1674
NOTES
similar type have been observed between bismuth and bromide ion,6 between bismuth and thiocyanate ions,6 and between iron(II1) and thiocyanate ions . 7 3 (5) Babko, Uniu. eta1 Xisv, Bull. Sci. Rec. Chim., 4, 81-100 (Russian), 103-105 (English translation) (1939). (6) W. D. Kingery and D. N. Hume, J . Am. Chem. SOC., 71, 2393 (1949). (7) 8.2. Lewin and R. 5. Wagner, J . Chsm. Ed., SO, 445 (1953). (8) H. 6. Frank and R. L. Oswalt, J . Am. Chem. SOC.,69, 1321 (1947).
SPECTROPHOTOMETRIC DETERMINATION OF 1:l COMPLEXES. INTERFERENCE OF HYDROLYSIS BY MICHAELARDON* Department of Physical Chemiatry, Hebrew University, Jerusalem, Israel Received June 6, 1967
Benesi and Hildebrand' developed a spectrophotometric method for the detection of 1 : 1 complexes and the determination of their equilibrium constants. McConnell and Davidson2 applied this method to aqueous metal-ligand complexes, of the type M 1 A 1 . They used the expression ab a n =1 -s+
1
(El
- E0)Kl
(1)
where a and b are the formal concentrations of the ligand and the metal, respectively, (a >> b). eo and el are the molar extinction coefficients of M and MIAI, respectively. K1 is the equilibrium constant, KI = [ M I A 1 ] / [ M ] [ A ] . D is the optical density of the solution. D' is the optical density of the solution sans ligand. If MIAl is the only complex in the solution one observes a linear dependence of ab(D D'] on a. In this case one can determine the value of el (from the slope) and the value of K1 (from the slope to intercept ratio). It was assumed in the above derivation that hydrolysis of the metal ion M+"is negligible. Lately314 this method was extended to the case where the first hydrolysis product M(OH)+(" - l) cannot be neglected. Burns and Whiteker3 derived an expression which includes the first hydrolysis constant KIH = { [ M ( O H ) + ( " - l)] [H+]]/[M+"] and the molar extinction coefficients EM and EMOH of M+" and M(OH)+(" - '1, respectively. While the hydrolysis constants of many metal ions are available from potentiometric measurements, the values EM and EMOH must be determined spectrophotometrically before the suggested method can be used. It will be shown here that (a) no prior knowledge of EM and EMOH is necessary for the evaluation of K1 and el, (b) the original method (1) can be applied for the general case where the solution contains all the possible monomeric hydrolysis products M+n, M(0H)+(" - l) . . , M(OH),+(" - m) and that only the hydrolysis constants must be known in advance. * Department of Chemistry. Cornell University, Ithaca, N.Y.
-
(1) H. A. Benesi and J. H. Hildebrand, J . A m . Chsm. Soc., 71, 2703 (1949). (2) H. McConnell and N. Davidson, ibid., 73, 3184 (1950). (3) E.A. Burns and R. A. Whiteker, ibid., 79, 866 (1957). (4) M.Ardon, J. Chem. Soe., 1811 (1957).
Vol. 61
Let us define [MT] as the total concentration of all free (uncomplexed) metal species. If no polymers exist in solution we get [MT] = [M+"]
+ + + By use of the hydrolysis constants K I H K ~.H. .
[M(OH) +(n - '1
[M(OH)m+("
m)].
. . . K,H (where K ~ H= [M(OH)i+(" - "1" [H+]/[M(OH)~+I+(~ - + I)]) we get the expression
KiH
It is seen from (2) that [M+n]/[M~]is constant if [H+] and ionic strength are kept constant. By similar reasoning it can be shown that all the fractions [M(OH)(+cn- i)]/[M~]are constant and therefore we can treat MT as one specimen (at constant [H+] and ionic strength). It follows that one can use the original function (1) and get ab -=-
1
a
D - D' e~ - eo -l- ( e l - eO)K where eo is defined at D'/[MT]. From the slope, one can measure el directly and from the ratio of slope to intercept one can measure K. K is the over-all equilibrium constant K = [M~AI]/[MT][A]. I n order to evaluate the true constant K1 = [MIA&' [M+n][A] we express!K in terms of KI and KiH with the aid of (2) and get the general expression ab
-==+
a
KIH l + - -[H+] +-
K~EKOH [Hf]?. + * " Kl(E1 - eo)
+
K I A . .. . K ~ E [H+I" (3)
in the special case* where all but M+n and MOH +(" - are negligible we get
KH
a
ab
-
jaq KI (a - E O ) l+
In order to ascertain that only M + n and none of the hydrolysis products combine with A to give MIAl one has to prove experimentally that K I remains constant at different H+ concentrations (but equal ionic strength). ELECTROMOTIVE FORCE STUDIES I N AQUEOUS SOLUTIONS OF HYDROCHLORIC ACID AND D-FRUCTOSE BY H. D. CROCKFORD, w. F. LITTLE A N D
w. A. W O O D
Contributed from the Venable Chemktrft Laboratory of the Universitu of North Carolzna, Chapel Hill, North Carolina Received October 4, 1966
This paper is a continuation of the studies being carried on in this Laboratory on the effects of mixed solvents on the thermodynamic properties of hydrochloric acid solutions. In this study electromotive force measurements have been made on the cell HP(HCl(m), D-fructose($), H20(y)[AgC1-Ag
a t 25' and in 17 and 25% by weight n-fructose solutions and with acid molalities from 0.01 to 0.20 m. The standard cell potentials, the activity coefficients
Dec., 1957
1675
NOTES
0.20900
A
0.20800
u2
3 +2
g
‘
v
0.20700
0.20000
-
0.20500
.
1
I
0.02
0.10 0.14 Molality. Fig. 1.-E‘ plots as function of ion size parameter.
of the acid and the ion size parameter have been calculated from the data obtained. One of the objectives was to determine the position of the E: - 1/D curve for D-fructose-water mixtures as related to the same curve for D-glucose-water mixtures. One of us1 pointed out on the basis of data then available that the E&-l/D curves for D-fructose-water mixtures2 and Dglucose-water mixturesa appeared to coincide. However the D-glucose data covered a 30% range whereas the D-fructose data covered only a 10% range. The higher concentrations of D-fructose studied in this paper produced essentially the same concentration range for the two carbohydrates. Experimental The procedures for purifying the chemicals, measuring the densities and cell potentials and calculating the vapor res sures were the same as those used by Crockford and &kh: novsky.2 I n the absence of dielectric constant data the corresponding D-glucose values taken by Williams, et al. ,8 were used. These were 74.3 and 72.0 for the 17 and 25% solutions, respectively. All electromotive force data were corrected to 1 atm. of hydrogen. Values are the averages of a t least three cells. These usually agreed within 2~0.05mv. The times necessary for equilibrium were comparable to those found by Williams, et aZ.3 The results are expressed in international volts.
Calculations and Results The function E’, defined by equation 1, was used in determining the standard cell potentials. E’ = E
0.18
0.00
A& + 0.1183 logm - 0.1183aBdz 0.1183 log (1 + 0.002mMxx,) (1) +
in which E‘ is the apparent molal potential, E is the observed electromotive force corrected to 1 atm. of hydrogen, m is the molality of the acid, A and B are the Debye-Hiickel constants, c is the concentration of the acid in moles per liter, and M,, is the mean molecular weight of the solvent. (1) H. D. Crookford, “Electrochemical Constants.” National Bureau of Standards Circular 524, 153, 1953. (2) H. D. Crockford and A. A. Sakhnovsky, J . Am. Chern. Soc., 73, 4177 (1951). (3) J. P. Williams, 8. B. Knight and H. D. Crookford, ibid., 7 8 , 1 2 7 7 (1950).
Table I gives the observed electromotive force values, the acid molalities and the E’ valoues calculated for an ion size parameter of G.G A. for the various solutions. Table I1 gives the values for the constants of equation 1.
TABLE I m
17% n-fructose soln.
0 . 0 11528 ,022950 .040185 ,048865 ,058292 ,075509 ,085885 ,095238 ,10598 .13738 .18272
25% I)-fructose soln.
E
E‘
m
0.44403 .41041 .38330 ,37397 .36543 .35309 ,34689 .34201 ,33681 ,32435 .31036
0.20890 .20885 ,20880 .20886 .20878 .20881 ,20878 .20885 ,20868 .20855 .20800
0.025324 ,029956 .035946 .046334 .054200 .Of32852 ,070857 .079821 ,086450 .OD5443 .11177 .12404 .19948
E
E’
0.39965 .39101 .38253 .36998 .36255 .35550 .34995 .34390 .34031 .33575 .32796 ,32260 .29920
0.20241 .20187 .20215 .20199 .20185 .20187 .20203 .20181 .20185 .20198 ,20169 ,20126 .20030
TABLE I1
0
CONSTANTS OF EQUATION 1 A
17% n-fructose 25% n-fructose
B
M~~
0.55334 0,33788 21.28 0.58007 0.34323 23.26
a,
A.
6 .0 6.6
D 74.3 72.0
The usual procedure for obtaining the best value for the ion size parameter by plotting E’ versus the molality for various values of this parameter was followed. Three such plots for the 1741, solution are shown in Fig. 1. The value of 6.6 A. gives a line of zero slope in the lower concentration range thus establishing it as the best value for the ion size parameter. This value was found in the work with ~ - g l u c o s and e ~ for the lower concentrations of D-fructose.2 The values of the standard cell potentials estabIished by the same plots are, for the 17 and 250/, solutions, 0.20886 and 0.20200 volts, respectively. The value of E& for the 17% solution is precise to *0.05 mv., the same variation as was found with the individual solutions. Due to increased difficulty in obtaining check electromotive force measurements in solutions below 0.02 m for the 25% solution EL for this concentration is considered precise to rtO.10 mv. As seen in Fig. 1 sat-
1676
NOTES
Vol. 61
Figure 2 gives the E: versus 1/D plots for D-glucose and D-fructose. It is noted that two distinct curves are obtained each essentially straight lines. Both of course originate a t the point having values of E; and 1/D for the cell when pure water is used as the solvent.
0.2200c
NOTE ON CONTROLLED VALENCY PROCESSES I N OXIDE SOLID SOLUTIONS AND LATTICE PARAMETER VARIATIONS
0.21500 h
ro
BYA. CIMINO
M Y
E
Instituto d i Chhimica Generale ed Inorganica dell’ Universita, e Centro per la Chimica Generale del C.N.R. Roma, I t a l y Received June 6 , 1067
W
0.21000
0.20500
0.20100 0.0127
0.0130
0.0135
0.0140
I/D. Fig. 2.
isfactory data were obtained for the 17(% solution down to an acid molality of 0.01. Density data fitted the empirical equations
+ 0.0178m + 0.0173~~
d (17% soln.) = 1.06675 d (25% soln.) = 1.1019
(2) (3)
The mean activity coefficients of the acid in the two solutions were calculated from the experimental data by the equation logy,
= (Eom- E)/0.1183
- log m
(4)
The values given in Table 111 were obtained a t rounded molalities from a large scale plot of the calculated values. The experimental values checked quite closely, except in the higher concentrations, with those calculated from the theoretical equation log z/*
=i
-
A&
1
+ uB&
- log (1
+ O.O02nzM*,)
(5)
TABLE I11 MEANACTIVITY COEFFICIENTS OF HYDROCHLORIC ACIDIN D-FRUCTOSE-WATER MIXTURES 17% D-fructose
25% D-fructose
Molality
Eq. 4
Eq. 5
Eq. 4
Eq. 5
0.01 .02 .03 .05 .07
0.895 .865 .849 .822 .804 .797 .785 .775 .767 .756
0.898
0.886 .858 ,842 .811 .792 ,785 .775 .769 .763 .754
0.894 .854 .842 .813 .794 .786 .773 .762 .748 .731
.os
.10 .12 .15 .20
.869 ,848 ,822 ,803 .795 ,783 .772 .760 .742
Considerable attention from different fields has been focussed recently on the possibility of varying the electronic structure of oxide semi-conductors by the addition of small amounts of ions of valency different from that of the host ions. The addition of cations of different valency will change (a) the concentration of interstitial atoms or vacant lattice sites, and (b) the valency of the host ions, if this is feasible. The second case, with which the present note is concerned, is known as “controlled valency’’ and was first studied by Verwey and coworkers.’ The controlled valency process is restricted to systems in which certain geometrical and energetic features, such as similarity of ionic radii between host and additive ions, are observed. The incorporation of LizOin NiO is a good example: in this case some nickel ions become substituted by lithium ions, and there is a variation of the valency of some nickel ions from two to three. I n addition, therefore, to the well-known changes in electrical properties, there will also be a change in the lattice parameter due t o the presence of a certain number of ions with different, effective radii. Since the elastic approach2 to a crystal containing point imperfections has been satisfactorily applied both to metals3 and to ionic crystal^,^ it is tempting to try to predict changes in lattice parameters of oxides based on this model and to compare them with the observed values. Few systems have so far been investigated. Some of them, such as Fe203 Ti02,6 ZnO Li,O and ZnO Gaz03,6do not lend themselves to this treatment on account of anisotropic expansion effects and, moreover, it is not easy to calculate expansion effects due to interstitial atoms. There are, however, some cubic systems for which the treatment is of interest. The effect of an additive on the lattice parameter must be calculated with respect to an originally pure and stoichiometric phase. Some oxides, however, e.g., CdO and NiO, are not stoichiometric under normal conditions of preparation. I n these cases the lattice parameter for the stoichio-
+
+
+
(1) E. J. W. Verwey, P. W. Haayman, F. C. Romeijn and G.W. van Osterhout, Philips Res. Rpl., 6 , 173 (1950). (2) J. D. Eshelby, J . A p p l . P h w . , 26, 255 (1954). (3) K. A. Moon, THIS JOURNAL, 59, 71 (1955). (4) D. Binder and W. J. Sturm, Phgs. Rev., 96, 1519 (1954). Phys. SOC.(Lon(5) L. D. Brownlee and E . W. J. Mitchell, PTOC. don), 865, 710 (1952). (6) A. Cimino, M. Marerio and A. Santoro, t o be published.
I
