NOTES
1670
verted slowly to intermediate I1 upon standing in water. The optical properties and X-ray patterns of the intermediates differ from those of calcium phosphates heretofore reported. Solutions of the intermediates in 5% acetic acid yield pyrophosphate chromatograms. Intermediate I crystallizes as colorless spherulites with occasional projecting monocrystal zones suitable for some optical measurements. The refractive indexes vary among preparations, and are Q = 1.527-1.535, p 1.535-1.537, y = 1.552-1.557. The crystals are biaxial, probably (+). Angle 21' is large. Different preparations of intermediate 1 yield identical X-ray patterns notwithstanding the variations in refractive indexes. The spacings, d , and intensities, I, are shown in Table I. The chemical compositions of different preparations place the empirical formula within the limits Hl.2P207.2H20to Ca1.5HP207.2H20.
Vol. 61
AN INHERENT DIFFICULTY I N SPECTROPHOTOMETRIC STUDIES OF ION-PAIRS BY STEPHEN R. COHEN Contribution from Metcalf Research Laboratory, Brown Univeraity, Providence, R . I . Recaived August 14, 1067
In the last few years a large number of studies have been made of the association of complex ions (usually cations) with oppositely charged i0ns.l Most of these studies have been carried out spectrophotometrically; upon mixing the complex cation and associating anion a new absorption band was produced in the visible or ultraviolet regions, or the ultraviolet absorption edge of the anion was displaced toward longer wave lengths. I n these cases it has been assumed that an electron was transferred from the anion of the pair to the complex cation, or a t least from the anion to a water molecule in the first hydration layer surrounding the cation (or vice versa). If true, then only the ionTABLE r pairs with the associating ions in close proximity X-RAY PATTERNS (Cu K a RADIATION;CAMERA DIAM., are detected. Even when, as with the association 14.32 CM.) of Ba++, Mg++, and K+, with Fe(CN)d-, the -Intermediate IIntermediate I1 change in absorption spectrum seems to be due to d, b. I a, A. I d, A. I polarization of the complex ion, only short range 10.7 VS 8.01 S 2.32 VW ion-pairs can be detected because of the decrease 6.74 VW 6.95 S 2.23 WM of the polarizing electric field with distance. I n 6.08 VW 5.48 vw 2.09 WM some cases, where the ions are associated by co4.66 W 5.20 2.00 w VW valent, or other more or less specific short range 3.58 M 4.47 vw 1.89 W "chemical" bonds, distant ion-pairs contribute 3.43 W 3.98 1.73 WM W little and may be ignored. I n others the bond is 3.14 VS 3.73 F 1.56 WM almost entirely due to electrostatic attraction be2.78 VW 3.42 1.54 W M tween the oppositely charged ions. With such 2.69 W MS 1.48 W 3.21 systems the Bjerrum-Fuoss theory predicts that if 2.30 W 3.10 MS 1.44 W they are multiply charged, two ions may be sep2.03 MS 1.40 W 3.04 M arated by a comparatively large distance and still 2.01 WM 2.95 1.38 W WM form an ion-pair. It follows that spectral measure1.83 VW 2.76 WM 1.36 W ments, and other methods of measuring association 174 vw 2.65 M 1 33 w which do not detect distant ion-pairs, will give 1.57 W W W 1.17 2.50 lower association constants for electrostatic ion1.53 WM 1.14 W pairs than conductivity and electromotive force 1.39 vw measurements which do. 1.34 VW The difference in equilibrium constants can be estimated following Bjerrum's derivation of the Intermediate I1 crystallizes as colorless euhedral triclinic prisms of parallelepipedon habit. The equations for ion-pairing.2 The association conusual forms are the (OlO), (001) and (201), modi- stant for an ion-pair is fied commonly by a small (hkl) form. Crystals K = (4~N/1000) 'r2dr e-mz2e3/DrkT (1) frequently are elongated along a and sometimes S a along b and c. The parallelepipedon profile where r is the distance between the centers of two angles are 120.5" (201 A OOl), 77.5" (on 201) and ions and D is the dielectric constant of the medium. 108" (201 A OlO), which corresponds to the y I n this treatment two oppositely charged ions beof X-ray. The crystals are biaxial (+) with 2V tween a, the distance of minimum approach, and (calcd.) = 68.6". The refractive indexes are a = q = -xlx2e2/2DkT, .the minimum value of the 1.540, 0 = 1.549, y = 1.568. The chemical com- integrand, are considered to form an ion-pair. position indicates an empirical formula of Ca2P207. In the usual derivation equation 1 is transformed to 2H20. K = -(4~hr/1000)(z,z~ea//okT)a&(b) (2) The powder X-ray pattern of intermediate I1 is shown in Table I. The lattice constants, as deter- where &(b) is defined by mine! by single-crystal X-ray diffraction, are a = 6.70 A., b = 7.38 A., c = 8.31 B., a = 85" 2', p = 102" 48' and y = 107" 23'. The unit cell contains 2(2Ca0.Pz05.2H20). The calculated density (2.(1) See S. R. Cohen and R. A. Plane, THISJOURNAL, 61, 1096 51 g./cc.) is in good agreement with the density (19571, for references to typical studies. (2.46 g./cc.) estimated from the indexes of refrac(2) N. Bjerrum, "Selected Papers," Einar Munkagaard, Copention by means of the Gladstone and Dale equation. hagen, 1949, p. 108.
-
I i \ I
t
!
i 1 1
t I
tI
i
i c
!
and b
= -zlzze2/aDkT
(4)
If only ion-pairs between a and p < p are detected, rather than all Bjerrum-Fuoss ion-pairs, the limits of integration in equation (1) should be from a t o p rather than from a to p. Equation (1) now becomes K' = (4rN/1000) r2dre-zlzne*/DrkT -
[-*
s," rZdre-~~~d/DrkT](1')
which is transformed t o K' =
1671
NOTES
Dec., 1957
-(4
d / 1000)(zlzze2/DkT)3&(b ')
(2 ')
where
QW) = Q ( b ) - Q(b"),
(5)
b" = -zlzze2/pDkT
(6)
and
ion-pairs becomes less. However even with the highly associated 4-2 electrolytes, distant ionpairs easily increase the equilibrium constant 15 or 20%. Unfortunately, at present we have no really satisfactory direct method for estimating distant ionpairs, and consequently no adequate experimental method for checking any proposed theory of ionpair formation. Although the indirect methods of conductivity measurements or ionic activity measurements detect the effect of ,distant ion-pairs, the extent of association which is computed depends on the validity of the theoretical or empirical equation used to compute the conductivity, or ionic activity, of the solution in the absence of ion-pairing. Without a "natural" generally accepted definition of an ion-pair (as distinguished from the diffuse ionic atmosphere about an ion, or from an essentially covalent bond between two oppositely charged ions) the ion-pairs in a system must remain defined by the method used to study them.
Using Equations 3 and 4,b' and the corresponding apparent distance of closest approach a', may be found . As an illustration, the error caused by not detecting long range ion-pairs was computed a t 25" for ISOTOPIC OXYGEN IN THE STUDY OF THE aqueous solutions (D78.5$).3 The distance of ap- SOLID REACTION OF SILVER SULFATE proach was taken to be 5 A,, a typical value for sysAND CALCIUM OXIDE tems involving one complex ion, and the maximum B Y ELLINUTON M. MAQEE' separation of measurable ion-pairs t o be 8 .if., which Contribution from the Chemistyy Department, University of Wisconsin, allows for two molecules of water between the ions. Madzson, Wisconsin Values of &(b) were taken from Harned and Owen.4 Received J u l y 16, 1067 The results are tabulated below. Similar results may be found with other assumed values of q, p , T, Recent experiments on the kinetics of the solidand D. solid reaction EFFECT OF NOT DETECTINQ DISTANT ION-PAIRS Electrolyte t Y P,"
4.
a, PI A.
4,A. K K' a',
A.
2-1
3-1
5 8 7.1 9.9
5 8 10.7 44.5 21.7 0.84
12.4
9.49
These calculations clearly show that the observed equilibrium constant for an electrostatic ion-pair mill be decreased significantly if the experimental method used does not detect distant ion-pairs. Conversely, as the calculations for a 2-1 electrolyte show, the observed equilibrium constant will be increased significantly if the experimental method detects fortuitous ion-pairs which are separated by a greater distance than the maximum distance for ion-pair-ng considered by the theory. (Because p is 3.57 A., which is less than the assumed a in these calculations, 1-1 electrolytes were not considered. As they show little or no electrostatic ion-pairing in water, any observed equilibrium constant is almost certainly the result of "chemical" bonding or fortuitous ion-pairs.) Somewhat unexpectedly, as the charges on the associating ions increase, and the maximum interionic distance for a BjerrumFuoss ion-pair increases, the importance of distant (3) G. Akerlbf, Values given in H. S. Harned a n d B. B. Owen, "Physical Chemistry of Electrolytic Solutions," 2nd Edition, Reinhold Publishing Corp., New York, N. Y., 1950, p. 118,Table (5-1-3). (4) Ref. 3, p. 123 Table (5-2-3).
2-2or 4-1
3-2
5 8 21.4 1.47 x 103 0.07 X lo3 5.77
5
8 14.3 166 84 5.98
4-2
5 8 28.5 1.32 x 104 1.11 x 104 5.14
+ CaO +2Ag + '/so2 + Cas04
AgzS04
at temperatures around 5OOo2 indicate that the limiting factor in the rate of the reaction is the diffusion of the silver ion, It diffuses rapidly over the surfaces of the particles and then slowly into the interior of the calcium oxide particles. The present experiment using isotopic oxygen was carried out to determine by a different technique whether or not the diffusion of oxygen is a limiting factor. Calcium oxide containing excess oxygen-18 was prepared by shaking pure CaO with water containing 1.5 mole % ' of oxygen-18. The O18-water was obtained from the Stuart Oxygen Company of San Francisco, California. The Ca(0H)z was then heated for several hours to give CaO with excess 0'8. Stoichiometric amounts of dry AgtSO4 and the enriched CaO were mixed by grinding in a mortar and screening through a 200 mesh screen onto a 325 mesh screen. The part of the mixture on the 325 mesh screen was stored in a desiccator over NaOK. A Vycor tube, 20 mm. in diameter and about 4 inches long, had a ground-glass joint attached at one end and was sealed (1) Humble Oil and Refining Company, Baytown, Texas. (2) W. P. Riemen a n d F. Daniels, THISJOURNAL,61,802 (1957).
