7th Annual Summer Symposium-Developments in Titrimetry
Use of Chelating Agents as Reagents in Titrimetric Analysis A. E. MARTELL and STANLEY CHABEREK Clark University, Worcester, Mass.
'
The application of monodentate, and, to some extent, bidentate reagents to the titration of metal ions is limited by the formation of lower complexes before a specified end point is reached, and by the fact that complexes made up of a number of particles tend to dissociate considerably at the end point, where the concentration of free ligand is necessarily low. The use of chelating agents with a large number of coordinating groups overcomes these difficulties through the formation of 1 : l metal chelates involving a rapid change of solution properties at the end point. These ideas are illustrated with examples of potentiometric curves of metal complexes and chelates, and by the calculation from solution equilibria of the effect of ligand concentration on metal ion concentration. Examples are given of titration analyses of metal ions with polyamines and polyaminopolycarboxylic acids. Various methods of detecting end points are described, including potentiometric and colorimetric determination of pH, as well as potentiometric and colorimetric determination of metal ion concentration.
I
S R E C E N T years a number of new titration procedures have been developed, which have been especially useful for the quantitative determination of metal ions. Many metals may non be titrated n i t h chelating agents a s a result of the pioneering work of Schwarzenbach ( 1 , fO-f9), and the subsequent application of the basic principles to specific problems by many other investigators. This revien presents the theoretical basis for metal titrations involving chelating agents and summarizes the work completed up to the present time. The basic principles involved in the titration of hydrogen ions have been well established and understood. Because metal ions and hydrogen ions behave like Lewis acids in aqueous solutions, a comparison of the behavior of these ions offeis a logical and reasonable approach to the investigation of the properties of metal ions in titration procemes. These acids are solvated in aqueous solutions. Reactions involving the combination of hydrogen ions 01metal ions n ith a ligand ( a Levis base) proceed by the displacement of nater from the coordination sphere by a stronger bace. .411 the folloning reactions proceed in thla manner. iegardless of the t \ pe of reactant: H+(HpO)z OH-(H?O), --+ H20 (2 y)H>O
+
aqueous solution. If 0.1X solutions are titrated, for example, and if the product, then 0.05MJ is to be no more than 0.1% dissociated a t the end point, the maximum allowable concentration of reactants is 5 x l O - ~ M . This would correspond to a stabilit? constant of 2 x 107. Since in a titration solutions are geneidllx more dilute than 0.05J1, stability constants of lo9 or higher a l e required for R 1: 1 reaction. -4number of unideritate donors might therefore serve as titrants foi metal ions. Consider, for example, the folloiring reaction? in which the mater of solvation has been omitted:
1%
+ S H 3zzS H 4 +
K =
109.3
H-
+ C S - zzH C S
K =
109.14
K
klkrkskc =
T_
Cd-'
+ 4CS--:-f-
Cd(CS)a--
=
Y
The free energy changes of these reactions seem to have a sufficiently high order of magnitude. It is readily seen in Figure 1, hoa-ever, that iyhile a rapid decrease in the (H?) concentration a t the end point is indicated by a sharp, almost vertical rise in the pH curve, t,he corresponding depletion of metal ions is reflected by a very weak inflection n-hich is unsuitable for a titration end point. Consequently, copper(I1) and zinc(I1) ions cannot be tit,rated n-ith these unidentate ligands. The titration curves of simple compleses such as Cu(THa)a++ and Zn(CN)r-- are not suitable for two reasons: the tendency to form loner eompleses before the end point is attained, and the greater tendency for the higher compleses to dissociate on dilution. FORMATION OF LOWER COMPLEXES
F
The first effect produces an appreciable decreaFe in the metal ion concentrntion before the end point is reached. The result is graphically illustrated by the sloping buffer regions preceding the inflections of the metal titration curves in Figure 1. .4 more detailed consideration of the interaction of cadmium(I1) and cyanide ions indicates the reason for this effect. Although the over-all stability constant for the formation of Cd(CS)r-is very high, the formation of this species occurs through a aeries of overkipping steps:
+ C S - zz C d C S C d C S - + C S - r z Cd(CS)2 Cd(CS)? + C S - z-fCd(CS)3Cd(CS)3- + C S - z Cd(CS)I-Cd + +
+ +
k,
= 1Oj.54
k2
= 105.04
k3 =
104.66
+ CS-(H,O)z--+ HCS(H20)m + (5 + z - nl)H?O Ji4 103.Z Zn'+(H20), + C S - ( H 2 0 ) , ---+ Zn(CN-)(HtO),'-, + (1 + -.)H20 I t is apparent, therefoic, that a single cyanide ion is not so stronglv bound to the metal ion as to a hydrogen ion ( k = Zn-+(H20), + H2SCH2CH2SH2(H20)d--+Zn(HeSCH2CH2NH2)(H20).+-+, + ( 2 + d)I120 and that the free energy changes for the individual steps H+(H20),
109.14),
The subscripts represent the average number of molecules of hydration for each species. They are significantly large values only for the positive ions, a s the solvation of the negative ions is of a much lower order of magnitude. If a reaction is to he considered suitable for a titration process, it must proceed rapidly and completely to a n end point in dilute
are comparable in magnitude If the total concentration of metal species is denoted by C u , then:
cv
= =
1692
+ [MC?:+l + [nI(cs),]+ [Rl(CW,-I + [ I f (CS)4- -1 [ A I + T ] + kl[ar+-][CS-l + . klkz[AI'+] [CS-I2 + kik?k3[II+'] [CS-13 [AI++]
1693
V O L U M E 26, NO. 1 1 , NOVEMBER 1 9 5 4 The terms may be rearranged to give:
Year the beginning of the titration [ C S - ] has its lowest niagnitude and the terms containing higher poa ers of I C s -1 have relstively less effect upon pM. Since kl > kl > kl > k4, in the general case, these loner [CN-] terms which are obtained directly from the formation of the lo\%-ercomplexes Fill result in a n appreciable increase in pM. Hence, it is apparent that the p?rI increase will occur before the complete formation of the highest comThis premature p11 rise decreaGes the plex, such as Cd(CN),--. magnitue of the pM change a t the end point and iesultq in a weak inflection in this region of the titration curve
A comparison of the degree of dissociation of these metal complexes near the equivalence point of a l O - z X solution for various values of the formation constants is given in Table I. These data indicate that a t a concentration of lO-"M, the 4 : l complexes are dissocisted to the greatest extent regardless of the magnitude of the stability constant and that the degree of dissociation diminishes as the number of donor groups is decreased. For example, the increase in metal ion concentration a t the equivalence point for a 1 : l complex having a stability constant of 1020 corresponds to 8 p?.I units, in contrast to a n increase of 1.9 units for a 4:l complex having a comparable stability. Even a 4 : l conq)le\ nmv hc satisfactory if its stahilit?- is sufficirntly high.
DISSOCIATION OF HIGHER COMPLEXES
The greater tendency of higher complexes to aissociate on dilution, even though the magnitudes of the stability constants are the same, is predictable from the mass action law. T h e stepwise formation of 1:1, 2:1, and 4 : 1 complexes may be represented by the following general equations:
Figure 2. Variation of .Metal Concentration at Titrinietric End Point with Stability Constant and Number of Donor Groups E. P.
The general shape of the hvpothetical titration curves for t h e complexes and log K values listed in Table I are illustrated in Figure 2 . Although the formation of intermediate complexes has been neglected here, it is readily seen that 4 : l complexes. n i t h stability constants as high as 1020 are unsatisfactory; on the other hand, 2 : l complexes c:tnnot be usrd unless K is considerably greater than 10'0 The shape of curves beyond the inflection in Figure 2 further illustrates this effect. The concentration of metal complex varies to onlj a s m d l extent in this region containing excess complexing agent. The slopes of the 1111 curves increase with a n increase in the number of bound donoi group.. This behavior decreases, in effect, the p M change a t the end point.
14
PM OR
PH
I
0
I
I
1
I
I
1 2 3 4 5 MOLE? OF LIGAND PER M0I.E VETAL
Figure 1. Titration of Hydrogen, Copper(II), and Cadmiuni(I1) with Cyanide and Ammonia
EFFECT OF CHELATIOR
- - - - - Titration of (H +) and Cu(I1) with NHa
-
The substitution of chelating agents for monodentate complexing ligands overcomes most of the difficulties described above. Their use in titration proceduies offers thrre distinct advantages:
Titration of ( H - ) a n d Cd(1I) with CiY-
Table I. of Donors 76
1 1
Effect of Log I< and Number of Donor Groups upon pM ~ ~ ~ b ~-pLI l , t ~Corresponding , t o Various Values of M a
Constant, LogK .U=OQn 10
3 0 3 0
4
: a
,!-1 = n f O l
6 0 -12 2 9
9 0 6 0
11 = n f l 10 0 8 0 4 0
20
3 0 3 0 3 0
11 0 7 5 4 9
19 0 16 0 10 0
20 0 18 0 14 0
3 0 3 0 3 0
16 0
30
10 9
29 0 26 0 20 0
30 0 28 0 24 0
4
1 2' 4
?l=n
6 9
I1olf.s of ligand added per mole of metal ion
End point
1. The elimination of lower coniple~es,which result in too rapid a rise in p M in the initial portion of the titration. 2. Less dissociation of the metal chelate a t and beyond t h e end point, since fewer ligands are bound per metal ion. 3. Considerably greater increase in p31 a t the end point resulting from the higher stability of metal chelates over corresponding complex compounds.
The interactions of copper(I1) and zinc(I1) ions with the polyamines, ethylenediamine (En), diethylenetriamine (Dien), triethylenetetraamine (Trien), and triaminoethylamine (Tren) illustrate well the influence of these factors upon the shapes of the corresponding titration curves. While both metal ions have a coordination number of 4, the spatial arrangements of the donor group are different. The copper(I1) chelates are square planar, while those of zinc(I1) are tetrahedral. The structure of t h e
1694
ANALYTICAL CHEMISTRY
copper(I1) chelates are shown in Formulas I1 to Y. Examples of the zinc(I1) chelates are shown in Formulas VI and VII. CHZ-CH?
I
\ /
.4mmonia
H?C--CH?
type shown have the advantage of 4 to 1 monodentate complexes in satisfying all the coordination requirements of the metal, and the added advant'age of a 1 to 1 complex in undergoing a lesser degree of dissociation a t and beyond t,he end point. Increased Stability of Chelates. It has long been recognized that the binding together of donor groups in such a way that coordination with B metal ion produces a cyclic five- or six-membered ring structure result,s in a large increase in stability of the resulting metal chelate, even though the number of coordination positions of the metal which are satisfied remains the same. This effect is readily seen by considering the stability constants listed in Table I1 for the copper(I1) and zinc(I1) polyamine chclatcs.
I1 Ethylenediamine (En) CHz-CH2
/
H*K
CH?--CHz
\." S'
/
\ / H1-
H21-
I11 Diethylenetriamine (Dien)
\
CH?--C& H'
IT- Triethylenetetraamine (Trien)
/
\ ,CH?CH,XH*
CHt-CH,
HA-
N DONORS
Figure 3.
\* Triaminoethylamine (Trenj
VI ( E n )
1-11 (Tren
Stepwise Complex Formation. T h e elimination of stepwise complex formation through chelation is readily apparent, as the combination of one molecule of a chelating agent with a metal ion results in the simultaneous coordination of all the available donor groups (barring steric factors). Hence, the interaction of tetradentate ligand uith a tetracovalent metal [Cu(II)Trien and Zn(I1)-Tren] can result on11 in the foimation of a 1 to 1 chelate. With the exception of ethylenediamine and diethylenetriamine, all chelates shown above do not undergo stepwise complex formation. -4decrease in the numbel of ligand molecules which are required to satisfy the covalences of the metal ion results in the supprepsion of the premature p?\I rise during the initial portion of the titration curve. Decreased Dissociation a t End Point. The gieater stahility of metal chelates at the end point of the titration follous from the considerations outlined above. The data in Table I and Figure 2 illustrate well the desirability of 1 to 1 interactions between a metal ion and ligand in titration processes. I t is readily apparent, therefole, that tetradentate chelates of the
BOUND
PER
METAL
Titration of Copper(I1) and Zinc(1I) with Various Polyamines
Foi. example, t,he binding of two molecules of ammonia corresponds to the log K of 7.6 units, while the coordination of one molecule of eth>-lenrdiamineresults in a log I< of 10.7. The formation of a five-iiicmhered ring, therefore, incrcaases the stabilit!, by approximately 3 log K units, in spite of the fact that in both cases two coordination positions are occupied. Similarly, the formation of two five-nienilwied rings by the binding of the three amino nitrogens of dictli!~lt~iietrianiiiieincrcares log I< by 5.5 units over the binding of 3 ammonia moleculrs. This chelate effect, therpfore, results in ttii increase of rtabilit!. for mch metal ion Tvith an increase in t,he number of coordiii:itrti donor groups and with the number of chelate rings that are formed. This etYect is important for analytical purpows, as it produces a greater pAl change at t,he titrimetric end point. Tahle 11.
Stabilitl- Constants of Copper(l1) and Zinc(I1) Amine Chelates T = 200
Ligand Ammonia En Dien
Tren
Formula
h": H2KCH2CH??iHz ,CHICHISH* HN \CH?CHA-H? CH,CH?NH?
/
1 ' -
c.
p
=u.1
Cu(I1)
Log K
Zn(I1) 2.2.2.3,
Reference
4.1,3.5, 2.9, 2 . 1 10.7, 9 . 3 16.0, 5 . 0
5.9, 5 . 0 8.9, 5 . 3
18.8
14.6
(1)
20.5
11.8
(13)
(2)
2.3, 2.0
(3) (10)
CHsCHA-H?
\
Trien
CHICHISHI HN-CH?CH2NH?
&H* AH?
\
HN-CHzCH?SH?
V O L U M E 26, N O . 1 1 , N O V E M B E R 1 9 5 4 The tit,rution curves corresponding to the interaction of copper(I1) and zinc(I1) ions with the chelating agents listed in Table I1 are illustrated in Figure 3. It is obvious that the binding together of two donor nitrogen atoms (ethylenediamine) markedly increases the pill change at the end point over that shown for ammonia. However, the end point is less satisfactory than those obtained with triaminoethylamine and triethylenetetraamine. The presence of two inflections for diethylenetrianiiue is due to the formation of a 1:l chelate with enough additional stability resulting from the coordination of a second mole of amine to produce a significant pM increase. Because thv zinc(I1) chelates have a lower order of stability than the corresponding copper( 11) chelates, the titration curves with et,hylenedianiine and diethylenetriamine are much less satisfactory; only trieth>-lenetetraamine and triaminoethylamine give satisfactory end points. The use of polyamines as titrant,s is restricted to copper(II), riii~kel(II),and zinc(I1). Interaction with cadmium(I1) and cobalt(I1) is considerably weaker and unsatisfactory end points arc obtained. The incoiyor~t~ion, however, of carboxylate groups into t,he amine structure extends the use of chelating agents in titi,imrt,ric analysis to many other metals which have little or no trntlency to coordinate amine nitrogen groups. T v o aininopol!,curboxylic acids, etliylenediaminetetraacetic acid (EDTA>Formula 1'111) and nit,rilotriacetic acid (NTA, Formula I S ) , havc proved to be highly successful a s titrants for the detc~i~minati:)n i i f many metal ions.
CH2C 0 0 €I
HOOCCH:!
\+
+/
1695 hydrogen is a considerably weaker acid. The dotted curve of the dipotassium salt, therefore, corresponds to that obtained by titrating the salt of a strong acid and strong base with standard hydroxide. I n the presence of a metal ion, the third proton becomes strongly acidic, and t,he titration curve (solid line) is similar in shape t.o that obtained by neutralizing a strong acid with a st,rong base. The p H change at the inflection may be determined either potentiometrically or by the use of a suitable p H color indicator.
PH
MOLES OH-/ MOLE NTA
Figure 4. Titration of Dipotassium Hydrogen NitriIotriacetate
- - - - - Titration of K2HA w i t h base
--
Titration of K2HA in presence of divalent m e t a l i o n
CH2COW +/ HT-CH2COOH
Titration with Standard Chelating Agent. Tit,rations may also be accomplished by t.it,rat.ingmetal ion solutions wit,h the strongly -OOCCII:, CHZCOOCH2COOH alkaline tripotassium nitrilotriacetate (K3.4). During the course of the t,itrat,ion, no strong acidification is observed, as all the hydrogens of the amino acid have been neut,ralized. The solution remains aciclic until t,he end point is attained. The addition of a slight excess of the highly alkaline reagent then results in a These amino acids-of the chelating agent for the metal ion. metal ions in buffered solutions using various dyes as indicators. The reawn for thiv hehavior is readily seen when one considers These compounds are actually p H indicators which have two or that, thew amino acids exist in aqueous solut,ion as zwitter ion!: more sensitive regions of color change and which form chelates and t,hat t,he (ahelation of a metal ion actually involves the diswith metal ions. -4s the color rhange a t the end point depends placement of a hydrogen ion from a weakly acidic positive amupon the removal of t,he nietal from the metal-dye chelate by the monium ion. For example, .thc int,eraction of dipotassiumstandard chelat'ing agent, the stability of the metal-dye chelate hydrogen-11itl.ilotriacetate (KJT-I) with a metal ion proceeds must be of a proper magnitude relative to that of the metal according to t,he r e a d o n : chelatr of the reagent and t,he removal of the metal must, be H.i-\I+11.1Hi rapid and reversible. 1Iany metals may be titrated in the presence of such indicators Hydrogrn ions are liberated during the chelation process. a s Eriorhromrwhwartz T, Murexide, and Tiron. This pH rffect, may be utilized in several wa>-s. Titration with Standard Potassium Hydroxide in Presence of JIETHODS BASED UPON CHANGES IN OXIDATIONExcess Chelating Agent. Schwarzenbach and Biedermann ( 1 4 ) REDUCTION POTENTIALS have applied this method to t,he determination of a number of metal ions using dipotassium hydrogen nitrilotriacet,at,e (K2H.4). The oxidation potential of a system may be interpreted qualiThe basis for the method is illustrated in Figure 4. Tlie first tatively a s a measure of the tendency of this system to undergo two hydrogens of this acid are strongly acidic, whilr the zwitter oxidation from a lolver to a higher oxidation state. The formaH--S--CH?C'H---S
/
-H
\
\
+
+
rz
+
-22.
+
1696
ANALYTICAL CHEMISTRY
tion of a very stable metal chelate with one of the oxidation states of a metal can cause a shaip change in the redox potential. This property of metal chelates has analytical applications. Potentiometric Titrations in Presence of Excess Chelating Agent. The oxidation potential of the cobalt(I1)-cobalt(II1) couple is so negative ( - 1.82 volts us. hydrogen) that even the stronger oxidants such as ceric sulfate cannot be used as a redox titrant ( E O = -1.61 volts us. hydrogen). The addition of ethylenediaminetetraacetic acid, hoTTever, shifts the potential about 1.2 volts [EOfoi cobalt(I1) ethylenediamine tetraacetate-cobalt(II1) ethylenediamine tetraacetate = -0.6 volt], so that a redox titration using ceric sulfate is feasible. Pfibil and conorkers ( 4 , 8) have devised procedures based on this principle for the determination of manganese and cobalt. Titration with Standard Chelating Agent. It is possible in some cases to titrate metal ions in buffered solutions with a standard chelating agent. I n this case the potential change at the end point is a result of the formation of a very stable virtually undissociated chelate with one of the oxidation states of the metal. PEibil ( 7 ) obtained excellent results in titrating iron(II1) with disodium dihydrogen ethylenediamine tetraacetate in an ammonium acetate buffer. The use of this method is dependent upon the availabilitj- of a suitable indicator electrodc and the rapid formation of a stable metal chelate. Polarographic Methods. Metal chelate formation generally results in a shift of the half-wave reduction potentials ( E l / ? )of the polarographic wave of the metal. This displacement in E l / , has been made the basis of a large number of amperometric titrations by many investigators. Literature references concerning this technique are too numerous to mention here. It is also possible to separate the reduction waves of several metals having comparable reduction potentials through preferential chelate formation. Because the spread in El/, values for the chelates is dependent a t least in part upon the relative affinity of the ligand for the metal ions, the proper choice of a chelating agent makes possible the resolution of the corresponding reduction waves. Numerous examples of this application may be found in recent literature. PEibil and coworkers ( 9 )have succeeded in resolving the waves of copper(II), lead(II), and thallium(1) by this method. Colorimetric Applications. The development of intense color
resulting from the interaction of a number of metal ions with chelating agents may be utilized for analytical applications. Spectrophotometric determinations of manganese, cobalt, and chromium have been reported by Pfibil and coworkers (6, 6). Sweetser and Bricker (20, 21) have recently reported simple and rapid procedures for the spectrophotometric titration of copper(II), nickel(II), iron(III), zinc(II), and cadmium(I1) ions using disodium dih] drogen ethylenediamine tetraacetate. The interest and the excellent progress in the application of chelating agents to specific analytical problems are evidenced by the fact that over 150 scientific papers have already been published on the uses of nitrilotriacetic acid and ethylenediaminetetraacetic acid alone in this important chemical field. The continuing investigations along these lines n ill certainly result in the development of nem- and useful analytical applications of this important class of chemical compounds. LITERATURE CITED
(1) Ackermann, H., Prue, J. E., and Schwarxenbach. G., A-ature,
163,723 (1949). (2) Bjerrum, J., thesis, Copenhagen, 1941. (3) Bjerrum, J., and Nielsen, N.,unpublished results. (4) Piibil, R., and HorLEek, J., Collectton Ctechoslou. Chem. C o w muns.. 14. 413 (1949). (5) Piibil, R., and Hornychorh, E., I b i d . . 15, 456 (1950). (6) Piibil, R., and Klubalovh, J., I b i d . , 15,42 (1950). (7) Piibil. R., Koudela, Z., and hlatyska, B., I b i d . , 16, 80 (1951). (8) Piibil, R., and gvestka, L., I b i d . , 15,32 (1950). (9) Piibil, R., and Zabranskg, Z., I b i d . , 16, 554 (1951). (10) Prue, J. E., and Schwarzenbach, G., Helv. Chim. Acta. 33, 985 (1950). (11) Schmarxenbach, G., A n a l . Chim. A c t a , 7, 141 (1952). (12) Schmarzenbach, G., Chimia, 3, 1 (1949). (13) Schwarzenbach, G., Hell;. C h i m . A c t a , 33, 974 (1950). (14) Schwarzenbach, G., and Biedermann, W., Ibid., 31, 331 (1948). ( 1 3 Ibid.. n. 456. i l 6 j I b i d . : b. 459. (17) Schwarzenbach, G., Biedermann, W., and Bangerter, F., I b i d . , 29, 811 (1946). (18) Schwarxenbach, G., and Gyding, H., I b i d . , 32, 1108 (1949). (19) Ibid., p. 1314. (20) Sweetser, P. B., and Bricker, C. E., SAL. C H E M , 25, 253 (1953). (21) I b i d . , 26, 195 (1954). RECEIVED for review July 29, 1954. Accel>ted September 29, 1954.
7th Annual Summer Symposium-Developments in Titrimetry
Interpretation of Data Obtained in Nonaqueous Media ERNEST GRUNWALD Florida State University, Tallahassee, Fla.
In media of low and intermediate dielectric constant, activity coefficients of ionic species deviate greatly from unity. The deviations may cause inaccurate inflection points in potentiometric titrations and troublesome salt effects on color indicators. The deviations are best described by assuming the formation of ion pairs. The physical nature of the ion pairs, the magnitude of their dissociation constants, and the calculation of ion activity for partly associated electrolytes are discussed. The available generalizations are applied to one particular potentiometric titration, and methods are proposed for improving the accuracy of the inflection point. A quantitative treatment of medium effects on color indicators for acid-base titrations is developed. For optimum results, the choice of an indicator is governed by the pH at the equivalence point and the solvent sensitivity indexes of the indicator and substrate.
I
X T H E classical approach to the theory of titrations, the l a w
of the dilute solution ( 2 3 ) are thought to be an adequate first approximation. This approach is certainly correct for aqueous titrations and, when applied only to nonelectrolytes, for nonaqueous titrations. However, electrolytes deviate so greatly from the laws of the dilute solution in solvents of low dielectric constant that the interpretation of results on the basis of the dilute solution approximation may lead to considerable error. For the sake of illustration, the experimental activity coefficients, y, for hydrochloric acid in a number of solvents are shown in Table I. I t is seen that y values for the 0.01JI acid decrease markedly with the dielectric constant, D, from 0.905 in water (D = 78.5) to 0.138 in 82% dioxane (D = 10.6). The y values are compared with those predicted from the Debye-Huckel limiting law
- logy =
s d;
(1)
