738
F. R. MACDOUGALL
THE SOLUBILITY OF SILVER ACETATE I S AQUEOUS SOLUTIOSS OF SILVER S I T R A T E ASD OF SILVER PERCHLORATE. COMPLEX IOSS FORMED FROM SILVER A S D -1CETATE IOSS’ F. H. MAcDOUGALL School of Chemistry, Institute of Technology, Cniaersity of Minnesota, Minneapolis, Minnesota Received March 26, 1942 INTRODUCTION
In a previous publication ( l ) , relating to the solubility of silver acetate in aqueous solutions of some other acetates, evidence was presented in favor of the view that in such solutions appreciable amounts of diacetato-argentate ion, AgAl (where A- = acetate ion), were formed. The dissociation constant of this complex ion was found, in a preliminary estimate, to be 0.28 f 0.05. An analysis of the experimental results obtained in the present investigation indicates that acetatodisilver ion, Ag2A+, is also formed in significant amounts, especially when the concentration of silver ions is greater than that of acetate ions. EXPERILVESTAL PART
The experimental methods are described in a previous paper (1). The solutions, saturated with silver acetate and containing silver nitrate or silver perchlorate as added electrolyte, were analyzed volumetrically by titration with potassium thiocyanate (1). The concentration of silver acetate was obtained “by difference” and is therefore probably less accurately known for solutions containing a large excess of the added silver salt. In tables 1 and 2 are summarized the results obtained with silver nitrate and perchlorate as added salts. By mole fraction, x, we shall ordinarily mean the “normalized” mole fraction, that is, the true mole fraction multiplied (for aqueous solutions) by the factor 55.51. Also c1, cz and 21, zz will be referred to as the apparent molarities and mole fractions of silver ion and of acetate ion, respectively; the term “apparent” is used to indicate that the values of cl, cz, zl, and x2 are calculated on the assumption of complete ionization of the strong electrolytes and of no formation of complex or of intermediate ions. In figure 1 the ordinates give the values of 3 log z m and the abscissae denote values of the square root of the apparent ionic strength, S:&, . In this figure are represented not only the data obtained when silver nitrate is the added salt but also those obtained for sodium acetate, calcium acetate, strontium acetate, and sodium nitrate as added electrolytes, as reported and referred to in a previous paper (1). The curve for silver perchlorate is not included in the figure, since it coincides quite closely with that for silver nitrate.
+
1 This research was made possible by grants from the Research Fund of the Graduate School of the University of Minnesota. The author takes this opportunity to express his appreciation of this financial assistance. The experimental work described in this paper was carried out by Mr. Martin Allen, M. S.
739
BOLUBILITY OB SILVER ACETATE
TABLE 1 Solubility at 86°C. of silver acetate i n aqueous solutions of silver nitrate
-
DENSITY OF
I O L A L I I Y OF SILVEP NIIPATE
0.04920 0.07063 0.09491 0.1059 0.1990 0.2009 0.3104
YOZNJTY
SILVER ACETATE
SATmAIW SOZWIION
0.04896 0.07026 0.09439 0.1053 0.1973 0.1992 0,3068
PPAPENI Y O L E FPACTlON OF
OF
1.0119 1.0142 1.0175 1.0187 1.0304 1.0302 1.0452
A-
0.05008 0.0.1555 0. 04107 0.03991 0.03145 0.03135 0,02745
0.04984 0.04531 0.04085 0.03968 0.03118 0.03103 0.02714
0.09894 0.1157 0.1353 0.1450 0.2286 0.2303 0.3338
0,04990 0.04536 0.04087 0.03970 0.031 19 0,03105 0.02712
TABLE 2 Solubilitv at W C . of silver acetate i n aqueous solutions o silver perchlorate UOLALIIY OF SIZYEP P E P CHLORATE
YoLAPITy OF
1
DENsll'YoP YOLALITY OF YOLAPITY OF SILYEP ACETATE SILVER ACETATE ~
~
s ~ " , ~ ~ s~~~~ ~ -
0.05089 0.1028 0.1996 0.3007
1.0136 1.0205 1.0352 1.0507
+
0.04916 p.03907 0.03129 0.02925
0.04891 0.03879 0.03095 0.02879
I
PPAXENI MOLE APPAXENT MOLE FRACTION OF FRACTION OF
As+
0.09969 0.1111 0.2286 0.3261
*-
0.04898 0.03887 0.03103 0.02891
FIG.1. Plot of (3 log ZIZZ)against the square root of the apparent ionic strength. Curve I , sodium nitrate; curve 11, strontium acetate; curve 111, calcium acetate; curve IV, sodium acetate; curve V, silver nitrate.
740
F. E. MACDOUQALL
Now, just as curve IV (sodium acetate) when compared with curve I (sodium nitrate) suggests (see reference 1) that increasing amounts of a complex ion (e.g., AgA;) are formed with increasing excess of acetate ion, so curve V (silver nitrate) points to the formation of a complex ion (e.g., AgZA’), the concentration of which increases as the excess of silver ion becomes greater. The theory to be presented shortly assumes, of course, that these complex ions are present even in solutions of sodium nitrate saturated with silver acetate, but in such a case their concentrations will always be small and in a constant ratio to that of the dissolved silver acetate. Hence curve I (sodium nitrate) is of ,the same type that would have been obtained if there had been no formation of complex ions. “FIEORETICAL PART
Solutions containing only uni-univalent salts The equilibria that we assume to exist are represented, along with the corresponding equilibrium constants, in the following equations. Note that, because of our use of “normalized” mole fractions, an equilibrium constant K‘. is numerically equal to the equilibrium constant K”’ for a given reaction.
I./ AgA(s) = Ag’
+ A-;
G = G = ang+aA-
(1)
From these equations we find
We make the approximately valid assumption that In a-given solution all univalent ions have equabctivity coefficients. Then equations 4 reduce to
For solutions for which equations 5 are valid, we can write CASAF
-
-
%
.
CAgiA+
- xAmAC
-
u1
-
(6)
1 - 2%’ CAg+ %As+ 1 21(1 where u1 and ua are constants at a given temperature. In t e r n of these constants equations 5 may be written %A-
C=E
(A -
2 ) ; K; = 4
- 2)
(7)
Bearing in mind equations 1, 2, 3, and 6 and the meaning w i p e d previously to the symbols c1, q, XI, and G, we find
741
SOLUBILITY OF SILVER ACETATE
and hence
car+ = (1
- 2%)
(
cA- = (1
- 2uJ
(
Cl
-u2 c.-) 1 - 2u2
Similarly, CP
-
u1
1 - 2Ul
~
cAgt)
From equations 8 and 9 we obtain Cnn+ = (1
- 2UdCl - czuz)
(10)
1 - UlUP
Corresponding equations for xAg+,xA-, etc. can be derived from equations 10 to 13 by replacing c1 by XI and cz by z2. Expressions for the ionic strength of a solution will depend on the nature of the added salt. We have three cases: 'A. The solution contains silver acetate (cl) and sodium acetate (c, - c J : In this case, we find for S, the true ionic strength,
s=
c2 - ClUl
- czuz + CZUlUZ
1 - u1u2
or, with sufficienct accuracy, since u1and uPare small compared with unity,
s = c2
-
ClUl
- c2uz
(15)
.
B. The solution contains silver acetate (c2) and silver nitrate.(cl case, instead of equation 15, we have
s = c1 - ClU, - c2uz
-
cz): In this
(16) C . The solution contains silver acetate (c) and sodium nitrate (c,) : In this case, equations 10 to 13 are still valid if we set in them c1 = cz = c (and 51 = x2 = 5). Thus we obtain: (1 - 2Ul)(l - uz)c Cap+ = (17) 1 - u1u2
742
F. H. MnCDOUGALL
with analogous expressions for xAK+, xA-, etc. For the ionic strength when the concentration of the added sodium nitrate is 6 , we have
s = c,+
41 - Ud(l 1
-
- u2)
Ulul
or, with sufficient accuracy,
+ c(1 - u1 - uz)
s = c.
(22)
Theory of Debye and Huckel The theory of Debye and Huckel, when applied to the present problem, gives the fundamental equation (for 25"C.),
where A may be interpreted to mean an effective ionic diameter a , multiplied by the factor 0.3286 X 10'. In view of equations 10 to 13 and the statement immediately following this set of equations and in view of equations 15,16, and 22, the fundamental equation (23) assumes the following forms in the typical cases indicated: (1) Added salt, sodium acetate:
= log KT
-
-
1.0184(~2 C I U ~ (24) 1 A(& - clul - C Z U Z ) ~ ' ~
+
(2) Added salt, silver nitrate:
(3) Added salt, sodium nitrate: log x2
+ log (1 - 2Ul)(l -12-u m - u d l - uz) UlUZ
In connection with these equations it may be remarked ( a ) that when an
SOLUBILITY OF SILVER ACETATE
743
acetate is the added salt, the ratio cJct = xl/xt becomes small, the variable term log (1
-
9
ul) approaches zero, and the term clul is of minor importance
in the exprbssion for the ionic strength as the acetate concentration is increased; ( b ) that when a silver salt is the added electrolyte, the ratio c2/cl = x2/xl bel - ?! approaches zero, and the term ( x 2 ) czu2 is of minor importance in the expression for the ionic strength as the silvercomes small, the variable term log
u2
ion concentration is increased; (c) that when sodium nitrate is the added salt, the quantities C U I and cuz diminish in importance the larger ca is in relation to c, and hence that equation 26 becomes approximately equivalent to
?;ow when MacDougall and Rehner (2) applied the Debye equation to the solubility of silver acetate in sodium nitrate solutions, they assumed both salts to be completely ionized but took no account of the possible formation of complex ions. The activity product, aAg+uCI-, which they found may be called the stoichiometric activity product, Ktt. In view of equation 27 it is seen that the relation between the true activity product, K ; , and the stoichiometric equilibrium constant, K:t, is given with some accuracy by the equation
MacDougall and Rehner found K i t = 2.815 X
Determination of the constants ul, u2,and K; In a previous paper, MacDougall and Allen (1) had calculated us (in that paper denoted merely by u) from the results obtained in solutions containing sodium acetate or potassium.acetate. They found a value of about 0.0094, which led to 2.71 X lop3as a preliminary value of K;. A study of equations 24, 25, and 26 and the results of calculations have shown that the values of us obtained by applying equation 24 to solutions containing sodium acetate or potassium acetate depend only slightly on the value assumed for ul. Similarly, when equation 25 is applied to solutions containing silver nitrate or silver perchlorate, the values of u1obtained depend only slightly on the value assumed for ut. With u~ = 0,0094, and K ; = 2.74 X equation 25 mas applied to the silver nitrate and the silver perchlorate solutions to give a set of values of ul. The average value of u1 so obtained with us = 0.0094 gave a new and more accurate value of K ; by means of equation 28. This new value of ZC;, along with u2 = 0.0091, was used with equation 25 for the silver nitrate and silver perchlorate solutions to obtain a presumably more accurate value of ul. The new values of u1 and of K; were now used in applying equation 24 once more to the sodium acetate and potassium acetate solutions to obtain a new set of
744
F. R. MMDOUGALL
values of U Z . The new values of u1 and uz were employed in equation 26, which was applied to the sodium nitrate solutions to give a more nearly correct value of K; which could be used once more in the application of equations 24 and 25. As an illustration, we give the series of values of u1 obtained by applying equation 25 to the silver nitrate solutions listed in table 1, For these solutions, in order from the most dilute to the most concentrated, we obtained u1 = 0.0307, 0.0325, 0.0325, 0.0350, 0.0315, 0.0315, and 0.0282; average, ut = 0.0317. Similarly, from the sodium acetate and potassium acetate solutions we found 0.0105 as an average value of uz. Summarizing, we find u1 = 0.0317; ut = 0.0105; KY = K ; =2.48 X log KY = 3.394. TABLE 3 Values of log Kf with u~ NaNOi SOLWIIONS A = 1.3
1
/I I/
1
&NO* A
-
SOLtlTlONS
1.2
Molarity of
KclHiOr
3.396 0.05064 3.392 3.401 0.1021 3.390 3.399 0.1974 3.395 3.405 0.2960 3.407 3.394 3 I393 (3.360)
0.0
0.9198 1.0106
0.0817 and u, = 0.0106
NaCalOt SOLUTIONS KCJIlOI SOLVTIONS A31.2 1.2 A log K;
0.5602 0.7400
-
3. 95 3.394 3.394 3.391 3.398
1
-____
Numerical check of the hypothesis of complex ions In order to justify our assumption that the complex ions AgtAf and AgA; are formed in any solution that contains silver ion and acetate ion, we might have presented in detail the series of values of u1 and u2 calculated for the various solutions. It seemed, however, simpler and more direct to make a check of the present hypothesis by calculating for each of the solutions investigated a value of log K;, using the appropriate equation (24, 25, or 26), and the values of u1 and u2 just obtained, oiz., 0.0317 and 0.0105, respectively. For the sodium nitrate solutions we have taken A = 1.3 and for the other solutions, A = 1.2. It should be emphasized that if A = 1.3 is used in all cases, the agreement among the calculated values of log K is only slightly diminished. The results of the calculations are shown in table 3. In finding an average value of log K:, the values enclosed in parentheses were omitted from the calculation.
SOLUBILITY OF SILVER ACETATE
745
Dissociation constants of the complex ions Referring to equations 7 and adopting the values U I = 0.0317, uz = 0.0105, we fmd for the dissociation constant, K;, of the diand K ; = 2.48 x acetato-argentate ion, AgA;, = 0.23 f 0.02
K; =
and for the dissociation constant, K;, of the acetatodisilver ion, AgzA',
K;
=
K; = 0.073 f 0.007
We have estimated the uncertainty in these values of K ; and K; a t about 10 per cent. Undissociated silver acetate It may be objected that we have left out of account the probable existence of an appreciable concentration of undissociated silver acetate in all our solutions. It may be suggested that the relatively high value of 5122 (or of cis) for a solution containing a considerable excess of acetate, as compared with the value of x2 (or c') for solutions which contain only sodium nitrate as added salt, is obtained because, when acetate is greatly in excess, the silver in the undissociated silver acetate may be a considerable fraction of the observed zl; hence, correcting for the concentration of undissociated silver acetate may give a value of xAg+ so much smaller than 21 that the true value of xAg+xA-for acetate solutions may approach the true value obtained for sodium nitrate solutions. It is easy to test the hypothesis that our results can be explained solely by assuming that a suitable concentration of undissociated silver acetate exists in the solutions. In the first place, the activity of undissociated silver acetate must be the same in all the solutions; in the second place, since undissociated silver acetate exists as electrically uncharged molecules, the activity coefficient of undissociated silver acetate will not, in all probability, differ much from unity. Hence we infer that all our solutions must contain virtually the same concentration or mole fraction of undissociated silver acetate. When pure water is saturated with silver acetate a t 25°C. the molar concentration of the salt is about 0.066. Let us assume that the dissolved salt is 2 per cent undissociated. This gives co = ZO = 0.0013 as the concentration of undissociated silver acetate. We first subtract this amount from the observed values of c (or x) in the sodium nitrate series and obtain, on the present hypothesis, the true values of xA~+xA- for solutions of various ionic strengths. We then go to the sodium acetate solutions and calculate for each solution what quantity, 20, must be subtracted from the observed values of z1 and xz in order that ZAS+ZA-
=
(XI
- 20) ( 2 2 - ZO)
shall equal the value obtained for a sodium nitrate solution of the same ionic strength. Actually we find that the values of zo so obtained increase with the
746
E”. H. MaCDOUQALL
acetate concentration and in the more concentrated solutions are five or six times as large as 0.0013. When we turn to the silver nitrate solutions, we obtain a similar result, except that in the solutions of highest concentration the required value of xo is eight or ten times as large as 0.0013. Similar results are obtained if we assume that the silver acetate is 3 or 4 or 5 per cent undissociated. It is probably possible to assume a sufficiently large value for the per cent undissociated so that consistent results can be obtained for a pair of sodium acetate solutions and the corresponding pair of sodium nitrate solutions, but in this case there nil1 be no agreement for the remaining sodium acetate solutions and still less for the silver nitrate or silver perchlorate solutions. ]Ire can safely conclude that our experimental results cannot be accounted for solely by taking into account the concentration of undissociated silver acetate. It is, of course, very probable that silver acetate is not completely ionized, but our calculations show that the presence of undissociated silver acetate is of minor importance in explaining why the observed solubility product, x1z2, increases more rapidly with the ionic strength when sodium acetate or silver nitrate is the added salt than when sodium nitrate or potassium nitrate is the added electrolyte. We doubt if our experimental data are accurate enough (even if the theory of Debye were exact) to lead to a quantitative measure of the per cent of undissociated silver acetate in our solutions. It is partly because of the view presented in these paragraphs that we have attached an uncertainty of about 10 per cent to our calculated values of u1 and up.
Structure of the complex ions The existence of the diacetato-argentate ion, [Ag(CH&OO)J, does not seem strange in view of the tvell-established occurrence of other complex ions of apparently analogous structure, such as [.4gC12]- or [Ag(CS)z]-. All these ions fit into the scheme in which the central atom, Ag, is assigned the coordination number 2. At this time no more detailed picture of the diacetato-argentate ion will be attempted. The acetatodisilver ion, [Ag2CHsC00]+, seems to deserve more consideration, especially when one notes that it is actually more stable than the diacetatoargentate ion. The stability of the acetatodisilver ion is probably due to an appreciable resonance energy. The two structures between which resonance occurs may be represented by the two formulas: 0-Ag+ CHs-C
I
/ \\
O...Ag+
I1
In each of these formulas, both oxygen nuclei are a t the same distance from the carbon nucleus to which they are bonded. This distance should correspond to a bond which is intermediate between a single and a double bond. The normal
ISOMORPHISM AND ALLOTROPY I N COMPOUNDS
A&O(
747
state of this complex ion is of course not represented by either formula I or formula I1 but is a configuration in which both silver ions are in identical states and in which both oxygen atoms are in identical states. SUMMARY
1. The solubility of silver acetate at 25OC. in aqueous solutions containing various amounts of silver nitrate and silver perchlorate has been determined. 2. The results obtained are interpreted by means of the theory of Debye and Hiickel and by assuming the formation of diacetato-argentate ion and of acetatodisilver ion, 3. The dissociation constants of these complex ions have been determined. 4. It is suggested that the stability of one of these ions is due to resonance. 5. The true activity product for silver acetate has been calculated. REFEREKCES (1) MACDOUGALL, F.H., AID ALLEN,MARTIN:J.'Phys. Chem. 46,730 (1912). (2) MACDOCGALL, F.H.,AND REHNER, JOHN,JR.: J . Am. Chem. SOC. 68,368 (1934).
ISOMORPHIShl AKD ALLOTROPY I S COMPOUKDS OF THE TYPE AZO4 M. A. BREDIG Vanadium Corporation of America, 4.90 Lezington Avenue, New York, New York Received Januaru 7 , 19@
In a number of previous publications, experimental work on the conditions of formation and on some structural relations of calcium phosphates, calcium silicophosphates, and calcium alkali phosphates has been described (5, 7, 8, 13, 14). In the present paper a more detailed interpretation and general discussion of the x-ray data, as obtained in those investigations and published previously (13, 14), is given. It is believed that the results may contribute to the knowledge of the structural relations between various substances with tetrahedral anions, and of the mechanism of crystal transformations in chemical compounds in general. I . POLYMORPHISM OF CALCIUM POTASSIUM PHOSPHATE, a- AND O-CaKPO, Calcium potassium phosphate, CaKPO4, has been shown to exist in two distinctly different crystal modifications' which, on account of the similarity in 1 In the former paper (14) the titles of the x-ray diagram were badly misplaced. Proofs were not submitted to this author. Since the corrections could not be published, they are given below: FIG. 1. Equilibrium diagram of the system potassium sulfate-sodium sulfate. FIG. 2. Equilibrium diagram of the system sodium sulfate-calcium sulfate. FIG.3. a-Potassium rhenanite, containing carbonate.
