J . Phys. Chem. 1988, 92, 6368-6373
6368
Analysis of Thermodynamic Data for the Adsorption of Organic Molecules at Polarizable Interfaces with Consideration of Medium Effects W. Ronald Fawcett,* Gilles Y. Champagne, Scott Komo, Department of Chemistry, University of California, Davis, California 9561 6
and Artur J. Motheo Instituto de Fisica e Quimica de Sao Carlos, USP, Sao Carlos, SP, 13,560, Brazil (Received: February 26, 1988; In Final Form: May 3, 1988)
The adsorption of acetamide and N,N-dimethylacetamide has been studied at the mercury/solution interface from aqueous solutions containing an electrolyte at constant concentration. The change in electrolyteactivity with organic solute concentration was monitored with specific ion electrodes. It was found that electrolyte activity increased markedly with organic solute concentration, the change in the activity of the anion being greater than that of the cation. A new method of analyzing thermodynamic data for these systems is proposed that involves estimating the function Y- = y + uE- + r+p,, where y is the surface tension, u the electrode charge density, E- the electrode potential measured with respect to an anionic reference electrode, r+the surface excess of cations, and pLsthe chemical potential of the salt. Accordingly, the first derivative of Y- with respect to the chemical potential of the organic solute pA for constant u and r+gives the relative organic surface excess PA. The present method is compared with methods used previously, and the extrathermodynamic assumptions involved in estimating +'I are discussed.
Thermodynamic Analysis
Introduction
The adsorption of organic molecules at polarizable electrodes such as mercury has been traditionally carried out by using electrolyte solutions of constant concentration together with a reference electrode of constant potential.' This procedure was strongly criticized by Mohilner and Nakodomari,2 who pointed out that the electrolyte activity is expected to increase at constant concentration when an organic compound is added to an aqueous solution. In addition, the change in salt activity results in the measured potential of the polarizable electrode not having thermodynamic significance. A third effect is that the activity coefficient of the organic compound with respect to Henry's law is not constant as assumed in previous work' but varies with organic compound concentration when the latter is high.2 Mohilner and Nakodomari2 recommended that the experiments be carried out at constant electrolyte activity with a thermodynamically valid reference electrode and that the activity of the organic solute be measured as a function of its concentration. The first requirement generally adds considerable tedium to carrying out these experiments since a recipe describing the electrolyte concentration as a function of organic solute concentration must be obtained so that interfacial thermodynamic data may be obtained at constant electrolyte a ~ t i v i t y . ~ - ~ The purpose of the present paper is to describe a simple method by which medium effects may be treated when data are obtained at constant electrolyte concentration. The analysis requires that the potential scale, which may originally involve a constant reference electrode, be corrected to a thermodynamically significant scale by using a specific ion electrode responding to one of the ions in the electrolyte solution. The results of the analysis are illustrated with data for the adsorption of acetamide and N,Ndimethylacetamide at mercury from aqueous solutions. The present analysis is also compared with that of de Battisti and T r a ~ a t t i ,who ~ , ~ have argued with the net effect of the change in salt activity with concentration on derived surface excesses is negligible when a constant reference electrode is used. ( I ) Damaskin, B. B.; Petrii, 0. A,; Batrakov, V . V. Adsorption of Organic Compounds on Electrodes; Plenum: New York, London, 197 1. ( 2 ) Mohilner, D. M.; Nakadomari, H. J . Electroanul. Ckem. 1975, 65, 843. ( 3 ) Nakodomari, H.; Mohilner, D. M.; Mohilner, P. R. J . Pkys. Ckem. 1976, 80, 1761. (4) Mohilner, D. M.: Kakiuchi, T.; Taraszewska, J . Can. J . Ckem. 1981, 59, 1872. ( 5 ) de Battisti, A.; Trasatti, S . J . Electroonul. Ckem. 1974, 54, I . (6) AM-el-Nabey, B. A.; de Battisti, A,; Trasatti, S . J . Electround. Ckem. 1974, 56, 101.
0022-3654/88/2092-6368$01.50/0
Consider the system HglMX
(C
MI, A
(X
M), H2OIHgJ21Hg
(1)
where MX is a 1:l electrolyte at constant concentration c M, whose ions adsorb negligibly at the polarizable mercury electrode, A is the organic substance whose concentration x M is varied, and Hg2X2 is an insoluble mercurous salt involved in the reference electrode which responds to the activity of X in solution.' The Gibbs adsorption isotherm (GAI) for this system may be written -dy = a dE- + r+dps + FA dpA (2) where y is the interfacial tension, u is the electrode charge density, E- is the potential of the polarizable electrode measured with respect to the reference electrode, F+ and FA are the relative surface excesses of the cation and organic solute, respectively, and ps and pAare the chemical potentials of the electrolyte and organic solute, respectively. It follows that =
-(d?/aFA)E.,rr,
(3)
Le., that the relative organic surface excess can be obtained from interfacial tension data measured for varying organic activity at constant potential and constant electrolyte activity. This is exactly the procedure used by Mohilner et aL2s3 It is clear that data obtained by using cell (1) cannot be analyzed by using eq 3 because of the variation in g, with pA. One may avoid the requirement of constant electrolyte activity by defining a new function Y-, where Y- =
+ a ~ +- r+ps
(4)
Taking the total derivative of Y- and substituting in eq 2, one obtains the equation -dY- = -E- d c - p s d r + + r A dpA (5) Now, the relative surface excess of the organic substance is given by r.4 = -(aY-/awA)o,r+ (6) and is found from the change in interfacial tension with organic activity at constant electrode charge density and relative surface ( 7 ) In fact, the electrolyte of choice would be N a F or KF, but H&Fz is not stable in water and cannot be used to construct a reference electrode reversible to the F ion. On the other hand, when CI- or Br- salts are used, the reference electrode is stable but the anions adsorb strongly on mercury. However, although the cell is a fictitious one, it can be used to illustrate the principles of the analysis proposed.
0 1988 American Chemical Society
Adsorption at Polarizable Interfaces
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6369
excess of the cation. According to the Gouy-Chapman theory of the diffuse layer in the absence of ionic adsorption, r+is given by8
r+= (A/F)[exP(-f$d/2) - 11
(7)
where $d is the potential drop across the diffuse layer, A = ( 2 ~ R T t t ~ c ) t' /being ~ , the dielectric constant of the solvent and to the permittivity of free space, a n d f = FIRT. For 1:l electrolytes
It follows that when the electrolyte concentration c and the electrode charge density are constant, r+is also constant provided at the dielectric constant of the medium does not vary with organic solute concentration and ionic adsorption is absent. Thus, as pointed out earlier by de Battisti and T r a ~ a t t idetermination ,~ of relative surface excesses at constant charge density also implies that I'+ is held constant, at least within the context of the Gouy-Chapman model. This point is examined in more detail below. To calculate Y-, one must have values of u, E-, r+,and p,. The electrode charge density a is calculated in the usual way from capacity or interfacial tension data obtained at constant solution composition. The changes in p, with solution composition are estimated by measuring the mean ionic activity coefficient of the electrolyte, and r+is estimated by the Gouy-Chapman theory. Thus, Y-may be defined as Y- = y
+ aE- + 2 r + R T In (y,c)
(9)
where y* is the mean ionic activity coefficient for the electrolyte, and the constant associated with the standard state of the electrolyte is taken to be zero. Since r+is calculated from a model, the values of Y- are based on an extrathermodynamic assumption. The effect of this assumption on derived values of r A is discussed further below. By defining a function
x = Y + r+p, the GAI may be written -dX = 0 dE-
(10)
- /.lS d r + + I'A dpA
(11)
so that rA
pA)E-,r+
=
(12)
However, in general r+is not constant when E- is constant, so that the conditions necessary to determine at constant E- and +'I are not easily met. It follows that analysis of thermodynamic data obtained at constant electrolyte concentration with consideration of medium effects are preferably carried out at constant electrode charge density. The cell traditionally used to study the adsorption of organic molecules at mercury is HglMX (C M), A
(X
M), H2O)ISCE
(13)
where the reference electrode is a constant one such as the saturated calomel system (SCE). The potential scale obtained, E,, is related to the thermodynamic scale by the equation E- = E, (RT/F) In a, constant (14)
+
+
where any changes in liquid junction potential with solution composition are assumed to be negligible. The GAI for cell (13) may then be written as -dy = u dE, (aRT/F) d In yx 2 r + R T d In ( 7 ~ 7 ~ r )A dpA (15) where yMand yx are the individual ionic activity coefficients for
+
+
+
(8) Delahay, P. Double Layer and Electrode Kinetics; Wiley-Interscience: New York, 1965; Chapter 3.
ions M and X, respectively. Recognizing that u = F ( r - - r+), eq 15 becomes -dy = CT dE, + r + R T d ln 7~ r R T d In yx dpA (16) de Battisti and Trasatti5 argued that y Mand yx should be approximately equal to the mean value ya and wrote eq 16 as follows:
+
-dy =
u
dE, 4-
+
(r++ r - ) R T d
In 7, +
r A
dpA
(17)
Accordingly, medium effects are absent only at the point of zero charge (pzc), where r++ r- = 0. They become more important as the potential moves in either direction from the pzc, the magnitude of the effect depending on the change in In y+ with organic activity. Since organic adsorption is often studied in the presence of sulfate salts,' it is useful to examine the corresponding relationships for 1:2 electrolytes. For the cell HglMzS04
(C
M),A
M), HzO(Hg2SO4IHg
(X
(18)
the GAI is
+
+
-dy = u dE- ( r + / 2 ) dp, dpA (19) where E- is now the potential of the polarizable electrode measured with respect to the sulfate reference electrode. The appropriate definition of the function Y- is thus
+
+
Y- = u ~ -r + 4 2 or, in correspondence with eq 9
+ uE-+ Y2r+RTIn (y,c) From the Gouy-Chapman theory, r+is given by9 r+= (A/F)[(l + 2 exp(-f4d))1/2 - 3]iZ] Y- = y
(20) (21) (22)
and 4d is found by solving the equation
+
e ~ p ( 2 f 4 ~ ) 2 exp(-f4d) = ( u 2 / A 2 )+ 3
(23)
Application of these equations requires that specific adsorption of the sulfate anion be negligible, a condition that is met for low electrolyte concentrations at or negative of the pzc.'O It is obvious from the above that medium effects are somewhat more complex when nonsymmetrical electrolytes are used. If cell (1 8) is replaced with one with a constant reference electrode such as HglM2S04
(C
MI, A
the GAI becomes -dy = udE, r + R T d In
+
yM
(X
MI, HzOIISCE
(24)
+ r-RT d In yso42- + r A dpA
(25) where the potential of the polarizable electrode with respect to the constant reference electrode; E, is related to the thermodynamic potential scale E- by the equation E.. = E ,
+ (RT/2F)
In uSo42-+ constant
(26)
Since single ion activity coefficients are not directly available from experiment, evaluation of the medium effects in cell (24) can be made only after a series of extrathermodynamic assumptions. Experimental Section
Differential capacity against potential data were obtained for two systems, namely, the adsorption of acetamide (AC) from aqueous solutions of 0.25 M N a F using cell (13), and the adsorption of N,N-dimethylacetamide (DMAC) from aqueous solutions of 0.15 M Na2S04using cell (24). The differential capacity was measured on a ac bridge modified with operational amplifiers to provide potentiostatic control of the mercury electrode." The pzc was determined against the same reference electrode by using a streaming mercury electrode. The cell and configuration of the counterelectrode and reference electrode were similar to that described previously." The experiments were carried out at 25.0 (9) Grahame, D. C. J . Chem. Phys. 1953, 21, 1054. (10) Payne, R. J . Electroanal. Chem. 1975, 60,183. (11) Borkowska, Z.; Fawcett, W. R. Can. J . Chem. 1981, 59, 710.
6370
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
TABLE I: Mean Ionic Activity Coefficients for 0.25 M NaF in Water-Acetamide Solutions Containing Varying Concentrations of Acetamide at 25 OC A C concn mean ionic AC concn tnean ionic cAc, M act. coeff, y* cAC, M act. coeff, yi __ 0 0.69 1 0.4 0.730 0.063 0.696 0.63 0.753 0.1 0.701 1 .oo 0.790 0.16
0.706
1.60
0.858
0.25
0.714
2.53
0.971
f 0.1 “ C in the case of AC and at 35.0 f 0.1 OC in the case of DMAC. A fluoride ion specific electrode (Orion Model 94-09) was used to convert the E, potential scale of cell (1 3) to an E- scale (cell (1)) by measuring the potential difference between the fluoride electrode and the S C E in each of the AC solutions studied. At the same time, the potential difference between a sodium ion specific electrode (Orion Model 97-1 1) and the fluoride electrode was measured in the same solutions so that the change in mean activity of N a F with AC concentration could be estimated. In the case of the DMAC study, a similar procedure was followed. The potential of a mercury/mercurous sulfate electrode was measured with respect to the SCE in each of the DMAC solutions so that the original E, values could be converted to the E- scale (cell ( 1 8)). Simultaneously, the potential difference between the sodium ion specific electrode and the sulfate electrode was measured in the same solutions so that the change in the mean activity of Na2S04with DMAC concentration could be monitored. Acetamide (Fisher certified grade) was purified by recrystallization from water, and N,N-dimethylacetamide (Fisher certified grade) by distillation. The salts, NaF and Na2S04,were also recrystallized from water before use. All solutions were made in triply distilled water. Solutions were deaerated with purified N 2 or Ar before electrochemical measurements.
Fawcett et al.
I
/
P
‘A(*
Figure 1. Plots of the change in activity coefficient, Ayi, against concentration of acetamide cAc for 0.25 M NaF: mean ionic activity coefficient (A); activity coefficient for Na’ (0); activity coefficient for F (0).
Results and Discussion Acetamide-NaF- Water System. Data were obtained for I O solutions with a constant concentration of N a F (0.25 M) and varying concentration of AC as follows: 0,0.063, 0.1,O. 16, 0.25, 0.40,0.63, 1 .OO, 1.60,and 2.53 M. On the basis of thermodynamic data tabulated by Hamer and Wu,” the value of the mean activity coefficient for 0.25 M N a F in the absence of AC was estimated to be 0.691. The potential drop across the cell Na+-specific electrodellx M AC, 0.25 M NaF, H,OI(P-specific electrode (27) was measured for x = 0, and the value for unit activity determined by using the known activity of NaF. Values of yi were then determined in the various AC solutions from the corresponding values of the potential drop in cell (27) by using this constant. From the results given in Table I, it is clear that the electrolyte activity increases markedly with AC concentration. The potentiometric data obtained by measuring the potential of either specific ion electrode against the constant SCE were used to estimate changes in the activity coefficients of the Na+ and Fions individually. These data are presented in Figure 1 from which it is clear that the activity of the fluoride ion is much more strongly affected by the presence of AC than that of the sodium ion. As a result the assumption made by de Battisti and Trasatt? that leads to medium effects being absent at the pzc is not valid for this system. Differential capacity against electrode potential data are illustrated in Figure 2. It is apparent that adsorption is rather weak, the capacity being only slightly depressed in the most concentrated solutions with respect to its value in the solution with no AC. In fact, its value at the most negative potentials is higher than that in 0.25 M NaF, reflecting the fact that the salt activity is increasing with AC concentration. No adsorption-desorption peaks characteristic of systems with strong organic adsorption are (12) de Battisti, A.; Trasatti, S . J . Electroanal. Chem. 1973, 48. 213.
I 0.5 1.0 1.5 Ecr
v
Figure 2. Plots of the differential capacity of the mercury/solution interface against electrode potential E, for the acetamide-NaF-water system with 0.25 M NaF and varying amounts of acetamide as indicated.
apparent. Qualitatively, similar results were obtained by de Battisti and Trasatti12for the acetonitrile-NaF-water system for a smaller concentration range of the organic compound (0-0.5 M acetonitrile). Thus, the adsorption of AC is considerably weaker at Hg than that of acetonitrile, a compound of similar polarity. The capacity data were integrated twice with respect to electrode potential, once to obtain the electrode charge density (r and again to obtain the relative interfacial tension Ay. The integration was carried out from the pzc for equal increments in u, A y being assigned initially the value zero at the pzc. The relative value of the function Y- was then estimated on the basis of the equation AY- = Ay iaE-
+ 2T+RT In ( y g )
(28)
by using the Gouy-Chapman theory to estimate r+(eq 7). To obtain values of AY-referenced to a charge density where adsorption is absent, we subtracted the value of AI‘- at the most negative charge density ( u = -24 g C cm-2) from all other values at a given AC concentration. Thus, estimation of the surface excess of AC was based on AY,, where AY, = [AY- AY-(a=-24)],A,
The assumption that organic adsorption is negligible at
(29) = -24
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6371
Adsorption at Polarizable Interfaces
0.3
1
n
'5 s a
E Y
L' 0.1
-
Figure 3. Plots of the surface pressure II against acetamide concentration, cAc, at the pzc. The surface pressure was estimated by using the functions AY, (O), A& (A),and A&' (0) as described in the text.
pC was confirmed by the observation that AY, was independent of AC concentration within experimental error at other large negative charge densities. To compare the present analysis with that of de Battisti and Trasatti: we also estimated the relative value of Parsons' function on the basis of data with a constant reference electrode At,. Following the above procedure, the change in A[, can be defined at constant AC concentration as
At, = Ay
+ uEc
(30)
When values of At, are referenced to the most negative charge density where adsorption is absent, one obtains
In view of the fact that thermodynamic data for organic adsorption were sometimes obtained in previous work with a thermodynamic reference electrode but without consideration of the change in salt activity, comparison was also made with the function At,', where
At- = Ay
+ uE-
(33)
Values of the surface pressure II based on the three quantities AY,, At,', and At, are shown in Figure 3 as a function of AC
concentration for data obtained at the pzc. The surface pressure based on At, is quite close to that based on AYr, the value at the highest concentration being smaller by -6%. This result is clearly due to the fact that the activity coefficients for the individual ions in solution are not equal. Considering the fact that the surface pressure must be differentiated to obtain the surface excess, the use of At, will lead to a larger error in r A C . On the other hand, the use of At,' will obviously result in values of r A C that are seriously in error. The surface excess of AC, r A C , was estimated from the change in surface pressure with AC concentration, ignoring possible changes in its activity coefficient with solution composition. This assumption is probably valid for this system since the mole fraction of AC does not exceed 0.05 and Henry's law is expected to hold.2 From eq 6, one may then write rAC
= (l /RT)(d
n/a In
CAC)e,r+
(34)
The surface pressure against In cAC data at constant u were fitted to a cubic equation by ieast-squares analysis, and r A C was estimated from the first derivative.13 The resulting values of r A C based on AY, and A[, are shown as a function of bulk AC concentration in Figure 4. As expected, r A C estimated on the basis of A[, is lower, the error at the maximum bulk concentration being 11%. It is interesting to note that the relative error associated with using the approximations introduced by de Battisti and (13) Fawcett, W. R.; Kent, J. E. Can. J . Chem. 1970, 48, 47
lr f 2 /
I
1
CA,, M
Figure 4. Plots of the relative surface excess of acetamide, r A C , against bulk concentration cAC. The data designated (0)were obtained by using the function AYr and those designated (A)by using the function A&. TABLE II: Mean Ionic Activity Coefficients for 0.15 M Na2S04 in Water-N,N-Dimethylacetamide Solutions Containing Varying Concentrations of N,N-Dimethylacetamide at 35 OC DMAC concn mean ionic DMAC concn mean ionic cDMAC, M act. coeff, ya CDMAC, M act. coeff, y+ 0 0.10 0.16 0.25
0.395 0.410 0.420 0.433
0.40 0.63 1.oo 1.60
0.458 0.498 0.570 0.709
Trasatt? does not vary significantly with electrode charge density negative of the pzc, where AC is adsorbed most strongly. As noted above, this reflects the fact that yx changes more rapidly than T~ in the bulk, whereas the surface excess of cations r+is increasing and that of anions r..decreasing. N,N-Dimethylacetamide-Na2S04-Water System. Data were collected for solutions with a constant concentration of Na2S04 (0.15 M) and varying concentration of DMAC as follows: 0, 0.0063, 0.01, 0.016,0.025,0.040, 0.063, 0.1,0.16, 0.25,0.40, 0.63, 1.O, and 1.6 M. The mean activity coefficient of 0.15 M Na2S04 at 35 "C was estimated to be 0.395 on the basis of the data reported by Harned and Owen.I4 The mean activity coefficients in solutions containing DMAC were determined from potential difference measurements in the cell Na+-specific electrodellx M DMAC, 0.15 M Na2S04, H20IHgzSO4IHg (35) in a manner similar to that described above for AC (see Table 11). As expected, the electrolyte activity increases with DMAC concentration. The potential of each specific ion electrode was also measured against the constant S C E to assess the relative changes in the single ion activity coefficients. In this case, it was assumed that the ratio In yNa+/lnyso4z-is equal to 1/4, that is, the limiting ratio expected from the Debye-Hiickel theory. The , ys0,z- are presented in Figure 5. resulting data for ya, Y N ~ + and It is clear that the activity coefficient of the anion is more strongly affected than that of the cation, a result that precludes simplifying assumptions in the application of eq 25 to data obtained in a cell with a constant reference electrode. Differential capacity data are shown in Figure 6 as a function of electrode potential for several DMAC concentrations. It is clear that DMAC is adsorbed more strongly than AC, adsorptiondesorption peaks being observed at both positive and negative potentials. In the case of DMAC, maximum adsorption occurs at -9 pC cnr2, whereas for AC, maximum adsorption was observed at -3 pC (14) Harned, H. S.; Owen, B. B. Physical Chemistry of Electrolyte Solutions, 2nd ed.; Reinhold: New York, 1950; p 415.
6372 The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
'.O
Fawcett et al.
4
t
1.0
0.4
1.6
1.2
0.6
Conn3 M
Figure 5. Plots of the change in activity coefficient against concentration of N,N-dimethylacetamide,cDMAC, for 0.15 M Na2S04: mean activity coefficient (A);activity coefficient for Na' (0);activity coefficient for
so>-(0).
CoMnc8
M
Figure 7. Plots of the surface pressure II against DMAC concentration cDMAc at the pzc. The surface pressure was estimated by using the functions AY, (0),A[, (A),and A&' (0) as described in the text.
lfi I
60
'E u
401
U
1
2oti
Y
0.6
1.2 &MAC
I
0
-1
v Figure 6. Plots of the differential capacity of the mercury/solution interface against electrode potential, E,, for the N,N-dimethylacetamide-Na2S04-water system with 0.15 M Na2S0, and varying concentrations of DMAC as indicated. E,
The capacity data were integrated twice with respect to electrode potential to obtain values of u and A y for equal increments in surface charge density u. The relative value of the function Y- was estimated on the basis of the equation
1Y- = Ay
+ uE- + ?J+RT
In (y,c)
(36)
with I'+ estimated on the basis of eq 22 and 23. Values of the functions AY,, At,, and A&' were then calculated by using the method described above, the most negative charge density used as a reference point where adsorption is absent being u = -26 M C cm-2. The corresponding values of the surface pressure II at the pzc are shown in Figure 7. For this system, the values of rI are considerably higher than those for AC because of the stronger adsorption of DMAC. The surface pressure based on At, is -4% lower than that based on AY, at the highest concentration because of the difference in the effect of the organic compound on the individual ionic activity coefficients. Similarly to data for the A C system, the estimates of the surface pressure on the basis of At, are seriously in error and could not be used to estimate r D M A C reliably. The surface excess of DMAC, r D M A C was estimated in a similar manner on the basis of the relationship
The results, presented in Figure 8, show that the estimate based on A& is lower than that based on AY,, the error at the highest concentration being -8%. It was also noted that the relative error
I
M
Figure 8. Plots of the relative surface excess of DMAC, rDMAC, against bulk concentration cDMAC. The data designated (0)were obtained by using the function AY, and those designated (A)by using the function A&.
in r D m C was independent of electrode charge density in the region where adsorption is strongest. Evaluation of the Extrathermodynamic Assumptions. The assumption made in the above analysis is that the surface excess of cations is independent of organic concentration at constant electrode charge density. This can be questioned on the basis of two facts, namely, that the activity of the electrolyte and the dielectric constant of the solution change under the same conditions. However, some comment should first be made about the use of the Gouy-Chapman theory to estimate r+.If the electrolyte activity and dielectric constant did not change, one would expect r+to be constant at constant electrode charge density in the absence of ionic adsorption. Nevertheless, the value obtained from the Gouy-Chapman estimate may not be correct so that the resulting values of Y- would be in error. Since the ultimate goal is to determine changes in Y-with the chemical potential of the organic solute, possible errors in the magnitude of r+are not important at constant electrode charge density. The increase in the activity of the electrolyte on addition of the organic compound is due to a change in the electrostatic environment of the ions in the bulk of the solution. A similar change may occur in the electrostatic environment in the double layer at constant electrode charge density, that is, for constant electrical field at the outer Helmholtz plane. The extent of such a change is very difficult to assess. However, it is reasonable to assume that it would not be greater than that observed in the bulk of the solution. If one replaces salt concentration in the AC system by its mean activity and estimates r+assuming that the constant A is given by A = ( 2 7 7 R T t ~ ~ a * )r+ ~ / decreases *, by -2-3% with increase in organic concentration, the exact change depending on
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
Adsorption at Polarizable Interfaces surface charge density. If the effective concentration determining the concentration profiles for ions in the diffuse layer is closer to the mean activity than to the actual concentration in the bulk, the effect on the estimates of r+is rather small and will not lead to significant errors in the estimates of AY-. The change in the cationic surface excess due to change in the dielectric constant of the solvent can be assessed somewhat better within the context of the Gouy-Chapman theory. The most concentrated AC solution (2.53 M), which corresponds to a mole fraction of 0.05, is estimated to have a dielectric constant of 80.15 Accordingly, the value of r+on the basis of eq 7 would be N 1% higher at the highest organic concentration than that estimated on the basis of the dielectric constant of pure water. In the case of DMAC, the most concentrated solution (1.6 M) has a mole fraction of DMAC equal to 0.03 and a dielectric constant of 76.15 As a result, the estimate of I’+ from use of eq 7 is 1% lower at the highest organic concentration. Obviously, the effects related to the change in dielectric constant alone are not large for the concentration range considered. In spite of the fact that small changes in r+at constant electrode charge density are expected in systems such as those considered here, it is easily shown that these changes will have a negligible effect on the estimated values of the organic surface excess. When values of the function AY- are estimated according to eq 28, errors in r+will result in errors in AY-, which become more significant as the concentration of organic compound increases. However, when AY, is calculated from AY- by subtracting off the value of AY- at the most negative charge density (eq 29), the error due to r+is reduced to a negligible level. This follows from the fact that the change in r+with dielectric constant or effective salt concentration is approximately independent of electrode charge density. This conclusion was tested by estimating values of AY, for the AC system by using activity instead of concentration to estimate I’+. The resulting surface pressure data were then differentiated to obtain r A C . Differences between surface excess data estimated by the two methods were negligible. Finally, the above analysis was carried out by assuming that the organic activity follows Henry’s law for the concentration range considered. Mohilner and Nakodomari2 observed departures from Henry’s law for 2-butanol solutions with organic mole fractions greater than 0.012 (0.7 M) and for 2-methyl-2-propanol solutions with organic mole fractions greater than 0.02. The extent that the solution departs from ideal behavior can be related to an increase in organic character of the molecular solute and the degree to which it promotes water structure in its vicinity. As water molecules become more involved with solvating organic molecules, the water remaining to solvate electrolyte ions decreases and the effective salt activity increases. Thus, the extent of departure of the activity of the organic solute from Henry’s law behavior is connected to the increase in salt activity.
-
(15) Rohdewold, P.; Moldner, M. J. Phys. Chem. 1973, 77, 373.
6373
Some indication of the importance of deviations from Henry’s law can be obtained by measuring the coefficient (a In a,/ d In c ~ )or~(d, In a,/a In aA)c,.Mohilner and Nakodomari2 found that (a In a,/a In aA)c,was greater than 10 for 2-butanol solutions in the high nonideal concentration range. For the present systems, (a In a,/a In c ~ ) was ~ , never greater than 1 . Thus, we conclude that departures from Henry’s law behavior are not important for the AC and DMAC systems discussed here. This conclusion is reasonable when one considers the fact that the amide compounds used in this study have less organic character than the alcohols studied previously.
Conclusions The technique described above permits one to obtain precise values of surface excesses for organic adsorbates from interfacial thermodynamic data obtained for solutions with constant electrolyte concentration. Data obtained previously that ignored the variation in salt activity with electrolyte concentration can easily be corrected when the variation in electrolyte activity is monitored by using specific ion electrodes. In situations where the change in salt activity with organic activity is high, one should also monitor the activity of the organic solute as a function of its concentration. An important feature of the proposed analysis is that one avoids carrying out organic adsorption studies at constant electrolyte activity. The tedium involved in finding the correct electrolyte concentration to maintain constant activity with varying organic concentration is thus avoided. However, one should note that the establishment of constant electrolyte activity is easily achieved if one always works with solutions that are saturated with the electrolyte. This normally requires using a relatively high electrolyte concentration. The suggestion by de Battisti and Trasatti that changes in electrolyte activity are eliminated by a compensating change in the potential of the polarizable electrode when a constant reference electrode is used is not supported by the present data. The addition of amides to aqueous NaF and Na2S04solutions in water resulted in the activity of the anion increasing more than that of the cation. In the case of a study of the dimethyl suIfoxide-Na2SO4-water system,I6 the activity of the cation was observed to change more than that of the anion when dimethyl sulfoxide was added to aqueous Na2S0, solutions of constant concentration. It follows that the activities of cation and anion vary differently when an organic solute is added to an electrolyte solution. Thus, the error introduced by the assumptions made by de Battisti and Trasatt? will depend on the nature of both the organic adsorbate and electrolyte and is expected to be high at high organic concentrations. Registry No. Hg, 7439-97-6; NaF, 768 1-49-4; Na2S04, 7757-82-6; acetamide, 60-35-5; N,N-dimethylacetamide, 127- 19-5.
(16) Scatena, Jr., H.; Motheo, A. J.; Gonzalez, E. R., unpublished results. (17) Hamer, W. J.; Wu, Y. C. J. Phys. Chem. Ref Data 1972, 1, 1047.
