334
Langmuir 1992,8, 334-335
Notes Degree of Dissociation of Counterion i n K+-Montmorillonite by the Diffusion Potential
concentration; (c) an increasing fraction of the counterions in betonite are immobilized.3 Supposedly surface solution is feasible
M. Tschapek
tKt = cK+/(cKt
+ CCI-) >> uKt/(uK++ uCl-) tC1- = cCl-/(cCl+ CK+) >> uCI-/(uCI-+ UKt)
National Research Council, CONICET, Serrano 669, 1414 Buenos Aires, Argentina
Thus the transference numbers of K+ and C1- in negatively charged material (K+ montmorillonite) should depend principally on their concentrations
Received June 6,1991. In Final Form: August 7, 1991
Miller and Low1have recently asserted that only a small percentage of the counterions of montmorillonite are in the diffuse Gouy layer. A similar idea on the distribution of counterions in clays and soils between the Stern and the Gouy layers has also been stated many years ago by other authors (ref 2). I t is true that our knowledge of soil properties (water, exchange) and plant growth in soil indicate that only few counterions are in soil water (solution). If all counterions were in soil solution (at moisture content < field capacity), then ita osmotic pressure would be -50 atm, whereas the real osmotic pressure of Onormal" soils solutions =1-2 atm. The analogous conclusion, that only a few of the counterions are in the Gouy layer, can also be reached from the study of the transference numbers of counterions. The transference number (the fraction of carried current) depends on the concentration C, mobility U , and valence z: in the bulk solution C+ = C-and z+ = z-, therefore the transference number t depends only on the mobilities
1 1 t-=
where U+ and U- are the mobilities of cation and anion, respectively. Equation 2 results in enhanced concentrations of cations and decreased concentrations of anions near the surface (2)
where C*and COare the concentrations of ions within and beyond the electric double layer (edl) and e, $, z , k, and T are their common meanings. As a consequence, the fraction of cations is greater than 0.5 and that of anions is less than 0.5, as shown by eq 3 1 L C,/(C,
+ Cco)L 0.5
0.5 1 C,,J(Cco
(5)
0.5 L tcl- = Ccl- + (Ccl- + CK+) 1 0 tK* is calculable from the diffusion potential measurementa. The transference number of counterion K+ in a K+-montmorillonite (A = 7 X lo6 cm2 g-l and Z = 1 mequiv gl)at different thickness of M KCl solution is studied by measurement of the diffusion potential. The diffusion cell used is shown 2 x lo3 KCI
salt
-bridge
(G)
K* montmorillonite -in lo3 M KCi
1x
KCI
M
salt
bridge*
(Cl)
The diffusion potential is measured with a Model 616 Keithley electrometer, which has an input resistance >2 X 1014 fl and a sensitivity A. From the Henderson equation: it follows that for diffusion potential
t+= 0.5 4- o.5E/E0 (7) where EOis the maximal value of E at t+ = 1. It seems that the present method of determination of transference number, based on the E measurement in the diffusion cell, is sufficiently sensible.s16 For electrolyte solutions (HC1, NaC1, KC1, LiC1) the calculated values of t+ coincide with tabulated values up to third sign.' The K+montmorillonite samples were equilibrated with M KC1 solution. In equilibrium the product of counter- and co-ion concentrations (activities) should be equal at any distance from surface (Donnan equilibrium)
(3)
+ C,) 1 0
where C, and C, are the concentrations of counter- and co-ions, respectively. Nothing is known of the mobilities of the ions of the edl, counter- and co-ions. But the following facts should be mentioned: (a) eqs 2 and 3 show that in the surface solution CK+>> Ca-; (b) in the bulk solution UK+= UCI-(=0.50), being independent of the (1) Miller, S. E.; Low, P. F. Langmuir 1990, 6, 572. (2) Mattaon, S. Soil Sci. 1929,28, 179.
1 L tK+ = cK+/(cK+ + CCI-) 2 0.5
E = (2t+ - l)RT/F In C2/C1 (6) where t+ is the transference number of cation and R, T, and F are their common meanings
u-/(u-+ v')LO
C* = C, exp(re$z/kT)
(4)
where hl,h2,and h, are the distances from charged surface. From (8) it follows that at any h (CK*CC1-)1'2 = c,
(9)
where COis the concentration of solution in equilibrium. (3) Cremenr, A.; Laudelout, H. S.S.S. Am. Pr. 1966,30,570. (4) Henderson, P. 2.Phys.Chem. 1907,69, 168. ( 5 ) Tschapek, M.; Grazan, A. M. Clays Clay Miner. 1973,21, 97. (6) Tschapek, M.; Torres Sanchez, R. M.; Wasowski,C. ColloidPolym. Sci. 1976. 254. -,516. ---
-.
~
(7) Wasowski, C.; Torres Sanchez, R. M.; Tschapek, M. Ann. Quim. 1978, 83, 433.
0 7 4 3 - 7 ~ 6 3 / 9 2 / 2 4 0 ~ - 0 3 3 ~ ~0~ 3 . 0001992 / American Chemical Society
Langmuir, Vol. 8, No. 1, 1992 335
Notes
\. .
O.1/ 0.6
I
IO
7
1. t‘k*
1. -e‘
20
I
1’
30
+
h nm Figure 1. Transference numbers t’K+ + t”Kt as a function of h: h is the thickness of solution between particles in nm; t ’ ~is the apparent transference number (ifall counterionswere in solution); tffK+is the real transference number (from diffusion potential).
I
-u’ \ +
’ Y
‘u
h nm Figure 3. Ratios C’’K+/C’K+ and C”K+/C”CI-as a function of h. h is the thickness of solution between particles in nm; C’K+= ZJhA.
-
I L
I
10
20
30
h nm Figure 2. Real concentrations of the counterion, C”K+,and the co-ion, C’’CI-,as a function of h. h is the thickness of solution between particles in nm.
In Figure 1 are presented two t ~ +(a) : t ’ ~ +calculated , by supposing that all counterions are in solution, that is the Gouy diffuse layer; (b) t ” ~ calculated + from the diffusion potential measurement t’K+
C’cl- = L-1
mol
t”K + 0.5 + O.sE/Eo Because CK+>> C’CI-,t ’ ~ + 1, whereas t ” ~ calculated + from diffusion potential measurements is always > UK+/(UK++ UcI-> Virtually the t ~in+the surface solution is definable by the concentration only tK+ = CK+/(CK++ Cc1-1 Knowledge oft^+ and CO(concentration of the solution in equilibrium) permit calculation of the real concentrations of the counter- and co-ions in the surface solution
c K + = CO[tK+/(l- tK+)11/2 The degree of the dissociation is definable by the ratio CK+/CK+, where the numerator and denominator are the real and the total concentrations, respectively. The ions in the Stern layer are immobile and are not involved in the transfer of current. Registry No. K, 7440-09-7; montmorillonite, 1318-93-0.
