March 20, 1953
COXVERSION O F
[ COXTRIBUTIOX FROM
THE
CO(NHB),H~O+++ TO C O ( K H ~ ) ~ SAT O ~~ +Q U I ~ I R R I U M
GEORGE HERBERT JONES LABORATORIES, cNIVERSITY
OF
1463
CHICAGO]
The Study of a System Involving Equilibrium between Inner Sphere and Outer Sphere Complex Ions : Co(NH,),H,O+++ and SO,= BY HENRYTAUBE AND FRANZ A. POSEY RECEIVED OCTOBER 10, 1952 The fractional conversion of Co( NH3)sH20f++t o Co( NH&SO4+ a t equilibrium is observed to be almost independent of the concentration of sulfate ion over a wide range above ca. 0.01 ill. The behavior is understood if the aquo ion is assumed t o be converted t o a sulfate complex ion by outer sphere association a t low concentration of sulfate ion. The interpretation is confirmed by observations on the ultraviolet absorption band of C O ( N H ~ ) ~ H ~ Oin+the + + presence of varying amounts of sulfate ion. The change from the sulfato ion t o the “isomeric” outer sphere complex ion is governed by the energy quantities: AH = -4.0 += 0.3 kcal. mole-‘, A S = - 13 cal. deg.-’ mole-’. The reactions are first order in the concentration of Co(II1). An increase in lability is observed with increase in sulfate ion concentration. The reactions are catalyzed by hydrogen ion. The activation energy for the change of the sulfato ion t o the aquo ion is 19.3 i 0.5 and for the reverse change is 23.7 zk 0.5 kcal. mole-’.
I n considering the structure in solution of a complex ion the stoichiometry of which has been established, the question arises as to its distribution between two forms, in one of which the addend is directly attached to the central ion occupying a position in the first sphere of coordination, and in the other occupying a position outside the first sphere of coordination. The latter type of structure can be expected to have considerable stability when the central ion has a high charge and when the addend is an ion of high charge. The importance of association of this type in water solution has been proven by the work of Davies,l Linhard2 and Kat~enellenbogen~using complex cations of the type CO(NH3)6+++. Replacement of NHa by the anion does not take place under the conditions which were chosen and, in fact, the observations on the spectra2 suggest that the first sphere of coordination is little disturbed in forming the outer sphere complex ions. It is evident that inert complex ions are extremely useful in defining the type of association under study, owing to the great difference in the speed a t which association in the inner sphere and outer spheres takes place. For labile complex ions the distinction between the two types is much more difficult to make because the two forms are not readily separately characterized. We have made use of an inert complex ion system also in our study. Substitution of water by water or other groups in Co(NHa)bH20+++ takes place very s10wly.~ Our data with this cation and with SO4= as an anion provide a dramatic demonstration of the presence in the solution of outer sphere complex ions, and furthermore, since H20 and SO4= are eventually exchanged, have made possible a comparison of the stabilities of inner sphere and outer sphere “isomeric” forms. The desirability of a more complete study of this system was indicated by work done on the water exchange rea ~ t i o n . The ~ experiments we are reporting supplement those described by Ade1l.j His study was limited to the range of dilute solutions ((SO4=) lop2 or less) and therefore did not expose some of the interesting phenomena we have observed.
-
(1) C. W. Davies, J . C h e m . SOL.,2421 (1931). (2) M. Linhard, Z. Elektuochew., 60, 224 (1943). (3) E. R . Katzencllenbogen, Paper No. 23, Division of Physical a n d Inorganic Chemistry, American Chemical Socicty Meeting, September, 1950. (4) A . C . Rutenbergand FI. Talihe, .T. Chein Phvs , 2 0 , X l ’ i f I ! l . ? Z ) . ( 5 ) n. Adell, Z. auoi’R. n l i p r m . C h m . , 246, 303 (1!3121,
Experimental The procedure was t o follow the extinction of a solution containing initially the ion Co(NHa)bSO,+ or Co( NH& HzO+++in an environment of known composition as a function of time. In all cases equilibrium was approached from both sides, and in every case the final values of the extinction agreed to within 1%. For numerous solutions the rate was followed as a function of time starting for a given environment both with the sulfato and the aquo ion. I n every case tested the specific rates k (defined as below), forward and reverse, agreed to within 3% if only total sulfate were present in sufficient excess. The values of the initial optical densities for the sulfato and aquo forms, and of the final optical density make possible the calculation of the equilibrium quotient, and these data, together with the specific rate for approach t o equilibrium, lead to the specific rate of aquotization and sulfato formation for each solution. The optical densities were measured using a Beckman spectrophotometer. The wave length 560 mp a t which the extinctions were measured lies on the long wave length side of a band with a maximum a t 515 mp for the sulfato and 495 for the aquo ion. The two maxima in the visible for the ions are not sufficiently well separated t o make them useful in analyzing the solution. While the strong ultraviolet band does differ markedly for the two substances, light of longer wave length was preferred since it permitted the use of Corex cells. The extinctions of Co(NH3)6HzO+++ and C O ( S H ~ ) ~ S OaIt+ X 560 mp are changed somewhat (cf. Table I ) as the environment changes, but only slightly as compared t o the ultraviolet band. I t was shown that the cobalt cations obey Beer’s law in the solutions studied 11ithin experimental error. The extinctions change slightly with temperature-for example, there is an increase of ca. 3yo in the extinction of the sulfato ion in 0.05 N KazSO1 as temperature rises from 25 to 31O-hence for a series all extinction measurements were made a t constant (&lo) temperature. In studying the variation of equilibrium constant with temperature the solutions which had been stored a t different temperatures were all brought to the same temperature for comparison of optical densities. No significant readjustment in the inner sphere of coordination took place during the temperature change. The substance [Co(KHg),SO4]HS04,2H20was the source of the sulfato ion. I t was prepared as described by Jorgensen.6 The content of Co and SO, were found to be 15.80% (theoretical, 15.79) and 51.4270 (theoretical, 51.47). Co( NH~),HzO( ClO,), was prepared as described elsewhere, and served as the source of the aquo ion. The agreement of final optical densities starting with both salts shows that the aquo salt was a sufficiently good preparation. Other reagents were of A . R. quality, used without further purification. Solutions were macle up using redistilled water. Conditions and Definitions.-In all experiments except expt. 11, Table I , the concentration of sulfate was in excess of the concentration of the complex ion by a factor of 8 or greater. Over the greater part of the range investigated, the specific rate as well as the equilibrium distribution is not very sensitive to the concentration of SO.=, and the initial recorded values which differ a t most by 7 or 8% from the equilibrium values, serve as sufficiently good de-
Vol. 75
HENRYTAUBE AND FRANZ A. POSEY
1464
KO.
1 2 3 4 5 6 7 8= 9 10 1Id
TABLE I DISTRIBUTION AND RATEAS FUNCTION OF SULFATE CONCENTRATION DATAON EQUILIBRIUM Temperature 31.1 f 0.02", except in expt. 8; SO,' as Na2SO4 except in expts. 5 and 6 Qe kn X 10' k s X 10' 2 Is04-I Z[H+] k X 10' Do9 D Do 6.6 4.7 1.42 2.90 0.30 0.213 11.3 0.328 0.491 4.6 3.7 1.25 .11 1.15 .339 .214 8.3 * 495 3.7 3.1 1.18 0.57 .050 ,213 6.8 .345 .501 .156 .015 4.8 ,499 .345 .214 1.17 2.6 2.2 .156" .015 4.3 ,499 .347 .214 1.14 2.3 2.0 .156b .015 5.2 ,502 .348 .215 1.16 2.8 2.4 .052 .010 4.1 .506 .352 .214 1.12 2.2 1.9 .010 17.0 .506 .371 ,214 0.86 7.9 9.1 .052 .021 .010 3.4 .508 .345 .217 1.28 1.9 1.5 .0140 ,010 2.8 .510 .341 ,217 1.36 1.7 1.2 0061 ,512 .321 .221 1.91 .00216 MgSO,. Temperature 43.8'. (RS04HS0,) = 0.00108 M; (HC104) = 0.005 M. No other electrolyte.
.
KSOI.
scriptions of the sulfate concentration prevailing. Except where otherwise recorded, sulfate was introduced as Xa2SO4. Z[SO4'] refers to total SO,' present, whether complexed or not (and differs but slightly from uncomplexed sulfate as noted above) Z[H+] represents concentration of H + present in all forms R represents the radical Co( NH& [A! represents the total concentration of species containing R H 2 0 + + + [SIrepresents the total concentration of species containing RSO4+ DoR, DoA and D , represent the optical densities (log loll) of solutions containing S initially, A initially and the equilibrium mixture, respectively. For all solutions, cd = 0.0150 cm. mole 1. - I . k is the specific rate of change as measured in a plot of log I D , - D, I versus t. I t is equal to the sum kA $. ks where these specific rates refer to the processes
kA S+A ks
A + S
QB represents the ratio [A]/[S] a t equilibrium and is
equal t o k r / k s . Specific rates are expressed with time in minutes. I
Results In Fig. 1 are presented typical data on the change of optical density with time, starting in one experiment with the aquo salt and in another with the sulfato salt. Table I contains a summary of results obtained a t relatively low acidity with [SO,'] as the principal concentration variable. Acid was present in all solutions to suppress the acid dissociation of RH1O+++. The results reported later show that (H+) (or (HS04y)) is not an important variable a t the levels used in the series in Table I. Table I1 is a summary of the data obtained on the variation of Qe with temperature. The data are shown plotted
TABLE I1 VARIATION OF EQUILIBRIUM CONSTANT WITH TEMPERATURE Medium 2[S04=1 ZH +
0.10 0.08
-. 0.06 8
Q I 0.04
6
-0.03
0.02
1.67 1.28 1.44
0.30 .OlO .010
2.90 0.052 0.021
at
31.1
43.8'
1.42 1.12 1.27
1.11 0.86 1.01
-4.1 f 0.3 a t 2.6 M SO1-4.0 f 0.3 a t 0.052 M Son' -3.6 & 0.3 a t 0.021 M so4' Table I11 presents data obtained for solutions containing also sodium perchlorate, Table IV for solutions with varying amounts of NaHS04 and Table V for solutions with varying amounts of NaHSO4 and HtSO4. In Table VI some data dealing with the changes in extinction for the ultraviolet band of R H 2 0 + + +as SOa' is added, are presented. The study of the spectra in solutions of various compositions is itself a major undertaking and more complete data for this and related systems will be presented in a future publication.
.-.-
__
Discussion
The most interesting feature of the equilibrium data is t h a t the ratio Qe is almost independent of (sod-)over a wide concentration range, extending from 0.02 to 2.6 M. It is further remarkable t h a t this ratio instead of diminishing a t high (SOI'), in fact shows a slight increase in this concentration region. These observations suggest that the principal equilibrium operating over the range studied is RSOn' 4- H20
10 20 30 Time, hr. Fig. 1.-The variation of optical density with time medium, Z[SO,-] = 2.90 M,Z[H+],0.3 M . Upper curve, sulfato salt approaching equilibrium ; lower curve, roseo salt. P same for both.
Qe
in Fig. 2 to yield values of AH in kcal./mole which are as follows for the change: S .--) A.
I
0.15
24 9 '
KI
RH2O+++.SOd'
(1)
If ion pair formation is essentially complete even a t 0.02 111 so4=the change S to A involves species of the same stoichiometry with respect to Co(II1) and Sod- and hence also of the same charge. Therefore the effects of salts, including SO4-, is expected to be relatively slight. I n the region of
1465
CONVERSION OF Co(NH3),H20+++ TO Co(NH3)&304+ AT EQUILIBRIUM
March 20, 1953
TABLE I11 THEINFLUENCE OF NEUTRAL ELECTROLYTE Temperature 31.1 '
ks X 10' kr X 104 Do5 DC Qa 0.021 0.010 0.93 1.92 0.516 0.225 4.40 1.57 0.355 .054 ,010 .71 2.56 .511 .223 2.13 1.74 0.82 3 .156 .010 .54 4.38 .506 .218 1.28 2.46 1.92 4 .054 .010 2.00 2.04 .524 .226 2.68 1.49 0.554 5 .156 .010 1.70 2.68 .507 .218 1.39 1.56 1.12 The series was planned a t constant p, but insufficient NaC104 was inadvertently added in this experiment. NO.
Z[H+]
2[SOb-]
k X lo4
(NaCIO4)
1 2"
a
TABLE IV, THEINFLUENCE OF BISULFATEI O N TemDerature 31.1' No.
(NazS04)
(NaHSO4)
(NaClO4)
k X lo4
1 2 3 4 5 6
0.054 ,054 .054 .54 .54 .54
0.10 .30 .70 .10 .40
0.60 .40 00 1.40 1.10 0.00
3.61 4.62 6.34 5.25 5.85 9.02
.
1.50
Do8
DC
Qe
k A X lo4
ks X IO4
0.506 .500 .499 .503 .500 .500
0.215 .215 ,214 .224 .219 .214
1.47 1.35 1.44 1.07 1.13 1.42
2.1 2.6 3.7 2.7 3.3 5.4
1.5 2.0 2.6 2.5 2.6 3.6
zero ionic strength and 25'. The conclusion is TABLE V DATAFOR SOLUTIONS CONTAINING directly proven by the data in Table VI on the RATEAND EQUILIBRIUM ultraviolet extinctions of RHzO+++in the presence NaHSOl AND &SO4 of varying concentrations of Sod-. Marked Temperature 31.1' changes in the extinction are observed in the ultra(Na(Hz- k X kA X ks X
NO. HSO4)
1 2 3 4 5 6 7
0.00 1.00 3.00 0.00 3.00 5.00
0.00
SO1)
104
Do5
Qe
10'
10'
3.00 2.00 0.00 6.00 3.00 1.00 9.00
16.1 12.5 10.2 27.5 21.0 18.5 36.0
0.488 ,496 .496 .485 .488 .490 .460
2.87 2.14 1.61 2.26 1.94 1.69 1.40
11.9 8.5 6.3 19.1 13.9 11.6 21.
4.2 4.0 3.9 8.4 7.1 6.9 15.
violet band, with the extinctions a t 240 and 235 mp approaching saturation values when (sod-) is only 6 X M . More complete data will be required to, obtain values of equilibrium con-
I
TABLE VI THE ULTRAVIOLET EXTINCTIONCOEFFICIENTS OF CO(NH&H20+++AT VARIOUSCONCENTRATIONS OF SULFATE
0.2
-
0.1
-
1
1
ION
Temperature 27 f 1'. E = l/cdlog & / l i n 1. mole +ern.-*; (RHzO(C104)a) = h.0 X M; (HCIO.) = 0.01 M e at Z(Sot-)
I
X in mrr
0.000
0.0062
0.0125
0.0416
0.1040
270 260 250 245 240 235
15 31 143 336 762 1620
26 76 257 503
34 89 288 538 1010 1940
42 112 338 613 1120
44 118 360 650 1180
990 1910
d
s"
low sulfate ion concentration the equilibrium RHzO+++
+ Sod'
KII
= RHzO+++*SO4'
(11)
0.0
presumably becomes important and RHzO+++ as well as RHzO+++.S04- contributes to [A]. At high concentration of Sod', Qe will be altered by salt effects on equilibrium (I) or by further association of sulfate with the complex ions. However, the affinities of RHlO+++.S04- and RS04+ for sulfate ion appear to be about the same, since Qe changes only slightly even a t high sulfate concentration. 2.9 3.0 3.1 The conclusion t h a t RHzO+++ and SO1- are 1/T x 10'. strongly associated is supported by Davies' calculations' for the similar system Co(NH3)6+++ Fig.2.-The variation of Q. with temperature. Curves and SO4- which yielded 3.3 X lo3 as the equi- are in order for 2.90, 0.021 and 0.052 M , Z[SOd-] reading librium constant for the association reaction a t from top to bottom.
stants, particularly because successive stages of association apparently must be taken into account. This is e\ idenced by t h t obscri-atioii that the rate of approach t u saturation cxtinctioii 7 dues is different at different wave lengths. If the assumption is made that the ratio (RHeO -.SO4=)/ IRS04 ) rcinains coiistarit below 0.03 -11SO4=,anti is riicasured by the ratio Qc a t this sulfate ioii concentration, the value of k-11for expt. 11 is calculated as 1 I X io1. 'Il'hen corrected for the difference in p , this value will be close to that rvportvc! bv 1hvic.s tor Co(SH1)c arid SO,-. The measured heats of reaction o n tlie interpretation suggested apply to reaction I. I t should be noted t h a t the change is exotheriiiic. I t is interesting that the heat of transfer of SC Ii from inner sphere to outer sphere does not change appreciably as (SO,=)changes from 0.0; to 2.0 J/. The decrease in , ! J I ' at lower (SO4=)can be attributed to participation by equilihriuni ( I I ) . Using the observed values of equilibriuin coiistmt and AI1 a t 0.05 . I1 SO4=, A S a t this Concentration of sulfate is calculated as -13 e.u. .in entropy decrease can be expected since ions of opposite charge are separated in transferring SO4= from inner sphere to outer sphere, thus increasing the interaction with the solvent. The effect of NaC104 on the equilibrium [-I], [SI is presumably largely in increasing the concentration of KHzO t i- ' relative to IIHiO t i .SOa= RSOe-. There niay also be an effect O T ~the ratio (RH&+' +.SO4=) ( R S 0 4 + ) ,but this is impossible to decide from the data. ;issuiiiing that the ratio is unaltered hy n'aC10, iiitl is given 1 3 ~ the value of QP a t 0.05 -11 SO,:, tlic quotient I i t i for expt. I , Table 111 i i calculated LO, and for expt. 2 of the same tablc, .it soinewhat loner ionic strength as 20. The larqe chanqe in A L Eiron1 the conditions of expt. 11 to those ohtaininq in the experiments of Table 111, I \ i n line w t ! ~the l x g e value of Az? for reaction (11 The data of Table I V suggest that salts do affect the ratio (IiH?O 4 - SOs-') ( IIS04-j K'liile in dilute solution (expts. I, 2 , :3, Table I!-) NaC101 and NaHSO4 influence Qe i n a1)prouiimtely the same way, in more concentrated solution (expts. 4, 3, (i) replacing NaCIOl by NaHSO: enhances the ratio. For concentrated electrolyte solutions effects due to changes i n the activity of watcr must become important. The decrease 111 Qc :is thc concentration of sulfuric acid is increased i i
