Fcb., 1W2
~ l S S o C I . \ T I O X&jVILlBItl.l
OF \ ~ A T E RBY A CONUUCT.1NCE h I W H O I )
225
L)I3TEItMIN,iTIOK OF THE DISSOCIATION EQUILIBRIA OF WATER BY h CONDUCTANCE METHOD BY 11. C. DUECKER ASD W. IIALLER ,\'afional Bureau of Standards, Washingfon, I). C. Recewed June 81, 1061
Electricd conductivity nieasurcmcnts have been made at various temperatures on clcctrophorct ically purified water with v:rrying impurity content. T h e temperature cocficients of conduction are detcrniined at 18 and 25' for cwh frsotmn. A11 expression is dcrivcd for the rictivatioti energy of conduction of very dilute :tqucous solutions as it function of clcctrical c:onduc:tivit,y. Upon sul)stii.rltion of the c a l d a t c d activation encrgies of conduction into this cxpreasion, thc theoretical c*orlduotivity of pure water IS calciilated to be 0.0373 x 10-6 ohm-] cm.-' at 18', a value 3 % lower than predicted by Kohlrauach 00 years ago. T h e dissociation constmlts for water c:ileulat,ed from this value, the cquivalcnt, conductance of the ions and the density, however, agree with t,hose detorniincd from the e.m.f. of galvanic cells.
ultra-low-conductivity water having n residual ionic Introduction impurity coiitciit of only one-third of thc minimum Siiicc postulation of thc theory of ionic dissocia- previously rrportcd in the literature. 13rcnuw this tion by Xrrhcniusl in 1857, many workers have more closely approachrs the ideal purity, and i n ticen cngagcd i n the quantitative description of thr view of thc fact that, bettcr supporting clcctrochemdissociation equilibria of chemical compounds. ical data with confirmed accuracy arc available Vcry early cfforts w r c devoted to thc study of the today, the authors were convinccd that a rcprtition suhtaiicr, watcr, hecawe of its importancc to the of the coiiductaricc method ~vouldhclp verify thc physical ecienccs a i d its iiniquc rolc as a mineral prcsently accepted valucs of tlic fuiidamcntal clccarid lifc-supporting liquid, rather than becauw of trochcmical properties of the water-substance. cxperinicnt a1 convcnicnce. Kohlrausch and I-Ieydweillcr nicasurcd thc clccIt apprarcd rather tempting to exploit the most trical conductivity of water fractions of varying apparcnt proprrty of an ion, its capacity to carry purity around 18" aiid prcsented thcir data by thc electrical charge, for tho dctcrmiriatiori of ionic use of a linear cqiiation of the form, dk/dl' = n conccntration. Yct, in the cas(>of water, the direct bk, wherc dk/dT is the temperature dependencc of determination of hydrogrn and hydroxyl ion con- the conductivity and u and b arc constants. From centration by clcctrical conductivity measuremciits the tcmperaturc dependence of the rquivalcnt conis compliratcd l)y the very mmll dcgrcc of dissocia- ductivities of the EI+ arid OH- ions and froni the tion, nhich yiclds approsimatc.ly one ion pair for hcat of neutralization of strong acids and bases, cach 1 0 9 \vat cr m o l c c i h . This means that a rra- they further predicted a valur for the temperature soiiablc degree of accuracy may he obtained only if dcpcndence of conductivity for pure watcr. Subimpurity ions arc rrduccd to a comparably low stituting this valuc into the above empirical equalevcl. In 1894, Koh1r:tnsch and IScyciweiller2 rc- tioii thcy arrived at a value for thc thcorrtical coilportcd the electrical conductivity of lvater which ductivity of purc watcr. I n evaluating thcir data they had purificd by 3 6 vacuum distillations in glass the authors of this present paper did riot iisc Kohlcquipnieiit 1thic.h had hcrn Icached wii h watcr for rausch and Heydwciller's empirical clxtrapolation tcn ycais. 12rom this (lata arid knon-n valucs of thr procedurc but derived a different method on thcoequivalent ionic conductances, they cstiniatcd thc rctical grounds. concentration of thc hydrogrn arid hydroxyl ions to Theoretical tie 0.8 X cquivalcnt pcr liter at 18". Thr coriduc'tivit y mcthod for dctcrmination of the disThc conductivity, k. of an ion may tx cxprcssed sociation caonst ant has not sinrc hrrn used h ~ a u s c ~as the product of its equivalent conductan(v, A. arid of thc difiiculty i n preparing and niaintaining mater its concentration, 2 . Upon cvnsidcration of thc of 1111 ra-low-coiiduct ivity. Today's h t acceptrd tmipcratiire coefficients of conductivity and the values are from mcthods which do not ncccssitatc thcrmodynamic law for the distribution of encrgirs, the prcparatioii of ultra purc watcr, such as the oiie can show that the activation energy for thc mtasiircmcnt of thc elrctrical potential of cells. conduction of the ion, &, is givc.n by the rclation This method was iiscd us tarly :is 1893 by OstkE = xh' f E . (1) mald3 and r l r r h ~ n i i ~ ~contt~mporariw ,4 of Kohlwhcrc A B is thr minimum thermal energy the ion rausch, biit was not pcrfccttd until the 1930's by must h a w in order to particiipatc in the conduc1I:Lrncd arid ro-workcrs.5 thr energy required for dissoI n a prcvious put)lic*ation,6thc authors of the tivitv process and ciation pcr eciuivalcnt ion formed. p r c w r i t paper drw-ibcd ail elcctrophorctic purifivaS o w the total conductivity of thc purc suhstancc tion proccdure ( q x h l e of producing and maiiitaiiiirig watrr is equal to the slim of the contluctivitics of ( 1 ) S 'irr'h?niii? Z physrl, Chem 1, Bdl (1RR7). thc IT,jO+ a n d OH- ions. By I I P C of similar thcr(2) I ' I F 3.0 V a
11
\ ~ A I . U E SUSEUI N TIIIS PZmmFOR THE
OF
2 .o 2
Krr Kp1/2 ( = m )
3
1 0 3 ~ '( = p )
1
VARIOUSI'rzormvrIEs
PURE\VATER
18 0 . J 7 9 X IO-" 0 . 7 ( i l X 10-7
Temperature, 'C.
25
1 , 0 0 8 X lo-" 1.0O.i X 10-7
I. 0
0.0"
~
4
8
I2
I6
20
24
5 fi
XOH
X.,
= XII
7 XEw 8 =lC 9 kfiw
0.0070.f4 340.8 198.3 548, 1 2723 (i710 9133
U.!)H&?.iOS
31.i.5 173
4 AH
4- Xon
488.6
203 & 089 I 98-43
eqiiiv. l00U g. water
g./ctn.3
cm.2 c q i i i v - l ohm-1 crri 2 iviiiiv.-l ohin-1 ctn.2 eqiiiv:l cnl. cquiv. -1 cal. equiv.-l cnl. equiv.-l
oiiiri-1
The values of li, del crmincd by the extrapolation in Fig. 2 arc subject tc? t,hc CJKW in tho dctcrmjnation of k E w as indicated abovci, and thus makc t,hc following det'crmination of t hc theoretical coiiducitivity subject to an error estimated to bc 270, ill25' the least, mean squarcs linc through our data 5212.:39 11.8261 log 1' - - has a slope of 240.07 aiid an ordinate intercept of 7' 4932, as shown in Fig. 2 . Using cquat,ion 4 we tf In h-,,:?': ohm-' em-l. At .,E = 117'2 -- 11994.2 - 11.i49Y' - 0.01!J51ti1'2 calciilatc I., to bc 0.0547 X cl2' 18" tha ?lope is 174.47 aiid the intercept is 5103 so ohm-' em.-'. (On the Csing this csprossion ive get mE' = (;!I22 cal./ that I;,. = 0.0373 X basis of thcir condiictivity valiies, Kohlrausch and cquiv. a t 18' and 6'75.5 cal./cquiv. at 25'. 'l'hc values of p,E are det,ermiiicd from tat)lcs of Heydwcillcr2 predicted the conductivity of purcst wntm to be 0.0384 x ohm-' cm.-l at 18' and density as a func:lion of tcmpcrat'urc to bc -45 ohm-' ( i r n . - I at, 25', valucs which eal./cquiv. at 25' arid -31 cal./equiv. at, 18'. 0.0569 x Thus, tS>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-
