some TABLE I difliculty with water purification, reproducible yields of peroxide mere obtained in the irradiat,ion PEROXIDE YIELDSI N 10-4 n/l K'f3r SOLUTIONS CONTAINING of neut,ral air-sat,urated water. The result,s agree PEROXIDE, OXYGEN A N D ACID closely with those of Allen and Holroyd.' The (EInOd. (Os), 1 M x 10' A4 X 104 p H Q(H2Ozf Go - Q(HzOP) Acid line representing peroxide concentration a.s a func1.40 HzSOa 0.168 tion of dose has an intercept of about. 0.25 p M , 2.7 3.8 1.19 3.8 - ,019 1.11 HISO( which is of about the same magnhude as that found 1.58 2.7 3.8 - .30 by Allen and I-Iolroyd, and presumably arises from 0.84 H2S04 2.38 2.7 impurities. The yield of peroxide G(H202) obtained - .84 3.8 2.7 .58 H2SO4 3.96 2.7 3.43 - .93 .54 H2SOr from the slope of the line is 0.87, in good agreement 6.44 .76 HzSOr with their value, 0.85. In acid solutions the repro4.30 2.7 3.43 - ,405 ducibility seemed a litt'le better than in neutral 2.15 2.7 3.43 .093 1.23 HZso4 solutions. Values of the peroxide yield in air3.43 .38 1.93 HzSOI 1.29 2.7 sat,urated water are shown in Fig. 2 as a funct,ion of 2.7 3.43 - .226 0.88 H~SOI 3.43 These (I1+)1'3 where (H+) is defined as lo-". 2.7 3.12 .045 1.14 H2SO4 3.90 values for each pH are herein:tfter called Go. 2.7 3.12 -1.13 0.49 Ha04 10.33 Solutions in which peroxide as well as oxygen 2.7 3.12 -0.44 .73 HzSOc 6.62 was added initially gave peroxide yields which - ,760 2.7 3.12 .59 H~SO.L 7.78 could be cither positive or negative, depending on 5.24 2.7 3.12 - .235 .87 HzSOi the amount of peroxide present. The results oh2.85 - .li .90 HBOI 7.77 2.7 taincd in neutral solution are shown graphically in 1.28 II2SOr .I 6 5.02 2.7 2.85 Fig. 3,tin which the quantity l/(Go - G(H?Oa))is 2.7 2.85 - .37 0.76 IlnSOr 10.33 plotted against the ratio of the oxygen to peroxide 2.7 2.85 ,079 6.20 1.16 H2SOr concentrat,ion. Similar results have been preseuted 4.14 2.7 ,335 1.64 IInSOc 2.85 by Allen and Schwarz.s The present data are 2.7 3.05 HCI 0 1.09 4.54 much more extensive and precise. The initial 2.7 3.05 -0.40 0.76 HCl 7.76 yields obtained for acid so1ut)ionswith peroxide and TIC1 3.88 2.7 3.05 ,117 1.25 oxygen initially present are shown in Table T. 2.7 11.6 3.05 - .83 0.57 €IC1 2.7 3.05 -1.24 .46 TIC1 Discussion 15.5 13.0 3.12 -0.84 .56 &so4 18.7 Neutral Solutions.-The mechanism of the reac14.9 33.0 3.12 .67 112SOc - .55 tion in neutral solutions has been discusscd by 13.0 11.2 3.12 .76 lI?S04 .39 Sworski9and by Allen and 8chwarz.8 If we denote 13.0 3.12 - .13 .95 HzSOr 7.46 the reducing radical produced in water radiolysis as 13.0 3.12 .38 3.74 1.84 F-IzSOd H and t,he oxidizing radical as OH, the equs't t'ions IIQSO~ 6.56 3.12 ,097 4.95 1.21 representing the mechanism appear as
-
+H, OI-i, H,,
HzOi Br- = Br OHBr 1 1 ~ 0 2= HOz H + BrH IIn0i OH 1120 I1 0 2 = HO, HzO OH
+
_____._
(9)
+ +
+
+
21102 =
T.J. Sworski, .I. Am. Cliem.
€1202
+ + + + 0 2
S o c . , 76, 4687 (1954).
(1) (2)
(3) (4) (6)
7.47 3.70 12.37 9.91 5.2G 4.20 6.29 7.34
6.56 6.56 6.56 6.56 2.7 2.7 2.7 2.7
3.12 3.12 3.12 3.12 3.03 3.03 3.03 3.08
-
-
.29 .29 .77 .67 .143 .025 .34 .46
0.82 1.58 0.59 0.62 0.95 1.13 0.80 0.73
HBOt HzSOr H&3On 132s04 IIClOc HClOa HC104 J-ICIO~
species. When perovide is addcd ini tialls, howcvcr, thc diffcrencc Go G(I1202)produced by the presence of the peroxide will depcnd only on thc yicld of radicals produced in the basic form, which docs react with hydrogen peroxide. Thus the intercept in Fig. 3 is a measure of the quantity of radicals produced in tho morc reactive basic form. This may be shown formally if we introduce another radical, I I ' , into the scheme which is assumed always to react with oxygen in the solutions. To the abovc scheme we formally write as the initial equation
-
0.8
'
I
I
0.I
0.2
I "+If,
Fig. 2.--Pcroxide yields in air-saturated solutions of AI KBr at, different acidities: 0 , I-12SOd; 0 , IICIOd.
RIO --+H2, H202, OH, H, H'
and add the cquation H' 4- 02
= 110s
(5)
Including ( 5 ) in the scheme me find for G and Go
+ 21 (GH + GH' - Gon) 2Gx G = Go 1 + ikdOz)lk3(I-Mh)I
Go = Grinas
_I_-
Thus thc intercept of Fig. 3 refers only to GII, not to Gs'. A word may be said here about the notation to be used in cquations such as the above, which tends to become very confusing. There is a growing belief that the basic form called H in the above I 2 3 4 equations really is to be thought of as a solvated electron, which for purposes of balancing chemical ( 0 2 ) I (HZOz). Fig. 3.-Initial peroxide yields in neutral Ill KBr equations is most convcniently represented as HzO-. solutions cont,aining O2 and added H202: 0 , saturated with Oxidation-reduction equations such as the above air; A, with 100%02;0, rvith50.6OJoO~;X, with 5.15% 02. can be written in equivalent forms for either forThe solubility of oxygen a t 1 atm. total pressure and room mulation of the reducing radical without changing temperature (22.5")was talcen as 1.29 m M . the Eignificance of the reactions in any way, since the postulated forms differ only by thc presence or This mcchanism prcdicts that the initial peroxide absence of a proton in the formulas of the reacyield in dilute bromide solution containing oxygcn tants and products. Thus equations 3 and 4 above but no peroxide is given by lo could be written GO
Gnzoz
+ 51 (GII - GOR)
(A)
and that the yield in the prescncc of addcd hydrogen peroxide is
+ +
€120-
H30-
Hi02
0 2
=
= HO2
+
+ +
OH OHHzO OH-or 02- H20
+
(3)
(4)
without affecting any conclusions to be drawn from the reaction mcchanism. The value of the total yield of reducing radicals G 2 " (B) G(E'z02) = Go - 1 + [k4(Oz)/ka(H202)] has been determined a t neutral pH from the yield The data. of Fig. 3 show that equation B is accu- of peroxide in solutions containing hydrogcn and rattly bornc out by experiment. The slope and intcr- oxygen,*.11formate ion and oxygcn,12 and ethanol ~ best valuc, 2.8, is obtained cept of the line of Fig. 3 were dctcrmiricd by a and 0 ~ y g e n . l The number of separate lcast rncan square calculations, from the hydrogcn-oxygen solutions. A 4ightJy using diffcrcnt, mcthods of weighting the individunl higher value appears from the ethanol solut ions, points. 'l'he statistical probahlc error in the inter- but licre the conccnt,ration of cthanol as well as cept is only about, iOyo,and in thc slope much oxygcn was somewhat higher and the valnc of GH less; but, the different weighting schemes gave may have becn somewhat elevated due to scaveng"best" intercepts corresponding to values of GH ing of radicals from the spurs. If we accept the ranging from 2.73 to 3.01. We believe, therefore, value 2.8 for the total yicld of the reducing radical, the data indicate that GH probably lies between 2.7 the results of Fig. 3 show that essentially all of and 3.0, and writc t 7 ~= 2.85 i 0.15, where the thcee radicals are produced in the hasic form, which limits represent ((probable error." From thc ratio is reactive with hydrogen peroxide, and littlc or none in the acid form. This conclusion is in direct of slope to intercept, IC& = 2.0 f 0.1. If same of the reducing radicals are produced in conflict with the proposal by the Durham workers6a6 an acid form which reacts preferentially with oxy- of an independent yicld of the acid form, arising gen then the peroxide yicld, with no peroxidc added from their interpretation of thc hydrogen yields initially, will be governed by the total yield of both (11) C. J. Hoohsnadel, J . Phys. Chsm., 56, 587 (19523. (IO) The initial yields of the wster radiolysis products are denoted by Girzoi, GH, ctc. The net observed yield of hydrogen peroxide is denoted by G(ITz0n).
(12) E. J. Hart, J . Am. Chsm. ,900.. 76, 4108 (1854). (13) G. G. Jayson, 0.Scholea and J. Weiss, J. Chem. Soc., 1358 (1957).
in ncutml solutions of orgsnic compounds. Sincc the chcmistry of thc pcroxide-oxygen system srrm=i clcaii arid simple conipared to that of most organic syst cms, we hclirvc that] thc prcsciit conclusion sliould be given inore weight, arid that! some other interpretation of the hydrogen yields obtained iri solutions of organic compounds should be looked
foiiiid
for.
Acid Solutions.-The discussions of Barr and Allen? and of Allen arid Schwarzs show that the form of hydrogen atom produced by free radical oxidation of H2 reacts preferentially with oxygen and much more slowly with hydrogen peroxide. The work of IIayon3F4 appears to show that thc form produced in water radiolysis is converted to an acid form by simple bjmolecular reaction with hydrogen ion. If the form resulting from oxidation of H2 is the same as that produced on reaction of the water radiolysis product with acid, then the kinetics of peroxide formation in acid solution should give evidence of simple competition for the radical between H202,O2and H+. The expected mechanism then would consist of reactions 1, 2, 3, 4, 5, 6 and H+H+=H‘
(7)
if we denote the form produced in the radiolysis of m t c r as 11and that produced by reaction with acid as 11’. A more reasonable-looking form of (7)is €120-
+ Hf
=
H20
+ 11
Tn the above mechanism with its double competition the following expression is obtained for the peroxide yield as a function of the initial concentration of H202,O2 and 11+ G(1ILh) = Go
Fig. 4.-Results of the peroxide yield determinations in acid solutions, plotted as dcscribed in the text: 0 , I12S0,; 0, I-IC1; 0, HClOa.
I
-
-
4
+ [kr(O?)/k.3(H2?X)]+ [k.i(Hf)/kr(Nz02)1 ”G.
1
The results of Table I consist of a number of experimental series, the initial oxygen and acid concentration in each series being held constant while the peroxide concentration was varied. For each of thcsc series a plot was made of the same quantity shown in Fig. 3, but with only five points to each plot. Because of the scatter of the points and their small number, the lcast-squares value of the intercept in these plots was quite uncertain and the best liiirs were drawn by assuming an appropriate value of Grr to fix the intercrpt. Since the total GI1 is known to increase with increasing acidity, and since it is not known whether the additional H formed in acid solutions is produced in the acid or the basic form, two calculations were made for each plot: one assuming GIh0 dellGhas oht,iiricd a value for t'his ratio of the order of 1000. E.
(15) C. ,J. lIoi:lianarld, in "Comgarativo Effccts of Radiation," ed. b y M. Riirtiin, .J. S. Kirby-Smith and .J. I,. Rlnpcc, John Wiley rind Sons, Inc., New Y i r k . N. Y., 1960, p. 167.
THE THERMAL EXPANSION OF LEAD' BY THORRUBIK!IT. L. JOHXSTON AND IIOIVARD W. ALTMAN Cryogenic Laboratory of T h e Ohio State L'niversity, Colilmbus 10, Ohio Received J u l y 26, 106'1
hlcasurements of the expansion coefficients of lead from 20 to ?,00"K. havc bcen made by use of a Fizeau Interferomctcr. A correlating function of heat capacity and expansion coefficients has becn derived by means of which it has becn shown that lead obeys Gruneisen's law between 25 and 300'K. A mct,hod for calculating thc compressibility of lead as B function of ternpcrature between 25 and 300°K. has been suggestcd. h correlation of the expansion coefficient data for lead with those for copper and rock salt has hecn given.
Introduction The apparatus and experirncntal technique for determination of the cxpansion coefficient of lead were the same as those described for synt,hct,ic rock salt3 and single crystal copper.2 The lead, obtaincd from thc Xational Bureau of Standards, was melt.iiig point purity material containing 99.99% lead. It was used without further purification. The samplc was cut to three pillars filed to the samc length within wave length of sodium-D radiation. These pillars served to separate the interference plates. Results The absolute values for the expansion coefficients are given in Table I. vI2 and vZ2arethe squares of the apparent fringe diameter measured at temperature equilibrium by means of a filar microrncter eye picce. The optical constant, 0, is a measure of the change in the square of the fringe diameter on increasing the fringes by one order. The values for 0 are those which result from smoothing according to the method already outlined.3 F is the number of fringes passing a fiduciary mark whcn the temperature changed by A?' dcgrcc, lo = 0.49670 cm. is the length of the sample mcasured at 2 5 O , T('K.) is the mean of the initial and final temperature of a dctcrminatiori and cy is the cxpansion coefficicnt. Runs 24 to 28 inclusivc are dctcrmined by use of the standard thcrmocouplc alone. The rest of the measurements were obtaincd by using a resistancc thermornetcr wound on the cell in coriiunction with the thermocouple. Thc data from this resistance thcrmometer wcre smoothed and tabulated at, (1) This work was supported in part by the Air Material Command, Wright Field. (2) T. Rubin, 13. W. Altrnnn and 1-1. I,. Jolinston, J. A m . Chem. Soc.. 76, 5289 (1934). (3) T. Rubir., 11. I,. Johnston and IT. W. Xltman, .I. Phus. Chrm., 66, 65 (1961).
equal temperature intervals betwecn 30 and 300'K. This resistance data table was used to calculate the temperatures of the cell above 30'K. All temperatures were based on The Ohio State University Cryogenic Laboratory temperature scale.4 All fringe measurements were referred to length measurements in terms of the mean wave length of sodium-n radiation. Seven sets of length (arbitrary) temperature measurements are exhibited in Table I. They begin at r i m 1, 9, 13, 24, 33, 36 and 40 where T average in most cases is given three significant figures to the right of the decimal, In each of these series the a-valucs were computed by the method of divided diff erences.6,6 Only third divided differences and first divided differences were used to calculate the derivative of length wit,h respect to temperature. Errors.-The absolutc temperature values are known to about 0.03'K. Tempcrature intervals measured by the thermocouple arc precise to about 0.02'K. Intervals measured by means of the resistancc thcrrnometer are precise to a few thousandths of a degree. The error in the length measurementjis about 0.008 fringe order. I€o\wver, because of the rather large heat capacity of the sample, thermal equilibrium was much more dificult, to obtain for thcse measurements than in thc case of the rock salt. A smooth curve was drawn within 0.2% of all data above 40°K., except for runs 36 and 37 which could not be reconciled with the rest of the data. Nix and MacSair' have determined integral expansions for lcad a t a number of temperatures ( 4 ) T. Kubin, 11. I,. Johnston and 11. Altman, .I. Am. Chem. Soe., 73, 3401 (19Sl). (,5), 1.: A. Willers, "Pructical Analysis," Dover Piil>licntions, 10.17, p. 77. (0) J . H. Scartiororigti, "NlimrrioaI Matiieiniltid .\nnlgsi~.".Jolins IIorikinn Prrss, Hattimore. Maryland, 1930, p. 115. (7) F. C. Nix nnrl D. MncNnir, I'hyn. Ir'eu,, 61, 7 1 (1912).
