COOPERH. LANGFORD AND WARREN R. MUIR
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Thermodynamics of the Formation of Co( NH,),CP+ from Co( NH,) ,OH,a+: Separation of Environmental Effects'
by Cooper H. Langford and Warren R. Muir Moore Laboratory of Chemistry, Amherst College, Amheret, Massachusetts 01002
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(Received January 61, 1967)
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Although over-all formation constants for complexes have often been evaluated at a few temperatures and thermodynamic parameters calculated from conventional log K - ( l / T ) plots, such plots are not too often linear. A maximum value of K in the neighborhood of room temperature may be found. Thus, AH" may actually change sign. This study reports the equilibrium constant for the reaction C O ( N H ~ ) ~ O H ~C1~ +% C O ( N H ~ ) ~ C ~ ~ + at temperatures from 25 to 86" at unit ionic strength and pH 3. Substantial curvature in the dependence of the observed concentration ratio [ C O ( N H ~ ) ~ C[~C~O+ (]N / H)~OH~~+] on chloride concentration is interpreted by means of separation of the outer-sphere ion association equilibrium from the outer-inner-sphere ligand interchange equilibrium.
+
+
Equilibrium constants for the two reactions CO(NH~)E,OH~~+C1K2
KI
CO(NH~)~-
OHz3+.. 'C1- and C O ( N H ~ ) ~ O H* .C1~~+. Co(NH3)~C12+ may be identified and are designated K I and K2. K 1 goes through a maximum at 57" but K 2 increases monotonically with temperature.
Introduction When a reaction in a polar solvent involves a change in charge types of participant species, simple electrostatic considerations suggest that environmental effects will lead to a substantial AC," (change of the heat capacity) in the reaction. Thus, the equilibrium constants obtained will not have a simple temperature dependence characterizable by a single value for the standard enthalpy change AH" over a moderately wide temperature range. This point has been carefully developed theoretically by Gurneys2 The simple electrostatic model predicts occurrence of maxima in the equilibrium constant-temperature function. Experimentally, the expectation has been fully realized for dissociation of weak organic acids in aqueous media2 and for the few appropriate complex formation equilibria which have been examined over a suffciently wide temperature range. The latter include the formation of Cr(OH2)6NCS2+ and the formation of Co(NH&Br2+ from CO(NH~),OH~~+.* In both cases, there are temperatures not far from room temperature at which the formation constants pass through a maximum. The Journal of Phyaical Chemistry
Gurney's ideas suggest that more useful thermodynamic parameters for complex formation equilibria might be obtained if the effect of the electrolytesolvent environmental factors could be partially eliminated by resolving the reaction into two steps, (1) formation of an outer-sphere complex (ion pair) and (2) ligand interchange between the inner and outer coordination spheres. This resolution is shown in eq 1 . Ki
(a) C O ( N H ~ ) ~ O -IH ~C1~+ C O ( N H ~ ) ~ O H. .C1~~" (1) Kz
1
(b) C O ( N H ~ ) ~ O H * uC1~~+*
Co(NH3)5C12+.. *OH2 (1) Work supported by the Petroleum Research Fund of the American Chemical Society under Grant No. P R F 2329-A5. (2) R. W. Gurney, "Ionic Processes in Solution," McGraw-Hill Book Co., Inc., New York, N. Y., 1953,Chapter 7. (3) C. Postmus and E. L. King, J . Phys. Chem., 59, 1217 (1955). (4) J. B. Swaney, B.A. Thesis, Amherst College, Amherst, Mass., June 1966.
FORMATION OF Co(NH3)&12+ FROM Co(NH&OH2*+
We define K1 and K2 as the conditional equilibrium constants for the outer-sphere and the inner-sphere formation reactions, respectively. From a limited point of view, in reaction l b there is no change in charge, thus, one might expect the value of K2 to display a less complex temperature dependence than the over-all formation constant. If so, some important environmental effects have been excluded from consideration and "separated." The over-all react'ion may be studied spectrophotometrically by observing the total concentration of the aquo and chloro complexes. Calling the spectrophotometrically observed ratio [Co(NH3)5C12+]/[Co(NH3)sOH23f]KO,the resolution into two steps implies a chloride concentration dependence of KOat constant ionic strength given by eq 2.
For small K1 values, the dependence of KOon [CI-] reduces to K1K2[CI-] in eq 2. This is a limitation encountered in the studies of the formation of Co(NH&Br2+ and Cr(OH2)6NCS2+which permits only determination of over-all formation Constants. The results reported here for the formation of Co(NH3)6Cl2+ in media of unit ionic strength (maintained with NaC104) are free from this limitation. Marked curvature is observed even at relatively low [Cl-1. It proves possible to achieve the desired resolution under the assumption that specific ion efects on activity in these media are attributable to association and to show that the maximum envisioned in Gurney's theory occurs in K1 while K2 increases monotonically with temperature. Within the (limited) precision attainable in this study, a single value of AH" may be fitted to the K2data.
Experimental Section
Materials. [ C O ( N H ~ ) ~ O H ~ ] ( C was ~ Omade ~ ) ~ from [CO(NH~)~CO~]NO? and recrystallized five times before use. [CO(NH~)~CI](NO~)~ was also made from the carbonatopentaammine. The [Co(NH&CO3]N03 was dissolved in distilled water. An excess of HC1 was added until the evolution of C02 gas ceased. The deep red solution was then heated on a steam bath for about 3 hr at 60'. The purple precipitate [Co(NH& C1]Cl2 was collected by filtering and washed with ethanol and ether. A 6-g sample of this salt was put in a mortar and ground in the presence of 60 g of NHdNOa and 50 ml of HZO. After several minutes, the residue was filtered and the product retained by the filter was returned to the mortar. The above procedure was repeated twice. The product was washed with cold
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water, ethanol, and ether and was recrystallized several times from water. Verification of these syntheses was made by comparison of visible spectra. Wavelengths of maxima and extinction coefficients ( E ) were found in agreement with literature values ( .t0.3a/o).6 At 532 mp, Co(NH3)6C12+has an E extinction coefficient of 50.8. At 491 mp, C O ( N H ~ ) ~ O H has ~ ~an + E of 47.6. Baker Analyzed sodium chloride was used to make a 1.000 f: 0.001 M solution. This was acidified to pH 3 with HC104. A 1.00 f 0.01 M solution of NaC104 was made by reacton of Baker Analyzed HC10, and NaOH in the appropriate amount of distilled water. This solution, too, was acidified to pH 3 with HC1O4. Equilibrium Study. Approximately 2 X M solutions of the pentaammine salts a t various chloride concentrations were placed in rubber-capped &in. test tubes and put in a temperature bath. Bath temperatures were maintained with a Tecam Tempunit to f0.1 Equilibria were determined approximately every 10" from 25 to 85". Temperature baths were covered to protect the solutions from light. That solutions were at equilibrium was verified in each case by either checking that both the original chloro and aquo pentaammines had reached the same point or by following the kinetic course of the reaction with the spectrophotometer. When equilibrium was attained, the solutions were rapidly cooled to 15-20' and filtered through a micropore filter. The absorbance was read in 5-cm silica cells with a Beckman DU spectrophotometer equipped with a Gilford absorbance indicator. The wavelength used was 555 mp. At this wavelength, extinction coefficients of the aquo and chloro complexes are 16.8 and 46.2, respectively. The ratio [Co(NH3)&I2+]/[ C O ( N H ~ ) ~ O H ~ ~ + ] was calculated from the extinction coefficient observed at each temperature and concentration of chloride. Outer-sphere association (added chloride) has no effect on the extinction coefficient of C O ( N H ~ ) ~ O Hat~ ~ + 555 mrm.
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Results Typical plots of the concentration ratio [Co(NH3)5Clz+]/[ C O ( N H ~ ) ~ O Has~ ~a +function ] of chloride concentration are presented in Figure 1. Curve B is the 25.0" data and curve A is the 76.7" data. The curves shown indicate the success of the procedure used to analyze the data. They are obtained by fitting the data to eq 2 by employing a trial and error "hill climbC. Blair, l w g . Syn., 4, 171 (1953). (6) H.Taube, J . Am. C h . Soc., 82, 524 (1960).
(5) J.
Volume 71, Number 8 Julg 1967
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COOPER H. LANGFORD AND WARRENR. MUIR
2.0 1.0
-.
0.8
0.6
2:
2
0.4 0.4 0.2
c 30
0.2
0.4
0.8
0.6
[Cl-1, M.
ing" approach to the choice of K1 and K z with a leastsquares error criterion. (The program employed for the calculations is straightforward and obvious.) Best choices of K1and K2 were determined to two significant figures. Table I lists K1 and K2 values as a function of temperature with the values of standard deviations of the fit. Data points (20-50) for each other temperature have been filed as a supplementary document.' Figure 2 shows the value of the outersphere association constant K1 as a function of temper& ture. Note the maximum near 55". Fitting log K2vs. (l/T) to a straight line by a linear least-squares procedure yields the thermodynamic parameters for complex formation: AH" = +0.4 kcal/mole, hs" = $1.6 eu. The standard deviation of the leashquare fit is 0.1. Table I: Computed Values of Equilibrium Constants K1, M-
K2
25.0 35.0 47.0 57.0 65.7 76.7 86.0
0.9 1.2 1.4 1.6 1.5 1.3 1.3
1.5 1.4 1.5 1.5 1.7 2.3 2.3
Std dev
4.47 x 4.72 x 8.20 X 3.24 X 3.07 x 4.55 x 3.98 x
lo-' 10-9 lo-' 10-1
lo-* lo-*
Discussion As often as not, the fundamental interest in determining thermodynamic parameters for complex formation is to make comparison of various metalligand bond interactions (e.g., the theory of hard and The Journal of Phyeical Chemistry
BO
T,OC.
Figure 2. The value of the outer-sphere association constant K1 as a function of temperature ('C).
Figure 1. The concentration ratio [Co(NH&CP+]/ [Co(NHa)&OH2a+] as a function of chloride concentation. Curve A is 76.7' data; curve B is 25.0"; p = 1.00 with NaClOa; pH 3.
T,ac
70
60
soft acids and bases).s From this point of view, environmental effects are a nuisance. Especially the dominance of the thermodynamics of complex formation by environmental effects implied by the frequent occurrence of changes of Sign in AH" (maxima in the temperature dependence of K ) is more than a nuisance. The main thesis of this report is that the maximum in the plot of the formation constant as a function of temperature may originate in the electrostatic effects on outer-sphere complex formation. The temperature dependence of the outer-sphere-inner-sphere complex equilibrium constant ( K z )may be expected to be subject to much simpler interpretation. It may even allow use of a single value of AHo over the whole temperature range of interest. The thesis is supported by the values of the thermodynamic parameters obtained for KS. The rather small value for A#" would be considered surprising if the reaction from outer-sphere to inner-sphere complex were seen by the aqueous environment as a charge-destruction process. It is interesting to note that the product KlK2 corresponds to the over-all formation constant usually measured. For Co(NH&,C12+,the value at 57" is 2.4 M-l (K1 = 1.6, KZ = 1.5). Under comparable circumstances, the value for formation of Co(NH3)aBr2+ is 0.51 M-1.4 Since no curvature was observed in the plots of [ C O ( N H ~ ) ~ B [~C~O + (] N / H~)~OH~~+] vs. [Br-1, we may conclude that K1 is 2.5 in the bromide (7) A more detailed form of this paper has been deposited as Document No. 9422 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. 20640. A COPY may be secured by citing the document number and by r e mitting $1.25 for photoprints or $1.25 for 35-mm microfilm. Advance payment is required. Make checks or money orders payable t o : Chief, photoduplication vi^^, Library of Congress. (8) R. G. Pearson, J . Am. Chem. SOC., 85,3733 (1963).
FORMATION OF Co(NHa)6Cla+FROM CO(NHJ~OH~*+
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case. The importance of resolving formation constants into outer-sphere constants and inner-sphere-outersphere interchange constants is suggested by noting the relationship of these numbers to the “hard” and “soft” behavior of the acid. The “inner-sphere” acid behavior appears “soft”; the formation of Co(NH&Br2+ is favored over formation of Co(NH&CI2+. The “outer -sphere” acid behavior is “hard”; formation of C O ( N H ~ ) ~ O H‘(31~ ~ + *is favored over C O ( N H ~ ) ~ O H .~-Br-. *+. Finally we must remark on the reasonableness of outer-sphere constants (KI) determined by the indirect methods of this study. They will be wrong to the extent that higher association (e.g., Co(NH&OHz*+* C12) may be important. They may be compared to constants determined from effects of outer-sphere association on the spectra in the ultra~iolet.~By this method a value of 3.2 f 0.4 was obtained (and is r e
ported elsewherelo) for the outer-sphere association constant (formation of Co(NH&.OHa. .C1-). This was recorded at 25’ for a lower chloride concentration range. It is in reasonable agreement with the K1 value derived from our equilibrium data but does suggest some higher association in the present case.ll The agreement is reassuring in its support of the physical significance of the separated variables from this study. A very similar value for K1 was obtained from analyzing the chloride dependence of the rate of formation of C O ( ~ H & . C ~ ~ + . ’ ~
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(9) M. G. Evans and G. H. Nanoollas, Trans. Faraday Soc., 49,363 (1953). (10) C. H. Langford and W. R. Muir, J . Am. Chem. Soc., 89, 3141 (1967). (11) The value 3.2 may be a better value for the outer-sphere ion
association conatant since the present equilibrium data probably include more of the effects of higher association.
Volume 71, Number 8 July 1967
