Spectrophotometric extractive titrations—V1

Tahta.

1968. Vol. 1% pp. 771 to 779.

Pcrgattton Press. Printed in Northern Ireland

SPECTROPHOTOMETRIC EXTRACTIVE TITRATIONS-V* THEORETICAL

APPROACH

TO TITRATION

OF A SINGLE

CATION

AFTANAS GALfK Lachema, N.C., Kaznejov, Pilsen-North, Czechoslovakia (Received 13 December 1967. Accepted 17 January 1968) Sammary-_The general equation of the titration curve for spectrophotometric extractive titrations is derived. The graphical location of the end-point is assumed and the significance of the general equation is discussed. Simple formulas for threshold pH and for sensitivity are obtained. An increased selectivity of spectrophotometric extractive titrations in comparison with that of the usual spectrophotometric extractive methods is demonstrated.

RECENTLY a technique for the determination

of microgram amounts of metals, based on extractive titration followed spectrophotometrically without any sampling of aqueous or organic phase, has been developed .l In order to make the method applicable to reagents other than dithizone, which was used in the earlier work, and because of the need to predict theoretically the optimum conditions of titration, a mathematical treatment of the spectrophotometric extractive titration has been developed. GENERAL

EQUATION

OF THE

TITRATION

CURVE

At any point during the spectrophotometric extractive titration of metal ion MM+ in the presence of metal ion NN+ with chelating agent HA, the absorbance, A, of the organic phase is given by: A = &MM,~- b%J,

+

&NAN .

[NM,,

+

&HA.

[HAI,,,)

(1)

are concentrations of the metal chelates [NANL~, and D%, and free HA in the organic phase, &MAX, aNAXand EEAare the molar absorptivities of the species indicated and I is the light path-length. It is assumed throughout that equilibrium has been reached. Then the extraction constant2 may be used to express the concentrations in equation (1). The extraction constants are defined by:

where b%lorg,

K = [MAado, [HIMand x = M N WI [W:g

[NANI~~~[W

PI D-W%, ’

(2)

where [H] is the equilibrium concentration of hydrogen ion. Here and elsewhere the charges of ions are omitted for the sake of simplicity. If KM > KN, the equilibrium concentration of free titrant [HA],,, is determined by KM and l/M

WA1erg= [HI( yM;;;d ) The equilibrium concentration, * Part IV-Talanta,

.

(3)

[MAJOrg, must be derived having regard to the

1967, 14, 731.

771

172

A~ANAS GAL~K

fact that the reaction of the chelating agent with metal ion M will not generally be quantitative under the conditions of titration, i.e.,

[MA,I,,, = E%,

(4)

where E is the degree of reaction and cu* is the total concentration of the chelating agent in the organic phase at the given stage of titration (calculated according to the volume of the organic phase, V erg, present in the titration cell at the start of the titration). The equilibrium concentration [NAN& and the equilibrium concentrations [M] and [N] in the aqueous phase may be derived from the mass balances:

NWorg = ;&I~ - WI,, [M]

=

cM _

- WMbJorg),

(5)

LMAM9 ’ ‘0,)

[N] = cN -[NA,],,,

(6)

. +,

(7)

where CM,cN denote the initial concentrations of metal ions in the aqueous phase of volume V. Flaschka,3 who dealt with the theory of chelometric photometric titrations in the aqueous phase, introduced the useful idea of the equivalent ratio of titrant to metal ion, a. For a metal ion of valency Mf the equivalent ratio is given by:

Solution of equations l-8 gives the general equation of the titration curve in parametric form : A = I. E&@&2

V

l/M

+ VOF%

EHABMM

l/M

4% NIM

+ (BM&a

where Q = KM/KN and BY is the ratio [HIH. (%)“-’

lKM. cMM. iU”I.

,

(96)

Spectrophotometric extractive titrations--V

773

Values of A and a for various values of the product Ea (0 < Ea < 1) may be calculated so it is possible to obtain the whole titration curve for given initial concentrations [HI, CMand CN, assuming that K,, KN, Y and V,,, are known, (Figs. l-5).

0

2

I

a FIO. I.-Titration en&=

of univalent cation.

V

1; S=l; V

I FIG. 2.-Titration

cx=o;

a

E==O.

2

of bivalent cation.

AFTANAS GALL

774

A

0.5

0

2

I

a FIG. 3.-Titration &PAM&

of tervalent cation.

V org=1.

zl. ‘y

c ‘N

=o.

8 3AA=

0.

DISCUSSION

Location of the end point

If the metal ion M is to be titrated after its preliminary separation from all other metal ions extractable with the titrant, the equation of the titration curve contains only the terms concerning the properties of reagent and of metal chelate MAM. Further simplification may be achieved by assuming that the titration is followed at the wavelength of maximum absorbance of the chelate MAM, at which in most cases the absorbance of the unreacted reagent is negligible. In such a case it is usual3 to establish the end-point as the abscissa of the intersection of two straight lines, one of them passing through the origin and through the point when half of the titrant has been added, the other passing through the points when 50 and 150 ‘,?$excess of the titrant has been added. It is in principle possible to continue the titration far beyond the end-point, and so to obtain points on the curve where the slope is essentially zero. This simplifies the considerations derived below, because the second straight line may be parallel to the axis on which the volume of titrant is plotted, and pass through the point of maximum absorbance. Threshold pH

The prediction of the proper conditions for successive spectrophotometric extractive titration requires a knowledge of the pH range of the solution being analysed which will give the results to the accuracy demanded. Straight lines can be drawn through the experimental points of the titration curve in terms of the general equations @a) and (9b). The first line is drawn through points a = 0, A = 0 and a = 0.5, A = A,.,; the second has zero slope and goes through the point A = Iey+CM v/ VW, 3 as a + co, where all the metal ion M is completely extracted. If it is assumed

Spectrophotometric

extractive titrations--V

775

that the permissible analytical error is ~1% it may be concluded that the degree of reaction E,,.&at a = 0.5 must be >O-991. Introduction of these values into general equations (9a) and (9b) (when cN = 0, aaA = 0) gives the critical values of B, and equations for the minimum satisfactory or threshold pH shown in Table I. TABLE I.-CAL

VALIJES Ih’ THE TlTRATION OF WJTAL ION M

Charge on the metal ion

Criticai BM value

I

2.338 x IO--$

2.63 - log KM - log CJZ

2

1.321 x 1O-5

3

4723 x 10-e

4

2.125 x IO-‘”

2.14 _ log - KM - log CM 2 1.97 _ ‘*g - K&f - log c,M 3 , .82 __‘og Ksf - log cx 4

Threshold pH*

* Supposing that V = Borg.

It must be noted that the errors considered above are positive, but negative errors may arise, e.g., if titrant absorbs at the same wavelength as the chelate. The highest pH value suitable for titration depends on the ease of hydrolysis of the metal ion in aqueous solution and the dissociation of the organic reagent, which limits the validity of equations (l)-(9), as in substoichiometric separations by extraction.2 Usually the knowledge of the threshold pH is the most significant, because near this pH the titration is most selective.

The sensitivity of most methods of trace analysis depends on the variability of the procedure blank, but this factor will not be considered in the discussion below, which deals with the limitations of the method. The sensitivity is dependent on two factors; (i) the extraction process, and (ii), the measurement of absorbance. (i) The least determinable amount of metal ion may be computed from the equation for threshold pH, if it is borne in mind that the maximum value of threshold pH is limited by at least three conditions: (n) the general equations of the titration curve, (9a) and (9b) must be valid, i.e., the dissociation of the reagent in the aqueous phase must be negligible-VIA] < [HA],,,VQV,,,; this rule is fulfilled for hydrogen ion concentrations lower than pKnA + log PHA + log F&,fV, where Kn, is the dissociation constant and P,, the distribution coefficient of the reagent; (b) the threshold pH must be lower than that at which the precipitation of hydroxide of the metal ion titrated begins; (c) the threshold pH must be lower than that at which the precipitation of hydroxides of metals other than the titrated one begins, otherwise losses due to co-precipitation may be expected. These conditions may be conveniently expressed as PHt < PI%n*

(10)

where pH, is the threshold pH and pH,,, is the lowest value of pH given by condition

776

AFMNAS GAL~K

a, b, or c. Formulae for the lowest determinable concentration of metal ion (c&in were calculated from equation (10) and Table I, and are shown in Table II. TABLE IL-SENLWWITY

Charge on the metal ion

OF THB TITRATION

Log minimum concentration suitable for titration

1 2 3 4

2.63 2.14 1.97 1.82

-

log KM - pH,dt i) log KM - pH,fit 4 log KM - pH&t & log KM - pHcrit

(ii) When the spectrophotometric extractive titration is followed at the wavelength of maximum absorbance of the chelate formed, it is desirable to determine at least five distinct points on the first branch of the titration curve, so the absorbance due to metal chelate formed compared to that of all the metal present must be at least five times that which is reliably measurable by the spectrophotometer used. Then the least determinable amount of metal M is given by

(11) where Amin is the minimum absorbance measurable. From equations (10) and (1 l), it is evident that the theoretical sensitivity of spectrophotometric extractive titration is lower than that of the usual extractive spectrophotometric methods. Nevertheless, it must be noted that in spectrophotometric extractive titrations so far developed 4*6the real sensitivity was limited mainly by the reproducibility of the procedure blank. Selectivity

When the analysed solution contains metal ion M together with metal ion N which also reacts with the titrant, it is not possible to simplify the basic equations (9a) and (9b). The shape of the titration curve in this case is that shown in Figs. 4 and 5. It is evident that the slope of the branch of the curve after the end-point is not generally zero. The end-point may be located by extrapolating the straight lines going through points A,, A,., and A2+, Aa.o. From the line before the equivalence point, if A,, = 0, then Al = 2A,,.+z, and from the line after the equivalence point, Al = 2(A,., -

A,.&

+ A,., -

5(A,., - A,.,).

Rearrangement gives an equation for a and since at the equivalence point a should be 1.00, the error A, expressed as equivalents, is given by A

=

A,., - Ws-i, - As.,)_ , &4,.s - As., + 4~)

(12)

where the subscripts denote the stoichiometric ratio of added titrant to total metal M present. Calculation of the appropriate Ai from equations (9a) and (9b) for a given system enables the systematic error to be predicted. These calculations, however, are very

Spectrophotometric extra&e 1.5

titrations-V

I

777

I

1.0 A

05

I l FIG. 4.-Titration E+‘Q

= 1;

I

I

I

2

ct of univalent cation M in the presence of tenfold excess of univalent cation N. Easaar= 5&f+;

B&f= lo-“. , --I, G3 V

FIG. 5.-Titration &~&&f=l;

I

I

I

2

a

&m=O;

of bivalent cation M in the presence of tenfold ems cation N. Q&=

5 &RAN; By=lO-‘;

v,,,=l. v

K&j = 106.

of bivalent

, cm = 0; KM = 10”.

778

AFTANAS

GAL~K

tedious as no general expression for Ea as a function of equivalent ratio a is possible, so they are not presented here. It is much more important to compare the selectivity of spectrophotometric extractive titration with the usual spectrophotometric analytical method where an excess of extractive agent is used. From the data used in preparing Fig. 4 it was concluded that approximately +2 ‘A error arises in the presence of tenfold excess of metal ion N which forms a chelate with a molar absorptivity one fifth that of the metal titrated, at the wavelength chosen, if Q = 103. In the case of a spectrophotometric extractive method where an excess of chelating extractant is used, 99 % extraction of metal ion M is secured at concentrations of hydrogen ion lower than IHl

=

KM.

[HA]o,, *

99

If Q = 103, the distribution ratio of metal ion N is

[NAN]~w= KN. [HA]~~, PI

[H]

-

103

10-z

*

=

0.1

’

If cN = l&M and 5&N&= &M&I’a 19 % positive error will arise. In order to diminish the error to the level obtained by titration, only 1.5 % extraction of metal N may be allowed, which means that the extraction constant of metal ion N must not exceed the value 1.5 [H] = 1.5 x 102. KN = 98*5[HA],,, In other words, the ratio K,:K, must be >6*7 x 103. It is evident that the spectrophotometric extractive titration is more selective than the usual spectrophotometric method. CONCLUSION

It has been shown that the spectrophotometric extractive titration of a single cation is theoretically less sensitive than the usual spectrophotometric method with extractive separation, but the titration is more selective. It is concluded that the use of spectrophotometric extractive titration for the determination of microgram quantities of metals is advantageous. Znsammenfassnng-Die allgemeine Gleichung der Titrationskurve spcktrophotometrischer extraktiver Titrationen wird abgeleitet. Es wird graph&he Ermitthmg des Endpunktes angenommen und die Bedeutung der allgemeinen Gleichung diskutiert. Man erhiilt einfache Formeln fur die pH-Schwelle turd die Selektivitat. Es wird eine verbesserte Empfmdlichkeit spektrophotometrischer extraktiver Titrationen demonstriert, verglichen mit den tiblichen spektrophotometrischen Extraktiwerfahren. RCsam&-On Ctablit l’equation g&r&ale de la courbe de titrage pour les titrages spectrophotometriques par extraction. On admet la localisation graphique du point de fin de dosage et discute la signification de l’equation gentrale. On obtient des formules simples pour le seuil de pH et pour la sensibilitb. On demontre une sdlectivite accrue des titrages spectrophotometriques par extraction par comparaison a celle des mtthodes spectrophotometriques par extraction usuelles.

Spectrophotometric

extractive titrations-V

REFERENCES 1. 2. 3. 4. 5.

A. Gal& Tulanta, 1966, 13, 109. J. Sta@, The Soluent Extraction of Metal Chelates, Pergamon Press, Oxford, 1964. H. Flaschka, Talunta, 1961,8,381. A. Galik and M. KnQek, ibid., 1966,13, 1169. A. Galik, ibid., 1967, 14,731.

779