Stability Constants of Copper-Organic Chelates in Aquatic Samples Mark S. Shuman" and George P. Woodward, Jr. Department of Environmental Sciences and Engineering, School of Public Health, University of North Carolina, Chapel Hill, N.C. 27514
A procedure similar to an amperometric titration of a ligand with copper was used to determine the conditional formation constants of copper-organic chelates in several fresh water samples a t controlled pH. The titration curve was constructed using anodic stripping voltammetry to detect unreacted copper. An equation for this curve was developed and revealed that both the stoichiometry and the formation constant of the complex formed during the titration could be obtained. The ligand in the water samples responsible for copper binding was characteristic of a conjugate base of a weak acid, the acid being almost entirely ionized a t neutral pH. Estimates of the conditional formation constants for these complexes ranged in value from 0.32 X l o 5 to 5.2 X l o 5 a t pH 6.5. Matson ( I ) introduced an electrochemical method consisting of a complexometric titration combined with anodic stripping voltammetry (ASV) for estimating the concentration of organic ligands in natural waters. This method and additional procedures were used by Matson to estimate formation constants of metal-organic complexes found in natural waters (I,2). Shuman and Woodward ( 3 )described a similar titration from which the formation constants for 1:l complexes could be calculated directly. The work reported here extends the usefulness of the latter method to include any stoichiometry and applies it to several natural water samples.
Theory and Procedure The procedure is similar to an amperometric titration of a ligand with metal, but in this case, ASV is used to gain sensitivity for application to very dilute solutions. Serial additions of a concentrated metal solution are made to a sample containing titratable ligands held in a three-electrode electrochemical cell. Figure 1 is a pictorial representation of the procedure where for simplicity a buret represents the micropipet actually used for additions and a beaker represents the electrochemical cell. With each addition of metal there is a reaction between the metal M and the ligand L to form M&b according to aM
+ bL s M,Lb
the anodic stripping current, is. Second, it is assumed that is = K { [MI [ M L I ] [ M L I I ]. . . [MLp,]Jwhere LN represents ligands other than the ligand of interest, and where K is the ASV response to all soluble forms of the metal not bonded to the ligand of interest. The numerical value of K is obtained from the slope of the upper region of the titration curve. A third assumption is that a t any point along the titration curve, the concentration of titratable ligand remaining is [L'] = [ L ] [ H L ] [H&] . . . [H&] [ M I L ] [ M I I L ] .. . [ M N L ] where M N are metals more weakly bound than the titrant metal and therefore displaced by the titrant metal and ,where n is the number of displaceable protons associated with the ligand. Other assumptions are that the ligand is in excess of titrant metal present in the solution prior to metal addition, and that M,Lb does not kinetically dissociate appreciably during the period of metal accumulation a t the mercury electrode. With regard to natural waters and the nature of the ASV experiment, these assumptions are reasonable. I t is likely that the predominant organic ligands encountered in natural waters would be either polypeptides or humic materials which form large multidentate complexes with metals. Reduction of these complexes, if it takes place a t all within the range of the potentials available to the mercury electrode, is irreversible and the dissociation rate of such complexes is slow ( 5 ) .This means that a potential can be selected that will not be in the range that reduces the metal complex. On the other hand, simple inorganic and bidentate organic complexes are much more easily reduced and their contribution to the stripping current, except for slight differences brought about by their diffusion coefficients in solution, is the same as would be expected if all the metal existed as the simple aquated ion. In any event, the sensitivity of the ASV experiment to all these simpler forms is accessible in the slope K . With regard to the large organic molecules to be encountered in natural waters, the quantity CL is interpreted as the concentration of individual functional groups acting independently as ligands and is not necessarily the concentration of individual molecules. Because of the complexity of these molecules, the functional groups may include a variety of
+
+
+
+
+
+
+
+
+
(1)
The concentration of metal not bound to L , designated M', and which is in equilibrium with Ma& is determined by ASV after each addition and gives an ASV response i, = h [ M ' ] , where i, is the peak current of the stripping curve, and K is a proportionality constant. The titration curve has two regions, a lower region where the ligand is titrated and the ASV response is low because most of the metal has reacted with L , and an upper region after the endpoint, where there is normal ASV response to the increasing concentration of uncomplexed metal. The shape of this curve is similar to a conductometric or colorimetric titration in which the product of the titration does not produce a response. The endpoint of the titration is the point a t which the analytical concentration of added metal, C M , is equal to ( a b ) CL, where C L is the analytical concentration of ligand. This point is determined by extrapolation of data points in the two regions to a point of intersection using guidelines suggested by Rosenthal et al. ( 4 ) . Several assumptions are made about this titration. First, it is assumed that the complex, M,Lb, does not contribute to
1 I COMPLEX
-
P
r
P
a
l==f Y
0 1
a
START
BEFORE ,ENDPOINT
iM'I=O
I M ' I = C,.,-IMLI IL'I = C L - I M L I
lL'l=CL
'0 l
AFTER ENDPOINT
IM'I-'~-c~ IL'lfO
I
0
CL
ADDED M E T A L , C y
Figure 1.
Procedure for titration of ligand with metal Volume 11, Number 8, August 1977 809
configurations and molecular weights. This simplifying assumption is common to other studies in which bonding of copper to large multifunctional molecules such as polypeptides and proteins is investigated (6). With reference to Reaction 1, a conditional formation constant can be written
+
+
and since [M’]= & / t i , CM = [M’] a [M,Lb] and CL = [L’] b[M&], the conditional formation constant expressed in terms of the experimental parameters is
This can be rearranged into a polynomial in is and the substitution CM = ( a / b )gCL made so that
+ ($)a
($)u+b
cLb((I -gb)
where g is the fraction of the stoichiometric quantity of titrant. For the important case of a = b = 1,this equation is a quadratic with the solution
is -.
lmax
1 2
- -([g - 1 - (KLLCL)-ll
+ [(l- g + ( K L L C L ) - ~+) ~4 g ( K h L C ~ ) - ’ l ~ ’ ~(5) ) where the term,,i = t i C ~is introduced to make the equation dimensionless. From this equation, the titration of a 1:1 complex depends only on the product K L L C where ~ K h L is the conditional constant for the 1:l complex. Theoretical titration curves calculated from Equation 5 for three values of K’CL are shown in Figure 2 and indicate that considerable dissociation occurs if K’CL is small. Lines drawn in the figure represent the extrapolation to the endpoint at g = 1.0. For a “break” in the titration to be easily observed, K’CL must be greater than unity. Values for the conditional constants could be obtained by comparing experimental with theoretical curves. However, a simplified method for analyzing the data is available. During the first additions of titrant and for reasonably large formation constants, [M’] = is/ti
