New and Improved Techniques for Applying the Mole Ratio Method to the identification of Weak Complexes in Solution C. D. Chriswell and A. A. Schilt Department of Chemistry, Northern Illinois University, DeKalb, Ill. 60 115
A detailed mathematical analysis of the Mole Ratio method has produced three novel and effective techniques for Identifying weak complexes In solution. Experlmental tests of these techniques demonstrated that they are both reliable and practical. Meaningful results were obtained using these techniques where conventional techniques were totally lneffective. Moreover, all three techniques afford the significant advantage of revealing the stoichiometry of a weak complex rather than simply the molar ratio of Its components. MOLE RATIO OF REACTANTS
Comprehensive investigations of metal complexes will generally include the use of some technique for determining their stoichiometry in solution and their conditional formation constants. Such information is particularly useful when a complexing agent is evaluated for possible use in analytical procedures. The formation constant and stoichiometry of a complex are of value in determining if a complexing agent will be useful as a separation reagent, masking agent, or scavenger; and if the complexing agent is used as a chromogenic reagent, such information will aid in choosing experimental conditions where Beer's law deviations due to complex dissociation can be avoided. The mole ratio method ( I , 2) is a widely used technique for identifying complexes in solution and determining formation constants. It consists of making appropriate concentration dependent measurements on a series of solutions prepared to contain the same analytical concentration of one component of the complex but different analytical concentrations of the other component. If the complex is relatively completely formed at the equivalence point, a plot of any measurement that is directly proportional to the concentration of the complex (e.g., absorbance) vs. the ratio of the analytical concentrations of the components will exhibit a sharp break a t the equivalence point, i.e., a t the mole ratio of the components of the complex (Figure 1, line A). The conditional formation constant of the complex can also be determined from the data. For the general reaction a A bB = A,Bb, the conditional formation constant is defined by Equation 1.
+
If only the forms of A and B indicated in Equation 1 are present in solution, or if all other forms are present only in negligible amounts, Equation 1 can be rewritten in the form
The value of the conditional formation constant, K , can thus be calculated with this expression from measured concentrations of A,&, known analytical concentrations of A and B (CA and CB);and values of a and b deduced from the mole ratio plot. If the complex is less completely formed a t the equivalence point, the mole ratio plot will be curved and the molar ratio will be difficult to determine (Figure 1,lines B,
Figure 1. Representative mole ratio plots of complexes of various stabilities Line A is typical of a relatively completely formed complex. Lines 8,C , and D are typical of successively weaker cornpiexes
C, and D). The weaker the complex, the greater is the curvature and the more uncertain is the identification of the molar ratio of the components of the complex. In such cases, not only is it difficult to identify the complex but also any error in the stoichiometry will result in an incorrect value of the formation constant. Even if the plot is not significantly curved, the mole ratio method gives only the ratio of the values of a and b, and thus the value of one parameter must be independently determined or assumed. The curvature of a mole ratio plot may be lessened in some circumstances by altering experimental conditione, for example, temperature or ionic strength of the solution ( 3 ) . However, varying the experimental conditions may change the stoichiometry as well as the conditional formation constant of the complex in solution. The curvature may also be reduced by increasing the concentrations of both components of the complex by a proportional amount. The log ratio modification of the mole ratio method introduced by Diehl and Lindstrom (4)has been widely used for identifying complexes in solution, but is no more applicable to appreciably weaker complexes than is the basic method. Meyer and Ayres ( 5 ) have devised techniques for applying the mole ratio method when several complexes are formed between a metal and a complexing agent, provided the stepwise formation constants differ by a factor of a t least 600. The method of continuous variations introduced by Job (6) and the refinements and modifications of the method introduced by Vosburgh and Copper (71, Schwartzenbach ( 8 ) , and Likussar and Boltz (9,IO) may also be used advantageously to determine the molar ratio of the components of a complex and its conditional formation constant in solution; however, the reliability of these methods also suffers when applied to very weak complexes. The slope ratio method (11)may be used in some instances for identifying very weak complexes in solution, but is applicable only to 1:l complexes. The work reported here concerns the development of a firm theoretical basis for the mole ratio method, the use of this basis to determine the limitations of the method, and the development of improved techniques for applying the mole ratio method to very weak complexes in solution. ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
1623
MATHEMATICAL ANALYSIS OF T H E MOLE RATIO METHOD In order to understand this method so as to utilize it to the fullest possible advantage, a theoretical general equation that accurately predicts experimental data and shapes of experimental mole ratio plots is necessary. One such equation has been previously described (12); however, its form is not sufficiently simple for complete interpretation, nor does it lend itself well to practical applications in treating or analyzing data. The following derivation was found to yield the desired equation in a simpler more useful form. Derivation of a General Equation Describing the S h a p e of Mole Ratio Plots. a is defined as the fraction of the analytical concentration of A in the form of the complex A,Bb, and R is defined as the ratio of the analytical concentrations of A and B (Equations 3 and 4 ) . @
= ~[&B,]/CA
R = CB/C,
(3) ( 4)
Equation 3 can be rearranged to yield an an expression for the concentration of A,& (Equation 5 )
(5) which when substituted into Equation 2 yields the expression
Equation 6 is rearranged to yield
Substitution of R for CBICA into Equation 7 yields the desired general equation (Equation 8) that describes the shape of mole ratio plots (a vs. R ) in terms of simple fundamental quantities.
F e a t u r e s of the General Equation. If Equation 8 is rearranged to form an expression with R as the independent variable (Equation 9),
product K ’ C A ~ + has ~ - ~a constant value. All systems with the same value for this product will exhibit identical mole ratio plots. The larger the value of this product, the greater CY will be, and the less the curvature will be for any given mole ratio plot. There are a t least two important consequences of such a feature. First, it predicts that an increase in analytical concentration of the reactants will indeed tend to decrease the curvature of the mole ratio plot. Such an increase has the same effect as would be manifested by a higher conditional formation constant. Second, it predicts that a single set of mole ratio plots will describe any complex of a given stoichiometry. This will be seen to have considerable practical significance in that it greatly simplifies treatment and handling of data for identification of complexes. Using the Fortran program t o evaluate CY by a process of successive approximations, a set of simulated mole ratio plots was prepared for each of the 36 different stoichiometries represented by integer combinations of a and b ranging from one to six. Some representative simulated mole ratio plots are shown in Figures 2 through 4. The entire group of 36 sets of simulations or the program used to generate the data can be provided on request. More Detailed Analysis of the General Equation. I t is observed that, in some instances, both experimental mole ratio plots and the simulations appear to possess inflection points. Momoki and coworkers recognized that, in certain specific cases, the position of the inflection points is related to the stoichiometry of the complex (12). I t was of interest to verify mathematically the existence of inflection points and to discover what parameters determine their location in mole ratio plots. Such information could conceivably provide useful information about complexes or permit differentiation between two or more possible stoichiometries. Use of the calculus to locate inflection points, based on the fact that the second derivative goes to zero a t such a point, is a well known procedure. By taking the second derivative of Equation 8 (d2aldR2)and setting it equal to zero, Equation 10 was derived relating the a-coordinate of the. inflection point (referred to as ainf) to the stoichiometry of the complex.
(a - l ) d i n f+ 2 a i n f - ( b - l ) / ( a +. b - 1) = 0 (10) When the value of a is one, the expression for the value of can be determined from the expression:
ainf
the resulting expression is mathematically equivalent to each of two equations previously derived by Momoki and coworkers (12) to describe the shapes of mole ratio plots of metal complexes in solution: (1) an equation for the case when the analytical concentration of metal is held constant and the analytical concentration of complexing is varied, and ( 2 ) an equation for the case when the concentration of metal is varied and the concentration of complexing agent is held constant. Because a is a function of the concentration of A,Bb, an experimentally independent variable, the most useful expression describing the shape of a mole ratio plot would have a as its independent variable. Unfortunately such a general equation has proved impossible to derive. Furthermore, equations derived for specific values of a and b are so complex as to be impractical. Fortunately, it is possible, as well as practical by present day computer methods, to evaluate a by a process of successive approximations. A Fortran program was written to perform this task. A salient feature of the mole ratio plots predicted by Equation 8 is that the forms of the plots will be independent of the individual values of K’ and CA provided the 1624
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
ainf= ( b - 1 ) / 2 b
(11)
When b has a value of one, the inflection point will always occur a t the origin. For all other values of a and b, the value of ainfcan be derived by solving Equation 10 to give Equation 12.
ainf= { [ ( a b ) / ( a + b - 1)]’/? - 1} / ( a - 1) ( 1 2 ) An expression for the R-coordinate of the inflection point is derived by substituting the expression for ainfinto Equation 9. In the resulting equation (Equation 13)
the terms R A and R B are constants the values of which are determined only by the values of a and b. The slope of the mole ratio plot of a relatively completely formed complex approaches the value of alb. Since the maximum slope of a mole ratio plot will occur a t the inflection point, it was of interest to evaluate the slope a t that
I.
1.0
-
4
a
I
a
.
I
J
a
4
-
I
.
a
0 MOLE
I .o
RATIO
2.0
Figure 2. Simulated mole ratio plots of complexes in which a and b have values of one
MOLE
Line A represents the plot of a completely formed complex. Lines E,C, D. E, F, G. H. i, and J are plots of complexes having values of the quantity K/cAs+b-lof 90.0,20.0,7.78,3.75.2.00,1.11, 0.612,0.313,and 0.124, respectively ~~
~
Table I. Mole Ratio Plot Inflection Point Parametersu
4
3.0
.o
RATIO
Figure 3. Simulated mole ratio plots of complexes in which a and b have values of 1 and 2, respectively Line A represents the plot of a completely formed complex. Lines E, C. D, E, F, G, H, I, and J are plots of complexes having values of the quantity K'CA'+~-' of 225, 25.0, 6.48,2.34, 1.00,0.463. 0.219,0.0977,and 0.0343,respectively.
Stoichiometry Inflection p u i n t ]:nmI.?ctL'rS
of t h e carnplm 1
b
1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4
1 2 3 4 1 2 3 4
0.0000 0.2500 0.3333 0.3750 0.1547 0.2247 0.2649
0.0000 0.5774 0.7937 0.8801 0.0000 0.3290 0.5718 0.7036
1
0.0000
0.0000
2 3 4 1 2 3 4
0.1124 0.1708 0.2071 0.0000 0.0883 0.1381 0.1706
0.2314 0.4640 0.6100
Oiinf
0.0000
RA
0.0000
0.1788 0.3969 0.5479
RB
Y
1.0000 0.5000 0.7698 1.0000 0.3969 1.5000 0.2347 0.0000 1.0000 0.1547 1.4526 0.3371 0.8932 0.5298 0.5713 0.0000 1.0000 0.0749 2.1313 0.1708 1.4649 0.2761 0.9851 0.0000 1.0000 0.0442 2.8086 0.1036 2.0964 0.1706 1.4635 values of a and b up to 6 0.0000
Parameters for stoichiometries with have been determined and are available on request. a
point to determine if useful information about the complex could be elucidated. An expression for the slope of the mole ratio plot a t the inflection point is derived by taking the first derivative of Equation 8 (da/dR) and substituting the previously derived expressions for ainfand Rinf into the resulting expression, giving
(da/dR),,, = (n/b)/IX(l/K'CAa+b-i)i/h + 11 (14) In Equation 14, the term X is a constant for any given stoichiometry. The values of the terms a,,f, RA, RB, and X have been calculated for a large number of different stoichiometries and their values are listed in Table I. Since the value of alnfis dependent only on the stoichiometry of a complex, its value can aid in identifying a complex in solution. Furthermore, the expressions for the values of Rlnfand the slope of the mole ratio plot a t the inflection point are both dependent on the conditional formation constant and thus conceivably can be used also to determine its value. By solving Equation 14 for [1/ K , C A ~ + ~ - and ~ ] ~substituting '~ the resulting expression for it into Equation 13. an expression is derived (Equation 15)
I .5
3.0 MOLE
4.5
0.u
RATIO
Figure 4. Simulated mole ratio plots of complexes in which a and b have values of 1 and 3, respectively Line A represents the plot of a completely formed complex. Lines 6.C, D. E, F, G. H, I, and J are plots of complexes having values of the quantity K'CA'+~-' of 333, 18.5,3.20,0 868, 0.296.0.114,0.0463.0.0181,and 0.00565,respectively
mined by a and b (X, RA, and RB), and experimentally measurable quantities (Ri,f and da/dRinf). This equation may aid in the identification of complexes in solution.
TECHNIQUES FOR IDENTIFYING COMPLEXES From the foregoing detailed analysis of the mole ratio method, several new or improved techniques have emerged for identifying very weak complexes in solution. These techniques are described in separate sections below. Technique Based on Inflection Point Parameters. This method is applicable only to those complexes that yield a mole ratio plot which exhibits an inflection point that can be accurately located. In such cases, the slope of the plot a t the inflection point and the coordinates of the inflection point are useful parameters that can aid the identification of the complex in question. Depending on the quality of experimental data, it is possible to eliminate all but a few possible stoichiometries from which the correct one may be more readily identified or determined by additional measurements. The first step in this procedure is to determine an upper limit or maximum mole ratio (b/a)maxfor the components in the complex. This is given by the slope of the plot a t the inflection point. Rearrangement of Equation 14 provides the rationale for and the definition of (b/a)max: = ($)[I
+
X{K'C,"+b-f}i/b] 1 =
(i)
(16)
max
-
containing only a and b, constants whose values are deter-
The measured slope at, the inflection point will always be ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
1625
OF K ' o GREATER
TrAN ZERO FOR
ZACH S T O I C r i I O h E P R Y CALCULATE RSD IN K ' S GREATER TAAN ZERO FOR L A C E
ZRAGE V A L E OF
t7 STOP
Figure 5. Flow chart of Fortran program used to provide values of K'CAaib-' and RSD values for use in identifying complexes by method of self-consistent constants
greater than bla, but its value sets an upper limit to possible values for bla. In certain cases (e.g., when K' or CA are very large) this upper limit may closely approximate the true mole ratio bla. The second step in the procedure provides further discrimination by eliminating stoichiometries that are inconsistent with the experimentally obtained value of ainf. This step consists of comparing the experimental to the theoretical values of ainf for all of the different possible stoichiometries (listed in Table I) to find those which agree within the experimental error of the measured value. Those found by this step, which have a mole ratio greater than the (b/a)maxfound in the previous step, can be eliminated. A third step, if necessary to achieve further discrimination among the remaining possibilities, is to compare the experimentally observed value of Rinf with values calculated from Equation 15. The experimental value of (daldR)inf together with each set of a and b values indicated by the prior techniques (and the values of RA, RB, and X associated with them, listed in Table I) when introduced in the equation yield a different value of Ri,f. That set which yields a value closest in agreement with the observed Rinf is the set which best identifies the stoichiometry. If the complex is still not conclusively or unambiguously identified after performing the above three steps, recourse to the following procedure is recommended. Repeat the mole ratio experiment, this time reversing the roles of the two components; vary that concentration which was previously held constant, and vice versa. This will result in a mole ratio plot that is different from that of the first in all cases except for the stoichiometry in which a = b. When the new curve parameters qnf,slope, etc. are treated and considered in the same way as were those before, all but one possible stoichiometry should be eliminated. It is important to emphasize here certain theoretical as1826
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
pects pertaining to inflection points in mole ratio plots. The absence of an inflection point in any curved plot (excluding the origin) is conclusive evidence that the parameter b (where CA is held constant and CB is varied in preparing solutions of A,Bb) has a value of one. If the roles are reversed, so that the concentration of B is held constant while that of A is varied, the absence of an inflection point (excluding the origin) is conclusive evidence that both parameters a and b are unity. Complexes of stoichiometry such that a = 1 and b # 1 or a # 1 and b = 1 will give an inflection point in one but not the opposite experimental procedure. Complexes with stoichiometry where a # 1 and b # 1 will give inflection points in both mole ratio plots. The use of inflection point parameters to identify complexes is thus seen to be a very informative and effective technique; since, in contrast with the ordinary mole ratio method and similar methods, the actual stoichiometry can be determined, not merely the mole ratio of the reactants. Technique of Self-consistent Constants. A conceptually simple technique for identifying a complex in solution is to substitute experimental data into either Equation 2 or Equation 8 and calculate a value of the formation constant for each experimental data point and all possible values of a and b. The values of a and b giving the most consistent value of the conditional formation constant will indicate the identity of the complex. While the technique is conceptually simple it involves a large number of tedious calculations. The use of the Fortran program in Figure 5 greatly simplifies its application. The program calculates a value of the quantity K'CA'+~-' for each data point and the 36 different combinations of values of a and b ranging from one to six. After eliminating any impossible values of the constant, the program calculates the relative standard deviation of the remaining values for each combination of a and b. The selection of the most likely stoichiometry is based on the relative standard deviations. This technique affords the significant advantage of using all experimental data instead of special or selected portions of the mole ratio plot. Curve Matching Technique. This method depends on the availability of appropriately complete sets of simulated mole ratio plots ( a vs. R ) , based on Equation 8. Such sets, as noted previously, were generated for use here. The simulations can be utilized as overlays for matching purposes to find that theoretical plot which most closely resembles the experimentally obtained plot. Since no two plots will match exactly unless they have the same values of the quantity K ' C A ~ + ~ -and I , because a single set of plots will describe any complex of a given stoichiometry, the stoichiometry of the matched plots should be identical. For improved certainty of identification two or more experimental mole ratio plots can be determined, each based on a different analytical concentration of reactant of A. As with the technique based on self-consistent constants, this technique utilizes the entire mole ratio plot. Deviations from ideal behavior, if present, will generally occur a t low values of R when lower order complexes are formed or a t high values of R when higher order complexes are formed. Such deviations are generally readily apparent when using the overlays, and can be taken into consideration when identifying a complex by this technique.
TECHNIQUES FOR DETERMINING CONDITIONAL FORMATION CONSTANTS In order to determine the conditional formation constant of a complex, it is necessary to determine (1)the stoichiometry of the complex and ( 2 ) the equilibrium concentrations of all the pertinent species in one or more solutions. Ordinarily the mole ratio method provides sufficient informa-
tion to satisfy both requirements, and Equation 2, or some simple form of it, is commonly employed for calculation of the constant. Complications arise, however, when the complex is either too weak or too strong. The stoichiometry of a very strong complex can be identified with certainty, but its conditional formation constant can not be reliably determined from the same mole ratio data. This is evident by inspection of Equation 8; as CY approaches unity, the experimental uncertainty in (1 - C Y ) and the relative error in K' increase enormously. On the other hand, if the complex is very weak, the conventional mole ratio method will not reliably identify its stoichiometry, even though it does yield equilibrium data suitably precise for calculation of K' if the stoichiometry were known. The new techniques described here for treating mole ratio data overcome this particular problem enabling reliable identification of stoichiometries of weak complexes and calculation of conditional conWants. One of the techniques proposed here, the so-called technique of self-consistent constants, not only identifies weak complexes but also simultaneously generates a value of the quantity K'Ca+b-l from which the value of K' can be readily calculated. This method is essentially a modification of the use of Equation 2 but with the advantage that manual calculations are eliminated. Two other possible methods for determining the conditional formation constants of certain weak complexes were revealed by the detailed analysis of Equation 8. Both depend on the presence of an inflection point in the experimentally obtained mole ratio plot, and hence both are limited in applicability. If an inflection point is observed, then its location on the R-coordinate can be employed together with Equation 1 3 to calculate K'. An alternative approach, the second method, consists of using the measured slope a t the inflection point and Equation 1 4 to calculate K'. Although of theoretical interest, neither method is sufficiently accurate or convenient to recommend over the above conventional methods.
Table 11. Values of R Required for Complete Complex Formationa \'alui 01 R 3t n'iicli c o l - p l e k iornilition \lolar Stoichiometq a
-
lBIcB
01
tI
d u c s ot
Y ' C A b + b - i 1,stcd
1
1
104
100
106
1.00 2.00 3.00 4.00 0.50 1.00 1.50 2.00 0.33 0.67
At some excess of B, CB,,,, all of A can be forced into the form of the complex and the absorbance of the solution, A,,,, is given by the expression:
(22) The concentrations of A,B, and B can be expressed once again in terms of the analytical concentrations of A and B: =
+ [BlmaxEB
[kBblmaxcA,Bb
[%Bblmax
[Blmax =
=
cBmax
(23) (24)
CA/a
- b~A/a
When these expressions are substituted into Equation 22 and the equation rearranged the following is obtained: Amax -
CB,,€B
= C A ~ , A , B-~ /~~C A E B / ~(25)
Combining Equations 21 and 25 yields the desired relationship between CY and experimentally measurable quantities: CY=
4 Amax
(I7)
The concentrations of A,Bb, A, and B can be expressed in terms of the analytical concentrations of A and B, CA and CB, and CY (Equations 18, 19, 20).
\
These three expressions are substituted into Equation 17, and the resultant expression rearranged to yield:
I t will be shown in this section that the proposed techniques derived for identifying complexes in solution can be applied t o spectrophotometric data and that they enable the identification of very weak complexes in solution. Spectrophotometric Determination of CY.The foregoing theoretical treatment of the mole ratio method was general in nature and not based on any particular experimentally measurable quantities. Since the method is most commonly used as a spectrophotometric technique, it is desirable to demonstrate that the theoretical relationships can be applied to spectrophotometric data and to examine any limitations of the method when used as a spectrophotometric technique. For the problem a t hand, it must first be shown that the term CY is obtainable from spectrophotometric data. The absorbance of a solution containing the complex A,& is defined as AT and can be expressed as the sum of the absorbances due to A,&, A, and B (Equation 17). iA1cA
ratio,
b l a
b
ipproached for t h c
LL
1.0 E2 2.0 1.o 1.o 2 1.2 E l 3.0 2.1 2 .o 3 7.6 4 .O 3.2 3 .O 4 7.1 5 .O 4.3 4.1 1 5.0 E 3 5.0 E l 1.0 0.5 2 7.1 E l 8.0 1.7 1.o 2 2 2 3 1.9 E l 5.2 2.3 1.7 2 4 1.0 E l 4.6 2.8 2.3 3 1 3.3 E 5 3.3 E 3 3.3 E l 0.7 3 2 3.7 E2 5.8 E l 6.4 1.2 1.00 7.0 E l 1.6 E l 4.2 1.7 3 3 3 4 1.33 2.5 E l 8.9 3.7 2.1 4 1 0.25 2.5 E 7 2.5 E 5 2.5 E 3 2.5 E l 0.50 5.0 E3 5.0 E2 5.0 E l 5.5 4 2 1.4 E l 3.7 4 3 0.75 2 . 9 E2 6.4 E l 1.00 7.2 E l 2.3 E l 8.0 3.2 4 4 E n = lon (Example E2 = lo2) Values for stoichiometries with values of a and b up to 6 have been determined and are available on request
1 1 1 1
E X P E R I M E N T A L TESTS OF T E C H N I Q U E S FOR I D E N T I F Y I N G COMPLEXES
A, = [ & B ~ ] ~ A , B+,
complex
- (CAE,
+
CBcB)
(26)
- ( C A E A + CBma,cB)
Accordingly, CY can be determined from Equation 26 and the measured absorbance AT, since the absorbance A,,, and the molar absorptivities CA and t~ can be determined by separate independent measurements, and the analytical concentrations CA and CB are both known, having been prepared using measured volumes of standard solutions. In order to determine CY spectrophotometrically it is necessary that some realistically attainable concentration of B exists that will result in essentially complete complex formation. Since spectrophotometric measurements are typically accurate to not much better than &l%, it will be assumed that the complex is completely formed within experimental error if no more than 1%of the analytical concentration of A is uncomplexed. The value of R required to re-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9 , AUGUST 1975
*
1627
Table 111. Experimental Conditions for Mole Ratio Studies Conccntrotion
Table IV. Comparison of Techniques for Identifying Weak Complexes in Solution Using Mole Ratio Method Data
of 20:1:ponc-nt
~
Stud)
~
~ a
?
~
,
pi ~1 i
~
5o
L'OI 7ctn
or tilt C o n plcx I i d i l a t k d
c
\
L
I \LLt'ia'n
~!Idd c@!lstnnt, If
CU(II)-EDTA~ 1.7 2.00 x l o - ; CU(II)-EDTA 0.92 2.00 x 10-3 CU(II)-EDTA 0.62 2.00 >: 10-3 0.32 2.00 x 10-3 CU(II)-EDTA 0.02 2.00 y l o - ? CU(II)-EDTA Fe(I1)-TPTZC 5 .O 5.00 x lo-' Fe(I1)-TPTZ 3 .O 5.00 x Fe(I1)-TPTZ 1.5 5.00 x lo-' Fe(II)-PIQd 4.7 1.00 x 10-'3 Fe(I1)-PIPH' 4.7 1.00 x 10-3 Fe (11)-PIP' 4.7 1.92 x 10" Fe(II)-PPB' 4.7 2.40 >: l o - ' Fe(II)-MPBh 4.7 1.92 x lo-' TPTZ-Fe(I1) 5 .o 1.00 10'' 3 .O 1.00 10-J TPTZ-Fe(I1) TPTZ-Fe(I1) 2.2 1.00 x io-' 4.9 2.00 x 10-3 MPB-Fe(11) 6 .O 1.00 x lo-,; MPB-Fe(I1) Component of the complex whose concentration is held con-
I I1 111 IV V VI VI1 VI11 IX X XI XI1 XI11 XIV XV XVI XVII XVIII
Inflection
C:mc
Si.li-
potnr
Cmvmtisnal
t
:-atL~I.inL,
-~~ R
h
o
h
l
b
a
h
n
h
n l . O n n l 1 1 1 1 I I l l n 1 . 2 n n 1 1 1 1 1 I11 1 1 n 2.011 n 1 1 1 1 1 I V l l n 2 . 8 n n l 1 1 1 1 V l l n 4 . 7 n n l 1 1 1 1 VI 1 2 n 2.3n 1 2 ' 1 2 1 2 VII 1 2 n 3.511 1 Za I 2 1 2 VI11 1 2 n 6.6 n 1 2" 1 2' 1 2 IX 1 2 n 2.811 1 2 ' 1 2 1 2 X 1 2 n 2 . 4 n x x 1 2 1 2 XI 1 3 n 4.5n 1 3' 1 3 1 3 XII 1 3 n 4.5n 1 3h 1 3 1 3 XI11 1 3 n 5.1n 1 3' 1 3 1 3 1 n 0.5n n 1 2 1 2 1 XIV 2 a XV 2 1 11 0.911 n 1 2 1 2 1 stant in the mole ratio studies listed first. EthylenediaminetetraXVI 2 1 11 1.0 n n 1 2 I k 2 1 acetic acid. Tris(2-pyridyl)-1,3,5-triazine. 2-(2-pyridylj-3H3 1 n 0.611 n 1 3 1 3 1 imidazo[4,5-h]-quinoline. e 2-(2-pyridyl)-lH-imidazo[4,5-fl4,7- XLTI phenanthroline. 2-(2-pyridylj-lH-imidaz0[4,5-c]pyridine. g 2-(2XVIII 3 1 n 0.8n n 1 3 1"' 3 1 pyridyl)-5(6)-phenylbenzimidazole. 2-(4-Methyl,2-pyridyl)-benzSymbol n indicates the values cannot be determined by the imidazole. method. Symbol x indicates value was not determined. Technique cannot provide a unique identification; other indicated stoi, chiometries are c 2 : 3 . 2:4, 3:4, 3:6, 4:6. 2:3, 2:4, 3:4, 3:5, 3:6. 4:6. e 2:3, 3:4, 3:6.f2:4, 3:6. g 2 : 5 . 2:s. 1:4, 2:4, 2:5, 2:6, 3:6. '3:3. , 2:l. 4:l. 1
1
1
f
t
MOLE
RATIO
Flgure 6. Mole ratio plots of the copper(l1)-EDTA complex 0.5
All plots obtained by holding the analytical concentration of copper(l1) constant and varying the concentration of EDTA. Lines A, B, C, D. and E are mole ratio plots obtained at pH values of 1.7, 0.92, 0.62, 0.32, and 0.02, respectively
MOLE
1.0
RATIO
Figure 8. Mole ratio plots of t h e iron(l1)-TPTZ complex All plots obtained by holding the concentration of TPTZ constant while varying the concentration of iron(i1). Lines A, B. and C are mole ratio plots obtained at pH values of 5.0, 3.0, and 2.2, respectively
4
z
a A
4
0
2 MOLE
1
.o
4.0
RATIO
Figure 7. Mole ratio plots of the iron(l1)-TPTZ complex Ail plots obtained by holding the concentration of iron(ll) constant while varying the concentration of TPTZ. Lines A, B. and C are mole ratio plots obtained at pH values of 5.0, 3.0, and 1.5, respectively
duce the free concentration of A to this level was calculated for a number of different complexes and various values of K ' C A ~ + ~The - ~ . results of these calculations, compiled in Table 11, clearly indicate that in some cases it is experimen1628
ANALYTICAL CHEMISTRY, VOL.
47, NO. 9,
AUGUST 1975
tally impossible to obtain the concentrations of B required to force all of A into its complexed form. However, this limitation may often be overcome by merely reversing the roles of A and B. For example, consider a complex formed from one metal ion and three molecules of a complexing agent with an overail formation constant of lo9. If the concentration of ligand is held constant at 10-3M and the concentration of metal varied, from the data in Table I1 it is found that a value of R of 3.3 X lo5 is required for complete complex formation, which corresponds to a clearly unobtainable metal concentration of 330M. However, if the concentration of metal is held constant a t 10-3M and the concentration of ligand varied, the complex will be completely formed a t a value of R of 7.6 which corresponds to an obtainable concentration of 7.6 X 10-3M. The choice as to which component concentration to hold constant in the mole ratio study may sometimes be dictated on the basis of which leads to the lower value of R in Table 11. In the case
of metal complexes, the favored choice will generally be the metal ion concentration. A common practice is to assume that an apparently constant absorbance value over a wide range of molar ratios implies complete complex formation. As clearly indicated by the simulated mole ratio plots (Figures 2-4), cy can appear t o approach a constant value even when the complex is incompletely formed. As an example of the difficulties this can pose, consider the previously described complex requiring a value of R of 3.3 X lo5 for complete formation. Simple calculations show that the absorbance becomes nearly constant (dculdR = 0.01) a t a value of R of less than 10, a t which value the complex is only 70% formed and the absorbance is 70% of its theoretical maximum.
EXPERIMENTAL In order to demonstrate t h a t the proposed techniques can be used successfully to identify very weak complexes in solution, studies were performed on previously well characterized complexes. T h e complexes studied are all relatively completely formed a t the equivalence point when mole ratio studies are performed a t optimum conditions but, for the purpose of this study, the pH of their solutions and analytical concentrations were adjusted so that the complexes would be formed to a lesser extent a t the equivalence points. The complexes studied and the experimental conditions are listed in Table 111. All chemicals were of reagent quality or were specially purified. All absorbance measurements were made using a Cary Model 14 spectrophotometer. Matched cells of 10.0-cm pathlength were used in studies of the Cu(I1)-EDTA complex, and 1.00-cm cells were used for all other measurements.
RESULTS AND DISCUSSION Some of the experimental mole ratio plots obtained are shown in Figures 6 to 8. All experimental plots were interpreted by each of the three techniques described above to
determine the stoichiometries of the complexes. The known stoichiometry and those indicated by each of the techniques are listed in Table IV. In those cases for which it is applicable (specifically when b # 1) the technique based on inflection point parameters indicated the correct stoichiometry. When only a single mole ratio plot was interpreted, the technique did not provide a unique identification of the complex. However, in separate studies of the iron-TPTZ complex when the roles of the iron and ligand were reversed, the additional information made a unique identification possible. The technique of self-consistent constants gave unique, correct identifications in fifteen of the eighteen studies, and in the other three indicated two possible stoichiometries for each study, one of which was the correct one. In each and every case, the curve matching technique provided a unique, correct identification of the complex. For comparison purposes, the plots were interpreted by the conventional (extrapolative) mole ratio technique, and the correct stoichiometries were indicated in only four of eighteen cases.
LITERATURE CITED J. H. Yoe and A. L. Jones, lnd. Eng. Chem., Anal. Ed., 16, 11 (1944). J. H. Yoe and A. E. Harvey, J. Am. Chem. Soc., 70, 648 (1948). A. E. Harvey and D. L. Manning, J . Am. Chem. Soc., 72, 4488 (1950). H. Diehl and F. Lindstrom. Anal. Chem., 31, 414 (1959). A. S. Meyer. Jr., and G. H. Ayres. J . Am. Chem. Soc., 79, 49 (1957). (6) P. Job, Ann. Chim. (Paris), 9 ( I O ) , 113 (1928). ( 7 ) W. C. Vosburgh and G. R. Cooper, J . Am. Chem. Soc.. 63, 437 (1941). (8) G. Schwarzenbach, Helv. Chim. Acta, 32, 839 (1949). (9) W. Likussar and D. F. Boltz, Anal. Chem., 43, 1265 (1971). (10) W. Likussar, Anal. Chem., 45, 1926 (1973). (1 1) A . E. Harvey and D. L. Manning, J . Am. Chem. Soc., 72, 4488 (1950). (12) K. Momoki, J. Sekino, H. Sato, and N. Yamaguchi, Anal. Chem., 41, (1) (2) (3) (4) (5)
1286 (1969).
RECEIVEDfor review January 13, 1975. Accepted April 21, 1975.
Development of a Multistage Air Sampler for Mercury Patricio E. Trujillo and Evan E. Campbell Industrial Hygiene Group, Health Division, Los Alamos Scientific Laboratory, University of California, Los Alamos, N.M. 87544
The development and use of a multistage tandem sampler to separate and determine particulate, organic, and metallic mercury in air is described. The sampler consists of a prefilter for collecting particulate mercury and a two-section sampling tube for collecting organic and metallic mercury vapors. Mercury is determined by thermally desorbing the metallic vapor from the sampler into a flameless atomic absorption mercury detector. At 0.3 ng, the relative standard deviation of the analytical method is f5%.
In recent years, numerous publications related to the hazards of mercury and organomercurial compounds have appeared in the literature. Since many organomercurials are considered more toxic than metallic mercury ( I ) , it is essential that a distinction be made between the various forms of mercury present in a contaminated environment. Distinguishing the various forms of mercury is one of the major problems encountered in analyzing mercury in air. In recent analytical methods for determining mercury in air (2, 3 ) , metallic, particulate, and organic mercury were col-
lected simultaneously and measured as total mercury. Many published methods for metallic mercury vapor in air are based primarily on amalgamation with precious metals ( 4 , 5 ) and are not capable of detecting most organic mercurials. Conversely, these methods are frequently nonspecific for metallic mercury since interferences from particulate mercury and certain organomercurials can be expected. Recently a project was undertaken to develop a method for determining particulate, metallic, and organomercurial vapors in industrial working environments. The developed sampling device was designed to collect preferentially each of the three forms of mercury and for use with a personal air sampler. In conjunction with this project, an analytical method was also developed in which mercury was thermally desorbed from the sampler and determined by flameless atomic absorption.
EXPERIMENTAL Apparatus. The apparatus used to generate known concentrations of organic and metallic mercury vapors for the testing of the various sampling materials was similar to that of Nelson (6). Two
basic sections comprised the generating system. The first section ANALYTICAL CHEMISTRY, VOL. 47, NO.
9. AUGUST 1975
1629
