1096
STEPHENR. COHENAND ROBERT A. PLANE
Vol. GI
THE ASSOCIATION OF FERROCYANIDE IONS WITH VARIOUS CATIONS BY STEPHEN R. COHENAND ROBERT A. PLANE Contribution from Baker Laboratory of Chemistry, Cornell University, Ithaca, N . Y . Received April 6 , 1967
Absorption spectra of aqueous solutions of thallous chloride, potassium ferrocyanide and potassium ferricyanide were measured in the visible and ultraviolet regions. The spectrum of potassium ferrocyanide deviates from Beer’s law, the extinction coefficients for wave lengths from 320 to 250 mp decreasing slightly as the concentration is increased, or as potassium, barium or magnesium salts are added. Using this effect, the association constants (corrected for the activity coefficients of the ions by the Debye-Huckel equation) were found to be 237 for the assumed ion-pair K F ~ ( C N ) G -6.3 ~ , X lo3for the assumed ion-pair BaFe(CN)6’, and 6.5 X lo3 for the assumed ion-pair Mg(HnO)6Fe(CN)a- (or MgFe(CN)e-). There was some indication of the formation of the ion-triplet KJ?e( CN)6- v+th a large excess of added potassium ion. The distances of closest approach for these ion-pairs were computed by the Bjerrum-Fuoss theory of ionic association t o be 4.16, 6.00, and 5.69 A., respectively, which is in reasonable agreement with the distances 5.0,5.0 and 5.6 A. estimated from crystal radii. hleasurements of, the association constant for barium and ferrocyanide ions in mixtures of isopropyl alcohol and water (dielectric constant ranging down to 70.7) also indicate the validity of the Rjerrum-Fuoss theory. Absorption spectra indicated the association of thallous chloride, the interaction of ammonium and thallous ions with ferrocyanide ions, and guanidinium ions with ferricyanide ions. No significant changes in the spectrum of potassium ferricyanide were found to occur upon the addition of ammonium, tetramethylammonium, magnesium, barium or thallous ions. magnesium oxide in water. The excess magnesium oxide was filtered off, nnd the filtrate partially evaporated on a hot plate. The crystals of magnesium perchlorate hexahydrate, .\Ig(C10)zr.6H20,which separated were dried in an oven a t 100-110” and stored over anhydrous calcium chloride. The material was neighed as the hexahydrate. The mother liquor from the magnesium perchlorate gave no indication of ferric iron when tested with concentrated potassium ferrocyanide solution. Fresh Jlallinckrodt ( AR) isopropyl alcohol was used to prepare the mixed solvents. Apparatus.-Absorption spectra were measured with a Beckman D r spectrophotometer. One-cm. and 10-cm. silica cells were used to study the interaction of ferrocyanide ion with potassium ion, and 10-cm. silica cells were used with magnesium and barium ion. One-cm. cells with 9-mm. silica spacers t o reduce the light path to l mm. were used to measure the absorption spectra for potassium ferrocyanide and potassium ferricyanide solutions. Thermospacers maintained the temperature of 25.0 f 0.3” with the 1-cm. cells and 25 I1’ with the IO-cm. cells. Procedure.-Stock solutions of potassium chloride, barium chloride, magnesium perchlorate and potassium ferrocyanide were prepared gravimetrically, fresh potassium ferrocyanide solution being prepared for each set of runs. From these all the experimental solutions to be used in one Reagents.-Analytical reagent grade potassium ferro- run were made (at the same time) using a calibrated pipet. cyanide was recrystallized from hot water. The crystals The solutions were thermostated a t 25.0 f 0.1” for a t were dried for several weeks in an opaque desiccat,or over a least 20 min., and the spectra measured against distilled saturated aqueous solution of sucrose and sodium chloride13 water. The cells were calibrated with distilled water before and weighed as the trihydrate. AR potassium chloride was and after every two samples. To minimize errors from the dried a t 100-110’ and used without further purification. AR atmospheric oxidation of a trace of ferrocyanide ion to ferribarium chloride was dried a t 180-200° and weighed as the cyatiide ion, measurements were made between 278 and 284 anhydrous salt. Magnesium erchlorate hexahydrate was mp which bracket the isosbestic point for ferro- and ferriprepared by adding slightly fess than the stoichiometric cyanide. I n addition, the solutions were used in an order amount of 70y0 AR perchloric acid t o a suspension of AR which cancelled systematic errors from oxidation of ferrocyanide ion. The ionic strength was not kept constant by adding an indifferent electrolyte, R S is often done when (1) Abstracted from the thesis submitted b y Stephen R. Cohen to studying complex cations, bccause no cation was found the Graduate School of Cornell University in partial fulfillment of which definitely did not associate with ferrocyanide ions. the requirements for the degree of Doctor of Philosophy. (Because the change in the ferrocyanide absorption spec(2) M. Linhard, 2. Elektrochem., SO, 224 (1944). trum when an ion-pair forms is small, the absence of a de(3) M. Linhard and b l . Weigel, 2. anoru. allgem. Chem., 866, 73 tectable change in the spectrum with added salt could not be (1951). taken to mean that no associntion occurred.) (4) J. C. James, J . Chsm. Soc., 1084 (1950).
Introduction Recently there has been interest in the interaction of complex cations such as cobalt(II1) hexammine with anions in aqueous s o l u t i ~ n . ~ -Many ~ of the studies have been made spectrophotometrically, the appearance of a new absorption band in the ultraviolet being taken t,o indicate the formation of a n ion-pair or “outer sphere complex. ” Linhard2 has suggested that this interaction is essentially electrostatic ion-pairing. This explanation can be checked by seeing whether: (a) ion-pairing of comparable magnitude is found with complex anions and simple cations; (b) equilibrium constants agree with those calculated by the Bjerrum10t11-FuossL2theory of electrostatic ion-pairs; (c) increases with a decrease of dielectric constant of a mixed solvent such as isopropyl alcohol and water. Experimental
(5) E. R. Katzenellenbogen, Paper No. 23, Division of Physical and Inorganic Chemistry, American Chemical Society Meeting, September, 1950. (6) M.G.Evans and G. H. Nancollas, Trans. Faraday Soc., 49, 363 (1953). (7) C. Postmus and E. L. King, THISJOURNAL,S9, 1208 (1955). (8) F. A. Posey and H. Taube, J . A m . Chem. Soc., 78, 15 (1950). (9) A. L. Phipps and R. A. Plane, ibid., 79, 2458 (1957). (10) N. Bjerrum, Kgl. Danske Vidensk. SeEskob, 7 , No. 9, (1926). (11) N. Bjerrum, “Selected Papers,” Einar XIunksgaard. Copenhagen, 1949, p. 108. (12) R. M. Fuoss and C. A. Kraus, J. A m . Chem. Soc., 66, 1019 (1933). (13) I. M.Kolthoff and V. A. Stenger, “Volumetric Analysis,” Vol. 11, Interscience Publishers, Inc., New York, N.Y., 2nd Revised Edition, 1947, p, 302.
Results Observed spectra of 0.01 and 0.001 JI solutions of potassium ferrocyanide and potassium ferricyanide and the spectra of potassium ferrocyanide reported by Iiortum14 and by Iber? and DavideonL5 are presented in Fig. 1. Although they agree at longer wave lengths, the extinction coefficients for potassium ferrocyanide measured by the authors below about 340 mp are appreciably higher (see Fig. 1) than those given by Ibers and Davidson for a (14) G. Kortiim, 2. p h y s i k . Chsm., B33, 243 (1936). (15) J. A. Ibers and K.Davidson, J . Am. Chem. Soc.. 73,476 (1951)
.
ASSOCIATION OF FERROCYANIDE IONSWITH CATIONS
August, 1957
0.1040 F solution in a H2P04---HP04- buffer a t pH 6.8, and are somewhat higher than those reported by Kortiim a t some unstated concentration. The decrease in absorption was found to occur as solutions of potassium ferrocyanide were made more concentrated, or when salts of several cations were added t o solutions of potassium ferrocyanide. This effect apparently is due to the polarization of ferrocyanide ion when ion-pairs are formed with potassium ions or added cations. Quantitative measurement of this shift was used t o determine the equilibrium constants for the formation of several of these ion-pairs. As shown in Fig. 2, the decrease in the ferrocyanide spectrum with added salt is qualitatively similar for added magnesium, barium and ammonium salts. The Equilibrium Constant for Association with K+.-For the reaction M+" Fe(CN)6-4 MFe(CN)6+n- 4, the equilibrium constant is (if activity coefficients are assumed to be constanP)
109;
-I
30000
d 10000
+
K =
- X ) ( b - X)
X/(U
(1)
where x is the concentration of the ion MFe(CN)6+" - 4, and a and b are the formal concentrations of the ions Fe(CN)6-4 and M+", respectively. For such a solution D = (a
- X ) €1
+ zco
(2)
where D is the optical density (for a 1-cm. light path), and el and eo are the extinction coefficients of the ferrocyanide ion and of the ion-pair, respectively. Combining these we find that in the limit of slight ion-pairing D/a =
€1
+ inlb
(3)
where ml = K(eo - el), and in the limit of almost complete ion-pairing D/a =
€0
+ ms/(b - a )
where m2 = - (eo - el)/K.
(4)
From these
K = d-rnl/m2
(5)
-
(6)
and (€0
€1)
= d-rnlms
The optical densities of two sets of solutions of 0.001 14 potassium ferrocyanide with various concentrations of added potassium chloride were measured, and m2 computed by application of the method of least squares to the equations derived above. Similarly ml was found from three sets of solutions, 0.0001 M in potassium ferrocyanide. In the first set potassium chloride was added in various amounts up to 0.007 M ; the other two sets consisted of three solutions without added potassium chloride. For each of the four wave lengths, the three values of ml were combined with the two values of mz to give 24 estimates of the association constant which were then averaged. Typical data for solutions with slight association and with extensive association are listed in Table I. It should be noted that because of the very slight changes of optical density on association, and the apparent (16) In analyzing experimental data, attempts were made to estimate activity coefficients of the individual species; however, these attempts did not give results greatly different from nor so self consistent as the assumption that over the concentration range studied the pertinent activity coefficient ratios are constant. This assumption was therefore made; however (as discussed later), it was not assumed that the ratios are unity.
10 0
3
~
1
1
,
,
1
1
1
1
,
1
1
1
1
,
1
~
250
300 350 400 450 Wave length, mp. Fig. 1,-Absorption spectra of K4Fe(CN)G and KaFe(CN)6.
200
formation of an ion-triplet, neither limit was approached as closely as desired. The resultant errors are partly cancelled in the ratio ml/m2 because both slopes are decreased if their respective limiting conditions are not reached. In addition, since the square roots rather than the limiting slopes themselves are used to compute K , a fairly good estimate can still be obtained even with moderate errors in the measured slopes. These two features, plus the possibility of calculating many values of K from a few measurements of the limiting slopes, make this method, when applicable, preferable to the slope-intercept method used below for barium and magnesium. The value thus obtained of K = 104 f SI7 or K D H = 237 (see below) for this association constant agrees well with Davies"* estimate of K = 176 from conductivity data. The decrease in extinction coefficient upon association, (e1 - eo), is: 17.6 f 1.0 at 284 mp, 19.0 f 1.2 a t 282 mp, 19.4 f 1.3 at 280 mp and 20 f 2 at 278 m!J. With a large excess of potassium chloride the optical density of potassium ferrocyanide was found to be significantly less than the extrapolated value for complete association. This may be due to the formation of the ion-triplet, K2Fe(CN)6-. The Equilibrium Constants for Association with Ba++ and with Mg++.-As it was difficult to measure the limiting slopes, a somewhat different method was used to measure the constants for the (17) All estimates of error are the probable error, Pe = 0.6745 d \ / z P / ( n - l ) , where Pe is the probable error, 6 is the deviation of an individual value from the mean, and n is the number of values. They do not include any estimate of the systematic eriors. (18) C. W. Davies, J . Am. Chem. SOC.,69, 1760 (1937).
,
1
,
,
STEPHENR. COHENAND ROBERTA. PLANE
1098
Vol. 61
0 . 0 1 M MgCI$0.001 M K,Fe(CN), -0.002 M MQC12+onm2M K,,Fe(CN), -e---+-O,OI M BoC1,+0.001 M K,Fe(CN), -e---+0.002 M BaC12+o.ooo2M K,Fe(CN), +---~0.01 M NH4C1+0.001M K,Fe(CN),
250
260
270
280
Fig. 2.-Interaction
290 300 310 320 Wave length, mp. between K4Fe(CN)Band various salts.
TABLE I KFe(CN)6-a ION-PAIR I. Sli h t association Totaf
[K+la
x
108,
0.400 1.398 2.400 4.400 5.400 6.395 7.400
mr
282 mr
280 mr
278 mp
1044 1036 1045 1032 1038 1027 1027
1158 1149 1159 1144 1150 1141 1140
1282 1270 1279 1262 1270 1261 1264
1408 1393 1401
1381 1388 1382 1388
284
282
280
278
mr
mr
mr
mr
11. Extensive association Total W+lb
x
108,
M
l/(a
- a),
M-1
340
350
which reduces to the linear equation b/A = (U EO - €1) 1/K (eo - e l ) (8) where A = ( D / a - el), if association is slight enough so that %/(EO - el) may be neglected. Three sets of eight solutions 0.0001 M in potassium ferrocyanide and containing various amounts of added barium chloride were prepared, and three similar sets containing 0.0001 M potassium ferrocyanide and various concentrations of magnesium perchlorate were prepared. At each of the four wave lengths, the slope and intercept of a plot of b / A vs. (a b) were computed by least squares, and twelve values of K and (€0 - el) calculated for barium and twelve for magnesium. Representative data for barium and for magnesium are shown in Figs. 3 and
+
D / a a t A, mp
284
M
330
L
+
+
8.00 142.8 M - 1 1011 1124 1245 1368 TABLE I1 8.40 135.1 1012 1126 1247 1372 ASSOCIATION O F BA++A N D FE(CN)O-~ 9.00 125.0 1012 1127 1249 1372 I. K for BaFe(CN)n- Ion-Pair No. 3 Mean No. 1 No. 2 X, m r 10.00 111.1 1016 1128 1248 1373 284 1144 1515 1002 11.00 100.0 1122 1241 1364 1007 282 1232 1398 1059 1006 1120 1241 12.01 90.84 1364 280 1324 1283 1266 1003 1117 1237 14.01 76.92 1360 1381 1253 278 1359 1231 1354 999 1111 16.00 66.64 1262 1392 1139 (1.26 f 0.10) Geoa All solutions contain 0.9996 X M IirFe(CT\T)e. .411 Rolutions contain 0.9993 X 10-3 M K4Fe(CN)6. metric mean x 103
association of ferrocyanide ion with barium or magnesium ions. Combining equat'ions 1 and 2 we get ~/(D/U €1) = ( a b ) / ( e o - €1) 1/K(eo - €11 - X /
+
+
(€0
- €1)
(7)
11.
(el
284 282 280 278
-
to),
l./mole om.
120 124 129 120
125 131 143 147
132 138 140 144
*
126 4 131 f 5 137 f 5 140 i 7
XYANIDE IONS WITH CATIONS ASSOCIATION OF FERR(
August, 1957
4. (For clarity the graphs for 282, 280 and 278 m p are displaced upward 1, 2 and 3 units, respectively.) The equilibrium constants, and (EO e).for these two ions are given iii Tables I1 and 111. I n spite of some scatter of the data points, the close agreement of the individual values t o the average indicates that the average values for K and (eo - el) are accurate. TABLEI11 ASSOCIATION OF M G + + A N D FE(CN)e-' 1. K for MgFe(CN)a' Ion-Pair A, mp No. 1 No. 2
284 282 280 278 Geometric mean 11.
(e1
941 1114 1099 1029 1043
- eo), l./male
284 282 280 278
No. 3
1443 1652 1827 1683 1645
1207 1300 1290 1334 1282
137 139 148 154
163 167 180 183
Mean
1099
6 N
5
s5
N
2 4 VI-
2
h
a
2 v3 I
( 1 . 3 =!= 0 . 2 ) x 103
2
om.
147 152 162 171
149 f 8 153 10 164 f 11 169 f 10
*
Association in Mixtures of Isopropyl Alcohol and Water.-Using the same method as with water, the association between barium and ferrocyanide ions was measured in mixed solvents of dielectric constant, D. Three sets of solutions were prepared with 3.94 weight % isopropyl alcohol in water as the solvent, three sets with 7.80 weight 70 isopropyl alcohol and two sets with 12.1 weight Yo isopropyl alcohol. Typical values a t 282 mp are shown (Values at D = 72.9 and D = 70.7 in Fig. 5. are displaced upwards 1 and 2 units.) The average values together with values for water are listed in Table IV. The meaning of a and a,,+, are discussed below.
0
1
2
(a
3
4
+ b ) X 103, molejl.
5
6
Fig. 3.-Association of Ba++ with Fe(CN)s-'. 8
1
1
1
1
1
1
1
1
1
1
1
1
TABLEIV THE ION-PAIR BAFE(CN)e3 IN AQUEOUSISOPROPYL ALCOHOL Wt. % isopropyl alc. D 19 K x 10-3 0,
A.
aest, ((1
~
A.
- a t 284 - ea) a t 282 w - eo) a t 280 mp - eo) a t 278 eo)
mp (qt
0.00 3.94 78.54 75.7 1.2R=k00.1 1 . 8 f O . l 10.3 9.3 5.0 5.0 126 i 4
119
*5
128 zk 5
138 i 2
131 f 5
128 f 4
130 f 8
143 f. 5
137 =k 5
140
*5
142 i 2
148 i 10
140 f 7
149 i: 5
146 z!= 1
160 f 9
( I (?I
mlr
7.80 12.1 72.9 70.7 2.250.3 4.310.5 9.4 7.8 5.0 5.0
2 3 4 5 6 (a b ) x 108, mole/l. Fig. 4.-Association of M g + + with Fe( CN)6-'. 0
1
+
I n addition to measuring the equilibrium con- responding solutions of potassium ferrocyanide. In stants for the association of ferrocyanide ions wit'h both cases a maximum was found a t about 297 mp, potassium, barium and magnesium ions, and find- a minimum a t 237 mp, and an increase at shorter ing some indication of interaction with ammonium wave lengths, which correspond more or less to the ions, the authors also surveyed the interaction with absorption edge of thallous chloride solutions. Bethallous ion. Mixtures of 0.008 M thallous chlo- cause thallous chloride itself does not obey Beer's ride and 0.0008 M potassium ferrocyanide and law20 and is associated in solution,21this systeni was 0.0016 M thallous chloride and 0.00016 d4 potas- not investigated further. Solubility studies by sium ferrocyanide showed a marked increase in abTables of malar extinction coefficients from 320 to 230 mF sorption below about 380 mp as compared with cor- of (20) 0.01, 0.008 and 0.0032 M TIC1 are available from American Docu (19) G. Akerlaf, values given in H. S. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 2nd Edition, Reinhold Publ. Carp., New York, N. Y . ,1960, p. 118, Table (5-1-4).
mentation Institute, Library of Congresq. Washington, D. C . (21) R. P. Bell and .I. H. B. George, TTans. Faraday Soc., 49, G l ! l (1953).
1100
STEPHEN R. COHEN AND ROBERT A. PLANE
L
l
l
l
l
l
l
l
l
l
l
l
l
2 3 4 5 6 (a b ) X 108, mole/l. Fig. 5.-Association of Ba++ with Fe(CN)e-4 in mixtures of water and isopropyl alcohol (values a t D = 72.9 and D = 70.7 are displaced upwards 1 and 2 units.) 0
1
+
Bell and George21 have also shown association between T1+ and Fe(CN)e-4. An attempt was made t o extend this study to ionic associations involving potassium ferricyanide, but no significant changes in the spectrum were found upon the addition of ammonium chloride, tetramethylammonium chloride, magnesium chloride, barium chloride or thallous chloride. Some evidence of interaction was found with guanidinium chloride but this was not investigated as solutions of guanidinium chloride were found t o deviate from Beer’s law. Discussion From the observed equilibrium constant for the association between potassium and ferrocyanide ions, it is seen that a nearly constant fraction, 4%, of the ferrocyanide in aqueous solution, which is not otherwise complexed exists as a complex with potassium ions. T o compensate for this, the observed association constants with barium and magnesium ions were divided by 0.96. I n addition the equilibrium constants for ion-pairing were corrected for the ionic strength of the medium. Because each solution had a different ionic strength, an approximate correction at the intermediate ionic strength of s’/l = 0.10 was made, using the complete DebyeHiickel equation (for 25”) log y = -0.506~~~’/2/( 1 f 0.329aions’l))
(9)
to find the activity coefficients, and the following esK + = 2.66 A,, timated ionic diameters,22 Ba++ = 2.70 A,, Mg++ = 1.30 A., Mg(Hz0)6++ = 3.90 A., Fe(CN)6-4 = 4.40 A., KFe(CN)6-3 = 10.Oofi., BaFe(CN)a= = 10.0 A., MgFe(CN)6’ = 8.6 A,, and Mg(HzO)6Fe(CN)a-= 11.2 A. Since it was impossible to estimate either the ex(22) L. Pauling, “The Nature of the Chemical Bond,” 2nd Edition, Cornell University Press, Ithaca, N. Y., 1944, Chapters V, X.
Vol. 61
tent of association of the potassium ferrocyanide, or the activity coefficients in the mixed solvent, the association coiistants for barium and ferrocyanide ions in mixtures of isopropyl alcohol and water have not been corrected for either effect. From both the uncorrected and the corrected association constants, K and KDH,respectively, the distances of closest approach of the ions, a and (LDH, were estimated using the Bjerrum-Fuoss equation K = -(4?rN/1000)(zLzzeZ/DkT)*&( b) (10) where Q(b) is a tabulated functionz3of b = -zlxze2/aDlcT. Comparing a D H with aest (the sum of the radii of the ions comprising the ion-pair) and KDHwith Kest (the equilibrium constant computed from aest)in Table V shows that the observed association agrees fairly satisfactorily with the Bjerrum-Fuoss theory of ion-pair formation, especially when the approximations in the theory and in the computations are borne in mind. This agreement seems to indicate that the association is probably electrostatic. Depending on whether the radius of the hexaquomagnesium ion, the simple magnesium ion or some intermediate value is assumed, K e s t for the association of magnesium with ferrocyanide can be varied by a factor of seven, which shows the influence of the extent of solvation and structure of ions in COMPARISON OF K
TABLE V BJERRUM-FUOSS THEORY
NITH
a,
Ion-pair KFe(CN)a-3 BaFe(CN)r MgFe(CN)aMg(HzO)s(CN)s-
b
KDH
Kent
A.
237 G . 3 X 103 G.5 X 103 6.5 X lo3
1GG 13.3 X I O 3 4 1 . 1 X 103 7 . 0 X IO3
6.7 10.3 10.1 10.1
ami,
A.
aest,
A.
4.17 5 . 0 0.00 5 . 0 5.06 5.09
4.3 5.6
solution. Apparently, as the values of KDHand show, the smaller magnesium ion and the larger barium ion have nearly the same “Bjerrum-Fuoss” size in solution. This is evidence that magnesium ions are extensively hydrated in solution, much more so than barium ions; although it does not show the existence of hexaquomagnesium ion, or any other definite aquo complex. One of the best proofs of an electrostatic ion-pair is the change of association constant with dielectric constant as predicted by the Bjerrum-Fuoss equation; or what is equivalent, the distance of closest ionic approach computed by the BjerrumFuoss equation being independent of the dielectric constant of the medium. I n spite of errors from neglecting the activity coefficients of the ions, and the association of the potassium ferrocyanide, the nearly constant value (Table IV) of the computed distance of closest approach between barium and ferrocyanide ions as the dielectric constant of the solvent is decreased is consistent with the supposition that the association between these two ions is electrostatic. Acknowledgment.-The authors are indebted to the General Electric Company for a Fellowship in Chemistry to S.R.C. during the year 1955-1956. UDH
(23) H. S. Harned and B . B. Owen, ref. 19. p. 123, Table (5-2-3).
d
-
