April, lBG0
TRACER DIFFUSION OF I - I S D I ~ O 10s GI~
48 1
TRACER DIFFUSION OF HYDROGEN ION IK AQUEOUS ALKALI CHLORIDE SOLUTIOSS AT 25' BY L. A. ~ T O O L F ~ ~ ? Contribution f r o m the Department of Chemistry, liniverszty o j S e w England, .lrnzidale, S e w South V a l e s , A1icstralia Receteed ,Vovember 11, 1969
The tracer-diffusion coefficients of hydrogen ion have been obtained from diffusion measurements in 0.1-3.6 I\. potassium chloride, and 0.1-45 Jf sodium and lithium chloriJe solutions, respectively, as supporting electrolytes. The dependence of the tracer-tliffusion coefficient on concentration of the supporting electrolyte is found to be greater than that of other univalent ions. Lithium chloride solutions are found to have an abnormal influence on hydrogen ion transport; an explanation is suggested in terms of the proton jump transport mechanism. Frames of reference for tracer diffusion are hiefly mentioned.
Introduction The transport properties of hydrogen ion are of interest in many branches of aqueous solut,ioii chemistry. A previous publication3 described an application of the magnetically-stirred, porousdiaphragm cell4 with which t,he Oracer-diff usion coefficients of iodide ion were determined by a chemical method involving direct analysis5 of iodide. The chemical niet'hod enables a fairly rapid and quite accurate (cn. 0.4%) determination of the tracer diffusion coefficients of particles which, while not possessing suitable properties for radiochemical analysis, can be studied readily by conventional analytical techniques. The normal hydrogen isotope ion is in this category since it is not radioactive and the less common isotopes, deuterium and tritium, are unsuitable for use in the usual radiochemical niethods of studying tracer diffusion. Tracer diff usioii, xiid the somewhat erroneously termed self diffusion, measurements in solut'ioii, except t,hose involving only solvent and tagged solvent molecules, are made in systems of more than two components. In ot'her words t,racer diffusion represents a limiting case of diffusion in systems of three or more components. A recent, publication6 has correlated tracer-diffusion data for N a + in aqueous KCI with diffusion coefficient measurements in t,he system H20-SaC1-KCl, with both solutes at, finite concentrations. Thus the tmcer diffusion work of this paper may be described as diffusion of hydrogen ion in the ternary system H~O-;1ICl-HCl (where JI = Na, Iadof :wid in the voliiin this solution was :inalyzed ronduc~timetrically accurate value of the concentration of the supporting elwS to fill the lowrr comtrolyte. The acid solution T ~ used pa.rtment of the diaphragm crsll and allowed to diffuse into the acid-free solution in the tipper compartmiwt with the usual experimental technique 4 After a diffusion period of :;bout 30 hours the experimt:nt, \vas eontlnded m d the contvnts of the cell analyzed for hydrogen ion. Brom thymol I~lue its used as indicator for all the titrations, from w1iic.h ic carbon diosidc WI~S c,xrludr:d by p:rssage of it,rogcn. Tlic hydrogen ion con(*(mtratioiww r e by tit,rxt,ing with b:tririm hydrositlr! soliltions been stand:irtlizrd k)y titrations with s:irnplw of : t n : ~ l > icnal ~ t reagvnt qualit,y hydrochloric :tc.itl wliorc~strcwgth n x s linown from contIiic~t~:~r~c~c~ In(~:tsiirf~iii(,Iits.The, titrations re ~n:ttlcin dup1ii~:tt~c with :t r ~ , i ~ r o ( ~ i i ( ~ i lof i i l0.1 i t ~";, or better. (10) See, for euamyli~,ref. 7 nliere numerous references to such deations are iecorded. (11) 8. R. de Groat, P. rlc X a z u r and J . Th. G. Ovcrbi*ek. J . C'iiem Phiis., 20, 1825 (1952). nl
L. A. WOOLF
482
Yol. 6-1-
TABLE I" 10sC(C)EE.FI(,IESTS _._______
L'
D
ICCl D,'D
0.1605 7.958 0.855 0.4806 7.934 ,832 1.(10% 7 . 7 2 9 ,830 1.016 7 . 6 7 5 , 8 2 5 ,778 1.712 7 , 2 4 4 2.883 6.-$?;3 .6!)Ll 3.Wl 5.936 ,638 Units: concentration C,
?
O F €lyuRoGis;y 1o.u IS AQLXUCSai^,^.^^^ 7
SaCI
-
D D..'D' -22.86 0.1090 8 . 0 1 1 0.860 - 9.705 ,5418 7.473 ,802 - 5.550 ,8124 7.053 ,757 - 5.015 1,442 6 . 5 5 2 ,704 - 2.332 2.271 5.726 ,615 0.1363 3.570 4.316 ,464 0.2637 4.545 3.460 ,372 ino1e:'I.; tracer-diffusioii coefficient D , k
C
+
i\ (' tliliitioris of the initial 0.1 JI acid stock soliithe 1 J I ticid-free solution were made t o give solutions for the Iowx conipartinent of the diaphragm cell which enahled the diffusion mmFwements to cover the initial wid cwnc.eritration range 0.01-0.1 ;If (or, averaging the acid concent,ration over hot,h compartments of t,lie cell, 0.005-0.05 J I ) . The zipp:irent "diffusion coefficients" I)' then w r e plottcd agitinst initial (lower compartment) iori :ind estrnpolatrd linearly to zero d u e . The limiting diffusion cocfficierit U thus t:ilirn to be the tracer-diffusion coefficicnt of 1 the 1 J I sodium chloridc solution. prorcdiircl KLS repen,rtd for t w h solution of the threc 1's YnC1, KCl :illti IiC'i, rt9spect portiilp. c~lectrol>.t Tht: s1.1pportiiig c>lt.:ntrolytc Polutions ~vcr(2prclxtrid from c4thu cndytiral rtxtgent, qiidity s:i,lt, as in the rase of t,he SnC'i :inti KC1 solutions, or froin LiC1 prepared bj- tlie method of Stokes and Stokes . l a Doubly distilled xmtw was L1sc.d in tlic preparation of all solutions.
Results The extrapolation of the ('diffusion coefficieiits" D' measured in each supporting electrolyte solution at' fini1.e acid concentrations c' moles./l. of hydrogen ioii to give the tracer coefficient D at c' = 0 can be represeiitecl by the equation D' = D kc'. Both D' and 1; are complicated fuiictions of t>hediffusion coefficieiit s mid therniodyiiainic ternis specifying each €i20-~HCl-AIClsystem. In Table I the D and k values are listed for the various supporting electrolyk coiiceiitrations, C. The values of D / D o are aLo given since they allow a, direct comparison of the present results with the tracer diffusion coefficients of other ioiis. Here the limiting tracer diffusion coefficient Do is defined b y t,he Nernst equation Do = (IIT,/F?)XOII+ where R, I' and F are t'ha: g ~ cmistaiit, s ahsolute temperature and the faraday, rcqxcti\dy. and A(" + is t'he limiting equixraleiit coiiductaiice of hydrogen ioii in water. l 3
+
Discussion The extrapolation procedure for obtaiiiiiig the tracer diffusion coefficients has been discussed previously.3 Exteiisioii of the theory of diffusion in t'hc diaphragm cell to include multicomponent diffusion with iiiteractiiig solute flows enables a mathematical coiifirmation of the method.I4 It is hoped that the details n-ill he presented in a future publication. Some of the theory, together with approximate values of one croFs diffusion coefficieiit tem ~yater-pentaerythritol-sodium chloeeii given by Kelly and Stokes.15 I-iifortuiiately the diaphragm cell method caiiliw :ind 11. f1. Ftolws, Tills ,JoL-Rs.\L, 60, 217 (19.iIi). and Stukcs. " E l e c t w l j - t e Solutions," Butteri\-orth's Ycientifil, Publications, E:nnland, 1'353. 11. 434. , I'Ii,I>, Tlic~sis,Unix..crsity of New E n ~ l a n d A. I mi(13) f ' r i n t c ro:iiiiiuiiicati~,n, t o be yublialied.
k
CHLORIDE$ i i L r r I o s s
. i 25' ~
-
LiCl--
7
D
C
D ,D
h
0.08917 7.789 0.837 --52.65 ,4240 7 . 2 4 4 ,775 - 11.46 1.010 6.283 ,674 - 1.611 1.311 5,606 ,602 0.1453 1.586 5.298 .56Y 2.519 1.687 2.974 3.662 ,393 5,555 2,668 4.590 2.109 ,227 6.682 ern.2/sec. X 105; slope k , cin.Vl. ! m h :set. X 10'.
-36.38 - 8.467 - 4.701 - 1.859 - 0.3109
+
+
not be used for diffusion measurements at electrolyte conceiitrat'ioiis much less t'haii 0.1 J14; L e . , it cannot be used in the range n-licre the Onsager limiting law16 is applicable. Therefore, in the absence of theoretical descriptions of tracer diffusion a t the supporting electrolytc. conceiit'rations of this work, we are necessarily limited to comparison of our tracer diffusion results with those for other ions in solutions of the same supporting electrolytes, aiid to intercomparisons bet'n-een the results ohtaiiied in the three supporting elcctrolytes. This procedure illuutrates certain features of the concentration dependence of the hydrogeii ioii tracer diffusion. Previous publications17 have sliowii the sinii1arit)y of the tracer diffusion of the catioiis Sa+, Rb+ aiid Cs+, and the anions C Y , Br- and I-, respectively, in the same support,iiigelectrolyte solutions. I n Fig. 1 the results for hydrogen ion are compared with corresponding values for sodium iol117-20 represeiitiiig a typical u:iirnlent cation and iodide i 0 1 1 , ~ ,as ~ ~SL typical univalent anion. ,1 comparison, using the Onsager slopes,l 6 defined here by D/DO
=
1 - l;lv/(r
where C is the coiiceiitratioii of the supporting elect'rolyte in moles/l., shows that' t'he predicted values of D,/Do for hydrogen ioii at 0.1 -11 agree to about 2% 71-ith experiment', which is bett'er than the agreement observed wit'h either. of the other ions. However, the Onsager liinitiiig laTy has, even at, 0.1 11, been used for a coiiceiit'ration at which it should not theoretically apply. Therefore use of it, for further prcdictioiis at, even higher upport,ing electrolyte coriceiitrations cannot be justified, and one caii oiily observe that the disparity betmen the Onsager slope and t'he experimental curve becomes increasinglj- larger for hydrogen ion with iiicrease in C' than do t'he corresponding cases for sodium and iodide ions. Alteriiatively, if we ignore the coinpari.oii using t'he Oiisager slopes, we may note that, tlie hydrogeii ioii tracer diffusion varies ~iiorenith t h change i n supporting electrolyte coiiceiitratioii than does the diffusioii of either of the other ion?. The prcdomiiiating inflneiiccu 0 1 1 t r w e r diffusion for concentrat,ion ranges similar to those of this work haye heeii nttrilwted to the qolution iiiacroI,. Onsnper. . i n n . S.1'. A c a d . Sci., 46, 211, (1943). (17) K . hlills. TIIISJ O C R X ~61, L . 1 0 3 1 (1957): 63, 1873 (1959) (18) R.RIills and L. .1.IVnulf, ibid., 63, 2068 flQ.j
