J. Phys. Chem. 1983, 87, 121-125
121
Estimation of Medium Effect on Dissociation Constant of Ammonium Ion and Formation Constants of Silver( 1)-Ammine Complexes in Aqueous Solution Masunobu Maeda;
Genklchl Nakagawa,
Department of Applied Chemktty, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466, Japan
and Georg Bledermann Department of Inorganic Chemistry, Royal Instltute of Technology, 5-100 44 Stockholm 70, Sweden (Received: June 15, 1982; I n Final Form: September 2 1, 1982)
So that information concerning the influence of electrolytes on complex formation equilibria could be obtained, the equilibrium constants of the reactions, NH4+= H+ + NH3 ( K J , Ag+ + NH3 = AgNH3+(PI), and Ag+ + 2NH3 = Ag(NH3)2+(&), were determined at 25 "C by glass electrode potentiometry in LiN03,NaN03, KN03, LiC104,and NaC104 aqueous media of different concentrations (0.5-5 mol dm-3). The pK, values increased linearly with the increase of the electrolyte concentrations and showed little difference with different kinds of electrolytes. As for the Ag+-NH3 systems the formation constants were considerably lower in the nitrate media than in the perchlorate media. In the ionic media, with the exception of LiN03,the formation constants continued to increase monotonously with rising electrolyte concentrations. On the contrary, in the LiN03media, they appeared to decrease with electrolyte concentrations. These variations in the constants were discussed in terms of the specific interaction theory, in which interactions between ions of opposite charges were assumed. The constants thus calculated showed a reasonable agreement with the experimental ones, although in most cases the deviations between the measured and estimated values exceeded by far the experimental uncertainties.
Introduction So far, most of the complex formation equilibria have been investigated in solutions containing a background salt (ionic medium) at a concentration exceeding by far those of the reacting species in order to keep as small as possible the variation of the activity coefficients of the reacting species in a specified solution.' It is well-known that the equilibrium constants expressed in concentration terms vary with differing kinds and concentrations of the ionic media. However, few quantitative discussions have been made on the influence of ionic media on the variation of the equilibrium constants. In the present work, therefore, the complex formation equilibria for the systems H+-NH3 and Ag+-NH3, which were chosen because of their simplicities, were studied in various ionic media by potentiometry. The variations in the equilibrium constants expressed in concentration terms were discussed on the basis of specific interaction theory,2 in which interactions between ions of opposite charge were assumed.
Experimental Section Reagents and Analysis. Reagents Used. These were, unless otherwise stated, prepared and analyzed as has been described in a previous paper.3 Lithium Nitrate Stock Solution. Lithium nitrate of analytical grade was recrystallized twice from water, and the crystals thus prepared were dissolved in water containing a small amount of nitric acid. The lithium nitrate content of the stock solution was determined gravimetrically as LiN03 by drying at about 120 "C. Potassium Nitrate Stock Solution. Potassium nitrate of analytical grade was recrystallized twice from water, and the stock solution was prepared and analyzed by proce-
dures analogous to those for LiN03. Lithium Hydroxide Solution. The lithium hydroxide solution containing LiNO, as an ionic medium was prepared by dilution of freshly filtered concentrated LiOH (analytical grade) and the LiN03 stock solution. Ammonia of analytical grade was used by dilution without further purification. Chloroform of analytical grade was pretreated in the usual way,4 and then fractionally distilled just before use. Apparatus for Potentiometric Titrations. The allpurpose glass electrode, Beckman No. 39301, was used in combination with an Orion Digital pH meter, Model 801A (up to 0.1 mV). The silver-silver chloride reference electrode was prepared according to Brown.5 The titration cell was of the type designed by Tsukuda et a1.6 It was kept in a paraffin oil thermostat maintained at 25.00 f 0.02 O C in a room thermostated at 25 f 1 "C. To avoid losses of ammonia the titration vessel was kept tightly closed. Stirring was performed with a magnetic rod. Potentiometric Titration Procedures. Complex formation was monitored by measuring the equilibrium hydrogen-ion concentration with a glass electrode. The emf s were measured for the cell of the type GEltest solutionlref where GE denotes a glass electrode, and ref the reference half-cell, e.g., in the system of z mol dm-3 LiNO, medium 1.z mol dm-3 LiNO,l(z - 0.01) mol dm-, LiN03 and 0.01 mol dm-3 AgN031Ag-AgC1 From the emf s the equilibrium hydrogen-ion concentration was calculated according to the equation E = Eo 59.16 log h Ej
+
+
(1)
where Eo is a constant, which can be determined from
~~
(1)L. G. Sillen and A. E. Martell, Spec. Period. F'ubl.: Stability Constants, No. 17 (1964);Supplement, No. 25, (1970). (2) G. Scatchard, Chem. Reu., 19, 309 (1936);E. A. Guggenheim, "Application of Statistical Mechanics", Clarendon Press, Oxford, 1966. (3)M. Maeda, R.Arnek, and G. Biedermann, J.Inorg. Nucl. Chem., 41,343 (1979).
(4) D. D. Perrin, L. F. Armarego, and D. R. Perrin, "Purification of Laboratory Chemicals", Pergamon Press, Oxford, 1980. (5)A. S. Brown, J . Am. Chem. SOC.,56, 646 (1934). (6) H.Tsukuda, T. Kawai, M. Maeda, and H. Ohtaki, Bull. Chem. SOC. Jpn., 48,691 (1975).
0022-3654/83/2087-0121$01.50/0@ 1983 American Chemical Society
122
The Journal of Physical Chemistry, Vol. 87, No. 1, 1983
Maeda et al
TABLE I: Densities of Aqueous Solutions Containing Various Ionic Media with Different Concentrations at 25 "C concn/M
LiNO,
NaNO,
KNO,
LiC10,
NaC10,
0.5 1.o 1.5 2.0 3.0 4.0 5.0
1.018 1.037 1.055 1.076 1.114 1.151 1.189
1.026 1.053 1.080 1.106 1.158 1.209 1.258
1.027 1.058 1.088 1.117 1.174
1.029
1.037 1.077 1.113 1.152 1.228 1.303
1.060 1.090 1.121 1.181
solutions of known hydrogen-ion concentrations, and Ej a liquid junction potential arising between the test solution and the salt bridge. Since the -log h range from 3 to 9.8 was studied in the present work, the Ej value, which was mainly caused by H+ and OH- ions, was negligibly small. In the z mol dm-, LiN03 system as an example, a solution with the composition of, say, w mol dm-, AgNO,, x mol dm-, NH4N03,y mol dm-3 HN03, and (z - w - x - y ) mol dm-,LiN03 was titrated with an LiOH solution containing z mol dm-3 LiN0,. The titration procedures were designed in such a way that the total concentrations of the silver and ammonium ions were kept constant throughout the titrations. Density Measurements. The densities of the solutions containing salts alone with different concentrations were measured at 25 "C pycnometrically. They are tabulated in Table I. The values were used for the conversion of the equilibrium constants and activity coefficients of ammonia in molar concentration units into those in the molality scale. Measurements of Activity Coefficients of Ammonia. The effect of the ionic media on the activity coefficients of ammonia was studied by distribution measurements with chl~roform.',~A solution (30 mL) containing known quantities of a background salt and ammonia was shaken with 60 mL of chloroform in a separatory funnel. After the funnel was shaken in a thermostat at 25 "C until equilibrium was attained, it was left undisturbed overnight. The two layers were separated, and the concentration of ammonia in each phase was determined by titration with a standardized HC104 solution (bromocresol purple as indicator).8
Results and Discussion Dissociation Constant of NH4+and Formation Constants of AgNH,+ and Ag(NH,),+. The dissociation constant of the NH4+ ion and the formation constants of AgNH3+and Ag(NHJ2+ complexes were determined by the usual graphical and least-squares m e t h ~ d s . ~ The equilibrium constants, K,, for the reaction NH4+ = H+ + NH3 (2) in various ionic media are given in Table 11. The formation constants, & and &, of the two amminesilver(1) complexes, which are defined by eq 3 and 4,are tabulated Ag+ + NH3 = AgNH3+
PI
= [AgNH,']
Ag+ P2
/([&+I [NH3I)
(3)
+ 2NH3 = Ag(NH3I2+
= [Ag(NHJ,+l/([Ag+l [NH3I2)
(4)
also in Table 11. It is seen that the pK, values increase linearly with the increase of the electrolyte concentrations (7) H. M. Dawson and J. McCrae, J. Chem. SOC.,79,493 (1901). (8)H.E. Matthews and C. W. Davies, J. Chem. SOC.,1435 (1933).
The Journal of Physical Chemistry, Vol. 87,No. 1, 1983
H+-NH, and Ag+-NH, Complex Formation
123
TABLE 111: Activity Coefficients of Ammonia at 25 "C in Various Ionic Media with Different Concentrations (in Molar ( y )
and Molal (7) Units)
LiNO,
concn/M 0.5 1.0 1.5 2.0 3.0 4.0 5.0
y 0.983 0.942 0.925 0.917 0.856 0.761 0.677
KNO
NaNO, Y 1.05 1.10 1.14 1.18 1.28 1.46 1.58
Y 0.966 0.911 0.880 0.857 0.773 0.663 0.569
Y 1.03 1.06 1.09 1.10 1.16 1.27 1.32
Y 1.05 1.13 1.24 1.33 1.48
LiClO, Y 0.935 0.862 0.783 0.718 0.570
Y 1.02 1.08 1.16 1.22 1.28
NaC10, Y
Y 0.907 0.817 0.729 0.648 0.487
1.00 1.04 1.02 1.01 1.02 1.02
Y 0.974 0.982 0.948 0.914 0.87 1 0.825
0.02 0.2
0.1
?E EO.01 0
.;
B
xz xZ 0
0
r
,
-a0,
U Z 0
0.01
- 0.1
-0.21
0.oc
- 0.3 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CNH3/mo1 dm3 Figure 1. Plot of CRNV3 vs. CNH3in LiCIO, ionic media. CR,, is the concentration of NH, in chloroform phase, and C ,,, is the concentration of NH, in aqueous phase: (0)LiC104-free solubon; (A)0.5 mol dm-, LICIO,; (0)1.0 mol dm-, LICIO,; (0)2.0 mol dm-, LICIO,; ( 0 ) 3.0 mol dm-, LICIO,.
1
2
3
4
conc. of mediumlmol dm- 3
5
Flgure 2. Plots of log yNHs vs. salt concentration. The straight lines were merely drawn through the data.
trated in Figure 1. It is seen that all the plots yield practically straight lines. The same trend was observed in the other ionic media. These results indicate, as is apparent from eq 5, that the activity coefficient of ammonia in a specified salt solution is constant within the and show a little difference with different kinds of elecexperimental uncertainties over the ammonia concentratrolytes. As for the Ag+-NH3 systems the formation tion range covered in the present work. The activity constants are considerably lower in the nitrate media than coefficient of ammonia in each salt solution, YNH3/YoNH3, in the perchlorate media. In the ionic media, with the was calculated according to eq 5 from the slopes of the exception of LiN03, the formation constants continue to plots of CRNH3 vs. CONH and CRNH, vs. CNH3. The results increase monotonously with rising electrolyte concentraare summarized in Tabie 111. The activity coefficients of tions. On the contrary, in the LiN03 media, they appear NH, thus calculated in molar concentration units were to diminish with increasing salt concentration. converted into those in molal concentration units by use Activity Coefficients of Ammonia. If for two experiof the densities of the solutions containing the salts alone ments, one involving pure water and the other a salt solisted in Table I. The activity coefficients expressed in the lution, the concentration of ammonia in the reference phase (chloroform phase) is constant, eq 5 is d e r i ~ e d , ~ molality scale are also tabulated in Table 111. The dependence of YNH,'s on the ionic media is visualized in y0NH3CoNH3 = ~ Y ~ N H ~ C= ~YNN H H ~~ C N H ~ ( 5 ) Figure 2 by plotting log yNHB vs. the salt concentration. It is seen that the plots follow practically straight lines in the where b is a constant, YNH3 and CNH3 are the activity cases of sodium and potassium media, while they show coefficient and concentration of NH, in salt solution, relarge deviations from straight lines at high salt concenspectively, and the superscripts 0 and R are for the pure trations in lithium media. Figure 2 shows that at a given and reference phase, respectively. In this derivation it is salt concentration the values are in the order Li < Na < assumed that the reference phase is immiscible with the K irrespective of the type of the anions. This is consistent aqueous phase. with the increasing hydration of the cation from potassium The experimental plots of CRw3against C'NH, and .CNH~ to lithium. With the lithium ion among the three cations in LiC104 media with different concentrations are illusthe surrounding water molecules are most strongly oriented with their protons outward and the attraction between these protons and ammonia molecules may then be the (9) F. A. Long and W. F. McDevit, Chem. Reu., 51, 119 (1952).
124
Maeda et al.
The Journal of Physical Chemistry, Vol. 87, No. 1, 1983
TABLE IV: Values o f pKa Observed and Estimated in Various Ionic Media with Different Concentrations (in Molal Units) LiNO,
KNO ,
NaNO,
LiC10,
NaClO,
concn/M
obsd
est
obsd
est
obsd
est
obsd
est
obsd
est
0.j 1.o 1.5 2.0 3.0 4.0 5.0
9.29 9.37 9.45 9.53 9.69 9.84 10.01
9.34 9.38 9.41 9.47 9.57 9.6, 9.7,
9.33 9.43 9.52 9.60 9.78 9.94 10.12
9.37 9.44 9.51 9.58 9.74 9.9, 10.1,
9.32 9.36 9.47 9.55 9.73
9.37 9.44 9.52 9.60 9.78
9.31 9.44 9.52 9.63 9.88
9.35 9.40 9.46 9.50 9.6,
9.34 9.46 9.56 9.67 9.89 10.16
9.38 9.48 9.58 9.65 9.8, 10.2,
TABLE V : Values o f log p , Observed and Estimated in Various Ionic Media with Different Concentrations (in Molal Units) NaNO ,
LiNO,
KNO,
LiClO,
NaClO,
concn/M
obsd
est
obsd
est
obsd
est
obsd
est
obsd
est
0.5 1.o 1.3 2.0 3.0 4.0
3.21 3.22 3.19 3.17 3.14 3.07 3.03
3.2, 3.2, 3.2, 3.1. 3.1 3.0, 3.0,
3.27 3.26 3.26 3.24 3.21 3.19 3.20
3.3, 3.3, 3.2, 3.2, 3.2, 3.3, 3.3,
3.26 3.17 3.25 3.24 3.27
3.3, 3.3, 3.3, 3.3, 3.3,
3.30 3.41 3.43 3.48 3.54
3.3, 3.3, 3.3, 3.2, 3.2,
3.35 3.37 3.43 3.49 3.57 3.71
3.3, 3.4, 3.4, 3.4, 3.5, 3.70
.5.0
TABLE VI: Values of log p , Observed and Estimated in Various Ionic Media with Different Concentrations (in Molal Units) LiNO,
NaNO,
KNO,
LiClO,
NaClO,
concn/M
obsd
est
obsd
est
obsd
est
obsd
est
obsd
est
0.5 1.o 1.5 2.0 3.0 4.0 5.0
7.20 7.14 7.15 7.14 7.10 7.02 6.94
7.12 7.0, 6.9, 6.9, 6.8, 6.7, 6.6j
7.24 7.21 7.26 7.22 7.21 7.22 7.22
7.1, 7.1, 7.1, 7.1, 7.2, 7.3, 7.3,
7.22 7.13 7.21 7.22 7.25
7.1, 7.1, 7.2, 7.2, 7.3,
7.33 I .49 7.59 7.64 7.69
7.2, 7.2, 7.2, 7.3, 7.4,
7.36 7.50 7.59 7.70 7.79 8.00
7.3, 7.42 7.5, 7.6, 7.9, 8.2,
strongest, which could lead to the lowest activity coefficients in the case of the lithium salts. On the other hand, by inspection of the effect of the anions with a common cation on the activity coefficients of ammonia, it is seen that the activity coefficients are larger in the nitrate media than in the perchlorate media. A possible explanation for this may be as follows. The nitrate ions have a greater tendency to form ion pairs with the cations than the perchlorate ions, and ion-pair formation would reduce the orientation of water molecules around the cation, the attraction between the water protons and the ammonia molecules being diminished. The orientation of water molecules around anions, which is inverse to that with cations, would be very weak with large nitrate and perchlorate ions, and the effect would be negligibly small. The above qualitative interpretations were made only in terms of the NH, basicity. A more quantitative discussion may be possible based on the various salting-in and -out theories of nonelectrolytes.1° It will be presented in a subsequent paper. Estimation of Medium Effect on K,, pl, and & Values. In this section an attempt was made to evaluate the magnitude of K,, pl, and p2 in the different media on the basis of the activity coefficients of the relevant single electrolytes and those of ammonia. Since the activity coefficient data of the single electrolytes to be employed are reported as a function of molalities,ll the equilibrium constants in Table I1 originally expressed in terms of molarities had to be recalculated to the molality scale. The conversion was performed by use of the density data in Table I on the assumption that the density of a test so(10)C. V. Krishnan and H. L. Friedman, J . Solution Chen., 3, 727 (1974), and references cited therein. (11) R. A. Robinson and R. H. Stokes, 'Electrolyte Solutions", Butterworths, London, 1965.
lution be equal to that of a solution containing the solvent salt alone at the concentration of the chosen molarity level. The introduction of this approximation leads to a negligible error under the present experimental conditions. The equilibrium constants converted to the molality scale are tabulated in Tables IV-VI. The standard state was chosen in such a way that the activities of the reacting species approach their concentrations as the composition of the solution approaches that of the salt solution. On this scale, the relations between the activity coefficients of the species of interest and the equilibrium constants are represented by the equations log log
(YH+YNH~/YNH,+)
= log (Ka"/Ka(O)
(YAgNH3+/YAg+YNH3)
= 1% ( & o / b l ( 0 )
(6)
(7)
where y denotes the activity coefficient in the molality scale, and superscript 0 is for the limit of the concentration constant as the dilution is successively increased in a salt-free solution. The equilibrium constants expressed in terms of concentrations obtained by the ionic medium method at a certain level of total molality, I , are indicated by the functional notation, e.g., K, = K,(O. Equations 6-8 indicate that, if the equilibrium constants at infinite dilution are known and the y values of the reacting species are estimated, the equilibrium constants in an ionic medium of ionic strength Z can be evaluated. Since the y values of ammonia in constant ionic media have been obtained in the previous section and reliable values of K:, Plo, and pZohave been reported, the present problem is reduced to estimating the y values of the reacting ions in an ionic medium of ionic strength I. For the estimation of the y values of the ions, the specific interaction theory developed by Bronsted, Scatchard and Guggenheim2was
The Journal of Physical Chemistv, Vol. 87,No. 1, 1983
H+-NH3 and AS+-NH, Complex Formation
employed. According to this theory, the activity coefficient, yi, of an ion i of charge zi in a solution of ionic strength I (in terms of molality) can be expressed by the equation log yi = -z? D
+ CB(i,j,I)mj J
(9)
125
than those described above were estimated just by interpolation and extrapolation procedures. Since the activity coefficients of silver-ammine complexes have not been reported, they were estimated as follows. The present data obtained in 2 mol dm-3 NaC10, and 2 mol dm-3 NaNO, were used for the estimation of the interaction coefficients B(Ag(NH3),+,A-) for A- = C104- and NO3-,respectively. For the estimation the following reactions were considered:
where D denotes a term of Debye-Huckel type which at 25 "C is equal to -0.510711/2/(1 + 1.511/2),and the sumAg+ + NH4+ = AgNH3++ H+ (12) mation extends over all the ions j present in solution at molality mj. The B term, which is called an interaction Ag+ + 2NH4+ = Ag(NH3)2++ 2H+ (13) coefficient, is set equal to zero when the charge of ion j has the same sign as that of ion i. So that the often not negBy accepting log Plo = 3.37 and log P 2 O = 7.22l and the ligible ionic strength dependence of the B term would be present log PlKaand log &K,2 results, eq 14 was derived emphasized, I is included as a variable. By application of log 020 + 2 log K,O - log &(I-) - 2 log Ka(I) = eq 9 to a solution of a single electrolyte the B terms are I(B(Ag(NH3)2+,A-) + 2B(H+,A-) - B(Ag+, A-) evaluated from a set of log yij vs. concentration data obtained in a solution of a single electrolyte ij. 2B(NH4+,A-)) (14) (2) Estimation of log Ka(I). The log y o ~ 0 ?log , y 0 ~ ~ o 3 , from eq 9 and 13. Equation 14 contains a single unknown and log yoHC104 values (where the superscript 0 is introB(Ag(NH3)2+,A-). From eq 19 and 12 an analogous duced to denote an activity coefficient in a solution of a equation was derived for the AgNH3+species. By this single electrolyte) were taken from the tables by Robinson treatment were obtained the values B(Ag(NH3)2+,C104-) and Stokes.'l The values valid for, e.g., I = 3.3 m corre= -0.21, B(Ag(NH3)2+, NO3-) = -0.071, B(AgNH3+,C104-) sponding to 3 mol dm-3 were found by interpolation; this = -0.04, and B(AgNH3+, NO,) = -0.072. Since it is usually does not involve any appreciable loss in precision when the accepted that the B value is little affected by I, the above data are first converted to the form log y+ = -D + B(I)m, B values obtained at the 2 M concentration level may be then only the slowly changing B(I) has to be interpolated. utilized for systems of other ionic strengths. Since the solubility of ammonium perchlorate at 25 "C is The log &(I) and log p2(0values calculated according only 2.1 m, log yomlclo4at the hypothetical concentrations to eq 7 and 8 with the B values derived above and the yWB I = 3.5 and 4.9 m corresponding to 3 and 4 mol dm-3 had values in the corresponding ionic media are compared with to be estimated by extrapolation. For this purpose Bthe experimental ones in Tables V and VI. (NH4+,ClO,, I) was calculated on the basis of Esval and The results summarized in Tables IV-VI show a rather Tyree's isopiestic data.12 The resulting plot of B vs. log good agreement between the measured and estimated I proved to be linear and it was extrapolated to 3.5 and values in NaN03, KN03, and NaC104media. On the other 4.9 m. For pK,O the value of 9.245 reported by Bates and hand, although the deviations in LiN03 and LiC10, are Pinching13was accepted. Insertion of the y values estiseen to exceed by far the experimental uncertainties, esmated above and the pK,O values into the equation log pecially at high molality levels, the calculation reproduces KAI) = log K,O - log (YOHA/YONH A) - log Y N H ~(where A the direction of the variation of the equilibrium constants denotes NO3- and C104-) led to the results in Table IV. with the change in concentration of the ionic media except They are compared with the experimental ones. for the p1 values in LiC10, ionic media. A part of the (2) Estimation of log &(I) and log &(I). The yo hNB deviations in /3 values may be ascribed to the fact that the values were taken from the table by Robinson and Stokes. B(AgNH3+, A-) and B(Ag(NH&+, A-) values calculated in Since the log ~ o A g C 1 0 4values are not available, they were 2 mol dm-3 NaN03and NaC10, and B(Ag+,ClO,, I)values estimated on the basis of Kraft's datal4 as follows. He obtained in NaC10, media were utilized for the estimation proposed the standard potentials Eo(I)for Ag+ + e = Ag in the lithium salt media, i.e., slight deviations of the inat 25 "C of 792.4, 784.0, and 755.3 mV in 1, 2, and 3 mol serted B values from the "real" ones will lead to large dm-3 NaC104 media, respectively. On the conventional deviations in /3 values at high molality levels, because the scale of activity coefficients,E0(nis related to the standard equation employed for the estimation of /3 values contains potential valid in dilute solution Eo by the equation the term BI. The strong hydration of the Li+ ion may be &(I) = Eo + 59.16 log ( y ~ ~ + / y H + ) (10) a second reason for the large deviations in the lithium salt media. The Li+ ion strongly attracts water molecules to Equation 10 can be converted to eq 11 by use of eq 9. itself, which may reduce the degree of the hydration of the Ag+ ion, especially at high concentrations of the ionic Eo(I) = Eo + 59.16(B(Ag+,C104-,I) - B(H+, C104-,I))I media. Due to this reduction, the Ag+ ion will coordinate (11) more easily with NH, molecules. This may be a reason Assuming E" = 799.1 mV and taking the B(H+, C104-,I) why the observed 0values are larger than those estimated values derivable from Robinson and Stokes' table,'l Kraft's in the lithium salt solution. measurements were found to provide for B(Ag+,C104-,I) In conclusion, it may be said that although the devia0.007 (1.05 m), 0.01 (2.21 m),and 0.021 (3.5 m). Approxtions between the measured and estimated values exceed imate values for B(Ag+,ClO;, I) at ionic strengths I other in most cases the experimental uncertainties, the simple model expressed by eq 9 provides a first approximation (12) 0. E. Esval and S. Y. Tyree, Jr., J . Phys. Chem., 66,940 (1962). to the medium effect. Such approximations might prove (13) R. G. Bates and G. D. Pinching,J.Res. Natl. Bur. Stand., 42,419 to be useful in practice. (1949). (14) W. Kraft, Monatshefte, 98, 1978 (1967).
Registry No. NH4+,14798-03-9; Ag(NHJ2+, 16972-61-5.
