N A L
I C A L CHEMI
.I Registered in U.8.Patent Ofice
-
O F
~
@ Copyright, 1973, by the American Chemical Society
-
~ VOLUME 77, NUMBER 1 JANUARY 4, 1973
t and Anionic Complexation Constants of Silver Halides, etonitrile, N,N-Dimethylformamide, and Dimethyl Sulfoxide
. Chantooni, Jr., and I .
M. Kolthoff"
School of Chemistry, University of Minnesota. Minneapolis, Minnesota 55455 (Received June 73. 7972)
Solubility products, KsP, of silver halides, acetate, and benzoate and formation constants of AgX2- have been determined in methanol, acetonitrile (AN), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO). For the halides KsP and Kf(AgX2-) were determined from pa(M+) and pa(Ag+) measurements in solutions saturated both with respect to AgX and M X (M+ = Na+ or K+], pa(M+) being determined with a calibrated cation-sensitive electrode. Values of K5p and Kf(AgXz- ) thus obtained were in s,itisfactory agreement with those in the literature. For benzoate and acetate the above constants were found from potentiometric titration or from pa(Ag+) and pa(H) measurements in saturated solutions of AgX containing excess parent acid. From the total solubility the dissociation constants of the homoconjugate salts AgHXz and Ag(HX)ZX were determined. The mobilities in AN of the halide, acetate, and benzoate are approximately the same as those of their respective silver complexes, AgXz -, while those of the acetate and benzoate homoconjugates ((H0Ac)zOAc- and H(Bz)z-) are much smaller than the corresponding simple ions. An explanation for this behavior is proposed. Medium activity coefficients ( p W * y , A N ) of the various ions are presented. The difference (pWy*N(OAc-) - pWyAN(Bz-)) N= (pWy4N(HBAc) - p"y*N(HBz)) N l/z(pWy*N(Ag(OAc)z-) - pWrAN(Ag(Bz)z-)), indicating the large effect of the nonelectric part on pWy14N.This conclusion is independent of the assumption on the basis of which ~ " Y ~values ~ N were calculated
In previous studies, based on the tetraphenylarsonium tetraphenylborate assumption, the medium activity coefficient S ( l ) y , s ( z ) ,i being a halide ion, benzoate, or acetate, has been reported, S(1). referring to the protic solvent metltianol1,z and S ( 2 ) to the aprotic solventsl.2 acetonitrile (AN), D = 36.0, N,N-dimethylformamide (DMF), D = 36.7, and dimethyl sulfoxide (DMSO), D = 46.6. The solubility products of the corresponding silver salts were determined in S(1) and S(2) and py(X-) was calculated from the relation apK"(AgX) = py(Ag+) py(X-); pr(Ag+) having been found from the solubility product of silver tetrapbenylborate.2 33 From potentiometric titration of tetraalkylaimnon lum halides with silver nitrate using a silver wire electrode I t has been reported that silver ion forms the fairly stable anionic complex AgXz- in AN,4,5 DMF,4,6 hexamethylphosp&oramide,4 acetone, nitromethane,7 D M S 0 , 4 3 8 $ 9 sulfolane,lo and propylene carbonate.ll Simiiai complexes of silver with azide or thiocyanate have also been found in these aprotic s 0 l v e n t s . ~ In ~9 these solvents additional complexes Ag2X3- and Ag3X4-
+
are formed with iodide and thiocyanate i 0 n . ~ . 9From an analysis of the titration curve of X - with silver ion the values of KSP(AgX) = a(Ag+)a(X-)
(1)
(1) R. Alexander and A. J. Parker, J . Amer. Chem. SOC.. 89, 5549 (1967). (2) I. M. Kolthoff and M. K. Chantooni, Jr.. J Phys. Chem., 76, 2024 (1972), and references therein. (3) R. Aiexander, A. J. Parker, J. Sharp, and W. Waghorne, J. Amer. Chem. SOC.,94, 1148 (1972). (4) R. Alexander, E, C. KO, Y . C, Mac, and A. J. Parker, J. Amer. Chem. SOC.,89, 3703 (1967). (5) D. C. Leurs, R . I . Iwamoto, and J. Kleinberg, lnorg. Chem.. 5, 201 (1966). (6) M. Breant, C. Buisson, M. Porteix, J. Sue, and J. Terrat, J. Hectroanal. Chem., 24, 409 (1970). (7) J. C. Bardin, J. Electroanal. Chem., 28, 157 (1970). (8) N . Rumbaut and A. Peeters, Buil. SOC. Chim Belg.. 79, 45 (1970). (9) M . LeDemezet; C. Madec, and M. L'Her, Buii. SOC. Chim. Fr.. 365 (1970). (IO) R. L. Benoit, A. Beauchamp, and M. Deneux, J Phys. Chem., 73, 3268 (1969). (11) J. N . Butler, Anal, Chem., 39, 1799 (1967).
i
2
M. K. Chantooni, Jr., and I . M. Kolthoff
and
Kd(Ag(HX)2X-)
have been evaluated.4-9 It should be realized that such an analysis of the titration curve, which employs a single measured parameter, m(Ag+), may involve considerable uncertainty, particularly when an appreciable amount of undissociated AgX is present or when the stability of AgXz- is sinall and precipitation of AgX occurs in the early portion of the I-itration, e.g., in the reaction of acetate with silver ion in AN.4 In the prlesend paper values of KSp(AgX) and Kf(AgXa-) have tieen estimated from a(Ag+) and a ( M + ) (Mf = M + or Na+) measurements in AN,.DMF, and DMSO solutions saturated both with respect to AgX and MX, knowing Ksp(MX). In these solutions the following e~ec1;roneutral~~;y and conservation relations hold, neglecting AgzXs - and Ag3X;-
with silver benzoate and benzoic acid, or saturated with silver acetate and containing 0.5-1 M acetic acid, were studied. The latter system was also studied in methanol and DMSO. Also, the total ionic concentration in solations saturated with AgX and MX or AgX and containing UX (eq 3 and 8, respectively) was estimated from their conductivity, while a(Ag+) was measured potentiometrically with a silver wire electrode and a ( M + ) with a cation-selective electrode. Also a(M+) was calculated from the difference in total X and silver content, C(X) C(Ag), in solutions saturated with AgX and MX, Activity coefficients were calculated from the partially extented Debye-Huckel relation -log f = Ap1/2L(1 i- Bup1/2). For simplicity a was taken as 3.5 A for A%+, K + and Nac, a mean of 2.5, 4.5, and 3 A given for these ions by Kiellandl3 in water, while a was taken as 8 A for AgGlz --,AgBr2 - , and 12 *A for the homoconjugate ions. For A.N and DMF A = 1.5 and B = 0.47, and for DMSOA = 1.1and B = 0.43.
[ M i]
C'(Ag)
-+ [big+]= [X-] + IAgX2-1
[Agf] C [AgXz
~
(3)
1 i- [AgX] + 2[AgAgXz] + [MAgX2] (4)
C(X) = [I(-/ + 2 [ k g X a - - ]+ [AgX] + 2[AgAgX2]+ IMXI + 2[MAgXzl ( 5 ) C(Ag) = [M+] + [MX] + [MAgXzI (6) Kd(AgX) J: a{Ag')a(X-)/[AgX] f(AgX) = 1 (7)
C(M) = C(X)
'-
In eq 4--6 C(Ag), C(X), and C(M) represent total (analytical) concentrations. The following systems were studied under the above conditions: AN saturated with silver chloride (bromide) and potassium chloride (bromide), DMF with silver chloride and sodium (potassium) chloride, and DMSO with silver chloride and sodium chloride. Furthermore, when X- is an anion of a weak acid, whose dissociation constant, Kd(HX), is known, Ksp(AgX) has. been found from a(H+) and a(Ag.+) measurements i n solutioms eaturated with respect to AgX and containing a known concentration of HX. When the solubility of E-TX is not too great ( < 2 A4) the solution can advantageously be saturated both with respect to H X and AgX. The equilibrium concentration of H X under these conditions can be taken equal to the solubility of H X in absence of AgX. Particularly in AN, a protophobic aprotic solvent, formation constants of homoconjugate species of acetic and benzoic acids, HX2- and (HX)2X-, are large.12 This tiornoconjugation combined with the incomplete ionic dislsociation of AgHX2 and Ag(HX)ZX results in a marked iiricrease in the solubility of AgX (C(Ag) in eq 91, In solutio:ns saburated with AgX and containing H X the foll.owing relalions apply
+
+ [(HX),X-] + [AgX2-] [.A+'] -k [AgX] + 2[AgAgXz] + [AgXz -1 + [AgHXz] + [ A d H X h X ]
[Ag+] = [ X - - j jHXz-j
C(Ag) = C(X)
(8)
(9)
+
C(HX) = [HX] -1.- [AgHX2] -I-Z[hg(HX)zX] I- [HXZ-] 2[(HX)2X-1 K'(HXz-) E [HX2-]/[HX][X-] f(HX2-) = f(X-) (11)
Kf((HX)2X-'I --. iiHX),X-]/[H-1X]2[X-] f((HX)zX-) E f i x - ) (12) Kd(AgHXz) == c d & + )
[HX2-]f(HXz-) /[AgHX2] (13)
The Journai of Plrysica! Chemistry, Voi. 77, No. 7 , 1973
Experimental Section Reagents Acetonitrile,l* methanol,15 ~ ' , ~ ~ - d i ~ e t h y l f o r m amide,l6 and dimethyl sulfoxide12 were purified and stored as previously described. Silver acetate was a Baker product, recrystallized from water, while silver benzoate was prepared as described by Kolthoff, e t ~ ~ 1 Silver . ~ 7 chloride and bromide were prepared in the conventional way. Sodium chloride, potassium chloride, and bromide were Merck Reagent Grade. Tetraethylammonium acetate, and benzoic and acetic acids were used previously.12 Instrumental. The potentiometric cell used in the determination of a(Ag+) and pa(H) and the 0.01. M silver nitrate/Ag reference electrode in the same soh ent are those as described for pa(H) measurements in AN.18 A Beckman No. 39047 cation-selective electrode was used in the above potentiometric assembly for a( K +-)and a( Naf ) determinations in AN, DMF, and DMSO. Prior to use the electrode was soaked for at least 24 hr in a 0.01 M solution of sodium or potassium perchlorate in the organic solvent in which a(M+) measurements were made. It was calibrated in saturated and/or undersaturated solutions of the following salts in the three aprotic solvents: potassium chloride, bromide, perchlorate, and 2,4-dinitrophenolate, and sodium chloride and perchlorate. Solubility products of these salts in AN, DMF, and DMSO and dissociation constants of the various salts in AN have been tabulated elsewhere.2 Stable electrode potentials reproducible to within f 2 mV were obtained usually after SO min. Calibration curves in AN, DMF, and D 9 0 are reproduced in Figure 1. They are linear in the range a(M+) = 2 X 10-4 to at least 5 X 10-2 M , the slopcs being practically (12) I. M. Kolthoff, M. K. Chantooni. Jr., and S. Uhowmik. J. Amer. Chem. SOC., 90, 23 (1968). (13) J. Kielland, J . Amer. Chem. Soc., 59, 1675 (1937) (14) I . M. Kolthoff, S. Bruckenstein, and M. K. Chantooni, Jr., i. Amer. Chem. SOC., 83,3927 (1961). (15) I. M. Kolthoff a n d M K. Chantooni. Jr., A n a / , Chem.. 44, 194 (1972). (16) I. M. Kolthoff, M. K. Chantooni, Jr., and H. Smagowski, Ana/. Chem., 42, 1622 (1970). (17) I . M . Kolthoff, J. J. Lingane, and W. V Larsori, J. Amer. Chem. SOC., 60,2512 (1938). (18) I. M. Kolthoff and M. K. Chantooni, Jr., ,I, An7er. Cherri. Soc.. 87, 4428 (1965).
Solubility Product and Anionic Complexation Constants Nernstian, 59 f 2 mV/Apa(M+) a t 25.0". Measurements of pa(Nai-) were not made in DMF as McClure and Reddyl$ reported that millimolar levels of Na+ were required for proper electrode response in DMF, possibly because of sohation (of this ion by amine impurities in the solvent. Although similar electrode behavior was noted in this study in DMSO (Figure 1)this electrode was satisfactory a t the h'igh levels of a(Na+) encountered. The conductivity cell and bridge have been described previous-
3
-400
1
- 300
-200
ly.14
Total Solubility of AgX, MX, and H X . Prior t o the operations described below, acetonitrile solutions were taken to dryness and the residues titrated in water. This was not necessary in methanol, DMF, and DMSO solutions, as these solvents do not interfere with the titrations. In saturated silver and sodium chloride solutions in DMSO, the total silver and chloride contents, C(Ag) and C(Cl), are such to allow their estimation gravimetrically after flooding the sample with 20 volumes of water (yielding C(Ag)) or 0.1 M aqueous silver nitrate solution (yielding C(C1) as AgCl). In AN and DMF solutions saturated with AgX and M X (X = halide) an estimate of the difference C(X) - C(Ag) (eq 4 and 5) was made from potentiometric titration with aqueous silver nitrate of aliquots taken up in 1:10 water-methanol mixtures. In AN or methanol solutions s a h r a t e d with AgX and containing iylammonium acetate potentiometric titraum ibdide (silver wire electrode) yielded C(Ag). Benzoate an'd acetate do not interfere in the titration. The alkalirnet,ric determination of C(HA) in these solutions was made by flooding an aliquot of the solution with 10 volumes of hot water, cooling, adding 0.5 g of potassium bromide t~ precipitate the silver and then 2 ml of nitrobenzene to coat, the silver bromide, and titrating with aqueous sodium hydroxide using phenolphthalein as indicator. Identical results were obtained by extracting benzoic acid with ethyl ether from the aqueous solution of the residue obtairaed afcer evaporation to dryness of the AN solution saturcited with benzoic acid and silver benzoate. Total X (acetate, benzoate) in solutions saturated with AgX and containing HX or tetraethylammonium acetate was estimated by titration in AN with perchloric acid (in acetic acid) using a-naphtholbenzein as indicator.20 Methanol solutions were taken to dryness and the residue dissolved in 0.5 ml of anhydrous acetic acid and 3 ml of AN and titrated. w:ith perchloric acid. Results Ionic Mobilities. The following ionic mobilities, XO, have been reported in AN: Ag-i- 85;21 Cl- 91;22 Br- 95;21 K + 86;23 Et4N+ 85;24 benzoate 62.25 In DMF26 Xo(K+) = 30.8, ho(Na+) = W.9, and Xo(CI-) = 55.1. The value of ho(OAc-) i:n AN, equal to 107, was derived from the following conductivity data in solutions of tetraethylammonium acetate: C(Et+NOAc) = 1.44 X 10-3, 2.88 X and 5.75 X 10-8 M , h = 179, 170, and 165, respectively. From the specific conductivities of saturated silver chloride-potassium chloride and silver bromide-potassium bromide solutions in AN entered in Table I, Xo(K+), XO (Cl-1, Xo(Rr-) values and values of [ K + ] = {C(X)- C(Ag) - [K:X]J (see below) and [X-] from K s W X ) and a(&+), the latter determined potentiometrically with the silver electrode, waiuea of Xo(AgC12-) and Xo(AgBr2-) equal to 96 and 88, respectkvely, were estimated. At the low ionic strengths in saturated solutions in AN as compared to those in DMF the salts KAgXz were considered complete-
-100
0
+loo
L 0
1
2
3
4
paM'
Figure 1. Calibration plots of cation electrode in aprotic solvents: @, KCIO4 or NaC104; 0, KCI or NaCI; A , KBr, A, potassium 2,4-dinitrophenolate, and e , potassium p-bromobenzoate. Lines drawn with slope of 60 mV/Apa(Mi-)
ly dissociated. Incomplete dissociation of KAgXz would lead to considerably higher values of Xo(AgX2 -1, which are highly improbable. The following conductivity data were obtained in DMF a t various dilutions of the saturated silver chloride-sodium chloride solution: C(NaAgClz) = 3.19 X 5.75 X 9.57 X 1.23 X and 7.18 x 10-2 M (saturated), A = 91.4, 9 1 . g 9 92.5, 92.9, and 74.1, respectively. Fuoss and Kraus and A us. 1 , T p l o t s of the above data yield Xo(AgClz-) = 61 and Kd(NaAgC12) 0.04 assuming [AgCL-] >> [Cl-1. Since ho(AgClz-) Xo(C1-), the value of Xo(AgClZ-) found in this way would hardly be affected by relatively small amounts of free chloride ion present in the dilute solutions of NaAgClz. 0.03 Using the above value of Xo(AgClz-), IP(KAgCl2) was obtained from the conductivity of a saturated solution of silver chloride-potassium chloride in DMF (Table I). In similar fashion, ionic mobilities of Ag(Bz)2 -, Ag(QAc)z-, and (H0Ac)zOAc- in AN were calculated from the specific conductivities of solutions of saturated silver benzoate in Table IT or of saturated silver acetate in presence of tetraethylammonium acetate (Table I) or of acetic acid (Table 11), respectively. The concentrations of the various ionic species were calculated as described below. Using the above values of hO(Ag+) and Xo(Nz-) the following mobilities were found in AN a t infinite dilution: Ag(Bz)Z- = 62, Ag(OAc)z- = 103, and (HOAc)zOAc- = 74.
-
-
-
J. E. McClure and T. 6. Reddy, Anal. Chem., 40, 2064 (3968). I. M. Kolthoff, M. K. Chantooni. J r . , and S. Bhowmik, Anal. Chem.. 39,1627 (1Y67). P. Walden and E. Birr, Z. Phys. Chem., 144 (7929). A. Popov and H. Humphrey, J. Amer. Chem. Soc., 81, 2043 (1959). S. Mine and P. Werblan, Electrochim. Acta, 7 , 257 (1962). J. F. Coetzee and G . P.Cunningham, J. Amer. Chefn. Soc., 87, 2529 (1965). I . M. Kolthoff and M. K . Chantooni, Jr., J. Phys. Chsm.. 70, 856 (1966). J. E. Prue and P. J, Sherrington, Trans. Faraday SOC., 5 7 , 1795 (1961).
The Joumal of Physical Chemisrry. Vol. 77, No. I , 1973
M . K. Chantooni, Jr., and I. M. Kolthoff
4
I
I
D
O
Solubility Product of M X . The following values of pKSP(MX) have been reported: potassium chloride and bromide in AN, 8.0 and 5.7, potassium and sodium chlorides in DMF, 5.5 and 5.0, respectively, and sodium chloride in DMSO, 2.9. Values of [MX] in the various saturated solutions were calculated from the dissociation constants of M X in ref 2 and the above values of pKsP(MX) and are listed in Table 1. Dissociation and Homoconjugation Constants of Acids. Values of pKd(HA) of benzoic and acetic acids equal to 20.7 and 22.3 in ANI2 and pKd(HOAc) = 9.6 in methano12? have been reported. The following values of the homoconjugation constant, Kf(HX2-), for benzoic and acetic acids have previously been found in A,"J:I2 4.0 X 103 and 4.7 x 103, respectively. Stoichiometry of the AgC1,cn-l)- Complex in DMSO. From independent gravimetric analysis of a solution saturated with sodium and silver chlorides in DMSO as described in. the -experimental section, C(Cl), C(A.g), and C(C1) C(Ag) were found equal to 0.915, 0.436, and 0.484 M , respectively. The internal agreement between these quantities is good. Substituting the above values of C(Ag) and C(C1) - C(Ag) in eq 4 and 6, respectively, and [NaCl] = 0.030 (Table I) and neglecting [AgCl], [AgAgClz] and [Agf], [Cl-] 0.013 M . The mole ratio, n, of silver to chloride in the mixture of AgCl,(n-l)- and Na(,_l,AgCl, as given by n = (C(C1) - [Cl-] - [NaCl]\/C(Ag) (eq 4 and 5) turns out to be 2.00, indicating the presence of primarily the 1:1 silver chloride-chloride complex. In eq 4-6 [Agf] can be neglected, as a(Ag+) 1 x 10-8 (Table I). A saturated silver chloride solution in DMSO when flooded with 5 volumes of 0.01 M aqueous silver nitrate remains clear, indicating that [AgCl] 2[AgAgClz] 5 M . No attempt is made to estimate the dissociation constant of NaAgCla in DMSO. Solutions Saturated w i t h A g X and MX. From eq 3-5 C(X) - C(Ag) - [MX] - [MAgXz] M [E:-] -t- [AgXz-] [Mf], since [Ag+]
