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EQUILIBRIA IN PYRIDINE
Equilibria in Pyridine.
111. Behavior of Silver Bromide and Silver
Bromide-Hydrobromic Acid Mixtures in Pyridine by L. M. Mukherjee and J. M. Lukacs, Jr. Chemistry Department, Polytechnic Institute of Brooklyn, Brooklyn, New York 11301 (Received February 84, 1969)
The behavior of silver bromide in pyridine has been investigated by means of conductance measurements (at 25') as well as differential vapor pressure studies (at 37"). The results of these measurements .have been subsequently correlated with potentiometric studies involving the use of the cell Zn(Hg)IZnCl&/IAgBrin pyridine/Ag(s)at 25" In AgBr-HBr mixtures, the reaction AgBr
+ HBr
KC
AgBr-HBr
has been found to occur. The value of K , has been determined from measurements of Ag+ activity in AgBrHBr mixtures in pyridine.
Introduction Silver(1) chloride, cyanide, and thiocyanate were found to be extensively associated in pyridine.' The conductance behavior of these solutes was quantitatively accounted for by postulating equilibria involving triple ions and dimers as well as simple dissociation as monomers. Also, on the basis of these equilibria a satisfactory correlation with potentiometric measurements using a silver indicator electrode was obtained in each of these cases. On the other hand, the concentration dependence of the conductance of silver bromide solutions in pyridine appears to suggest even aggregation beyond dimers-format>ion of trimers seems quite probable in this system. The object of the present work was (i) to obtain quantitative information concerning the silver bromide equilibria in pyridine by means of conductance measurements as well as differential vapor pressure (DVP) studies, and (ii) to utilize these results in order to explain potentiometric observations using a suitable cell with a silver indicator electrode. Furthermore, in this connection it has been considered of interest to investigate the effect of addition of hydrobromic acid-a bromide electrolyte previously investigated2-to silver bromide solutions in pyridine. The study of the behavior of AgBr-HBr mixtures was made Ivyuse of potentiometric measurements. Theory The following reactions are postulated to account for the behavior of solutions of silver bromide and silver bromide-hydrobromic acid mixtures in pyridine.
+ Ag+
Kza
AgBr
+ Br-
Kzb
AgBr
Ag2Brt;
AgBrz-;
K aa
Ag,Br+
+ Br- J_ Ag2Br2;
AgBr2-
+ Ag+
AgBr
+ HBr
Ksb
__
Ag2Br2;
KO
AgBr. HBr;
K,
=
[AgBr HBr ]
I [HBrI
(5)
Reactions similar to the ones given by eq 1-3b were found adequate' in explaining the behavior of AgC1, AgCN, and AgCNS as mentioned before; the additional assumption of a trimer (Ag,Br8) (cf. eq 4)has been introduced to account for the tendency of silver bromide to (1) L. M.Mukherjee, J. J. Kelly, M. Richards, and J. M. Lukacs, Jr., J . Phys. Chem., 73, 580 (1969). (2) (a) L. M. Mukherjee and J. J. Kelly, ibid., 71, 2348 (1967); (b) L. M. Mukherjee, J. J. Kelly, W. Baranetzky, and J. Sica, ibid., 72, 3410 (1968).
Volume 73, Number 9 September 1968
3116
L. M. MUKHERJEE AND J. M.LUKACS, JR.
form higher aggregates in pyridine. Equation 5 describes the complexation reaction which is envisaged to occur in AgBr-HBr mixtures. Conductance of Pure AgBr Solutions. Assuming as before' that Kza= Kzb = Kz, one obtains from the electroneutrality rule
=
(XAg+
(10)
[AgzBr+] = [AgBrz-]
(6b)
xcAgBr
4- [AgBrl 4- 3[Ag~Br+l4
+ 3 [AgsBr31
(7)
+ K1[Ag+I2+ 3K1Kz[Ag+l3+ 2K1K2K3 [&+I4 + 3K13K4[&+I6
(8)
As is evident, assuming arbitrary values of K1,K z , K3, and K4, eq 8 can be used to calculate CAgBr for a given value of [Ag+]. A convenient way of verifying the validity of the assumed values of these constants would be to compare the observed equivalent conductance (A,) with the value of the same calculated from the equation1 A,
+ lAgBrz-1 + [AgzBrzI + f.Ag3Br31
As a consequence of eq 6a and Bb, eq 10 may be transformed to
Now, expressing [AgBr], [AgzBr+], [AgzBr2], and [Ag3Br3]in terms of [Ag+] according to eq 1-4 and using K2a = K2b = Kz (eq 2a, 2b) and setting KBa= K3b = K3 (eq 3a, 3b), eq 7 can be rewritten in the following manner.
[&+I
[AgzBr+l
4-
(sa>
2 [AgzBrzl
CAgBr =
[Ag+l -I- [Br-I -I- [AgBrl
CcAgBr
[Ag+] = [Br-]
Thus, the total concentration C A ~ can B ~ be expressed as CAgBr = [&+I
DVP measurements, for a given concentration (CA~B~) of silver bromide solution, may be expressed as
f A h - ) [Ag+l + (XAg*Br++ hgBr2-)K1K2[Ag'l3 CAgBr
using reasonable values for the sums of ion conduch B r - and XAgzDr+ XAgBra-. For the tances, h a t X R r - and XAgaBrt present purpose the sums X A g t XAgBrr- have been taken to be 80 and 40, respectively. X B ~ -is comparable to the (The value of 80 for sum of the reported limiting conductance^^&^^ of Ag+ (XOAg+ = 34.3) and Br- (XOB,- = 51.3) in pyridine. XAgBra- was arThe value of 40 for the sum X A g B r t rived at by taking one-half of the value (80) assumed for X A g t ABr-, as is customarily doneeac) I n order to arrive at the optimum values of K1, K P ,etc., various trial values of these constants were used until a satisfactory agreement was obtained between the measured conductances and those calculated according to eq 9. Diflerential Vapor Pressure Measurements. Pure AgBr Solutions. These measurements are considered important in providing further substantiation of the equilibria, viz. eq 1-4, assumed to govern the behavior of silver bromide in pyridine. The sum total molarity, ~ C A ~as Bobtained ~ , from
+ +
+
+
+
+
+
The Journal of Physical Chemistry
+ LAgJ3rzl + IAg3BraJ
2lAg~Br+l
(11)
Expressing [AgBrI, [AgzBr+I, [AgzBrz], and [AgaBrs] in terms of [Agf] in eq 11 one obtains C C A ~ B 2[Ag+J ~ 2&Kz[Ag+I3
+ KiIAg+Iz +
+ K1Kz&[Ag+l4 + Ki3&[Ag+]'
(12)
Equation 12 permits the calculation of xCAgBr for a given value of [Ag+] if K1, K z , K3, and Kg are known. The set of values of K1, Kz, K3, and K4 which most adequately explains the conductance behavior of AgBr can be used in these calculations. Subsequently, the CC, values so obtained may be plotted against the corresponding values of C A (cf.~ eq~8). ~ This plot can then be compared with the experimental one based on the molarities determined from DVP measurements of solutions of known stoichiometric concentrations. Superposition of the two plots would indicate the reliability of the parameters K1, Kz, etc., used in the treatment of the conductance data, and would also suggest the validity of the equilibria given in eq 1-4. Potentiometry. I . Pure AgBr Solutions. The emf at 26" of the cell (cell I) Zn(Hg) ZnC12(B) ref electrode ( AgBr Ag(s) can be expressed as
I
1
I
E (9)
2[Ag+] f [AgBr] f
=
EoAgt/Ag
- Eref
+ 0.05916 IOg aAgt
(13)
Based on eq 8 and the Debye-Huckel limiting law (-log!, = 8.1912/;) it is possible to calculate theoretically silver ion activities corresponding to different concentrations of AgBr'. Correlating these calculated activities with the data obtained from cell I, in the pre~ vious manner,l the value of E ' A ~ + ,isA obtainable using -0.788 V as the value for Emfzb vs. nhe. I I , AgBr-HBr Mixtures. When hydrobromic acid is added to silver bromide dissolved in pyridine it is assumed that an adduct, AgBr.HBr, is formed. If the initial concentration of AgBr is relatively low so that one can neglect the concentrations of AgzBr+, AgBrz-, AgzBrzand Ag3Bra in such a mixture, the silver ion activity can be expressed as4 (3) (a) W. F. Luder and C. A. Kraus, J. Amer. Chem. Soc., 69, 2481 Kraus, ibid., 70, 706 (1948): (1947): (b) D. S. Burgess and C. (0) H. S. Harned and B. B. Owen, Physical Chemistry of Electro-
t.
lytic Solutions," Reinhold Publishing Corp., New York, N. Y., 1968, pp 299-300.
(4) S. Bruckenstein and (1960).
L. M. Mukherjee, J. Phys. Chem., 64, 1601
3117
EQUILIBRIA IN PYRIDINE
0.8
where [AgBr] and [HBr] denote the equilibrium concentration of AgBr and HBr, respectively, and K A ~ and K H B r are related according t,o eq 15a and 15b
