COMMUNICATIONS TO THE EDITOR
1169
and mg are the adjusted concentration of the sodium ions and the concentration of the potassium ions, respectively, in moles per kilogram of HzO. Through a recently Published review Kaimakov and Varshavskaya~2we have now become aware that Hartley,3 when introducing the adjusted indicator method in 1934, had already derived this equation. This fact seems to have been overlooked in the literature that has appeared since then. (2) E. A. Kaimakov and N. L. Varshavskaya, Russ. Chem. Rev., 3 5 , 89 (1966). (3) G.8.Hartley, Trans. Faraday SOC., 30, 648 (1934).
KONINHLIJKE/SHELL EXPLORATTE EN L. J. M. SMITS PRODUICTIE' LABORATORIUM E. DUYvs RIJSWIJK, THENETHERLANDS RECEIVED JANUARY12, 1966 SOCIETY ACCEPTED AND TRANSMITTED BY THEFARLDAY DECEMBER 6. 1966
CENa+
+
= (c
caCl- =
CR-)e-e'/kT
(2)
Cee*/kT
(3)
where e is the elementary charge and $ is the surface potential inclusive of (negative) sign. Ultimately this leads to
-
dCR
-dr
= rR--kTm'
(4)
CR -
with
m'=1+
1
+ z(1 -
1
(5)
e2eJ.'kT)
and 2 = c / c R - . However, Chattoraj's statement is incorrect. In a diffuse double layer, surface excesses of ionic species cannot be obtained by application of the Boltzmann equation in one plane of- adsorption but should be calculated via integration over the whole double layer. According to the Gouy theory, the ratio of the surface excesses is given by
Comments on the Paper, "Gibbs Equation for the Adsorption of Organic Ions in Presence and
rcl- -
Absence of Neutral Salts," by D. K. Chattoraj
rNa+
Sir: It is now well established that in the interpretation of surface and interfacial tensions at air-water and oil-water interfaces the Gibbs equation should be used in the "one kT" form if neutral salts are present in excess to the surface active electrolyte, and in the "two kT" form if neutral salts are ab5ent.l In a recent paper in this journal, Chattoraj2 investigated how the kT coefficient varies between 1 and 2 in the intermediate salt concentration range. His basic equation (eq 8), in a slightly different notation, reads -dr
dCR = rR-----kT CR-
[
1
y is the interfacial tension;
+
1
l--
I"
(6)
-
After solving the integrals, eq 6.reads3
rcl- -rNa+
1
c
c
+
cR-
-eewkT -1
(7)
is the potential of the outer Stern plane, which also should replace $ in eq 5. Substituting eq 7 into eq 1 gives
$8
dCR
-
(8)
CR -
with
(l)
and rcl- are the surface excesses of surface-active anions, sodium ions, and chloride ions, respectively. It is assumed that the Na+ ion is common to both anions present; cR- is the concentration of the surface-active anion and c is the NaCl concentration, SO that cNa+ = c + cR-. k is the Boltamann constant and T is the absolute temperature. Chattoraj states that the ratio of the surface excesses, r C l - / r N a + , can be replaced by the ratio of the surface concentrations C'CI-/C'N~ + with rR-, h a + ,
CR-SOI
(e-''./''
- d r =Tkm-"--Rr-
rcl-c+ CR-
rNa+
+
- ee""/kT)dz
l ( 1
C
mr' = 1
+
.
1 1-
ee!bg/2kT
1
(9)
+ '[l - e-e+g/2kT - 1
In Figure 1, m' and mr' at 20" are compared for two value5 of $8. Although it is realized that $6 = - 5 mv is an unrealistically low potential, the correspond(1) See, e.p., J. T. Davies and E. K. Rideal, "Interfacial Phenomena.*#Academic press Inc.. New Yo& N.y,. 1981. . - 198, (2) D. K. Chattoraj, J . Phys. Chem., 70, 2687 (1966). (3) D.C.Grahame, Chem. Rev., 41, 481 (1947).
,
Volume 71, Number 4
March 1967
COMMUNICATIONS TO THE EDITOR
1170
higher than m'. At potentials more negative than $a = -30 mv, m' and m" both approach the parameter m as given in eq 5 of Chattoraj's paper m=l+-
10
30
20
50
X
Figure 1. m' and m'' w a function of salt ratio x: full lines, +a = -5 mv; broken lines, $6 = -30 mv.
ing values are given by way of illustration. $a = -30 mv also is a rather low potential but it may be encountered under certain conditions, and therefore it is worthwhile to note that even then m" is substantially
The Journal of Phyaieal Chemistry
1
l+a:
and line I of Chattoraj's Figure 1 applies. When specific adsorption of Na+ ions in the Stern layer occurs, the factor 1 - ( r c l - / I ' N s + ) in eq 1 approaches unity at lower z values than in the pure diffuse case. Under these circumstances the kT coefficient will be between m" and m. In conclusion, we can say that the kT coefficient in the Gibbs equation approaches unity only at high values of z, the deviation from unity growing progressively more than 1% when z < 100. B. H. BIJSTERBOSCH LABORATORY FOR PHYSICAL AND H . J . VAN DEN HUL COLLOID CHEMISTRY AQRICULTURAL UNIVERSITY WAQENINQEN, THENETHERLANDS RECEIVED JANUARY30, 1967
