COMMUNICATION TO THE EDITOR
1598
THE
Vol. 64
I N THE Go-60 RADIOLYSIS OF TABLE I AQCEOUS xal\;03 SOLUTIONS IS CERICSOLUTIOXS 0.8 5 THEGo= OBSERVED NaNOa BY H. A. MAHLMAN added,
(:OH
Oak Ridge National Laboratory,1 Chemistry Division, Oak: Ridge, Tennessee Received J u l y 11, 1960
In the radiiztion rhemi~tryof aqueous solutions an initial decomposition of solvent into H atoms and OH radicals is assumed. The detected molecular products Hz and HzOz result, from the reaction of like initial products while the reaction of unlike radials regenerates water. The yields are calculated from the total energy absorbed by the solution relative to the ferrous dosimeter assuiiiing the 100 e.v. yield of ferric ions to be 15.60. The reduction of Ce+4 in an 0.8 I\- HzS04 solution has been determined to be equal to 2G(azo,) -t GH - GOH [0.45 - G(H2)]. This yield is deduced from the reduction of ceric ion by H202 and €1 at'oms, the oxidation of cerous ion by OH2 and the lowering of the G(Hz) by ceric ion.3 When thallous ion is present the cerous yield beGH GOH [0.45 - G(Hz)]. comes 2G(HzOz) The thailous ion effectively converts t'he oxidizing OH radical into a redncta~nt4
M 0.1 .3 .5 c
. i
1.0 2.0 3.0 4.0 5.0
IN
HzSOa
G(Ce+*)a T1+
G(Ce+')b
aG(Ce+s)c
GOH
8.93 10.15 10.83 11.18 11.75 12.24 12.49 12.89 13.05
3.33 4.37 5.03 5.51 5.90 6.58 6.86 7.09 7.37
5.60 5.78 5.80 5.67 5.85 5.66 5.63 5.80 5.68
2.80 2.89 2.90 2.84 2.92 2.83 2.82 2.90 2.81
Ce+4-acid-NaS03-T1 (Ce+3) = 2G OH.
+.
Av. 2 . 8 6 Ce +4-acid-SaS03. AG-
+
irradiated with 10-3 Jf T1+ present. In Table I are presented the cerous yields obtained from Ce+4-acid-NaN03 solutions and Ce+4-acid-n'aNO3-T1+ solutions, as calculated from the total energy absorbed by the solution. This work confirms and extends previous work5 10-fold, from 0.5 t o 5.0 M NaN03. The calculated GOH is constant over the entire NaKO3 conceiitration from 0.1 to 5.0 ;If and equal to 2.86. This average TIC 'i. OH +T1+++ OH(1 1 GOH is exactly the same average o b s e r ~ e din~ the T l + ++ Ce+4 -+ Ce'3 + Tl+3 (2) range 0.02 t o 0.5 ik! NaKO3. and the Idifference in G(Cei3) from the solutions is A constant GOH indicates that the total energy equal to 2GoH. The "direct, action effect"I upon absorbed by the solution is effective in decompos?;aT\'03 should manifest itself by increasing the ing solvent. For example in a 5.0 ; I I NaKOa G(Ce+3)the same amount in both the CeL4-acid- solution the water absorbs only i 8 % of the total i?;aNOs and Ce+4-acid-Nan'03-T1+ systems. energy absorbed by the solution. If only this Therefore, t'he difference between the two ceric energy decomposed the water solvent. the expected systems should cont'iiiue to monit'or ~ G o H . OH radical yields would be 0.78 of that obserred. The solutions irradiated were 0.8 N HzS04, Possible reduction reactions of KO3- by OH 0.004 M Ce+4 and cont'ained t'he desired SaKOa radical iii 1.0 M , HN03 have been reported.6 concentration. The identical solutions also were All of these reactions yield products that reduce Ce+4 (ie., HOz,NOz- and HzOz)and would predict (1) Operated for the U.S. .4tomic Energy Commission by t h e Union a decreasing GO=. The constant GOH observed Carbide Corporation. ( 2 ) A. 0. Allen, Radiation Research, 1, 87 (1954). indicates that the OH radical does not react with (3) H. A. Mahlm;m, J . Am. Chem. Soc., 81, 3203 (1959). the nitrate ion. (4) T. J. iSworski. Radiation Research, 4, 483 (1956).
+
+
+
(6) G. E Challenger and B. J. Masters, ibrd., 7 7 , 1063 (1955)
( 5 ) T. J . i3worski. J . Am. Chem. SOC.,77, 4689 (1955).
COMMUNICATION TO THE EDITOR CERTAIN TR-INSPORT PROPERTIES OF BINARY ELECTROLYTE SOLUTIONS AND THEIR RELATIOK TO THE THERiLIODYNAA9IC8 O F IRREVERSIBLE PROCESSES Sir: J'or
:i iiiigle
1)iii;try ~ I w t r o l y t ediisohwl i l l
J, = -
2
L,, (G bPJ -k
2 3
2)
(1)
,=1 ,
for the f l o v J1mid J , of catioii aiid aiiioii Iiascd on solveut-fixed referelice frainc. it c:iii ~ 1 i o i v n that 2
:til u t i -
ionized solvent (Itkt1 water). the wctor tralispoit properties, i.r ., ciiffusioii, cwntluctance, and traiihference, call be expressed in terms of the therniodynamics of irieversible processes by nieans of the Onsager coefficieiits. Thus using the defining equations for these properties together with the expressioiil (in one dimension) (1) S. R. DrGroot "Tlir,rmodynamirs of Iii-px Prsiblr Frocev.r.i." lutarsririioe P'ublislirrs, Inc., ,Yew k urk, N. Y . , IH.51.
(3)
(2) R. W. T'aity, J . C h ~ m Z'livs., . 30, 682 (1959).has given ?xprossiou fur 1:. h , and .If in terms of the inveicr- clei!tii,tion uf ( I ) , I . c . , X, YKi,J,.
-
COMMUNICATION TO THE EDITOR
Oct., 1960
1599
where L i j denote phenomenological coefficients with L12 = L21,p i the chemical potential, zi the signed valence, 5 the faraday, C#J the electrical potential, 2 the distance, ti the transference number ( t l t2 = l), X the specific conductance, A the equivalent conductance, c the molarity, Do the solvent fixed diffusion coefficient, R the gas constant, T the temperature, y the molarity activity coefficient, r1 and r2 the ion stoichiometric coefficient, and r = r1 rp. M is defined by equation 4. Conversely, it can be shown from equations 2-4 that
+ + GI
a3
05
07
09
c
II
13
15
1.7
1%
Fig. 1.
Some preliminary values of Llz/c and L / I , where I is the ionic strength, have been calculated from experimental data at 25” for 1-1, 2-1, and 3-1 electrolytes and are plotted in Fig. 1; Llz/I seems to show a common limiting slope. Calculations are in progress for a number of other electrolytes. These results, comparisons with the Onrwlger-Fuoss expression, and the derivations will be the subject of a subsequent paper. Ternary systems will also be considered. The Ll, directly represents the interionic interaction, and hence is extremely important. Thus the law of independent ion mobilities at infinite dilution results from LlZbeing zero there. However, as the concentration increases, Llz increases rapidly at first and then more slowly. As it is of opposite sign from Lll and LtZ,it contributes heavily to the rapid decline of the conductance. For a second example, the empirical extension of the Nernst-Hartley limiting diffusion law4 is known to be in serious error6 even in solutions as dilute as 0.01 molar.4 However consideration of equation 5 with i = 1, j = 2 readily shows that (3) L. Onaager and R. M. Fuoss, J . Phbs. Chem., 36, 2689 (1932,. (4) R. A. Robinqon and R. H. Stokes, “Electiolyte Bolutions,” 2nd Ed., Academic Press, Inc., New York, N. Y., 1959, p. 288290. (5) We also note that since Do is the solsent-$sed diffusion coefcCI In $I/&) not to ficient, care must be taken in calculations of D / ( 1 use the usually reported coefficients Dv, as they are measured on a volume-fixed reference frame. Although the same at infinite dilution, Do and Dv &verge rapidly in concentrated solutions (c.o., see R. P. Wendt and L. J. Gosting, J . Phgs. Chem., 63, 1287 (1959)). The calculati-n of LN From D” requires knowledge of partial molal volumes, but lack of these data IS not aeiious aa It can be shown that Do/(l c b In g/&) = Dv/(l mb In y / b m ) . where m is the molality and y t h e molality activity coefficient.
+
+
+
difference between the right- and left-hand sides of equation 6 is
c
lOOORTr (1
+ c a In y/&)
r172
L12
IC
(7)
ie., the failure of equation 5 is due precisely to the existence of a non-zero Llz. It seems clear therefore that any serious theory of diffusion or conductance must focus its attention on the calculation of Liz. The thermodynamics of irreversible processes also yields an interesting conclusion on the possible influence of viscosity on the above properties. In the general case there is an additional entropy production term involving viscous forces and flowse besides those involving the vector flows and forces of equation 1. However according to Curie’s theoremla vector flows cannot result from tensor forces and similarly for tensor flows and vector forces. Since the forces of equation 1 are vectors (1st rank tensors) and the viscous force is a 2nd rank tensor, there can be no term involving viscosity in the linear laws (equation 1) for the vector J i . Consequently since the vector properties are completely determined by equations 1, there cannot be the direct connection between diffusion, etc., and viscosity, as there was between D, t, and A. Thus it is not surprising to find the quantitative failure of Walden’s rule and of other transport property “correction” factors involving the bulk viscosity. UNIVERSITY OF CALIFORNIA
G. MILLER LAWRENCE RADIATION LABORATORYDONALD LIVERMORE, CALIFORNIA RECEIVED JULY25, 1960 (6) Reference 1, p p . 120-122.
