dissociation constant generally is given) to units of cquixdcnts'cm.3. Using the values of these paramctcrs givcii i i i Table I , wc calculate the conductivity of purtst watrr to br 0.0371 X 1 0 F ohm-' cm.-' at (8' and 0.0549 x 10-6 ohm-' cm.-' a t "J0, s i h j w t to thc crror in the mcns.urcmeiit of the parameter? u r d . These values agree very favorably with the valiics we have obtained in this study. I n view of the above agreement (within the rangc of experimental error), wc conclude that the dissociation ccjuilibrium constant which could be calculated from these conductivity data is riot significantly different, from the values obt aincd from c.m.f. measureinents yivcn in Table I.
Conclusion The theorctieal conductivity of tho pure substance w t e r has becii dctermincd from conduc-
tivity data to bc 0.0373 X ohm-' cm.-I at 18' and 0.0347 X ohm-' cm-' at, 25", with an rstimated accuracy of 27%. While the valucs are about 3%. loivcr than predicted hy IS>4, owing to the increasc in the collision diamctcrs involved. Iiydrogeii flames are ptrhaps thr lcast romplcx examplcs and rich mixtures will produce mainly H,O and I 3 2 (and S2 if air is thc oxidant) as the important t hird-bodies. IIydrocarbonair fiamcs give fairly similar quantitics of H20, 1-12 and S2,with the addition of modcratrlv large quantities of CO? and CO also likely to be important in recombination. This paper reports some detailed measiiremcnts of [HI that have been made in propane-air mix-
turcs burning to a single temperatnrc of 2080'K. Abnormal [I-I] havr I)eru noted in thr t)iirnt ga m d our at tcn tion has b w n dirwt rd towzt following thr decay of tlicsr rxce purcly thcrmal zone. Experimental
fcrcnt valncs of the ratio 8. By plotting the niimcmtor of a against 8 (nrglwt ing reaction (i aiid thcrcforr any 8, trrm iti a ) , \-dues of 1.4 :md kj, attributed t o third-body . In hydrocarbon flames, 1c4 and /is,, also will The rxpcriincntal tcArhriiqur was almost iclrntical with iiicludc terms involving COZ and perhaps CO. COZ might be cxpccted to act in mnrh the samc Hrre \v:is nsctl u that rcportrd by l l d nncl \Vhwler shirldrd, p r c - m i d , prop:mci-air flarnr ou :I rirthclr smallcr manncr tinct with similar rfiicicncy as T1,O. CO, Mblcer t)iirnrr than previoudv, it s cliamc>trrbring 3.5 rm. To although diatomic, might, assist thc rccombinat ion the very crntral column of g:ws only, w r y m s l l liut rqrial :mounts of lit hiinn and sodium salts \wrc addrd by ittornim- significantly through cherniral action in rcacdons tion. T h r flames gcncrally wrre clcl;ignrti to brirn with as G and 3 ~ .11, itself might be important (mainly little vertical tcmprraturc gritdicnt as possil)lc (onr reason through Gc) in flames more oxygen-rich wherc 8 for thr Phielding). Tcmp(mturcs on t he cent rid iwis of t h r is larger arid can be greater than iiiiity. This latter flame \vwc mrasured visually by the sodium-u-linr rrversal cffcct might bc dctcct:tble i n I I ? flames iicar mothod using a tiingstrn st rip fil:imrrit 1~:trl~groiiridso1 stoichiometry as :L departure from lincnrity in thr Corriparibons w r v mndr at scvrral points on the A;tmc. B the intensity ratio, lithium rcd lirirsisodinm-r)-linc.P, which is nhove plot. sufficirnt to drtermine [l i ] at c w h point :is first dioivn by Thcrc arc practical difficwlties in making t hcsr Yugdcn itnd co-workrrs.2 Thc intrnsity mc~asurrnirntswrrr made photometrirally ttirough a small pl:tss-prismrd mono- photometric mrawrcmrnts i n the oxygep-rich as ihort, sharplychromator con5tructc~iin this Labor:itor\. .\ttclntiori \\ab flamcq. Thew h i r n gcrici confined to the rcgion sonic' niillirnrtcrs itbovr thr l ~ u r n wtop poiiitcd cones with rather p vertical tcmpcrawlirrr the ba1:tnre of thr reaction tiirc gradients. On our SI hirner, it was impossible to dcsign a srt of mixtures which could bc burned with thc desired icothcrmicity over a fairly ic; assumrd to he romplctc. licw%iori 7 acrounts l'oi ttw observrd rcduction in t h c linv iritcnsitg ratio from unitv. wide range in 0 arid yct at rclat ivriy high valurs of t'atcr. This prrcludcd for thc Knowing thr rquilibriiim roristarit for the rc:ic%ion, thtm [II] = (k',[Il~Ol lIAi])/[lJiOIr].The mcasurrtl intcrisity rntio is I f the intluriiw of C Y ) or 1-12, diroctly rrlatrd to [[A] / [LiOII]through an instrummi factor, was to opcratc with a hasr and t h r partial pressure of steam may ti(, rtLIrulatrd froin thc flninc>composition. The distance above thr I)urncJr top \VM flamcb of mixturc (prop:Liic./stoit.hioin(~tric propanc) = 1. I 6 whirh t)urnctl a t 2080'K. with the final converted to a rorrcspontfing t imr. wale bj u calciil~itionof thr vertird flow ratc of t h e hot c.qxinded gssrs. .I knowl- condition [0Hlp = [Ille or 0 = 1. The parametcr edge of the pr(4)urnt flow rate, initial trmpcrsturr, find a then reduces dirtct ly to fiarne temperature and the rrieasured fittnir t1i:rmctc.r givrs a = lh,,
sufficiently acruratu rcsults for our pnrposcs.1
Results and Discussion If only reactions 4, 5 and (i arc important in thc rcmoval of abnormal concentrations, then the intrgratrd expression for the final equilibration of [HI with time is
mhcrc thc parametcr a, constant, in any onr flame is =
2 {4 ( kl -
L
+ IC,') + (kTP+ kBr)e+ i+e
(n)
The apparent, second-ordcr constants k.,, k, and h.6 includc thc conccntrat'ions of third-bodirs. Taking rich hydrogcii-air flames as t,hc simplest, ca,se, only IIZO iiccd bc corisidercd an import:ints rccombiiiatioii center. In tho combiliation of iodine atoms, Itusscll and Simonsj cst,iniate the efficiency of 1 1 2 0 to be 10 t,imcs grr:Lt.cr than t8hat of cithcr Nz or TI,. 1;urthermorc reaction G can be ruled oiit if thc over-all cfficicnry of 11, is low or if e is very small (as ,is the ( m e in fuel-rich flames, both hydrogen and hydrocarbon). Rulcwics and Sugden6 succcssfully treated the t,t:rmolecular scheme by designing a set of hydrogen-air mixt tires which burned t'o t,hc samc tcmpcrnturo hiit, dif(4) A , G . Guydon arid 11. G . JVolftiard, "F'lnrries, 'Ylivir Slriic%ure, Radiation and Terii~,rraturi~,"Cliapiiian a n d Ilall, I,oniion, 1!4fjO. ( 5 ) K. E. Ruvvell tind .I. Siinons. I'roc. Row. SOC.(I.ondon), 8217, 271 (1953). (6) I?. XI. Bulewica and T.M.Sugdrn, Trans. Faradall Sac., 64, 1855
(1958).
+ k,, + kB* + k,, + ICs,
(11)
1Sach constant in cqimtion 11 is itsrlf compositc and clcprmls on t hc cwiccntrations of the wrioiis third-hodics. Even haking rcasonahle awimptioiis as to the importance of each (H,O tirid COZ in reactionh 4 and Zp, CO and 1 1 2 in k,Gc and pcrhaps 4c), tho twmplete elucidation of the rrsulting 11 ternary vclocit y const:mtk prcirnts tt formidable prohlcm. ITom.rver, in this particular basc flamc with 0 = 1 it was fcnsiblc to malic small indi\.idu:il additions arid hrnw cihaiigcs in thc (.oncent f tlic product, g a w whilc thc others rcniaint idly constant. Only minor furlry to maintain the air adj compoiition of th the tcmpcmtiirc~and thc condition [ IC. Some terms in cquatiori 11 thcrcforc could tw scparatcd at this particular tcniperatiirr, 2080'K. Flames with Added SO2.--\'cry smnl! quantities of SOz were mctcicd into thc vcry center of the flamr. This x i i prirnarily a t c i t to confirm the existrncc of abiiormnl [HI.At any otic point on the flame axis, it was c+dmt that e\wi tht. smnllcst addition would lo\wr the iiitctiiity of the lithium red lines while having no effect on that of the I)1inc.s. r'urthrrmorc, the dccay of [HI tip the flame axis was fo!lo\ved to thc mme constant valuc, [€I],,found in thc piire l x w flanic. 1Sxccssivelv high concwitrat ioiis then must flow from thc hot honndary iiito thc burnt gas region in these mixtures.
0, in the sitbscqucnt rwoinbi-
. 1:or thrsc small cxccsses in [HI, [HIralso was mcasiircd arid log ( ( [I4 J [IT],)/
+
([I-I] - [1IIe)] plotted against time after leaving the burner top. This should be a straight line of slope 0.8G8a[II],. Figure I shows thc quite good 1incl:wity obscrvctl for thc has(. flame and 5 others, cach with :L constant addition of SO2. 'rhe volume additions arc indic,ated as a pcr cent. 01-1 each line. For the hase flame, n = 3.2 x 1 0 - ' 3 molecule-' see.-' arid there is a progressive incrcaw from this as thc SOz added is raised. XIorcovcr, this increase is quit(' linear with the quantities of SO2 added here. Although the measurcments wcre made in the flame gases wc~ll past the hot boundary and the SO2 admixed had ample opportunity to form such radicals ns S, SO, etc., it, is evident from the linearity in thc parameter increase that the acc4elcration of the rccombiriatioii ratc in the biirnt gases is riot overdulv influrnced by dimers such as Sz or polymeric forms. SO1 being large and yuitc stable should bc the most important form, aeting mairilv through rcactioii 6c. In addition Iloolcy arid Whit tingham' h a w shown that the percentage oxidation of SO2 to SO3 is lo\wst, in pure hydrocarbon flanies. On this basis, a lernary rate constant kgciSOn) = 1.1 X IOz9 ems6 see.-' at 208O01hc2700-2850 cm.-l region. The ~ s i g n m e n tof those baiids has becn tho subjcct of several studies in rccent ycurs.’-* h singlc aldchydic C-€1 st,rctching vibration is cspected, hcncc n problem exists in choosing one or the othcr of these hinds as this fundtimcntal. lccrmi resonance5 involving thc C-13 stretching vibration has bccii suggcstcd as a sourcc of this doublet, prcsent~ingtho additional problem of the assignment of thc proper rcsonaiicc partner. l’ozcfsky and Coggcshall’ origirially suggested that the two infrared bands obscrvcd for aldehydcs in carbon tetrachloride solut,ion werc thc rcsult of a Fermi rcsonancc bctxecn t>hc aldehydic C-If stretching vibration and an overtolie or combinat.ion band of thc samc symmctxy. They tentativcly chose the overtotic of thc 1380 cm.-l methyl symmetrical bending vibration as the part,iicr in the rcsons1ricc. I n making the choice, howcvcr, they noted that hcnxaldchydc, which has no mcthyl group, also cxhibitcd tlicse c:h:tractcristic bands. Subscqucntly, l’inchas2 publishtd n st-udy of t\\-enty-savcn aldchydes, all of which exhibited this characteristic doublct. He assigncd the lowcr frequcricy hand, ccnl crcd a t approximately 2720 cm.-’, to tho aldehydic C-I3 strctching vibrat,ion, and t,hc higher band, at :ipproximatcly 2820 cm.-’, to tho first overtone of thc aldehydic in-plane (2-11 bending vibration. (1) A. Pozefsky and N. D. Coggrshull. Anal. Chem., 23, 1611 (1951). ( 2 ) S. Pinchas, ibid.. 27, 2 (1955). (3) D. F. Eggcrs a n d W. E. Lingron, i h i d . , 26, 1328 (1956). (a) 6. Pinch&.., ibid., 29, 334 (1957). (5) E. Fermi, %. P h y s i k , 71, 2.50 (1931).
The work of I’inchas2 w-ns followed by the intcresting paper of Eggers and 1 , i n g r ~ n . ~They reported a study of four monodeuteratcd aldehydes with thc deuterium atom replacing the aldchydic hydrogen. Upon dcut cration, both bands in thc 2700-2830 cni.-I rcgion and one in the 1400 cm.-l region disappeared. Two new barids appeared in the C-I3 stretching rcgioii and one in the C-D bending region. Thcir intcrprctatioii was that thc two bands i n the 2700-2830 cm.-I region w r c produced by a 1;crmi resonance betv ccii the fundamental aldehydic C-13 stretching vibration and the first overtone of thc aldehydic C-11 bending vibration. They pointed out that thc l’crmi rcso~iaricepersists in thc monodcutcratcd aldehydes. These results sccm rather conclusive. Howcver, I’inchas4 has rciterated his view that thc lowcr of thc two bands is the aldehydic C-H strctching vibration and ha? changed his assignment of the highrr frequency barid to that of a combination bctwcen thc 1380-1390 and 145.3-14’70 cm. -1 bantls. All of the work cited abovc has been concerned with the infrared spectra of aldehydes in solution, with c:irbon tetrachloridc thc solwilt in most enws. lcurthermorc, these papers wcrc ciscntially studics of the aldehydic group frcquclncics in a variety of molecules, rather than the vibrational assignment of a sperific moleculr. I h r i n g this period, the vibratioiial assignmciit of acctaldehgde had becn the subject of scvcral p a p c r ~ . ~ -These ~ studics wcrc concerned with the infrared spwtra in the (6) FI W I’lioiiiiison and G I’ IIarris, Trans Faraday S o e , 38, 37 (1942). (7) J C. Morri-, J . Chrm Pliys , 11, 230 (1911). (8) I< 5 Pitscr and \V Weltnor, J . A m Chem. S o c , 71, 2812 (1949). (9) J C Evans and 1%. J Bernstoin, Can J Chem., 34, 1083 (1956).
