of the trlnietapliosphite, which shows vory littlc adsorption, thc adsorhcd phosphates must cover Inorcly :L srn:d frwtion of the ndsorhtnt si1rfac.c even at the highest voiiuculruiioii irsod. ’l’hcsr pronounced diffcrcncm i n adsorption may be allributcd primarily to tho diffcrrncc>s in thc affinity of strontium iou for the various phosphat c ions. This afiriity may lw rclatcd to the soluhility of the iiidividual stroritium phosph thc ability of the phosphates to form c~omplcxcs with strontium. its thcrr arc few data in the litrraturc or1 the solubilitios of those salts, we studied the prccipitatioii of stronliiun with each of thct phosphatcs hy mcaiis of thc Tyndall effert. Tlie rniriirnum phosph:ite cuicrntrations at which a 0 02 111 strontium chloride solution bccarric t urhitl w:(w 2 x 10-4 .I[, I x 10-5 x, 4 x 10-5 -11,:~11d~ I X N C 1 X 10-1 JI, for the. o ~ t h o - pyrn-, ,~ tri-, and trimetaphosphates, respectively. Thcsc data siiggcst the familiar rclation that the smaller the solubility, the greater is thv adsorption. The stahility of the stroiitiuiri cornplcxw with thcse phosphates arc givcn in van Waxer uiid Callis’ comprcheiisivc review l o ; the pKn-raliics (ncgatirc logarithms of the dissociation constants) ur(1 1.52 for the ortho- and 3 3 5 for the triinetaphosphute. (9) Tliqodiiiiri salt uns used and tho p H of t h o systcm w a s 7.1 rit 1111~ ~ o i i c r i i t i a t i r ~j nu r t refrired to (lo) J R Van W w e r !uid C 1‘ Cnlhs, Chcm. ficus., 58, 1011 (1058).
Valiics for thr chain phosphates are lacking, but we worv uMc to cMimate them from thc relationship betneeii the rclutivc! ph’n-v:~liw for :ilk:iline cnrth cornplcxcs a d t h r ~iiiriiherof phosphorus at onis pcr vhain; the vnliics obtained are 4.8 and 6.1 for the pyro- and triphosphat (18, rclspcctivrly. Thcsc data confirm qiialitatively the expected relation l)ct,wccxi 1he cwinplrxing ahility and adsorption. The very sinal1 adsorption of thc trimctaphosphatc may bcx attributed, in part, l o Iho rigidity of its ionic striicturc As has been pointed out by liaist rick,ll thc rigid cyclic striictnrc, may prcvmt adaptation of the ioiis to tho vrystal latticct of st rnn t ium sulf at c . The inwhariism, which first n ~ quggrstcd ~ s to explaiii the inhibition of the cq~stalliaationof strontium snlfntc by triphoy~hxte,2 ha< been confirmed, and it, also swws to clxplnin thr rffcrt of the other condensed phosphates. T l i i b wot*li d s o may afford somc insight into the relatioii bet~recrithe tiehavior of tho cmdcnsrd phosphattcl and their ioiiic itriicture. We iiow urc wrkitig with tctra- and pentaphosphates to fiild out the rclatioiiship bctwcen tho kngth of thc ion aiid its cffcct 0 1 1 crystullizntion rate. Acknowledgment.-Tli(~ wiithors w5h to thank A h . A. M’cisebt~rgerfor hrr hclp in preparing the manuscript. (11)
n
Hni\tiirk
D z v i i i w i o r i ~I ’ n , o d a y
. i ~ t ) ~ o h i 1r:itc ( ~ c*oilst:tlits of thcir rcwatioiis. Information n i l both of these points can bc obtaiiird hy st iidyiiig solutions with high intensity tadintion. If it coiild he shown that thc active
spccics Iincirrgo cxclusively secoud-order tl15appcaruiicc it \ ~ o u l dbe stroiig cvidcncc for their radical charact#cr rather thnn tixcaitrd-stst o charactcr. Thc applicatioii of pulsed-beam techniques to an iiitciisi ty dependerit 3ystr.m mill yield information oii ahsol111rrate constmts. In 1956, Ghormlryz piiblislird h i s resulls or1 the irradiation of pure water with ail electron bcam. IIe observed a stcarlv-statc conccntrntion of hydrogrn pcrovidr whicih vttricd with the intensity. Upon placing a rotnting sector in froiit of the h a m , he deternniird that the lifetimc of thc ratc-controlwns of' thc ordcr of a xnillisccoiid under his (wildit ions. At that Iime, there was a plcthora of data on thc low-intcn cii t y radiation rhrmistry of dilute solutions of IF,, H,Oz arid 0 2 , which was not adequately undwslood. Couscyuently thr high intensity cxpeiimeiit,s could not bc intcrprctrtl. Quantitative agrcc'rnciit, b c t ~ ~ r cmu(+ n of the low intensity data :md a simple six-step mwhanism was rcnchcd by Allen antl Schwi.arz3in 1058 arid i t uppcarcd that, it mas timc to rccoiisidcr uiid exteiid the high intmisity nork. Experimental Tiiply-di.;fillt-d walcr was uscd in this work with tirid without l r i i Ihvr piiiihcrition bv pre-irrndiatjon Rith Cow -prays arid sul)scquerit p h o l o l ~SI\ by 2537 A. light t o dcstroy the hydrogeii peroxide Slightly diffcrent results obtsincd with t tit. t a o diffcrcnt prcpnrations, as will be evplaiiied i n the srrtion on rrsiilts. The iadiatinii d l s wcrc flat cylinders of Pvrex gluse, 14 min i 11 itrid iin avcragc of 3 . i mm. inside lcngtli in the dirw tiori (if t h r hcam. This is ahout half the ruiiKc of the r l w t r ( i i i ~ l'hc tront facc of the cc4 wus about 0.2 m m . t h i ~ k T h e w w n s n single cntranco to tho cell from the edge m,dr of 0 . 5 mm. 1.d. capillnry, 1 em. long, \+liicli was Icft o p m and hilcd w t h nutcr during the iriadiation l'hc m t r r for irradiation wus deaerstecl hy hulit~ling hrlirim through i t for h u t 1 lir. The helirini first was p a w d through a trap of nctivrttwl charcoal at Iiqiiid nitrog m tcmpcrtiture, through a fiitled disk into a tubc containing pure wntcr and tlirii thiougli a capillary huhblcr into the wtiter usrd for thr irratlirttion. Thc d m c r w d ,solution WUY forced into thr cells through a fine capillary with t sli rht helium prc'ssurr. Thcrc wrre no visible bubbles iii &e cells ~irforc.or aftcr irradiation. ..ideaeratetl solution standing in a ccll for an hour oxposed to the atinosplic.i(~c-ontninrd lws than 0.3,~lIOa.This time i b long c~oinpitirtlto thc timc hctwwn filling und iir:tcliatirig ti e r r l l s . l h h day thc cclk were filled i!ith deaer:ttrd u a t v xnd prrirriidintcd with the electron beam for about 100 t-wcnnda in order to clean the surface. They twit iiot r v p & to the nir until after they had been used illiring thc irradiation, the cell was plxc*c.rl hrh!nd a groiintlcd *ii4'' nliiminum plate, 3" in diamrtri with a lo mm. holc directlv in front of the cell Iirliincl thr ccll, n I/a" cdiiniinnm plim collected the (-iirreiit that wcnt through. A 0.05 mm. plutinum \ \ i r ( A a t t x d i r d to thc hnck platc u-as inscrtcd a few millimcteiq i n t o t h e neck of thc crll. The cc4 W:LS mounted with its window 9 rm. from thc window of the, mtlcshinr. At this distancci thc t ~ c u mh:ts divcrgrd ronsitlcrablv and onlv l l ? & of it ~ R ~ P Cthrough S t hc holr in the guard plate. Thc. intrnsitv distrihiition across thc ccll mas checlcrd b y irradiating blur rol1oph:m in a similar holdcr and wiis found to vary hv almrlt 45, from the cvntcr of th(A cc%llto t h outsidc (~lgc'. T h e ma\imum intensity viwiation from front to hiirk of the ( ~ ~ 1shoultl 1 not cxccrd & 137" of the avrr:ip.6
Hydrogen peroxide was dcteririiiird by tlir iwlide met hod of Ghormley.6 The w u p l e \\m r~iriovetlfrom thr I I I R C ~ I ~ tioxi cell with a11 evcdioppw siicl a 0 2OO-(r diqiiot inixcd with 0.114 cc. of the i r x g ~ i i ttlirec.11~in IL d i j Jlrckman microcell. The 0.13 of k i i o u i i sxmplr~n r i v rrprodncihlc t o 0.002 unit out of 0 15 0 I) u n i t The s~iiriof peroxide con( n i t i , h o i i p l u s twicc thc ovygrn coricentrstion W A S f o i i n r i 112 (OH) > (€I), and that reactions 7, 8 and 9 disappearance which is proportional to the average should be important reactions decreasing in that eoncentratlionof the rate controlling intermediate.'* (12) C . Crapski, private communication. This value is highei t h a n the valuc 1.85 reported in reference 3. It WRS determined b y t h e same method b u t with increased prccislon. (13) A. R . Anderson a n d E. J. H a r t , J Phys. Chem., 6 5 , 804 (1961). (14) H. A. Sch-arz a n d A. 0 Allen, J . A m . Chem. SOL.,77, 1324 (1955) (15)
E. It. .Johnson arid A . 0 Allen, zbid., 74, 4147 (1952).
(16) H. A. Schwarz, J. M. Caffroy and G. Scholes, h d . , 81, 1801 (1959). (17) A. 0. Alien, "The Radiation Chemistry of Water a n d Aqueous Solutions, ' U. Van Nostrand Co.. New York. N. Y., 1961, p. 97. (18) G. M. Burnett a n d 11. W. Melville, "Techniques of Organic Chemistry," Vol 8. "Investigation of Rates a n d Mechanisms of Reactions," Interscicnce Publishers, Ino., New York, N. Y., 1953.
In this wo~li,tho conconlratkm of Ihc measurable species are a t steady state and a diffcrcnt analysi? is needed. At steady state, the concentration of any species a t the beginning of one cycle must be the same ns it is at thc beginning of the ncxt. Hence the integral of the rate of production of any species over a complete cycle must be zero.
$ Rldt - $ Rzdt - $ R;dt - 2 f Itad/, etc. 7 is the time the beam is on. There are seven cqunlions of this typc, one for each species, analogous to the set of equations 1. The average rate of a reaction, during the cycle 8,is given by
f
Rdt = f i ( r
+1
) ~
where T is the ratio of the time the beam is off to 1he time it is on, 7.5 in the present case. These integral rate rquations combine into a set analogous to equations (3) Ri(r
+ 1)
A:(r +
1)
R ~ (+ T 1) = G H J
+ B,!r + 1) =
At this point, some assumptions about the relative lifetimes (2) of the three radicals, €102, O H and H must be made in order to obtain rate constants from the pulsed-beam H202 curve (Fig. 2). The most reasonable assumptions are that ZHO, >> brr >> IH. This is analogous to the earlier statement that (Hog) > (OH) > (H)made on the grounds that >> k z while the rate constants for reactions between €IO2 and the stable products are negligibly slow. The experimental data presented here are consistent with these assumptions, as it was found that R7 > R8 > R,. Since k,, IC8 and lie are probably of similar magnitude, this again gives (HO2) > (OH) > (H). If it is assumed that the eoncentration of NO2 is large enough so that it does not change appreciably during the cycle, then E; = k 7 ( I I 0 2 ) ( E ) and Rg = ke(IlOz)($ where (ofl)and (Is) are the average eon_ccntrations of 011 and €I over the cycle. Also, Rz = kz X ( 1 1 2 0 2 ) ( ~I&) , = Icq(Oz)(8)aiidR3 = k3fN202)(G), giving
Since u and l& are fixed all the average rates are fixed by equations 6, The yields assigned_ to the varioys rates in equati+s 6 apply here tjo R(r4-1); ie., RL(rf1) = 0.16, &(r+l) = 0.22, etc. While it would seem to be instructive to follow (0:) as a function of T , the lower precision of the analysis compared to HZOZ coupled with the other sourccs of error in the pulsed beam work were not encouraging enough to make the attempt attractive. The relationship bctween the observed peroxide steady state and the average radical concentration d-uring the pulse may be found from the relationship Rz(r+l) = Ria. (Superscript or subscript zero refers to steady-beam conditions a t the same intensity.)
The ratio (m)/(OI-I)o may be found by integrating the O H concentration over the cycle. The rate equation for (OH) when the beam is on is d(OH)/dt = G o d R8 - R1 - Rz - R7 - 2Re The assumption that i~
