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Extractive indicators in complex-formation titrations: theory and practice
Talanta. 1966. Vol. 13, pp. 1497 to 1516.
Pergamon Press Md.
Printed in Northern Ireland
EXTRACTIVE INDICATORS FORMATION TITRATIONS: PRACTICE
IN COMPLEXTHEORY AND
D . BETIERIDGE University College, Swansea, Wales (Received 3 December 1965. Accepted 11 May 1966) Summary-The use of conditional constants to predict the optimum conditions for titration in several complex-formation titrations, in which the end-point is detected by the formation of a coloured extractable complex, is demonstrated. The predictions have been tested by experiment. 2-(2-Pyridylazo)-1-naphthol is shown to be a useful extractive indicator for the copper-EDTA titration; dimethylglyoxine is not recommended as an extractive indicator for the nickel-EDTA titration; the titration of fluoride with aluminium, using I-hydroxyquinoline as an extractive indicator, is shown to be undesirable theoretically and experimentally.
it is difficult to observe the end-point in the titration of a coloured metal ion with EDTA because the colour of the EDTA complex formed masks the colour change of the indicator. In these circumstances the end-point must be detected instrumentally or with fluorescent or extractive indicators. Visual detection is often preferable and this paper is concerned solely with extractive indicators (which may be defined as indicators which form an extractable complex with the metal ion so that the end-point may be detected by a colour change in an organic solvent immiscible with water added to the titration vessel). The optimum conditions for such titrations are calculated theoretically, using conditional constants, and the predictions tested by the following titrations: EDTA with copper and nickel using 2-(2-pyridylazo)-lnaphthol (a-PAN) and dimethyl glyoxime (DMG) respectively as indicators, and fluoride with aluminium using %hydroxyquinoline as an indicator. In the normal extractive titration the metal ion is titrated with a complexing agent with which it forms a coloured extractable species. When an extractive indicator is used, however, the metal ion is titrated with the complexing agent of choice, e.g., EDTA, in the presence of an indicator, which forms an extractable species with the metal ion. If the free indicator is soluble in the organic layer and the metal-ion solution is the titrant the end-point is indicated by the extraction of the first excess of the metal-ion into the organic layer with consequent change of colour, so that the colour of the aqueous layer does not affect the detection of the end-point. In developing a theoretical approach we focus attention on the extraction, and consider the titration system to represent an extraction system in which the extraction of the metal ion is inhibited by a masking agent e.g., EDTA, whose concentration varies (i.e. the concentration of free EDTA decreases as increments of metal-ion solution are added). The use of conditional constants,* proposed by Ringbom1-3 and Schwarzenbach,a FREQUENTLY
* If the formation or stability constant for a reaction is Kf = - [Mb1 the conditional stability lM1[R-ln lMRn1 constant is defined as K’r = lMltOt~HRl~t,t where [M]M and [HR& tration of metal ion and reagent respectively. 1497
are the analytical concen-
1498
D. B-E
and propagated by Laitinen ,I Freiser and Fernando,6 and Butler,’ enables the optimum conditions for such titrations to be predicted fairly easily,s-@because the cumulative effect of side-reactions, e.g., with hydrogen ion, buffer solution or other masking agents, can be broken down into smaller parts. In this paper different systems from those discussed by StilP are considered and a different emphasise is used in the theoretical approach, although, of course, the treatments are equivalent. DERIVATION
OF EQUATIONS
General
The nomenclature of Laitinen,6 and Freiser and Fernando,6 with slight modifications, is followed. Thus tc is a coefficient relating to the effect of acid dissociation of reagents and p is a coefficient relating to the effect of masking agents on metal ions. To simplify the derivation of the equations the metal ion is assumed to be bivalent (M”+), and the reagent, HR, to be one that can either take up (H2R+) or lose (R-) a proton. This derivation is applicable to many chelate systems and the extensions to make it more general are obvious. An extraction system is quite complex because in addition to the equilibria associated with complex formation the equilibria of the distribution of the reagent and complex between the two phases, and the side-reactions of reagent and metal ion, must also be taken into account. Figure 1 represents schematically the possible reactions, except the formation of mixed ligand complexes, and indicates their equilibrium constants. (It is possible to view Fig. 1 as a flow diagram in which the order of reactions is from HRor, to MRgorg.) ORGANIC PHASE
=am
=a1
AQUEOUS
PHASE H,R+ _
HR +R-
h
+
ka
M’+ +
MR+ ;
MR 0
XllOH) %Y) II e
M(OH)+
MYa-
%OEl
*XIX) 11
M(OH)“-
~PIX)
11
MX+ _
MX,
M(Oii),-
FIG. I.-Schematic
diagram of extraction system.
For the extraction of the chelate the essential reactions are the formation of the anion of the reagent, complex formation in the aqueous phase to give uncharged chelate, and the transfer of the uncharged complex to the organic layer; these will be called distribution reactions. The formation of neutral and cationic reagent species and the formation of other metal complexes are side- or masking reactions. The treatment consists of seeing how the central distribution reactions are modified by the side-reactions.
Extractive indicators in complex-formation titrations
1499
The necessary constants are defined below. Subscripts have the following meanings: aq = aqueous phase, org = organic phase, tot = total analytical concentration,(D) =
taking distribution into account, (HX) = with respect to HX, a = acid dissociation, and numerals indicate the steps in a series of constants for which & is the overall formation constant. A superscript dash indicates that the constant is a conditional one. Concentrations rather than activities are used throughout, but wherever possible the constants used are those measured at an ionic strength similar to that used in the experimental part of this study. Distribution reactions The ratio of direct interest is the distribution ratio, D, which is the ratio of the total concentration of metal in the organic phase to the total concentration of metal in the aqueous phase. D varies with the conditions prevailing in the system.
Wltot,&Wtotaq.
D =
The partition coefficients for the complex (K,,) defined by
(1)
and the reagent (KDR) are constants
KDX
=
~MRzlore/[MRzlas
(2)
K DR
=
[HRlordWRlrw
(3)
and The overall formation constant of the complex (Ki> is given by (4) If MR, is the only metal-ion species present in the organic phase [M]totOrs = [MRJore and if the predominant metal-ion species in the aqueous phase is free metal ion so that WltotaP= [M2+],,, then D=KDxE
(5)
w D = KDxKr[R-1’.
(6)
This is the form of the equation widely usedlo to describe chelate extraction systems, for [R-l = j!& !!?!& the total concentration
when the uncharged form of the reagent predominates and of reagent is its concentration
in the organic phase, and .
A more generally applicable form of equation (5) is available if the side-reactions of the reagent and the metal ion are taken into account. Side-reactions of reagent. Although the concentration of the anionic form of the reagent in the aqueous phase is required in equation (6) it is more convenient to use the analytical concentration of the reagent in the system i.e., the amount of reagent added regardless of the species present. The relating of what is convenient to what is required theoretically is the function of the coefficients ccand @,which are defined below.
1500
D. BETITWDGE
If the number of moles of reagent in the system, in absence of metal ion, is represented by mtot the mass balance equation for the system can be written m tot
-
%2R
+
%ROrg
=
mH2R
+
lltHR
+
1 +
mHR
+
KDR F)
“R-
w
(8)
+
mR-
where mx is the number of moles of species X and Verg and Vaqare the volumes of the two phases. If the total concentration of reagent, [HR]tot, is defined as the concentration of reagent if it were all present in the aqueous phase, then [HR]tot = F
w
= [HsR+] + [HR]
The fraction of the total concentration anionic
1 + KDR $f)
w
+ [R-l.
of reagent present in theaqueous
phase in the
form is
1+ KDR
7 +K,*K,,) --) .
(12)
Thusa2(D) can be used to compute the effect of side-reactions-competing with the hydrogen ion. It is simple and convenient to plot a graph of log>20j VS.pH (Fig. 2). When the uncharged form of the reagent predominates, .
FIG.
2.-Log CC,,D) as a function of pH for various reagents when Vorg= V,, 3+x-PAN I-DMG 2-Shydroxyquinoline ~---O-PAN
(13)
Extractive indicators in complex-formation titrations
1501
KDR is usually large and the relationship between the total reagent concentration defined for equation (7), [HR] orB, and equation (lo), [HR]tot, is given by [HR]tot = [HRlore (VW/VW), so that equation (7) is readily derived. However, as(=) is most useful for those conditions when the simplifications are unjustified e.g., the extraction or iron with 8-hydroxyquinoline or the extraction of nickel with DMG. Side-reactions of metal ion. There are many possible side-reactions for a metal ion in solution, so, in principle, it is more convenient in equation (4) to use the total metal-ion concentration rather than the free metal-ion concentration. Thus p is defined as B = -[M2+JN _ - [M2+l/{[M2+l + [MR+l + [MU + [MY2-1 + [M(OH)+l P&t,, + [M(OH),I + [MPH,-)1 + [ML+1 + P=,I)
(14)
where Y4- represents the completely dissociated EDTA and L is some unspecified interfering ligand that might be present in the solution, e.g., an interfering component in added buffer solution. In general, ignoring charges, k
[MXI lCx) = [M][X]
(15)
and k
P4X21 2(x) =
[MX][X]
(16)
where X can be any ligand. The overall formation constant, Kf, is given by
K iCxj = k,k,.
. . kn-
[MRnl WI[Rl”
(17)
where n is the maximum number of ligands normally bound to the metal ion. Substituting the appropriate stability constants into equation (14) gives B = l/(1 + k&R-l + Kro,tR-I2 + Kr&Y4-l + k,(,,,tOH-1 [OH-l3 + k,o,[Xl + W,o,[X12}. + k,k,om [OH-l2 + k&&o,,
(18)
This apparently formidable equation is readily handled in practice because one term usually predominates. The terms containing the reagent concentration are for the concentration of the anionic species so that an a coefficient or conditional constant should be introduced for convenient working. For example, for the simpler case of [Mltot = [M2+] + [MR+] + [MR,], l/B = 1 + k,[R-1 + Kr[R-I2 = 1 + kla2[HR] + Kta22[HR]2 = 1 + k,‘[HR] + Ki’[HR12. In general it is not so simple to portray graphically the variation of log @ with pH or reagent concentration as it is to deal with log a, because the successive stability constants are too close together. Ringbomle3 has noted the additive nature of /3 3
1502
D. Barre~nx;~
coefficients. Thus if a value /3* were calculated on the basis of equation (18) and another masking agent, Z, were added to the system, the total masking coefficient, 1 1 /Itot, would be given by -!-tot = Ba _!_ + z - 1 whereK = 1 + ~dZ1 + Wz&la. B Obviously ,9 will vary greatly with changes in the system, but because of the additive nature of the coefficients it is easy to follow changes of @ with changes in the system. A more satisfactory derivation of a comprehensive extraction equation, then, is
U.MbJaq
(19)
D=KDx [Mltotaq
(20) D = K&xt%(Dj [HR12tot. Under appropriate
(21)
conditions it reduces to the limiting cases of equation (7) or to
In this study B and a,(n) are calculated for a variety of conditions and systems and D is calculated by use of equation (21) ; the predicted results are compared D = KD,.
with the actual results. Details of the calculation for the three systems studied are given in the experimental section. EXPERIMENTAL Calculations One of the great advantages of the use of conditional constants is that problems arising from systems involving complex equilibria may be solved easily because, when conditions are defined, many terms in the expressions for a and b can be ignored. It is tedious to calculate a and /I for a large number of conditions, and computer programmes have been devised to carry out some of the calculations. As the programmes are readily modifled to accommodate many systems and one set of data cards is adequate for several systems, there is some value in using a computer if it is available. A typical programme is given below in Fortran 2 for an IBM 1620 computer. The two most important general features are (1) the values of constants are introduced into the appropriate equations in the programme and (2) A is used for a, B for & and as far as possible chemical terms are transcribed into easily recognisible ciphers. The lirst of these eliminates sub-routines at the cost of changing a few cards for each modiiication of the programme i.e., each new system. Both features help an inexperienced operator to make his own modifications to the programme. Copper-EDTA-a-PAN a-PAN: EDTA:
system. The following values for the constants were used:“~” PK., = 3.0, pKs, = 9.5, log K~B = 4.2, log KDx = 3.6, log K, = 24. pK,, = 2.0, pKs, = 2.67, pK,, = 6.16, pKa, = 10.26.
OH: log KpI+ = 10.6
KSr., =
where
[‘&(OH),*+I~H+l*. [Cu*+p
These substituted into equations (13) and (18) gave a2,nj = 3.15 x 10-‘S/([H+]* + 15.8[H+] + rzI(BDTAj= 8.12 x lo-“/([H+]”
W
3.15 x 10-‘S)
+ 10-P[H]8 + 2.14 x IO-=[H]* + 1.48 x lo-“[H+] + 8.12 x lo-=)
l/j3 = 1 + 10zAa,*,n,[aPAN] *tot -t- 6.31 X 10” 2.51 x lo-“[Cup+]
[H+l*
aP(EDTd)
[EDTAh
f
&
i-
Extractive indicators in complex-formation
titrations
1503
These coefficients were calculated for differing values of pH and copper and reagent concentration, with v,, = I’.,,, and were substituted into equation (21) to predict how the distribution varied with these factors. The final form is D = l~“~~a,*~~~[a-PAN]‘,,I The following computer programme was also used. TITLE READ 2, N 2 FORMAT (13) M=O 4 M=M+l IF (N-M)18, 8, 8 8 READ lO,PH,YTOT,RTOT,CU 10 FORMAT (F10.2, 3E10.3) H=l*O/EXPF(2.303*PH) AR=3.15E-l3/(H*H+15.8*H+3.15E-l3) AY=8.12E-22/(H**4+1.E-02+H++3+2.14E-05*H*H+1.48E-ll+H+8.12E-22) P=l.+l.E 24+AR+AR+RTOT+RTOT+6.31E 18*AY+YTOT Q=l.E-08/H+2.51E-ll*CU/(H*H)
B=l./@'+Q) D=4.E 27*B*AR*AR+RTOT*RTOT BLQG=LGGF(B)/2.303 DLQG=LGGF(D)/2.303 12 PRINT 14,PH,YTOT,RTOT,CU,BLQG,DLGG 14 FORMAT (1H F10.2, 3E10.3, 2F10.3) GOT0 4 18 CALL EXIT END N is the number of data cards (169 in this case), Y = EDTA, R = a-PAN, and P and Q have to be used because the full expression for B (=p) is too long for one card. A selection of the results for various conditions is shown in Figs. 3,4 and 5.
FIG. 3.-Variation
of log B for copper-a-PAN-EDTA system as function of pH for various concentrations of EDTA. l-no EDTA 3-lo-% EDTA 2-lo-‘M EDTA
1504
D.
BETTERIDGE
PH
FIG. 4.-Extraction l-a-PAN, 2-a-PAN, ~--G-PAN,
of copper as a function of pH for various concentrations a-PAN and EDTA. 10-4M; EDTA, 10-*&f &a-PAN, 10-*&f; EDTA, 10-‘&f ~-U-PAN, 10-6M; EDTA, nil 10-4M; EDTA, 10-6M 6-a-PAN, 10-4M; EDTA, nil 10-SM; EDTA, lo-‘M O-a-PAN, IO-*M A-a-PAN, 10-5M
of
Aluminium-fluoride-Shydroxyquinoline system. The following constants were used,“-l4 AIF,‘*-“I+: log k, = 6.13, log ka = 5.02, log ks = 3.85, log k, = 2.74, log k, = 1.63, log k, = 0.47, log Kr = 19.86. HF: pZ&, = 3.17. Alm(OH),(*m-n)+: Values for both the acid dissociation constants of the hydrated aluminium ion,
KI* etc. KI* = [Al(;$+;[H+I 1
; KIB* = WdW,l[H+l’~ [Al*+]*
and the hydroxide formation constants, kn, are given. They are formally related by k,* = k,K,. A value of K, = 1.0 x lo-l4 is assumed. log kl* = -4.85, log k,k,k, = 26.96, log k,k,k,k, = 28.3, log Kaa* = -8.2. I-Hydroxyquinoline: pK,l = 5.10 pK,s = 9.71 log KD = 2.66. A value of log KfKnx = 31.9 is found by Star);. I8 This clearly differs from the predicted values of Langmyhr and StormY log k, = 12.5, log k, = 12.0, log k, = 10.5, log Kf = 35. Star-j+ value may be slightly low because the effect of hydroxy-complex formation has not been allowed for, but the experimental conditions of the measurement were such that the correction would be slight. From the same work K~x is shown to be at least 1Oaand so a value of log Kf = 30 has been used in the subsequent calculations. Because of the doubt surrounding these values, a reflection of the experimental difficulty of obtaining reliable results in a system prone to hydrolysis, a theoretical prediction based upon them must be treated with caution, though results of value to the analytical chemist may still be obtained.
Extractive indicators in complex-formation
1505
titrations
.D.TA),
pH
FIG. L-Extraction of copper as a function of p(EDTA) at various pH values and a-PAN concentrations, compared with extraction of copper as function of pH with no EDTA present : l--u-PAN, 10-sM; pH 5 &-PAN, 10-W; pH 11 ~-CC-PAN, 10-&M; pH 5 5-a-PAN, 10-6M; no EDTA; pH varied ~--SPAN, lo-“M, pH 9 &-PAN, lo-*M; no EDTA; pH varied The full expressions used to calculate tLz(nB,and 0 are lO-““1 a1(BB) = [H+] + 10-W’, a,(nJ = [H]’ + lO-W”[H+] + 10-I”+’ l//W)
-
= 1 + aJF-lt,tlO+’ + (altWtot)*10tl-5+ (al[F-]t,t)*1016 + (alF1-JtOt)SIO1*‘* + (allF-lt0t)s1010’8
+ (a1[F-]t,t)410”~7
= 1 +at(D,8 [HOX]*~O*~
The value for l/(&ex)) is somewhat arbitrary because of the uncertainty in the values of the formation constants. For this reason a computer programme was set up to calculate l/j+$r-) and l//?(cn_) only, and the rest of the calculations were made by hand. D =
10S"g~a*,~n,[HOX]'t.t.
A selection of the results is shown in Figs. 6, 7 and 8. Nickel-EDTA-dimethyglyoxine DMG: Ni-DMG: Ni-EDTA: N&OH:
system.
The following values of the constants were used:**‘s-l’
pK,, = 10.46, log KDR = -1.08. log klks = 17.24, kp/kl = lO_“*,
log kl
= 9.3, log KD~ = 2.51.
log Kf = 18.6 (table of conditional constants log k, = 3.36, log kp = 10.2, log k, = 13.0.
given by Ringbom.*~s)
1506
D. BETTERIDGE
PH
FIG. 6.-Variation
function I-F-, 2-F-. 3-F-; 2a, 3a and 4a are A simple modification
of log /I for the ahuninium-8-hydroxyquinoline-fluoride system as a of nH for various concentrations of fluoride (Al*+, 10-4K4): 4-F-, 10-“M; HOx, -10-W llii; HOx, IO-*M 5-F-. nil: HOx. 10-*&f IO-‘M: HOx. lo-*M 6-F-i nil; HOx; lo-%Z 10-4M; HOx; lo-*M continuations of 2, 3 and 4 in the absence of 8-hydroxyquinoline i.e., only F- and OH- are present.
of equation (10) is required because DMG and a-PAN dissociate differently. Ka [R-Isa -WRltot = a*‘D) = [H+] (1 + KDR) + Ka.
(22)
By arguments similar to those used above, equation (22) can be deduced. lO-‘O.&l a1(=) = [H+]lOW08+ lo-‘o’“e’ l/B = 1 + a1~o~tHRlt,t100’8 + a*,~~~[HR~atotlO”‘LE+ K~wY,[EDTAI. D = ~a*,(D,[HR]*1011’76. At this stage sufficient familiarity with the approach had been acquired to render extensive calculations superfluous. The salient points (Fig. 9) were calculated by hand.
Gkmware. Use grade A where possible. In these experiments only the micro-burette was not grade A. Photometric titrutor. An EEL photometric titrator. with standard cells. (It was not found necessary to use the special cells recommended by Galik, I* although they might have been useful.) Reagents Reagent-grade chemicals were used throughout. Metal-ion solutions were prepared in the usual way and standardised by a standard gravimetric procedure, unless otherwise indicated. EDTA and
Extractive indicators in complex-formation
1507
titrations
PH
FIG. 7.-Extraction I-F-, 2-F-, 3-F-, 4-F-,
of ahtminium as a function of pH in the presence concentrations of fluoride (HOX = 10-W). 5-F-, 1O-4M IM 6-F-, 10-6M 10-‘&f 7-F-, 10-aM lo-‘M 8-F-, 10-‘&Z equivalent to no F- present lO-+M
of various
sodium fluoride were taken as standards; EDTA was checked by comparison of the results from the standardisation of copper solution by EDTA titration (various indicators) and electrogravimetry. EDTA, O.lOOM ~ Copper( 0.1 OOM a-PANsolutions. Dissolve 0.0249 g of 2-(2-pyridylaxo)-1-naphthol (a-PAN)*, prepared according to the procedure of Betteridge et al.,” in 100 ml of carbon tetrachloride to give a 10-‘&f solution. Dilute to lo-‘M or 10-5M as required. These solutions have been found to be stable for at least 6 months. Chromium(ZZZ),O.lM Zron(ZZZ),0.1 M Vunudium(V) O.lM. Reduce to vanadium(IV) with hydrazine sulphate before use. CobaZt(ZZZ),0.1 M Aluminium(ZZZ),O.lOM. Prepare fresh and keep slightly acidic. Sodiumfluoride, 0.125M I-Hydroxyquinoline, 0.01 and O.lM. Chloroform solutions. * Independent work by Drs. A. Kawase and G. Nickless, communicated to the author recently, shows that the compound is 2-(2pyridylaxo)-l-naphthol and not 4-(2-pyridylazo)-1-naphthol as previously reported.
D. BETTERIDGE
1508
NF-1
FIG. 8.-Extraction
of aluminium as a function of pF at various pH; (HOx = IO-PM): 1-pH 3.5 3-pH 5.5 2-pH 4.5
FIG,. 9.-Extraction
of nickel as a function of pH at various concentrations (DMG, lo-*M) : l-EDTA, 10-4M 3-EDTA, nil 2-EDTA, 10-“M
of EDTA
Extractive indicators in complex-formation
titrations
1509
Nickel(IZ), lo-*M DimethyIg~yoxime, 10e4M in chloroform. Sodium acetate Bufer solutions. Standard buffer solutions of sufficient capacity to withstand the comparatively large change of pH during the EDTA titration. Procedures Normal titration. Take 5 ml of EDTA or F-, add buffer and sufficient water to give a final volume of about 50 ml, add 10-15 ml of indicator solution and titrate with the metal-ion solution. Exact control of volumes is most important in the aluminium-fluoride titrations, but for the other titrations the volumes of the phases may be chosen to suit individual preference and the type of titration vessel used. Photometric titration. Take 2 ml of EDTA or F-, add buffer and dilute to approximately 10 ml with water. Add 15 ml of indicator solution and titrate with the metal ion. Vigorous stirring between additions is sufficient to bring about extraction. The 15 ml volume of indicator solution was required by the geometry of the apparatus to give a good light-path. It is necessary to allow the layers to settle before reading the absorbance. Direct reading whilst stirring is not satisfactory because vigorous stirring is required and the best use of the extractive indicator technique is made when the aqueous phase is too highly coloured to allow the normal indicator change to be observed. Use a 605 filter for a-PAN-copper, 601 for 8-hydroxyquinoline-aluminium, and 602 for dimethylglyoxime-nickel. RESULTS AND DISCUSSION
The curves (Figs. 4-9) may be used to determine the feasibility of the titration, the optimum conditions, and the probable sharpness of the end-point. The first requirement for selecting the conditions is that the coloured chelate be extracted so that the end-point can be observed. There is a simple relationship between D and the fraction (%) of the substance extracted. If M = the amount of the substance distributed between the phases, E = the % of the substance extracted, and the subscripts have their previous meanings, V
1OOD~ D=
and E =
V84
V Ds+
1
Thus if Vorg = Vaq a value of D = 1 corresponds to 50% extraction. We will assume that this is the minimum distribution ratio that will result in an observable colour in the organic phase. If the volumes are not equal the value of D corresponding to 50% extraction can be readily calculated e.g., if Vaq/Vorg = 10, D = 10. The ratio of the phase volumes (aqueous:organic) is not likely to exceed 10 so it is simpler to consider log D = 1 as representing the minimum acceptable value. There will be little visual difference, at this volume ratio, between log D values of 2, 3 or 4, representing 90, 99 and 99.9% extraction respectively. The second condition for a satisfactory titration is that the end-point should not be reached before the equivalencepoint i.e., that extraction of the metal ion should not take place in the presence of a significant amount of masking reagent. The definition of a significant amount will depend upon the accuracy demanded of the titration and the concentration to be determined. If O-1% is considered the error permissible and the solution of determinand is 10-2M, no appreciable extraction must take place in the presence of 10-5M masking reagent. If it is assumed that 1 ‘A extraction represents the smallest determinable error in end-point detection for equal volumes then log D = -2 and for the volume ratio of 10 : 1 (aqueous : organic) log D = - 1. Thus if under a specified set
1510
D. BETTERIDGE
of conditions the value of log D in the absence of masking agent is greater than 1 and in the presence of a satisfactory minimum of masking agent is less than -1 the titration is feasible. The greater the difference between the curves the sharper the end-point. In common with other calculations for EDTA titrations, it is assumed that virtually all of the metal ion and EDTA are bound in the metal-EDTA complex and that values of pH or pEDTA on the graphs correspond to free M or EDTA close to the end-point. With the aid of these curves it should be possible to predict rapidly the feasibility of titration and optimum range of conditions. The following discussion compares the experimental results with the theoretical predictions. There are obvious practical limitations. Kinetic effects are ignored and in general the rate of attaining equilibrium by back-extracting the metal ion from the organic phase with the masking reagent (i.e., the direct titration) is so slow that normally a back-titration must be employed, i.e., the excess of masking reagent is titrated with metal ion. The visual limits for the indicator may determine the lower limits of titration; these would seem little point in titrating a lOaM solution with a theoretical sensitivity of 0.1% if the lowest observable concentration of indicator-metal complex is 10bM. Copper-EDTA-u-PAN Predictions. The practical visual limits for the concentration of a-PAN are lo-*M and 1OVM. The graph of log p us. pH is shown in Fig. 3. Figure 4 shows the variation of log D with pH for various concentrations of EDTA and shows that this is complex, because of the combination of a&,, terms with /I. Over the pH range 3-6 the effects of ionisation of the a-PAN and EDTA are equally opposed (EDTA is acting as a diprotic acid pK,, N p&s < 3). From pH 6-10 the EDTA is acting as a monoprotic acid pK,, N pK,, < 3). From pH 6-10 the EDTA is acting as a monoprotic acid (P&a, - 6) so that the extraction increases with pH (log D us. pH has a slope of 1). At pH 10 the EDTA is fully dissociated and the slope of log D us. pH increases to 2. The useful titration range is seen to be pH 4-9 for 10”‘M a-PAN and pH 5-10 for 10-6M a-PAN. Care must be taken not to go below these limits to avoid incomplete extraction at the end-point. A false end-point might be obtained at a pH higher than the limit and this is more clearly shown in Fig. 4, which shows the variation of log D with p(EDTA) at various pH values. The end-point at the lower limits would be detectable but poor owing to the excess of IX-PAN masking the colour of the complex. Experimentalfindings. Titrations carried out according to the procedure confirmed the validity of these conclusions. At pH 4.5-50 an end-point was observed with 104M or-PAN, but with 10~r’M a-PAN the end-point did not have good contrast. The colour change at the end-point, under optimum conditions, is from orange-yellow to red-violet; it is easily observed but a little slow. The normal visual observation of the end-point in a titration flask is satisfactory and the photometric detection is very sharp. The reaction takes place more rapidly at lower pH, but care must be taken to buffer the solution well because of the release of a considerable concentration of hydrogen ion from the reaction between O*lM EDTA and O*lM copper(I1). Solid sodium acetate was found to be effective. The reaction is reversible but the backextraction (i.e., titration of copper with EDTA) is so slow that if the end-point is overshot, it is simpler to add anexcess of EDTA, acidify the solution to pH 3-4, shake
Extractive indicators in complex-formationtitrations
1511
until the organic layer is yellow, adjust the pH to 6, and titrate the excess of EDTA with copper. Although o-PAN can be used its rate of reaction is much slower than that of a-PAN. Accuracy and precision
Because of the slowness of the reaction near the end-point it is possible to obtain readings which are precise but inaccurate. The accuracy was checked by titrating at different rates to see if the same answer was obtained and by titrating the same solution using other indicators. With practice the same end-point is obtained regardless of the rate of titration but there is a definite risk of over-titration because of the slow indicator change. For the comparison with other indicators the solutions were diluted to O*OlM. The results with different indicators were 0*0102& (Fast Sulphon Black F),8*1e O-102, M (1,2-dihydroxyanthraquinon-3-yl-methylamc acid)” and 0*0102& (a-PAN). The molarity of the parent copper solution was found by electrodeposition to be O-102,. The precision of the titration was estimated from 8, results obtained by titrating 25*00-ml aliquots of O*lOOMEDTA. The mean titre was 24.68 ml, the standard deviation 0.055 ml, and the coefficient of variation 0.22%. Comparison with other indicators
In the titrations of O*OlOOMEDTA described above it was noted that the end-point with a-PAN was superior to that obtained with 1,2-dihydroxyanthraquinon-3-ylmethylamine-N,N-diactic acid and comparable with that obtained with Fast Sulphon Black F. At higher concentrations a-PAN is preferable. No fluorescent indicator@% were at hand but past experience has shown that o-dianisidine-N,N,N,N-tetra-acetic acidzl is an excellent indicator for this titration at concentrations of O=lM. It functions over the same pH range and is truly reversible. If it is inconvenient to observe fluorescence the extractive indicator a-PAN is a useful alternative. o-PAN can also be used as an extractive indicator but the rate of reaction is so slow that a-PAN is clearly superior. E$ect of colour of the solution and back-titration of coloured ions
It was found that the colour of the aqueous solution did not greatly affect the end-point. If the aqueous layer is intensely coloured it may make some slight difference to the ease of detection by adding a reflected colour to the organic layer or by preventing the colour being visible through the aqueous solution. It should, in principle, be possible to use a-PAN as an indicator in the determination of coloured ions by adding excess of EDTA and titrating the excess with copper. Iron(III), chromium(III), vanadium(IV) and cobal! were determined in this way. In all cases sharp end-points were observed and the titrations seemed feasible. The colour of the chromium(III)/EDTA complex provided most screening and that of iron(III)/EDTA least. Standardisation of the iron(II1) and chromium(II1) solutions by other means indicated that the method was as accurate as would be expected. Procedure. Take 10 ml of approx. 0-M solution of the metal ion to be determined and add 25.00 ml of standard O*lOOMEDTA. Ensure the pH is 5.5-6.5, add 10-15 ml of 104Ma-PAN solution and titrate the excess of EDTA with standard copper solution.
1512
D. BEITERILEE
Aluminium-fluoride-8-hydroxyquinoline system That aluminium forms a very strong complex with fluoride ion is common knowledge; fluoride can mask aluminium in an EDTA titration. However, the formation of the hexafluoro complex depends upon an excess of fluoride ion, for although the overall formation constant is high (101g,8) the formation constant for the sixth ligand is only 10O47. The degree of complex formation i.e., the average number of fluoride ions per aluminium ion, fi, reflects the stoichiometry of the reaction, when it is considered for analytical purposes. It varies markedly with total fluoride ion concentrations, Table I. It is obvious that such a system would only be considered TABLE L-VALUES
p[F-I ii
0 6.0
OF li FOR DIFFERENT CONCENTRATIONS QF [F-l* 1
2
5.0
4.5
3 3.2
4 2.5
5 1.3
6 0.6
JW-1 + 2k&lF-I* + . . . +nk,k,. . . k,,[F-1” * ’ = 1 + k,[F-]
+ k,k,[F-]*
+ . . . +kJc~ . . . &[F-I”
under extreme circumstances and that great care would be needed to obtain any result at all. However, it is desirable to know whether the theory can predict how difficult the titration will be and if there are any conditions which could give reasonable results. Figures 6 and 7 by their irregular spacing with decade changes in fluoride concentration show the effect of the unequal stepwise formation constants. Figure 6 shows how l//I values are additive; part A of curve 2 is due to the predominance of fluoro-complexes, and part B to hydroxo-complexes predominating. Figure 7 indicates that the potential pH range is very limited (4.2-4.5) and that the minimum concentration of fluoride that could be titrated with less than a O-1% error is about 0.IM. It must be noted that although the maximum value of log D (log Knx) is arbitrary, because K,, and Kf have not been separately determined, the points on the slope of the curve are unchanged by the value of KD, as long as the product KDXKf remains unaltered. Figure 8 confirms the deductions made from Fig. 7. A further disadvantage accrues in the extraction titration because of the experimental limitation that 10-2M 8-hydroxyquinoline must be used to avoid hydroxide formation. Experimental jindings. Titrations of O.lM fluoride solution were made with aluminium solutions of varying molarity (0*014-0.038), using 10e2M 8-hydroxyquinoline in chloroform as an indicator. The photometric titration was used because the end-point is difficult to determine visually. It is poor even with photometric detection, and the difficulty in extrapolating what is almost a point of inflection is reflected in poor precision. The mean of seven results gave : Al : F = 6*7,, standard deviation = O-7,, coefficient of variation = 9.3 %. The high value of the fluoride to aluminium ratio indicates that an early end-point was being observed, as predicted by the theory, though the size of the error is greater than predicted. Nickel-EDTA-DMG
and nickel-EDTA-u-PAN
systems
DMG is soluble in chloroform to the extent of ca. lOaM. Figure 9 shows the relevant curves for predicting the feasibility of using DMG as an extractive indicator at this concentration. The only new feature is the flattening of curves 1 and 2 at pH 11, a result of the complete ionisation of both EDTA and DMG. The titration should
Extractive indicators in complex-formation titrations
1513
be feasible over the pH range 5-10. The extraction and stability constants for the nickela-PAN system have not been determined. However, it is reasonable to predict that the extraction curves would be similar to those for copper, but that for the same concentration of reagent an increase in pH of 2-4 units would be required to effect the same distribution ratio. a-PAN was compared with DMG as an indicator over the pH range 7-10. The predictions of theory were confirmed. DMG was ExperimentalJindings. useful as an indicator over the pH range 5-10 but at pH 4.5 the end-point was most indefinite. The end-point was of poor quality because of the low absorbance of nickel(I1) dimethylglyoximate solutions and compared very unfavourably with that obtained when a-PAN was used. a-PAN is a very good extractive indicator for nickel; the colour change is sharp and the colour contrast is good; in fact, with the photometer used, the change in absorbance was so marked that it proved almost impossible to follow the titration curve well enough to make an accurate estimation of the precision. It is possible, although it is not recommended, to use DMG as a visual indicator, but it was found that the results differed from those from the photometric finish. The visual titration was in agreement with the end-point obtained with o-PAN used as a conventional indicator, whereas the photometric detection gave rise to a higher titre which was conI%-med with fresh solution, standardised by electrogravimetry. The results were; by electrogravimetry 0*104,M, by EDTA with a-PAN as extractive indicator 0*102&f and by EDTA with DMG as extractive indicator (photometric) O-107&. The coefficient of variation for the last method, based on 7 results, was 4.0%. Clearly DMG is not to be recommended as an extractive indicator but a-PAN would be useful on those rare occasions when the system might demand an extractive rather than a conventional indicator. Interferences Still9 observes that one of the advantages of dithizone is that it leads to the EDTA titration being carried out at higher pH and thus at greater sensitivity. Most workers would feel that one of the advantages of a-PAN is that the copper-EDTA titration can be carried out at a low pH, because it is more selective. This raises the problem of selectivity when the extractive indicator is used. It is not easy to predict what will happen if the titration is carried out at so high a pH that another cation reacts with the EDTA. In the ideal case the metal ion used as a titrant would displace the interfering ion from its EDTA complex and the end-point would remain unaffected. But the equilibrium constant for this displacement reaction is the ratio of the stability complexes of the EDTA complexes of the metals concerned and if this is small compared with the conditional extraction constant of the metal-indicator complex an early end-point might result. A further complication arises if the indicator extracts the interfering ion. A simplified approach was made, using conditional stability constants and considering the case where the interfering ion did not react with the indicator, specifically the copper-calcium-EDTA-a-PAN system. Because in this system attention is focused primarily on the reaction of copper with EDTA, the added metal is assumed to participate in a side-reaction with EDTA comparable with that by hydrogen ions. In
1514
D. BETIXRIDGE
other words a4urDTd) can be modified to take this extra competition into account. Then
V-1
present) = [H,Yltot =
4~
=
v-3 [H,Yl
+
JVa&a3~a4/~[H14 +
Kda2~as~a4U
[H,ql+ +
+
[W3k
D-&Y1 +
+
WI
+
[W$&,3
+
WI
+
[MYI
(23)
D-U3JS,,&,3
(24)
h~y,M1
As normally expressed, a4 will be unaifected until the fifth term in the denominator becomes dominant when K alK a2K a3K a4K ~(MY)[MI>K~~K~~K~[HI’, and if %&Ml
>
1 --log
aP(M present) =
log J&my)
-
PM.
Thus the effect will be greatest when the conditional stability constant and interfering ion concentrations are high and will be dependent upon the concentration of the interfering ion. The modified a4 coefficient must be used to calculate the @coefficient to determine the working effect of EDTA, and obviously this will affect the distribution ratio (Table II). When substituted in the distribution equations for the copperTABLEII.-EFFETE
PH
4 5 6 7 8 9 10 11 12
log Kb&Y -2.7 0.1 2.2 4.2 6.0 7.4 8.4 lit4 10.6 10.7
OF CALCIUM ON MASKING CGEPPICIENT3 OF COPPER WEH
no Ca 13.4 10.6 8.5 6.5 4.7 2:; 1.3 0.5 0.1 0.0
-log ah lo-‘M Ca 13.4 10.6 8.5 x:; 3.7 4.4 5.4 6.2 6.6 6.7
EDTA
log KbuY
lo-*M Ca
10-*&f Ca
10-W Ca
13.4 10.6 8.5 6.5 4.4 5.4 6.4 7.4 8.2 8.6 8.7
5.4 8.2 10.3 12.3 14.1 15.1 14.4 13.4 12.6 12.2 12.1
5.4 8.2 10.3 12.3 14.4 13.4 2.4 11.4 10.6 10.2 10.1
EDTA-a-PAN system, these figures predict that when EDTA = lOAM, Ca2+ = 10-2M and a-PAN = lOAM, log D = 3.4 at pH 9, -2.6 at pH 7 and -5.8 at pH 5. The figure of 104M EDTA is chosen because it represents the defined limit of permissible error for titrating lo-lM solutions. The prediction that 10-2M calcium would interfere with the titration of copper at pH 9 but not at pH 5 was contimed experimentally. Sharp end-points were obtained at pH 9.6 and 5.0 when calcium was added to the EDTA before titration (photometric) with copper. At pH 9.5 the titre corresponded exactly with that predicted assuming the calcium was quantitatively held by the EDTA and at pH 5 it corresponded with that predicted on the assumption that calcium would not interfere at all. At pH 7, where the predictions are likely to be at their most erroneous, the theory predicts no interference from the calcium. The observed end-point was drawn out and the titre showed some calcium interference (16% of the amount taken). These results show that it is probably justifiable to modify the conditional constants in this way and that, because the complexing reaction takes place in the aqueous phase, the normal criteria apply for obtaining greater selectivity by pH control.
Extractive indicator in complex-formation
titrations
1515
General
The use of extractive indicators is likely to be limited for several reasons. They are more inconvenient to use than conventional indicators and so would only be recommended when the colour of the solution to be titrated prevents the use of conventional visual indicators. The chemical requirements are more rigorous; not only must the indicator form a complex with a metal ion, but the complex or the indicator must be extractable over the required pH range. It would have been very difficult to make predictions about the titrations without the use of conditional constants. With their aid it is comparatively simple to handle complex equilibria because attention is concentrated primarily upon the central reaction. Acknowlec@ement
author thanks Professors Quintus Fernando, S. West for their helpful comments and encouragement.
Henry Freiser and Thomas
Zusannnenfassnng-Der Gebrauch mediumabhiingiger Stabilitatskonstanten wird demonstriert, urn die optimalen Bedingungen fur die Titration in einigen Komplexbildungstitrationen, bei welchen der Endpunkt durch die Bildung eines farbigen extrahierbaren Komplexes gefunden wird, vorauszusagen. Die Voraussagen wirden experimentell getestet. Es wird gezeigt, da13 2-(2-Pyridylazo)-l-naphthol em brauchbarer extraktiver Indikator ftir die Kupfer-EDTA-Titration ist ; Dimethylglyoxim empfiehlt sich nicht ftir die Nickel-EDTA-Titration als extraktiver Indikator ; es wird gezeigt, dai3 die Titration von Fluorid mit Aluminium bei Gebrauch von I-Hydroxychinolin als extraktivem Indikator theoretisch und experimentell zu wtinschen tibrigRt3t. R&tnn&--Qn explique l’emploi de constantes conditionnelles pour p&oh les conditions optimales du titrage dans dit%rents dosages par formation de complexe, ou le point de virage est d&elk par la formation dun complexe color6 extractible. Les previsions ont ett6 soumises a l’epreuve experimentale. On montre que le 2-(2-pyridylazo)l-naphtol est un indicateur par extraction valable pour le titrage cuivre-EDTA; la dimethylglyoxime n’est pas recommandQ comme indicateur par extraction pour le titrage nickel-EDTA; on montre que le dosage du fluorure a l’aluminium, utilisant la I-hydroxyquinolbine comme indicateur par extraction n’est pas satisfaisant, tant theoriquement qu’exp&mentalement. REFERENCES 1. A. Ringbom, J. Chem. Ed., 1958,35,282.
2. Idem, in I. M. Kolthoff and P. J. Elving, Eds., Treatise on Analytical Chemistry, Part 1, Vol. 1, pp. 543-628. Interscience, New York, 1959. 3. I&m, Complexation in Analytical Chemistry, Interscience, New York, 1963. 4. G. Schwarzenbach, Complexometric Titrations, English Ed., Methuen, London, 1957. 5. H. A. Laitinen, Chemical Analysis, McGraw-Hill, New York, 1960. 6. H. Freiser and Q. Fernando, Ionic Equilibria in Anafytical Chemistry, Wiley, New York, 1963. J. N. Butler, Ionic Equilibrium, Addison-Wesley, Reading, Massachusetts, 1964. I: D. Betteridge, Proc. Sot. Anal. Chem., 1964, 1, 138. 9. E. Still, Tafanta, 1965, 12, 817. 10. G. H. Morrison and H. Freiser, Solvent Extraction in Analytical Chemistry, Wiley, New York, 1957. 11. D. Betteridge, P. K. Todd, Q. Fernando and H. Freiser. Anal. Chem., 1963,35,729. 12. A. E. Martell and L. G. Sill&, Stability Constants of Metal-Ion Complexes, Chem. See., London, 1964. 13. J. Starjl, Anal. Chim. Acta, 1963, 29, 132. 14. F. J. Langmyhr and A. R. Storm, Acta. Chem. Scat& 1961,15, 1461..
1516 15. 16. 17. 18. 19. 20. 21. 22.
D. D. H. A. R. R. R. G.
D. BETTERIDGE Dyrssen, F. KraSovec and L. G. Sill&, ibid., 1959, 13, 50. Dyrssen and M. Hennichs, i&-id.,1961, 15,47. Christopherson and E. B. Sandell, Anal. Chim. Acta, 1954, 10, 1. Gallk, Talanta, 1966, 13, 109. Belcher, R. A. Close and T. S. West., Chem. and Ind., 1957, 1647. Belcher, M. A. Leonard and T. S. West, J. Chem. Sot., 1958, 2390. Belcher, D. I. Rees and W. I. Stephen, Tafanta, 1960, 4, 78. F. Kirkbright, D. A. Rees and W. I. Stephen, Anal. Chim. Acta., 1962, 27, 558.
Pergamon Press Md.
Printed in Northern Ireland
EXTRACTIVE INDICATORS FORMATION TITRATIONS: PRACTICE
IN COMPLEXTHEORY AND
D . BETIERIDGE University College, Swansea, Wales (Received 3 December 1965. Accepted 11 May 1966) Summary-The use of conditional constants to predict the optimum conditions for titration in several complex-formation titrations, in which the end-point is detected by the formation of a coloured extractable complex, is demonstrated. The predictions have been tested by experiment. 2-(2-Pyridylazo)-1-naphthol is shown to be a useful extractive indicator for the copper-EDTA titration; dimethylglyoxine is not recommended as an extractive indicator for the nickel-EDTA titration; the titration of fluoride with aluminium, using I-hydroxyquinoline as an extractive indicator, is shown to be undesirable theoretically and experimentally.
it is difficult to observe the end-point in the titration of a coloured metal ion with EDTA because the colour of the EDTA complex formed masks the colour change of the indicator. In these circumstances the end-point must be detected instrumentally or with fluorescent or extractive indicators. Visual detection is often preferable and this paper is concerned solely with extractive indicators (which may be defined as indicators which form an extractable complex with the metal ion so that the end-point may be detected by a colour change in an organic solvent immiscible with water added to the titration vessel). The optimum conditions for such titrations are calculated theoretically, using conditional constants, and the predictions tested by the following titrations: EDTA with copper and nickel using 2-(2-pyridylazo)-lnaphthol (a-PAN) and dimethyl glyoxime (DMG) respectively as indicators, and fluoride with aluminium using %hydroxyquinoline as an indicator. In the normal extractive titration the metal ion is titrated with a complexing agent with which it forms a coloured extractable species. When an extractive indicator is used, however, the metal ion is titrated with the complexing agent of choice, e.g., EDTA, in the presence of an indicator, which forms an extractable species with the metal ion. If the free indicator is soluble in the organic layer and the metal-ion solution is the titrant the end-point is indicated by the extraction of the first excess of the metal-ion into the organic layer with consequent change of colour, so that the colour of the aqueous layer does not affect the detection of the end-point. In developing a theoretical approach we focus attention on the extraction, and consider the titration system to represent an extraction system in which the extraction of the metal ion is inhibited by a masking agent e.g., EDTA, whose concentration varies (i.e. the concentration of free EDTA decreases as increments of metal-ion solution are added). The use of conditional constants,* proposed by Ringbom1-3 and Schwarzenbach,a FREQUENTLY
* If the formation or stability constant for a reaction is Kf = - [Mb1 the conditional stability lM1[R-ln lMRn1 constant is defined as K’r = lMltOt~HRl~t,t where [M]M and [HR& tration of metal ion and reagent respectively. 1497
are the analytical concen-
1498
D. B-E
and propagated by Laitinen ,I Freiser and Fernando,6 and Butler,’ enables the optimum conditions for such titrations to be predicted fairly easily,s-@because the cumulative effect of side-reactions, e.g., with hydrogen ion, buffer solution or other masking agents, can be broken down into smaller parts. In this paper different systems from those discussed by StilP are considered and a different emphasise is used in the theoretical approach, although, of course, the treatments are equivalent. DERIVATION
OF EQUATIONS
General
The nomenclature of Laitinen,6 and Freiser and Fernando,6 with slight modifications, is followed. Thus tc is a coefficient relating to the effect of acid dissociation of reagents and p is a coefficient relating to the effect of masking agents on metal ions. To simplify the derivation of the equations the metal ion is assumed to be bivalent (M”+), and the reagent, HR, to be one that can either take up (H2R+) or lose (R-) a proton. This derivation is applicable to many chelate systems and the extensions to make it more general are obvious. An extraction system is quite complex because in addition to the equilibria associated with complex formation the equilibria of the distribution of the reagent and complex between the two phases, and the side-reactions of reagent and metal ion, must also be taken into account. Figure 1 represents schematically the possible reactions, except the formation of mixed ligand complexes, and indicates their equilibrium constants. (It is possible to view Fig. 1 as a flow diagram in which the order of reactions is from HRor, to MRgorg.) ORGANIC PHASE
=am
=a1
AQUEOUS
PHASE H,R+ _
HR +R-
h
+
ka
M’+ +
MR+ ;
MR 0
XllOH) %Y) II e
M(OH)+
MYa-
%OEl
*XIX) 11
M(OH)“-
~PIX)
11
MX+ _
MX,
M(Oii),-
FIG. I.-Schematic
diagram of extraction system.
For the extraction of the chelate the essential reactions are the formation of the anion of the reagent, complex formation in the aqueous phase to give uncharged chelate, and the transfer of the uncharged complex to the organic layer; these will be called distribution reactions. The formation of neutral and cationic reagent species and the formation of other metal complexes are side- or masking reactions. The treatment consists of seeing how the central distribution reactions are modified by the side-reactions.
Extractive indicators in complex-formation titrations
1499
The necessary constants are defined below. Subscripts have the following meanings: aq = aqueous phase, org = organic phase, tot = total analytical concentration,(D) =
taking distribution into account, (HX) = with respect to HX, a = acid dissociation, and numerals indicate the steps in a series of constants for which & is the overall formation constant. A superscript dash indicates that the constant is a conditional one. Concentrations rather than activities are used throughout, but wherever possible the constants used are those measured at an ionic strength similar to that used in the experimental part of this study. Distribution reactions The ratio of direct interest is the distribution ratio, D, which is the ratio of the total concentration of metal in the organic phase to the total concentration of metal in the aqueous phase. D varies with the conditions prevailing in the system.
Wltot,&Wtotaq.
D =
The partition coefficients for the complex (K,,) defined by
(1)
and the reagent (KDR) are constants
KDX
=
~MRzlore/[MRzlas
(2)
K DR
=
[HRlordWRlrw
(3)
and The overall formation constant of the complex (Ki> is given by (4) If MR, is the only metal-ion species present in the organic phase [M]totOrs = [MRJore and if the predominant metal-ion species in the aqueous phase is free metal ion so that WltotaP= [M2+],,, then D=KDxE
(5)
w D = KDxKr[R-1’.
(6)
This is the form of the equation widely usedlo to describe chelate extraction systems, for [R-l = j!& !!?!& the total concentration
when the uncharged form of the reagent predominates and of reagent is its concentration
in the organic phase, and .
A more generally applicable form of equation (5) is available if the side-reactions of the reagent and the metal ion are taken into account. Side-reactions of reagent. Although the concentration of the anionic form of the reagent in the aqueous phase is required in equation (6) it is more convenient to use the analytical concentration of the reagent in the system i.e., the amount of reagent added regardless of the species present. The relating of what is convenient to what is required theoretically is the function of the coefficients ccand @,which are defined below.
1500
D. BETITWDGE
If the number of moles of reagent in the system, in absence of metal ion, is represented by mtot the mass balance equation for the system can be written m tot
-
%2R
+
%ROrg
=
mH2R
+
lltHR
+
1 +
mHR
+
KDR F)
“R-
w
(8)
+
mR-
where mx is the number of moles of species X and Verg and Vaqare the volumes of the two phases. If the total concentration of reagent, [HR]tot, is defined as the concentration of reagent if it were all present in the aqueous phase, then [HR]tot = F
w
= [HsR+] + [HR]
The fraction of the total concentration anionic
1 + KDR $f)
w
+ [R-l.
of reagent present in theaqueous
phase in the
form is
1+ KDR
7 +K,*K,,) --) .
(12)
Thusa2(D) can be used to compute the effect of side-reactions-competing with the hydrogen ion. It is simple and convenient to plot a graph of log>20j VS.pH (Fig. 2). When the uncharged form of the reagent predominates, .
FIG.
2.-Log CC,,D) as a function of pH for various reagents when Vorg= V,, 3+x-PAN I-DMG 2-Shydroxyquinoline ~---O-PAN
(13)
Extractive indicators in complex-formation titrations
1501
KDR is usually large and the relationship between the total reagent concentration defined for equation (7), [HR] orB, and equation (lo), [HR]tot, is given by [HR]tot = [HRlore (VW/VW), so that equation (7) is readily derived. However, as(=) is most useful for those conditions when the simplifications are unjustified e.g., the extraction or iron with 8-hydroxyquinoline or the extraction of nickel with DMG. Side-reactions of metal ion. There are many possible side-reactions for a metal ion in solution, so, in principle, it is more convenient in equation (4) to use the total metal-ion concentration rather than the free metal-ion concentration. Thus p is defined as B = -[M2+JN _ - [M2+l/{[M2+l + [MR+l + [MU + [MY2-1 + [M(OH)+l P&t,, + [M(OH),I + [MPH,-)1 + [ML+1 + P=,I)
(14)
where Y4- represents the completely dissociated EDTA and L is some unspecified interfering ligand that might be present in the solution, e.g., an interfering component in added buffer solution. In general, ignoring charges, k
[MXI lCx) = [M][X]
(15)
and k
P4X21 2(x) =
[MX][X]
(16)
where X can be any ligand. The overall formation constant, Kf, is given by
K iCxj = k,k,.
. . kn-
[MRnl WI[Rl”
(17)
where n is the maximum number of ligands normally bound to the metal ion. Substituting the appropriate stability constants into equation (14) gives B = l/(1 + k&R-l + Kro,tR-I2 + Kr&Y4-l + k,(,,,tOH-1 [OH-l3 + k,o,[Xl + W,o,[X12}. + k,k,om [OH-l2 + k&&o,,
(18)
This apparently formidable equation is readily handled in practice because one term usually predominates. The terms containing the reagent concentration are for the concentration of the anionic species so that an a coefficient or conditional constant should be introduced for convenient working. For example, for the simpler case of [Mltot = [M2+] + [MR+] + [MR,], l/B = 1 + k,[R-1 + Kr[R-I2 = 1 + kla2[HR] + Kta22[HR]2 = 1 + k,‘[HR] + Ki’[HR12. In general it is not so simple to portray graphically the variation of log @ with pH or reagent concentration as it is to deal with log a, because the successive stability constants are too close together. Ringbomle3 has noted the additive nature of /3 3
1502
D. Barre~nx;~
coefficients. Thus if a value /3* were calculated on the basis of equation (18) and another masking agent, Z, were added to the system, the total masking coefficient, 1 1 /Itot, would be given by -!-tot = Ba _!_ + z - 1 whereK = 1 + ~dZ1 + Wz&la. B Obviously ,9 will vary greatly with changes in the system, but because of the additive nature of the coefficients it is easy to follow changes of @ with changes in the system. A more satisfactory derivation of a comprehensive extraction equation, then, is
U.MbJaq
(19)
D=KDx [Mltotaq
(20) D = K&xt%(Dj [HR12tot. Under appropriate
(21)
conditions it reduces to the limiting cases of equation (7) or to
In this study B and a,(n) are calculated for a variety of conditions and systems and D is calculated by use of equation (21) ; the predicted results are compared D = KD,.
with the actual results. Details of the calculation for the three systems studied are given in the experimental section. EXPERIMENTAL Calculations One of the great advantages of the use of conditional constants is that problems arising from systems involving complex equilibria may be solved easily because, when conditions are defined, many terms in the expressions for a and b can be ignored. It is tedious to calculate a and /I for a large number of conditions, and computer programmes have been devised to carry out some of the calculations. As the programmes are readily modifled to accommodate many systems and one set of data cards is adequate for several systems, there is some value in using a computer if it is available. A typical programme is given below in Fortran 2 for an IBM 1620 computer. The two most important general features are (1) the values of constants are introduced into the appropriate equations in the programme and (2) A is used for a, B for & and as far as possible chemical terms are transcribed into easily recognisible ciphers. The lirst of these eliminates sub-routines at the cost of changing a few cards for each modiiication of the programme i.e., each new system. Both features help an inexperienced operator to make his own modifications to the programme. Copper-EDTA-a-PAN a-PAN: EDTA:
system. The following values for the constants were used:“~” PK., = 3.0, pKs, = 9.5, log K~B = 4.2, log KDx = 3.6, log K, = 24. pK,, = 2.0, pKs, = 2.67, pK,, = 6.16, pKa, = 10.26.
OH: log KpI+ = 10.6
KSr., =
where
[‘&(OH),*+I~H+l*. [Cu*+p
These substituted into equations (13) and (18) gave a2,nj = 3.15 x 10-‘S/([H+]* + 15.8[H+] + rzI(BDTAj= 8.12 x lo-“/([H+]”
W
3.15 x 10-‘S)
+ 10-P[H]8 + 2.14 x IO-=[H]* + 1.48 x lo-“[H+] + 8.12 x lo-=)
l/j3 = 1 + 10zAa,*,n,[aPAN] *tot -t- 6.31 X 10” 2.51 x lo-“[Cup+]
[H+l*
aP(EDTd)
[EDTAh
f
&
i-
Extractive indicators in complex-formation
titrations
1503
These coefficients were calculated for differing values of pH and copper and reagent concentration, with v,, = I’.,,, and were substituted into equation (21) to predict how the distribution varied with these factors. The final form is D = l~“~~a,*~~~[a-PAN]‘,,I The following computer programme was also used. TITLE READ 2, N 2 FORMAT (13) M=O 4 M=M+l IF (N-M)18, 8, 8 8 READ lO,PH,YTOT,RTOT,CU 10 FORMAT (F10.2, 3E10.3) H=l*O/EXPF(2.303*PH) AR=3.15E-l3/(H*H+15.8*H+3.15E-l3) AY=8.12E-22/(H**4+1.E-02+H++3+2.14E-05*H*H+1.48E-ll+H+8.12E-22) P=l.+l.E 24+AR+AR+RTOT+RTOT+6.31E 18*AY+YTOT Q=l.E-08/H+2.51E-ll*CU/(H*H)
B=l./@'+Q) D=4.E 27*B*AR*AR+RTOT*RTOT BLQG=LGGF(B)/2.303 DLQG=LGGF(D)/2.303 12 PRINT 14,PH,YTOT,RTOT,CU,BLQG,DLGG 14 FORMAT (1H F10.2, 3E10.3, 2F10.3) GOT0 4 18 CALL EXIT END N is the number of data cards (169 in this case), Y = EDTA, R = a-PAN, and P and Q have to be used because the full expression for B (=p) is too long for one card. A selection of the results for various conditions is shown in Figs. 3,4 and 5.
FIG. 3.-Variation
of log B for copper-a-PAN-EDTA system as function of pH for various concentrations of EDTA. l-no EDTA 3-lo-% EDTA 2-lo-‘M EDTA
1504
D.
BETTERIDGE
PH
FIG. 4.-Extraction l-a-PAN, 2-a-PAN, ~--G-PAN,
of copper as a function of pH for various concentrations a-PAN and EDTA. 10-4M; EDTA, 10-*&f &a-PAN, 10-*&f; EDTA, 10-‘&f ~-U-PAN, 10-6M; EDTA, nil 10-4M; EDTA, 10-6M 6-a-PAN, 10-4M; EDTA, nil 10-SM; EDTA, lo-‘M O-a-PAN, IO-*M A-a-PAN, 10-5M
of
Aluminium-fluoride-Shydroxyquinoline system. The following constants were used,“-l4 AIF,‘*-“I+: log k, = 6.13, log ka = 5.02, log ks = 3.85, log k, = 2.74, log k, = 1.63, log k, = 0.47, log Kr = 19.86. HF: pZ&, = 3.17. Alm(OH),(*m-n)+: Values for both the acid dissociation constants of the hydrated aluminium ion,
KI* etc. KI* = [Al(;$+;[H+I 1
; KIB* = WdW,l[H+l’~ [Al*+]*
and the hydroxide formation constants, kn, are given. They are formally related by k,* = k,K,. A value of K, = 1.0 x lo-l4 is assumed. log kl* = -4.85, log k,k,k, = 26.96, log k,k,k,k, = 28.3, log Kaa* = -8.2. I-Hydroxyquinoline: pK,l = 5.10 pK,s = 9.71 log KD = 2.66. A value of log KfKnx = 31.9 is found by Star);. I8 This clearly differs from the predicted values of Langmyhr and StormY log k, = 12.5, log k, = 12.0, log k, = 10.5, log Kf = 35. Star-j+ value may be slightly low because the effect of hydroxy-complex formation has not been allowed for, but the experimental conditions of the measurement were such that the correction would be slight. From the same work K~x is shown to be at least 1Oaand so a value of log Kf = 30 has been used in the subsequent calculations. Because of the doubt surrounding these values, a reflection of the experimental difficulty of obtaining reliable results in a system prone to hydrolysis, a theoretical prediction based upon them must be treated with caution, though results of value to the analytical chemist may still be obtained.
Extractive indicators in complex-formation
1505
titrations
.D.TA),
pH
FIG. L-Extraction of copper as a function of p(EDTA) at various pH values and a-PAN concentrations, compared with extraction of copper as function of pH with no EDTA present : l--u-PAN, 10-sM; pH 5 &-PAN, 10-W; pH 11 ~-CC-PAN, 10-&M; pH 5 5-a-PAN, 10-6M; no EDTA; pH varied ~--SPAN, lo-“M, pH 9 &-PAN, lo-*M; no EDTA; pH varied The full expressions used to calculate tLz(nB,and 0 are lO-““1 a1(BB) = [H+] + 10-W’, a,(nJ = [H]’ + lO-W”[H+] + 10-I”+’ l//W)
-
= 1 + aJF-lt,tlO+’ + (altWtot)*10tl-5+ (al[F-]t,t)*1016 + (alF1-JtOt)SIO1*‘* + (allF-lt0t)s1010’8
+ (a1[F-]t,t)410”~7
= 1 +at(D,8 [HOX]*~O*~
The value for l/(&ex)) is somewhat arbitrary because of the uncertainty in the values of the formation constants. For this reason a computer programme was set up to calculate l/j+$r-) and l//?(cn_) only, and the rest of the calculations were made by hand. D =
10S"g~a*,~n,[HOX]'t.t.
A selection of the results is shown in Figs. 6, 7 and 8. Nickel-EDTA-dimethyglyoxine DMG: Ni-DMG: Ni-EDTA: N&OH:
system.
The following values of the constants were used:**‘s-l’
pK,, = 10.46, log KDR = -1.08. log klks = 17.24, kp/kl = lO_“*,
log kl
= 9.3, log KD~ = 2.51.
log Kf = 18.6 (table of conditional constants log k, = 3.36, log kp = 10.2, log k, = 13.0.
given by Ringbom.*~s)
1506
D. BETTERIDGE
PH
FIG. 6.-Variation
function I-F-, 2-F-. 3-F-; 2a, 3a and 4a are A simple modification
of log /I for the ahuninium-8-hydroxyquinoline-fluoride system as a of nH for various concentrations of fluoride (Al*+, 10-4K4): 4-F-, 10-“M; HOx, -10-W llii; HOx, IO-*M 5-F-. nil: HOx. 10-*&f IO-‘M: HOx. lo-*M 6-F-i nil; HOx; lo-%Z 10-4M; HOx; lo-*M continuations of 2, 3 and 4 in the absence of 8-hydroxyquinoline i.e., only F- and OH- are present.
of equation (10) is required because DMG and a-PAN dissociate differently. Ka [R-Isa -WRltot = a*‘D) = [H+] (1 + KDR) + Ka.
(22)
By arguments similar to those used above, equation (22) can be deduced. lO-‘O.&l a1(=) = [H+]lOW08+ lo-‘o’“e’ l/B = 1 + a1~o~tHRlt,t100’8 + a*,~~~[HR~atotlO”‘LE+ K~wY,[EDTAI. D = ~a*,(D,[HR]*1011’76. At this stage sufficient familiarity with the approach had been acquired to render extensive calculations superfluous. The salient points (Fig. 9) were calculated by hand.
Gkmware. Use grade A where possible. In these experiments only the micro-burette was not grade A. Photometric titrutor. An EEL photometric titrator. with standard cells. (It was not found necessary to use the special cells recommended by Galik, I* although they might have been useful.) Reagents Reagent-grade chemicals were used throughout. Metal-ion solutions were prepared in the usual way and standardised by a standard gravimetric procedure, unless otherwise indicated. EDTA and
Extractive indicators in complex-formation
1507
titrations
PH
FIG. 7.-Extraction I-F-, 2-F-, 3-F-, 4-F-,
of ahtminium as a function of pH in the presence concentrations of fluoride (HOX = 10-W). 5-F-, 1O-4M IM 6-F-, 10-6M 10-‘&f 7-F-, 10-aM lo-‘M 8-F-, 10-‘&Z equivalent to no F- present lO-+M
of various
sodium fluoride were taken as standards; EDTA was checked by comparison of the results from the standardisation of copper solution by EDTA titration (various indicators) and electrogravimetry. EDTA, O.lOOM ~ Copper( 0.1 OOM a-PANsolutions. Dissolve 0.0249 g of 2-(2-pyridylaxo)-1-naphthol (a-PAN)*, prepared according to the procedure of Betteridge et al.,” in 100 ml of carbon tetrachloride to give a 10-‘&f solution. Dilute to lo-‘M or 10-5M as required. These solutions have been found to be stable for at least 6 months. Chromium(ZZZ),O.lM Zron(ZZZ),0.1 M Vunudium(V) O.lM. Reduce to vanadium(IV) with hydrazine sulphate before use. CobaZt(ZZZ),0.1 M Aluminium(ZZZ),O.lOM. Prepare fresh and keep slightly acidic. Sodiumfluoride, 0.125M I-Hydroxyquinoline, 0.01 and O.lM. Chloroform solutions. * Independent work by Drs. A. Kawase and G. Nickless, communicated to the author recently, shows that the compound is 2-(2pyridylaxo)-l-naphthol and not 4-(2-pyridylazo)-1-naphthol as previously reported.
D. BETTERIDGE
1508
NF-1
FIG. 8.-Extraction
of aluminium as a function of pF at various pH; (HOx = IO-PM): 1-pH 3.5 3-pH 5.5 2-pH 4.5
FIG,. 9.-Extraction
of nickel as a function of pH at various concentrations (DMG, lo-*M) : l-EDTA, 10-4M 3-EDTA, nil 2-EDTA, 10-“M
of EDTA
Extractive indicators in complex-formation
titrations
1509
Nickel(IZ), lo-*M DimethyIg~yoxime, 10e4M in chloroform. Sodium acetate Bufer solutions. Standard buffer solutions of sufficient capacity to withstand the comparatively large change of pH during the EDTA titration. Procedures Normal titration. Take 5 ml of EDTA or F-, add buffer and sufficient water to give a final volume of about 50 ml, add 10-15 ml of indicator solution and titrate with the metal-ion solution. Exact control of volumes is most important in the aluminium-fluoride titrations, but for the other titrations the volumes of the phases may be chosen to suit individual preference and the type of titration vessel used. Photometric titration. Take 2 ml of EDTA or F-, add buffer and dilute to approximately 10 ml with water. Add 15 ml of indicator solution and titrate with the metal ion. Vigorous stirring between additions is sufficient to bring about extraction. The 15 ml volume of indicator solution was required by the geometry of the apparatus to give a good light-path. It is necessary to allow the layers to settle before reading the absorbance. Direct reading whilst stirring is not satisfactory because vigorous stirring is required and the best use of the extractive indicator technique is made when the aqueous phase is too highly coloured to allow the normal indicator change to be observed. Use a 605 filter for a-PAN-copper, 601 for 8-hydroxyquinoline-aluminium, and 602 for dimethylglyoxime-nickel. RESULTS AND DISCUSSION
The curves (Figs. 4-9) may be used to determine the feasibility of the titration, the optimum conditions, and the probable sharpness of the end-point. The first requirement for selecting the conditions is that the coloured chelate be extracted so that the end-point can be observed. There is a simple relationship between D and the fraction (%) of the substance extracted. If M = the amount of the substance distributed between the phases, E = the % of the substance extracted, and the subscripts have their previous meanings, V
1OOD~ D=
and E =
V84
V Ds+
1
Thus if Vorg = Vaq a value of D = 1 corresponds to 50% extraction. We will assume that this is the minimum distribution ratio that will result in an observable colour in the organic phase. If the volumes are not equal the value of D corresponding to 50% extraction can be readily calculated e.g., if Vaq/Vorg = 10, D = 10. The ratio of the phase volumes (aqueous:organic) is not likely to exceed 10 so it is simpler to consider log D = 1 as representing the minimum acceptable value. There will be little visual difference, at this volume ratio, between log D values of 2, 3 or 4, representing 90, 99 and 99.9% extraction respectively. The second condition for a satisfactory titration is that the end-point should not be reached before the equivalencepoint i.e., that extraction of the metal ion should not take place in the presence of a significant amount of masking reagent. The definition of a significant amount will depend upon the accuracy demanded of the titration and the concentration to be determined. If O-1% is considered the error permissible and the solution of determinand is 10-2M, no appreciable extraction must take place in the presence of 10-5M masking reagent. If it is assumed that 1 ‘A extraction represents the smallest determinable error in end-point detection for equal volumes then log D = -2 and for the volume ratio of 10 : 1 (aqueous : organic) log D = - 1. Thus if under a specified set
1510
D. BETTERIDGE
of conditions the value of log D in the absence of masking agent is greater than 1 and in the presence of a satisfactory minimum of masking agent is less than -1 the titration is feasible. The greater the difference between the curves the sharper the end-point. In common with other calculations for EDTA titrations, it is assumed that virtually all of the metal ion and EDTA are bound in the metal-EDTA complex and that values of pH or pEDTA on the graphs correspond to free M or EDTA close to the end-point. With the aid of these curves it should be possible to predict rapidly the feasibility of titration and optimum range of conditions. The following discussion compares the experimental results with the theoretical predictions. There are obvious practical limitations. Kinetic effects are ignored and in general the rate of attaining equilibrium by back-extracting the metal ion from the organic phase with the masking reagent (i.e., the direct titration) is so slow that normally a back-titration must be employed, i.e., the excess of masking reagent is titrated with metal ion. The visual limits for the indicator may determine the lower limits of titration; these would seem little point in titrating a lOaM solution with a theoretical sensitivity of 0.1% if the lowest observable concentration of indicator-metal complex is 10bM. Copper-EDTA-u-PAN Predictions. The practical visual limits for the concentration of a-PAN are lo-*M and 1OVM. The graph of log p us. pH is shown in Fig. 3. Figure 4 shows the variation of log D with pH for various concentrations of EDTA and shows that this is complex, because of the combination of a&,, terms with /I. Over the pH range 3-6 the effects of ionisation of the a-PAN and EDTA are equally opposed (EDTA is acting as a diprotic acid pK,, N p&s < 3). From pH 6-10 the EDTA is acting as a monoprotic acid pK,, N pK,, < 3). From pH 6-10 the EDTA is acting as a monoprotic acid (P&a, - 6) so that the extraction increases with pH (log D us. pH has a slope of 1). At pH 10 the EDTA is fully dissociated and the slope of log D us. pH increases to 2. The useful titration range is seen to be pH 4-9 for 10”‘M a-PAN and pH 5-10 for 10-6M a-PAN. Care must be taken not to go below these limits to avoid incomplete extraction at the end-point. A false end-point might be obtained at a pH higher than the limit and this is more clearly shown in Fig. 4, which shows the variation of log D with p(EDTA) at various pH values. The end-point at the lower limits would be detectable but poor owing to the excess of IX-PAN masking the colour of the complex. Experimentalfindings. Titrations carried out according to the procedure confirmed the validity of these conclusions. At pH 4.5-50 an end-point was observed with 104M or-PAN, but with 10~r’M a-PAN the end-point did not have good contrast. The colour change at the end-point, under optimum conditions, is from orange-yellow to red-violet; it is easily observed but a little slow. The normal visual observation of the end-point in a titration flask is satisfactory and the photometric detection is very sharp. The reaction takes place more rapidly at lower pH, but care must be taken to buffer the solution well because of the release of a considerable concentration of hydrogen ion from the reaction between O*lM EDTA and O*lM copper(I1). Solid sodium acetate was found to be effective. The reaction is reversible but the backextraction (i.e., titration of copper with EDTA) is so slow that if the end-point is overshot, it is simpler to add anexcess of EDTA, acidify the solution to pH 3-4, shake
Extractive indicators in complex-formationtitrations
1511
until the organic layer is yellow, adjust the pH to 6, and titrate the excess of EDTA with copper. Although o-PAN can be used its rate of reaction is much slower than that of a-PAN. Accuracy and precision
Because of the slowness of the reaction near the end-point it is possible to obtain readings which are precise but inaccurate. The accuracy was checked by titrating at different rates to see if the same answer was obtained and by titrating the same solution using other indicators. With practice the same end-point is obtained regardless of the rate of titration but there is a definite risk of over-titration because of the slow indicator change. For the comparison with other indicators the solutions were diluted to O*OlM. The results with different indicators were 0*0102& (Fast Sulphon Black F),8*1e O-102, M (1,2-dihydroxyanthraquinon-3-yl-methylamc acid)” and 0*0102& (a-PAN). The molarity of the parent copper solution was found by electrodeposition to be O-102,. The precision of the titration was estimated from 8, results obtained by titrating 25*00-ml aliquots of O*lOOMEDTA. The mean titre was 24.68 ml, the standard deviation 0.055 ml, and the coefficient of variation 0.22%. Comparison with other indicators
In the titrations of O*OlOOMEDTA described above it was noted that the end-point with a-PAN was superior to that obtained with 1,2-dihydroxyanthraquinon-3-ylmethylamine-N,N-diactic acid and comparable with that obtained with Fast Sulphon Black F. At higher concentrations a-PAN is preferable. No fluorescent indicator@% were at hand but past experience has shown that o-dianisidine-N,N,N,N-tetra-acetic acidzl is an excellent indicator for this titration at concentrations of O=lM. It functions over the same pH range and is truly reversible. If it is inconvenient to observe fluorescence the extractive indicator a-PAN is a useful alternative. o-PAN can also be used as an extractive indicator but the rate of reaction is so slow that a-PAN is clearly superior. E$ect of colour of the solution and back-titration of coloured ions
It was found that the colour of the aqueous solution did not greatly affect the end-point. If the aqueous layer is intensely coloured it may make some slight difference to the ease of detection by adding a reflected colour to the organic layer or by preventing the colour being visible through the aqueous solution. It should, in principle, be possible to use a-PAN as an indicator in the determination of coloured ions by adding excess of EDTA and titrating the excess with copper. Iron(III), chromium(III), vanadium(IV) and cobal! were determined in this way. In all cases sharp end-points were observed and the titrations seemed feasible. The colour of the chromium(III)/EDTA complex provided most screening and that of iron(III)/EDTA least. Standardisation of the iron(II1) and chromium(II1) solutions by other means indicated that the method was as accurate as would be expected. Procedure. Take 10 ml of approx. 0-M solution of the metal ion to be determined and add 25.00 ml of standard O*lOOMEDTA. Ensure the pH is 5.5-6.5, add 10-15 ml of 104Ma-PAN solution and titrate the excess of EDTA with standard copper solution.
1512
D. BEITERILEE
Aluminium-fluoride-8-hydroxyquinoline system That aluminium forms a very strong complex with fluoride ion is common knowledge; fluoride can mask aluminium in an EDTA titration. However, the formation of the hexafluoro complex depends upon an excess of fluoride ion, for although the overall formation constant is high (101g,8) the formation constant for the sixth ligand is only 10O47. The degree of complex formation i.e., the average number of fluoride ions per aluminium ion, fi, reflects the stoichiometry of the reaction, when it is considered for analytical purposes. It varies markedly with total fluoride ion concentrations, Table I. It is obvious that such a system would only be considered TABLE L-VALUES
p[F-I ii
0 6.0
OF li FOR DIFFERENT CONCENTRATIONS QF [F-l* 1
2
5.0
4.5
3 3.2
4 2.5
5 1.3
6 0.6
JW-1 + 2k&lF-I* + . . . +nk,k,. . . k,,[F-1” * ’ = 1 + k,[F-]
+ k,k,[F-]*
+ . . . +kJc~ . . . &[F-I”
under extreme circumstances and that great care would be needed to obtain any result at all. However, it is desirable to know whether the theory can predict how difficult the titration will be and if there are any conditions which could give reasonable results. Figures 6 and 7 by their irregular spacing with decade changes in fluoride concentration show the effect of the unequal stepwise formation constants. Figure 6 shows how l//I values are additive; part A of curve 2 is due to the predominance of fluoro-complexes, and part B to hydroxo-complexes predominating. Figure 7 indicates that the potential pH range is very limited (4.2-4.5) and that the minimum concentration of fluoride that could be titrated with less than a O-1% error is about 0.IM. It must be noted that although the maximum value of log D (log Knx) is arbitrary, because K,, and Kf have not been separately determined, the points on the slope of the curve are unchanged by the value of KD, as long as the product KDXKf remains unaltered. Figure 8 confirms the deductions made from Fig. 7. A further disadvantage accrues in the extraction titration because of the experimental limitation that 10-2M 8-hydroxyquinoline must be used to avoid hydroxide formation. Experimental jindings. Titrations of O.lM fluoride solution were made with aluminium solutions of varying molarity (0*014-0.038), using 10e2M 8-hydroxyquinoline in chloroform as an indicator. The photometric titration was used because the end-point is difficult to determine visually. It is poor even with photometric detection, and the difficulty in extrapolating what is almost a point of inflection is reflected in poor precision. The mean of seven results gave : Al : F = 6*7,, standard deviation = O-7,, coefficient of variation = 9.3 %. The high value of the fluoride to aluminium ratio indicates that an early end-point was being observed, as predicted by the theory, though the size of the error is greater than predicted. Nickel-EDTA-DMG
and nickel-EDTA-u-PAN
systems
DMG is soluble in chloroform to the extent of ca. lOaM. Figure 9 shows the relevant curves for predicting the feasibility of using DMG as an extractive indicator at this concentration. The only new feature is the flattening of curves 1 and 2 at pH 11, a result of the complete ionisation of both EDTA and DMG. The titration should
Extractive indicators in complex-formation titrations
1513
be feasible over the pH range 5-10. The extraction and stability constants for the nickela-PAN system have not been determined. However, it is reasonable to predict that the extraction curves would be similar to those for copper, but that for the same concentration of reagent an increase in pH of 2-4 units would be required to effect the same distribution ratio. a-PAN was compared with DMG as an indicator over the pH range 7-10. The predictions of theory were confirmed. DMG was ExperimentalJindings. useful as an indicator over the pH range 5-10 but at pH 4.5 the end-point was most indefinite. The end-point was of poor quality because of the low absorbance of nickel(I1) dimethylglyoximate solutions and compared very unfavourably with that obtained when a-PAN was used. a-PAN is a very good extractive indicator for nickel; the colour change is sharp and the colour contrast is good; in fact, with the photometer used, the change in absorbance was so marked that it proved almost impossible to follow the titration curve well enough to make an accurate estimation of the precision. It is possible, although it is not recommended, to use DMG as a visual indicator, but it was found that the results differed from those from the photometric finish. The visual titration was in agreement with the end-point obtained with o-PAN used as a conventional indicator, whereas the photometric detection gave rise to a higher titre which was conI%-med with fresh solution, standardised by electrogravimetry. The results were; by electrogravimetry 0*104,M, by EDTA with a-PAN as extractive indicator 0*102&f and by EDTA with DMG as extractive indicator (photometric) O-107&. The coefficient of variation for the last method, based on 7 results, was 4.0%. Clearly DMG is not to be recommended as an extractive indicator but a-PAN would be useful on those rare occasions when the system might demand an extractive rather than a conventional indicator. Interferences Still9 observes that one of the advantages of dithizone is that it leads to the EDTA titration being carried out at higher pH and thus at greater sensitivity. Most workers would feel that one of the advantages of a-PAN is that the copper-EDTA titration can be carried out at a low pH, because it is more selective. This raises the problem of selectivity when the extractive indicator is used. It is not easy to predict what will happen if the titration is carried out at so high a pH that another cation reacts with the EDTA. In the ideal case the metal ion used as a titrant would displace the interfering ion from its EDTA complex and the end-point would remain unaffected. But the equilibrium constant for this displacement reaction is the ratio of the stability complexes of the EDTA complexes of the metals concerned and if this is small compared with the conditional extraction constant of the metal-indicator complex an early end-point might result. A further complication arises if the indicator extracts the interfering ion. A simplified approach was made, using conditional stability constants and considering the case where the interfering ion did not react with the indicator, specifically the copper-calcium-EDTA-a-PAN system. Because in this system attention is focused primarily on the reaction of copper with EDTA, the added metal is assumed to participate in a side-reaction with EDTA comparable with that by hydrogen ions. In
1514
D. BETIXRIDGE
other words a4urDTd) can be modified to take this extra competition into account. Then
V-1
present) = [H,Yltot =
4~
=
v-3 [H,Yl
+
JVa&a3~a4/~[H14 +
Kda2~as~a4U
[H,ql+ +
+
[W3k
D-&Y1 +
+
WI
+
[W$&,3
+
WI
+
[MYI
(23)
D-U3JS,,&,3
(24)
h~y,M1
As normally expressed, a4 will be unaifected until the fifth term in the denominator becomes dominant when K alK a2K a3K a4K ~(MY)[MI>K~~K~~K~[HI’, and if %&Ml
>
1 --log
aP(M present) =
log J&my)
-
PM.
Thus the effect will be greatest when the conditional stability constant and interfering ion concentrations are high and will be dependent upon the concentration of the interfering ion. The modified a4 coefficient must be used to calculate the @coefficient to determine the working effect of EDTA, and obviously this will affect the distribution ratio (Table II). When substituted in the distribution equations for the copperTABLEII.-EFFETE
PH
4 5 6 7 8 9 10 11 12
log Kb&Y -2.7 0.1 2.2 4.2 6.0 7.4 8.4 lit4 10.6 10.7
OF CALCIUM ON MASKING CGEPPICIENT3 OF COPPER WEH
no Ca 13.4 10.6 8.5 6.5 4.7 2:; 1.3 0.5 0.1 0.0
-log ah lo-‘M Ca 13.4 10.6 8.5 x:; 3.7 4.4 5.4 6.2 6.6 6.7
EDTA
log KbuY
lo-*M Ca
10-*&f Ca
10-W Ca
13.4 10.6 8.5 6.5 4.4 5.4 6.4 7.4 8.2 8.6 8.7
5.4 8.2 10.3 12.3 14.1 15.1 14.4 13.4 12.6 12.2 12.1
5.4 8.2 10.3 12.3 14.4 13.4 2.4 11.4 10.6 10.2 10.1
EDTA-a-PAN system, these figures predict that when EDTA = lOAM, Ca2+ = 10-2M and a-PAN = lOAM, log D = 3.4 at pH 9, -2.6 at pH 7 and -5.8 at pH 5. The figure of 104M EDTA is chosen because it represents the defined limit of permissible error for titrating lo-lM solutions. The prediction that 10-2M calcium would interfere with the titration of copper at pH 9 but not at pH 5 was contimed experimentally. Sharp end-points were obtained at pH 9.6 and 5.0 when calcium was added to the EDTA before titration (photometric) with copper. At pH 9.5 the titre corresponded exactly with that predicted assuming the calcium was quantitatively held by the EDTA and at pH 5 it corresponded with that predicted on the assumption that calcium would not interfere at all. At pH 7, where the predictions are likely to be at their most erroneous, the theory predicts no interference from the calcium. The observed end-point was drawn out and the titre showed some calcium interference (16% of the amount taken). These results show that it is probably justifiable to modify the conditional constants in this way and that, because the complexing reaction takes place in the aqueous phase, the normal criteria apply for obtaining greater selectivity by pH control.
Extractive indicator in complex-formation
titrations
1515
General
The use of extractive indicators is likely to be limited for several reasons. They are more inconvenient to use than conventional indicators and so would only be recommended when the colour of the solution to be titrated prevents the use of conventional visual indicators. The chemical requirements are more rigorous; not only must the indicator form a complex with a metal ion, but the complex or the indicator must be extractable over the required pH range. It would have been very difficult to make predictions about the titrations without the use of conditional constants. With their aid it is comparatively simple to handle complex equilibria because attention is concentrated primarily upon the central reaction. Acknowlec@ement
author thanks Professors Quintus Fernando, S. West for their helpful comments and encouragement.
Henry Freiser and Thomas
Zusannnenfassnng-Der Gebrauch mediumabhiingiger Stabilitatskonstanten wird demonstriert, urn die optimalen Bedingungen fur die Titration in einigen Komplexbildungstitrationen, bei welchen der Endpunkt durch die Bildung eines farbigen extrahierbaren Komplexes gefunden wird, vorauszusagen. Die Voraussagen wirden experimentell getestet. Es wird gezeigt, da13 2-(2-Pyridylazo)-l-naphthol em brauchbarer extraktiver Indikator ftir die Kupfer-EDTA-Titration ist ; Dimethylglyoxim empfiehlt sich nicht ftir die Nickel-EDTA-Titration als extraktiver Indikator ; es wird gezeigt, dai3 die Titration von Fluorid mit Aluminium bei Gebrauch von I-Hydroxychinolin als extraktivem Indikator theoretisch und experimentell zu wtinschen tibrigRt3t. R&tnn&--Qn explique l’emploi de constantes conditionnelles pour p&oh les conditions optimales du titrage dans dit%rents dosages par formation de complexe, ou le point de virage est d&elk par la formation dun complexe color6 extractible. Les previsions ont ett6 soumises a l’epreuve experimentale. On montre que le 2-(2-pyridylazo)l-naphtol est un indicateur par extraction valable pour le titrage cuivre-EDTA; la dimethylglyoxime n’est pas recommandQ comme indicateur par extraction pour le titrage nickel-EDTA; on montre que le dosage du fluorure a l’aluminium, utilisant la I-hydroxyquinolbine comme indicateur par extraction n’est pas satisfaisant, tant theoriquement qu’exp&mentalement. REFERENCES 1. A. Ringbom, J. Chem. Ed., 1958,35,282.
2. Idem, in I. M. Kolthoff and P. J. Elving, Eds., Treatise on Analytical Chemistry, Part 1, Vol. 1, pp. 543-628. Interscience, New York, 1959. 3. I&m, Complexation in Analytical Chemistry, Interscience, New York, 1963. 4. G. Schwarzenbach, Complexometric Titrations, English Ed., Methuen, London, 1957. 5. H. A. Laitinen, Chemical Analysis, McGraw-Hill, New York, 1960. 6. H. Freiser and Q. Fernando, Ionic Equilibria in Anafytical Chemistry, Wiley, New York, 1963. J. N. Butler, Ionic Equilibrium, Addison-Wesley, Reading, Massachusetts, 1964. I: D. Betteridge, Proc. Sot. Anal. Chem., 1964, 1, 138. 9. E. Still, Tafanta, 1965, 12, 817. 10. G. H. Morrison and H. Freiser, Solvent Extraction in Analytical Chemistry, Wiley, New York, 1957. 11. D. Betteridge, P. K. Todd, Q. Fernando and H. Freiser. Anal. Chem., 1963,35,729. 12. A. E. Martell and L. G. Sill&, Stability Constants of Metal-Ion Complexes, Chem. See., London, 1964. 13. J. Starjl, Anal. Chim. Acta, 1963, 29, 132. 14. F. J. Langmyhr and A. R. Storm, Acta. Chem. Scat& 1961,15, 1461..
1516 15. 16. 17. 18. 19. 20. 21. 22.
D. D. H. A. R. R. R. G.
D. BETTERIDGE Dyrssen, F. KraSovec and L. G. Sill&, ibid., 1959, 13, 50. Dyrssen and M. Hennichs, i&-id.,1961, 15,47. Christopherson and E. B. Sandell, Anal. Chim. Acta, 1954, 10, 1. Gallk, Talanta, 1966, 13, 109. Belcher, R. A. Close and T. S. West., Chem. and Ind., 1957, 1647. Belcher, M. A. Leonard and T. S. West, J. Chem. Sot., 1958, 2390. Belcher, D. I. Rees and W. I. Stephen, Tafanta, 1960, 4, 78. F. Kirkbright, D. A. Rees and W. I. Stephen, Anal. Chim. Acta., 1962, 27, 558.