A Method for the Determination of Stability Constants of Unstable Complexes Lee Hin-Fat and Hln-Cheung Lee Hong Kong Baptist College, 224 Waterloo Road, Kowloon. Hong Kong For the reaction M"+ constant is expressed as
+ L-
-
[Co(III)]= [A] + [B]
MI,("-')+, the stability
T h e K values of stable complexes in aqueous solution can be determined by various methods such as spectrophotometry (I),polarography (Z), etc. A method for the determination of K values of unstable complexes has not been as easy to show to students. In this work stability constants of the complex dioxalatodiaquocohaltate(III), Co(CzO4)~(HzO)z-,with lactate ion and glycine ion can he determined by studying the kinetics of the decomposition of this complex in aqueous huffer solutions spectrophotometrically. The complex, Co(Cz04)z(HzO)~-,undergoes decomposition fairly rapidly in acid solution to give Co2+ and COz. The mechanism of this decomposition has been studied and suggested (3) as follows
T h e rate eqn. (4) can h e written as 2.3 log[Co(III)]-
[Co(III)I
- -Qt
+ const
(7)
where
BYassuming ka = 0, eqn. (8)becomes
Equation (9) shows that K can be found from the plot of 2IQ against [L-1.
Experimental All chemicals used were AR grade or pure grade and were not purified before use. where A = Co(CzO4)z**(HzO)z-, I is the intermediate CO(C~O~)**(C~~~)*(HZO)~-, and the superscripts * and ** refer to a unidentate and a bidentate ligand, respectively. By applying steady-state approximation to the intermediate, we have
and the rate law is
T h e integrated form of eqn. (3) is
where [Co(lIl)l, representing [Co(Cz04)2*'(H20)2-I at time t . is eiven hv ICo(1ll)l = lCo(Ill~l,,(D,- D,)I\Do - Dm).D ripr&ents the optiraidensity of (he solution, and~subscripts zero. infinity, and t refer to valuesat zero time,infinite time, and time t, iespectively. When the complex Co(C204)~(Hz0)~was allowed t o decompose in a buffer solution, a retardation in rate of decomposition was observed. I n addition to eqns. (1) and (Z), the mechanism includes eqns. (5) and (6)( 4 )
R&ssifnn ~ ~ x o b i s @ x a ~ l t s ~Conplex l l ~ ] F, This complex was prepared, purified, and analyzed as described by Palmer (5).The analytical results obtained confirmed its formula K&o~(Cz04)r(OH)2~3HzO (found: Co = 16.4 0.18, C1042- = 49.1 0.2%). The solution of this bridged cam~lexexhibits a soectral maximum at 608 nm ( r 260 M-1 em-'), which is in close agreement with an independent report (6).
*
-
-
*
Potassium Dioxalatodlaq~~~obaltat~ll~), KCO(C~O~)~(HZC&, Complex A Solutions of A are prepared by allowing a solution of F in at least 0.03 M perchloric acid solution to stand for not less than one minute at roan temperature (3, 7). For example, the solution (pH 3.01) composed of [Co(III)]o= 5.0 X 10-3 M, [Lactate]/[Lactic acid] = 0.10010.125, and ionic strength I = 3.00 can be prepared as follows. In a 250-ml volumetric flask, a sample of 0.4465 g of the complex F is dissolved in 20 ml of water, 30.42 ml of 6.00M perchloric acid is added with shaking, and the mixture is allowed to stand for one minute. 34.38 ml of 6.00 M sodium lactate and 120.83 ml of 6.00 M sodium perrhlorate are then added aep&ately. The mixture is dilutpd to the graduarion mark.Theahtion ofAerhihitsspectral maxima at 609 nmtr 94.2 M-I rm-l) and 422 nm(t 137 M - I om-').
-
-
Kinetic Study Solutions of complex A for kinetic study were freshly prepared as described above. All solutions for preparation and the water used for dilution were keut in an Haake thermostat, tnse FE, maintained at tr~ 2 30' 0 2 C andsamples were taken for s p e c ~ o p h ~ t o m eevery min. The d-mwsition of the comolex . . A was fallowed at 416 - nm ( . an" wavelenflh close to the maximum or the maximum 422 nm can he employed; for comparing the present data with those of our earlier work, 415 nm was used) by using a Perkin Elmer Model 124 recording spectrophotometer until the end of reaction. pH values of all solutions were measured by means of a Chemtrix pH meter, type 40. A solution composed of 0.01W M perchloric acid and 2.99 M sodiumperchlorate was taken as a standard: its DHwas assumed to 2.00. In all emerimmtc. imic strenpth w&co&olled to I = S.00 M by addition i f sodium p~rrhloratrsolution. ~
~
~
B%C~(C~O~)**(C~O~)*L(H~O):-
(6)
where B = C O ( C ~ O ~ ) ~ * * L ( H ~During O ) ~ - . the decomposition, I and the second intermediate CO(C~O~)*'(CZO~)*L(HZO)Zcompete for the complex C O ( C ~ O ~ ) ~ * * ( H ~ Thus O ) ~ - .we have
Volume 61
~~~~~
Number 10 October 1984
~
-
925
Klnetic Data tor DecompoeHlon ot CO(C~O.)Z(H.O)~- ~- In Lactate and Glyclne Buffer at 30°C and I = 3.00 M a ~
Lactate bufferb
Butfer base. mM
Glyclne buffers Buffer lo2 0. base. mM mln-'
1026 min-'
Temp. i0.2'C: 4NaCIO.): [Complex]. 415nm. 'pH = 3.0 0.3. 'pH = 2.0 ;t 0.4.
= 5.0 X
10-'mM: &&taken In 1 cm call at
+
I
0
100 200 [buffer basel rdJ
+
Results and Dlscuoslon Plots of log(Dt - D,) against time t are linear only up to about 80% of rgaction. A value of P in eqn. (7) is chosen so that a linear function is ohtained. In this way, the decomposition of the complex A was studied in various buffer concentrations. Results obtained are listed in the table. Plots of 216 against buffer base concentrations are found to be linear as shown the figure. A least-squares program on a Casio Model FX-502 calculator was employed to calculate the k l and K values. Results obtained are: for lactate ion, k l = 2.27 X min-l. K = 13.4 l.mol-': for elvcine. k , = 1.96 X 10-2 min-1, K = 2:ll.mol-1. The stabilit; cons&& found in these two buffers follow the base strength of the anion. I t should be noted that the P values have not been listed in the table, and that the structural effects of ligands on K can be ohtained by studying the decomposition in several buffer if one desires t o investigate these systems further.
926
Journal of Chemical Education
Determination of stabilily constants of C O ( C ~ O ~ ) ~ ( H ~ O temp.: ) ~ - ; 30 0.2 C: I = 3.00 MNaCI04): kinetic experimental reproducibility:ca. f 3%; Kvalues.
ca +15%.
Acknowledgment We thank M. H. Mok and J. W. Barrett for their encouragment, and thank W. C. E. Higginson for his stimulating discussions. Appreciation is expressed to our students for their laboratory assistance. Literature Cited (11 S k w , D . A.,and Weat,D. M.,"FundameofalsofAnalyti~lChemiatni,"3rdd.,Holf Rimhart. and Winaton Ine. N w York. 1976. o. 556.
...........
,.,,=. ..."
(3) In.Hln-Fal.and H#aa,nsun.W C E . J Chem Sa.IAI. 2836 ,1910,. 14, In h - F a 8 , e n d Hlggtnmn. W. C E , J ,.'hem &r ,A!. 2842819?0.. IS, Palmer. n'. C.."Lhvrtrn~ntalh o m k Chrrnmrv."I:ambnoae llncveniw PIPB.1954, pp. 550-554.
(61 Higginson, W. C. E.,high, 8.T.,andNightingale, R., J. Chem. Sm., 435 11962). (7) Lee Hin-fat and Higginmn, W. C. E.,J. Chem. Soc. (A), 2589 (1971).
