Thermodynamics and Kinetics of Ligand D. A. Sweigart Sworthmore College Sworthrnore, Pennsylvania 19081
I
Binding to Vitamin B,,, A
laboratory experiment
In recent years bioinorganic chemistry has become a very active area of research and study. We would like to describe an experiment in bioinorganic chemistry that has been used with success in several physical chemistry courses at this institution. Vitamin B12, (aquocohalamin) is a fairly stable cobalt(U1) complex (Fig.) that contains a water molecule coordinated to the cobalt above a planar corrin ring. Vitamin B12 itself contains a C N group in place of the water., Neither BIZ or BIZ, is active as a coenzyme in any known enzymatic reaction. The active coenzyme is generated by replacing the CN- or Hz0 group with a 5-deoxyadenosyl group. This is done in the body in a series of reactions reauiring. FAD. NADH. ATP, and alutathione. The active &enzyme is involvedin a numberof metabolic processes. The mechanism(s) of these reactions has been the subject of considerable research ( I ) . The experiment entails the study of eqn. (1) where L = SCNB, CBM-OHI L === CBM-L + H1O (1)
+
I:.,
Aquocobalamin is abbreviated CBM-OH2. The objective -l is to determine K,, . " = .ICBM-LlI(ICBM-OH21IL1) ., .. -.. ,. = k -, k-I by equilibrium and non-equilibrium (kinetic) techniques. It is fairly easy to measure K,, spectrophotometrically. It is also easy using the stopped-flow method to ~ thus allowing an indepenmeasure kl and k - separately, dent determination of K,, for eqn. ( 1 ) . As is discussed below, we feel that a number of important and frequently overlooked ideas concerning chemical kinetics are illustrated in a meaningful way to the student. The experiment is rather open-ended in the sense that the student can try to ascertain the probable mechanism of the reaction. To do this the student learns some inorganic chemistry and in view of his freshman laboratory experience, is perhaps surprised to find a cobalt(IlI) substitution reaction that is so rapid. The reasons for the excessive lability of ligand substitutions on Blza are only beginning to be understood. The Equilibrium Method
Two students are given a 10-ml vial containing 1 mg/ml of BIZ, (7.3 x 10-4 M), 0.8290 sodium chloride, and 0.02% sodium acetate. This is more than enoueh to do the entire experiment. The BIZ, solution is avaiable from Merck Sharp & Dohme under the brand name Alfa-Redisol. Two solutions of the following composition are made: Solution (I): CBM-OH2 = 2.92 X M; acetate buffer = 0.05 M (pH = 4.7); sodium perchlorate = 1.0 M. Solution (11): Same as (I) except sodium thiocyanate = 0.02 M. Stock solutions of buffer, NaSCN = 0.1 M, and NaC104 = 4.0 M a r e made available. Solutions (I) and (11) are then prepared by the student from the stock solutions. The buffer is used because hydroxocobalamin is formed at high p H ( p K , = 7.8) and a t low p H the nitrogen donor group (benzimidazole) situated trans to the H z 0 ligand (Fig.) will be protonated. The uv-visible spectrum of solution (I) is recorded and repeated after adding increments of solution (11). The 126
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Journal of Chernicai Education
Aquocobalamin (vitamin B e S )
total metal concentration never changes. As more and more of the CBM-SCN complex is formed the spectrum changes in accordance with published data (2). After all of solution (II) is added, a final scan is made after adding excess NaSCN (;.0.2 M). This last spectrum should be that of pure CBM-SCN. The student is told to choose the volume increments of solution (II) so that the CBMSCNICBM-OH2 ratio varies from about 0.1 to its maximum value. The analysis is straightforward. Writing the reaction as
and choosing wavelengths where X does not absorb we have, = [MI + [MX] C, = [XI + [MX] A = tu[M1 + r\l\[MXI = r\Cv + [MXl(tn, - t , , ) In these equations CM is the total metal concentration, Cx the total thiocyanate concentration, A the absorbance, and ci the molar extinction coefficient of species i. The final spectral scan containing =0.2 M NaSCN yields a . above value for C M X . A scan of solution (I) yields t ~ The equations are now easily solved for [MX], [MI, and [XI and hence we have KO,. One can of course use simple curve fitting techniques to get a "best" value for K,,. However, simply calculating a Kep for each data point (absorbance value) is quite satisfactory, particularly if the
values are weighted. The best wavelength to use is 350370 nm. Some students extended the experiment by using X = Br-. In this case the reaction does not go far enough to completion to allow a direct determination of C M and ~ so one must use a graphical technique (3)to get K,, 1 A A = - - [K...."-
-
1 + 4~
e,CM
x~. .
The Kinetic Method
Reaction (1) is sufficiently rapid that a stopped-flow technique is needed to study the kinetics. This may seem to be a significant deterent; however we found just the opposite. Many institutions have a stopped-flow apparatus and with a little instruction its operation becomes easy and there is little chance of serious damage to the instrument. Our students were receptive to an experiment involving measuring the rate of a reaction that seems to he "instantaneous." The experiment opens the door to rapid reaction techniques in general which are widely used in inorganic chemistry and hiochemistry. The tedium of following a reaction taking several hours is avoided. Naturally only a few students can use the stopped-flow device at a given time. This means that numerous other experiments must be carried out concurrently. But this is the ~ l when e expensive instrumentation is being used in a physical chemistry laboratory. We frequently find it necessarv to have a different exveriment for evew two or three students at a given laboratory session. Reaction (1) was studied in the forward direction with M . Pseudo first-order conditions were used CM = 5 X with thiocyanate ranging from 2 to 10 x 10-3 M . ~h~ ionic strength was maintained at 1.0 M with NaC104. The usual plot of k , ~ , versus [SCN-] is made. Its slope yields kl and intercept k - 1 . The rate constant k-I is also measured directly by following the rate of the reverse of eqn. (1). CBM-SCN
+
H,O
CBM-OH,
5 CBM-OH, + SCNOH-
CBM-OH
(31
(41
Hydroxide ion is needed to drive the reaction to comple. tion but studies by Thusius ( 4 ) show that the kinetics are ~h~~ the independent of the hydroxide ion rate is completely determined by eqn. (3). F~~our solu[SCN-] = 0 , M, ~ tions we choose CM = [OH-] = 0.05 Mwith NaC104 to 1.0M. The student is asked to derive the expressions for k,b,. Thus for eqn. (1) A,,,. = h,[SCN] + k-, In particular the student must relate the experimental obto a mechanism. We find that many sewable times students can readily write rate equations for a given mechanism, but when presented with (absorbance, time) data are at a loss to the data to the mechanism, To illustrate this point we ask the student to derive the k,b,
expression for eqn. (5). which is a plausible mechanism for the forward step in eqn. (1). K
IZ
MX (5) M+X=M,Xequilibrium step in eqn. (5) represents an outer sphere association commonly observed with substitution reactions a t six coordinate centers. The rate-determining steo is dissociation of the H z 0 l i ~ a n d ,whereupon the X hecomes bonded to the cobalt. Thus this mechanism is essentially a dissociative one. In eqn. (5) X, which is SCN-, is in great excess. Most students write rate = hK[XIM] which is correct, but k,a, is not therefore kK[X]. Ohviously a limit must he reached as [XI or K -. One must either realize or calculate (5) that the observed absorbance changes are first-order in [MI [M,X]. Thus
-
+
and
We also ask the student to prove that the hobSobtained is independent of the wavelength used. One need not search for a wavelength where the product absorbs and the reactant does not or vice versa.
. =-"..From experients performed by four sets of students the average K,, value a t m m temperature from spectropho100 M - I . tometric measurements was found to be 700 This is reasonably close to published (2, 6) values of about 101 The average kOb,values for eqn. (1) obeyed the relationship h,,,.(s-'I = 1.9 1200[SCN] (6)
*
+
From this K,, = 630 M - 1 . For eqn. ( 3 ) we found h-I = 1.9 s-I in agreement with eqn. (6). This experiment provides the student a direct link between thermodynamics and kinetics. It utilizes a rapid reaction technique, requires one to clearly understand the relationship hetween the hob, expression and mechanism, and involves the investigation of an interesting bioinorganic system. Finally it is open-ended and allows for further work by the student in the form of project-type experiments. Literature Cited ~
(11Sehrauzcr.G. N.,Aduan. Chem: Ser. 100. 1i19711: Abeles. R. H.,Advon. Chsm ser..%(1971). 121 ~ r a t tJ. . M . . B ~ ~ T ~ o I P . R . G . Chsm. .J Sor. fA1.187 (1966). (3) Rauutti. F. J. C., and R m ~ l f i .H.,"The Determination of Stability con8tanfs;. M ~ C ~ W - R CO.. ~ I NI ~BW Y~ O~, ~ 1961. , ~274. (41 ~ h u s i u a D. . . J A m e r Chem. Sor.. 93.2629(1971). ( 5 ) Fro"'. A. A.. and Peano". R. G.. "Kinetics and Mechanism." 2nd Ed.. John
.. .,
Wil.,.&
%"
