Formal Photometric Titrations of Weak Bases in Ion ExchangerAqueous Solution Medium Frederick F. Cantwell' and Donald J. Pietrzyk2 Department of Chemistry, The University of Iowa, Iowa City, Iowa 52242
A titration function, which considers all the equilibria, is described and experimentally verified for the photometric tltration of weak bases with HCI in an aqueous slurry of a strongly acidic cation exchange resin in a neutral counterion form. The effect of each variable, including basicity constant for the base, nonelectrolyte sorption coefficient for the neutral base, Ion exchange distribution coefficient for the charged form of the base, and the swamping electrolyte sorption Coefficient, is discussed. Self-indicating photometric titrations for bases which show no spectral change as a function of pH are performed In this medium. Very weak bases, which cannot be photometrically titrated in aqueous solution in the absence of resin are successfully titrated In the presence of resin. Compounds titrated Include 2-methylpyridine (p& = 8.03), nicotinamide (p& 10.67), dAp-3,4dihydroxyphenylalanine (pKb = 11.7), tryptophan (pKb = 11.6), and sulfanilamlde (p& = 12.0). Differentiating photometric titrations of bases with close ionization constants but different charge type become possible in the resin-solution medium. For example, a mixture of tryptophan (p& = 11.6) and sulfate ion (p& = 12.0) is readily titrated to the first equivalence point. The derived photometric titration function can also be used to investigate other weak base lnteractions with strong acid resin.
Photometric titrations are performed by monitoring the absorbance of a sample solution as a function of added titrant and are characterized by a change in the absorbance as the concentration of an absorbing reactant, product, and (or) titrant changes during the titration. The theoretical as well as practical aspects of this technique have been thoroughly reviewed before ( I , 2). Recently, a detailed investigation was reported for the aqueous heterogeneous system: strong acid titrant-weak base-strong acid resin ( 3 ) . The multiple equilibria in this heterogeneous titration medium were identified and the effect of each was demonstrated through potentiometric titrations that verified the derived titration function for the system. Because of the resin's perturbing effect on the system, it was possible to differentiate mixtures of certain weak bases even though they were very similar in strength. The present work describes the theoretical and experimental investigation of the influence of the strongly acidic resin on the photometric titration of weak bases with strong acid titrants in aqueous solutions. The titration is of a self-indicating variety since the only species that absorbs a t the wavelength chosen is the compound being titrated. Furthermore, it is not necessary that the chromophoric Present address, Endo Laboratories, Inc., 1000 Stewart Avenue, Garden City, N.Y. 11530. * Author to whom reprint requests should be sent. (1) R. F. Goddu and D. N.
(2)
Hume, Anal. Chem., 26, 1679 (1954). Headridge, "Photometric Titrations," Pergamon Press, London,
8. 1961. (3) F. F. Cantwell and D.J. Pietrzyk, Anal. Chem., 46, 344 (1974). J.
1450
properties of the sample change during neutralization in order to follow the titration photometrically. In addition to providing a useful analytical procedure for the titration of very weak bases, a theoretical photometric titration function, which includes all the competing equi!ibria is also derived and verified. This complements the potentiometric technique (3) and serves as an alternate procedure for the investigation of complex equilibria that prevail when bases are in contact with strong ion exchangers.
EXPERIMENTAL Apparatus. Spectrophotometric measurements were made with
a Beckman DB-G spectrophotometer using either 1.000-cm fused silica cuvets or a variable path length cell with fused silica windows (UV-0-1, Beckman No. 195651). The cell compartment cover of the DB-G was modified with rubber "curtains" (Beckman No. 70669) to allow passage of inlet and outlet tubes for flow-through operations. Spectrophotometric output was recorded on a Beckman 10-inch laboratory potentiometric recorder in the logarithmic mode using scale changes and scale expansion provided by a Beckman 73490 scale expander. The 1-ml micrometer buret used for the photometric titrations has been described previously (3). Reagents. Chemicals. Purification of 2-methylpyridine was described previously (3).Its assay was 99.5% by potentiometric titration. dl-Tryptophan (Eastman Chemicals Co.) and nicotinamide (USP grade) were assayed by nonaqueous titration with HC104 in glacial acetic acid using crystal violet indicator as 100.4% and 99.8%, respectively. dl-P-3,4-Dihydroxyphenylalanine (dopa) (Sigma Biochemical Co.) was assayed (100.8%) by the nonaqueous backtitration procedure of Nadeau and Branchen (4, 5 ) . dl-Sulfanilamide (USP grade) was assayed (100.6%) by the nonaqueous titration procedure of Tomicek (6): Sodium sulfate was reagent grade. Purification of water and preparation of 1F HCI titrant were described previously (3). Resins. The strongly acidic cation exchange resin (Dowex 50WX8,ZOO-400 mesh, Baker Lot 20541) was pre-conditioned and converted to the Li form as previously described and resin Li-2 was used in the present studies (3).A portion of the same resin lot was converted to the Na form by treatment with NaOH and NaC1. After this treatment, the sodium form resin was slurried with water and an amount of hydrochloric acid was added to yield a titratable acid content of the final moist resin of 8 X mequiv/ mequiv/gram (Resin Na-2). This gram (Resin Na-1) or 5.8 X was done to convert the carboxylate resin impurity (uide infra) to the carboxyl form. Procedures. Distribution Coefficients. Measurement of the distribution coefficients of 2-methylpyridine, H30+ and OH- between Li form resin and aqueous solution has already been described ( 3 ) . Titration Procedure. The vessel used for photometric titrations was constructed identically to that described previously for potentiometry ( 3 ) ,except that the holes for the electrodes were eliminated. Instead, a glass tube with a coarse glass frit on one end passed through the stopper so that the frit was immersed below the surface of the solution in the beaker. One-mm Teflon tubing was attached to the other end of this tube and to the inlet capillary of the UV-0-1 variable pathlength cell in the cell compartment of a Beckman DB-G spectrophotometer. Another length of Teflon tubNadeau and L. E. Branchen, J. Amer. Chem. SOC.,57, 1363 (1935). (5) J. S. Fritz, "Acid-BaseTitrations in Non-Aqueous Solvents," G. F. Smith Chemical Co., Columbus, Ohio, 1952. (6) 0. Tomicek, Collect. Czech. Chem. Commun., 13, 116 (1948). (4) G. F.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
ing connected the outlet of the flow cell to a tygon or Solvaflex tube (Technicon Corp.) in a peristaltic pump (Buchler Instruments, Polystaltic Pump), and a third Teflon tube led from the pump back into the titration beaker through a small hole in the stopper. Hence, solution from the titration beaker could be circulated through the spectrophotometer cell free of resin in order to monitor changes in absorbance during a titration. Temperature control was achieved by suspending the titration beaker in a constant temperature water bath. An additional hole in the large rubber stopper provided access for adding reagents. A 1-cm silica cell containing water was used as a reference. In the titration procedure, 10 grams of resin was weighed into a 100-ml titration beaker and aliquots of an electrolyte stock solution and of water were added. The system was flushed with nitrogen for about ten minutes except when volatile bases were being titrated. Simultaneously, the suspension was stirred and the solution pumped through the spectrophotometer cell. After adjusting the dark current and 100% transmittance value about 0.5 mequiv of the sample base was then introduced as either an aliquot or a weighed portion of powdered sample. The titration was started after the absorbance reached a constant value, that did not change for at least ten minutes, by adding an increment of titrant to the well-stirred suspension. The new absorbance reading was established. Additional increments of titrant were then added until the end of the titration. Stirring and pumping were continued throughout the titration. Equilibration times were generally three to ten times longer in photometric systems than in potentiometric ones ( 3 ) .This is due, in part, to the circulation of solution through the spectrophotometer cell and associated tubing. Although the volume of the aqueous phase was never less than 60 ml, it was necessary to calculate an absorbance correction for the dilution resulting from added titrant. When calculating theoretical titration curves. a value of 0.3 ml was added to the initial aqueous phase volume in order to obtain Vaq. This is the volume of water lost by the 10 grams of Li resin when equilibrated with 0.10F lithium chloride. Titrations in the absence of resin were performed in an identical manner.
with strong acid. If all equilibria are considered, the following titration function which describes the photometric titration is derived (7). (All symbols are defined a t the end of the text.)
n, =
Limiting Equation. Equation 3 can be simplified as the result of certain experimental conditions which will now be described. It may be shown (7) that the second and third terms in Equation 3 are rectangular hyperbolic or degenerate hyperbolic terms. T h e coordinates of the center of the hyperbola described by the third term are:
RESULTS AND DISCUSSION
Model. A physical model describing the equilibrium relationships which prevail in an aqueous-ion exchange resin medium containing a monofunctional base of B charge type has been described previously (3). T h e relevant equilibria are summarized in Equations 1 and 2. B,,
+
K , R’
KOaq === BH,,+
+
OH,;
and
(5) If it is assumed that in a typical titration n B = mole, then the third term in Equation 3 may be neglected if the base is sufficiently weak so that the value of n x calculated by Equation 4 is about lo4 times less than n B ( i e . , > Vaq; KIE.HWR >> Vaq/YH; and cB(Vaq KIE,BHWR) >> t g ~Vaq ( KD,BWR) then the titration function reduces to
+
(R-H;O)R t Liz,+
LiOHR
If the base has chromophoric properties, a titration function describing its photometric titration can be derived by imposing several simplifying experimental conditions. These are: a large excess of both resin exchange capacity and swamping electrolyte are used (3);it is assumed t h a t the only absorbing species in the aqueous phase are one or both of the conjugate forms of the base being titrated; Beer’s law applies t o each of the absorbing species. Titration Function. Under suitable photometric titration conditions, assume t h a t nB moles of base B is titrated
Equation 6 is referred to as the “limiting titration equation” and is applicable if the base being titrated is weak (PKb,B 1 lo), KIE,BHor CB is large, and KD,Bor QH is small. T h e limiting equation contains a linear and a hyperbolic term with the latter being responsible for curvature away from the ordinate in the vicinity of the end point. T h e significance of the limiting equation may be appreciated by considering that the two ion exchange distribution coefficients K I E , Hand KIE,BHappear in the equation only as a ratio of one to the other. Since titrations are carried out at near-tracer ion exchange conditions with a large excess of resin, the value of each of these is inversely proportional to the electrolyte concentration in the aqueous phase. Even though a significant change in the electrolyte (7) F. F. Cantwell, Ph.D. Thesis, The University of Iowa, December 1972
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
1451
08
- 0 0
hi \\ 0
2
i
4
n,l-
6
x
6
1
0
io4
nCl-x I 0
Figure 1. Theoretical photometric titration curves showing one effect of KD,B
Figure 2. Theoretical photometric titration curves showing a second effect of
K$.B = lo-'; Kw = 1.00 X m = 5.00 X mole: KE,BH= 0; KE,H = 0; Ks.0~= 0; CBH = 0; CE = 100: pathlength 1.000 cm; YH = yon = 1; Vaq = 0.05I.; WR(kg) = 0 (curve l), = 0.01 (curves 2 and 3); I(o,g = 1 (curve 2), = 10 (curve 3)
K$,B = lo-'; KW = 1.00 X rg = 5 X mole: &,BH = 0; &E,H = 0; Ks.0~ = 0; cg = 0: CBH = 100; pathlength = 1.000 cm;yH = yOH= 1; Vas = 0.05 I.: Uk(kg) = 0 (curve 1)- = 0.01 (curves 2-4): &,E = lo3 (curve 2), = io4(curve 3), = io5 (curve 4)
concentration during a titration will cause a significant change in the values of these coefficients, it will not change their ratio. Hence, it is not necessary to carry out photometric titrations, where the limiting equation applies, in the presence of a swamping amount of electrolyte. Using lower concentrations of electrolyte will yield larger values for KIE,Hand KIE,BHand increases the validity of the limiting equation. For example, a compound with a KIE,BHof 300 in 0.1M swamping electrolyte will have a KIE,BHof about 3000 in 0.01M electrolyte. Predicted Titration Behavior. An examination of Equation 3 will reveal the following predictable behavior. The first term is a linear term in which Aobsd, the observed absorbance, is a linear function of n,, the amount of added titrant, and yields a straight line connecting a point where n, is zero and
little contribution from the hyperbolic terms of Equation 3, and a linear titration curve is obtained. Figure 2 illustrates the second effect of K D ,on ~ the titration curve. In this example, the initial absorbance is zero since tg = 0, and is therefore unaffected by an increase in K D , ~However, . K D , also ~ influences the two hyperbolic terms in Equation 3. An increase in K D , produces ~ an effect similar to that produced by a decrease in K'b,B. That is, it generates a greater curvature in the part of the titration curve near the end point. This increase in curvature in the latter part of the curve is associated with the second term in the titration function. If the base, chosen for the illustration had been much stronger than pK'b,B = 7 , it would be evident t h a t an increase in K D , also ~ has the effect of decreasing the curvature in the early part of the titration curve which is associated with the third term in the titration function. The KIE,BHparameter will exert two distinct effects on the photometric titration curve. In Figure 3, a family of titration curves is shown for a hypothetical base B of pK'b,g = 10, for which both conjugate species have identical molar absorptivities. As KIE,BHincreases, a downward shift of the final limiting absorbance is observed. This is caused by a greater fraction of the BH+ species being removed from the aqueous phase onto the resin phase as KIE,BHincreases. For very large values, nearly all of the BH+ species is found in the resin phase and the limiting absorbance approaches zero. The second effect of KIE,BH is illustrated in Figure 4. Since t g ~ += 0, the limiting final absorbance is already a t zero and is, therefore, unaffected by an increase in KIE,BH. However, the KIE,BHparameter appears in the second and third terms (hyperbolic terms) of the titration function. The effect of an increase in this parameter is to cause the base to titrate as though it were stronger. T h a t is, it reduces the amount of curvature near the end point in the titration curve. If the strength of the base chosen for this illustration had been much greater than pK'b,g = 12, then it would also be evident that an increase in KIE,BHincreases the curvature in the early part of the curve. KIE,Happears only in the second term of the titration function and does not influence the value of the limiting initial and final absorbance, nor does it influence the curvature in the early part of a titration curve. I t does, however, influence the curvature (increases with increase in KIE,H)in the vicinity of the end point as shown in Figure 5 .
with a point a t n , = ng and
The second term in Equation 3 is a hyperbolic term which is responsible for the curvature occurring near the end point of a titration curve. This curvature is away from the ordinate and increases with a decrease in the strength of the base being titrated and with a decrease in its concentration. The third term is also an hyperbolic term, which is responsible for the curvature in the early part of a titration curve. In this region the curvature is toward the ordinate and increases as the strength of the base increases and as its concentration decreases. The influence of the various parameters on the overall photometric titration curve can be summarized by plotting theoretical titration curves using Equation 3 in which only one parameter is allowed to vary a t a time. This is shown in Figures 1 to 6 for a base of the charge type B. K D ,affects ~ the titration curve in two distinct ways. (See Figures 1 and 2.) First, in Figure 1, as K D , increases ~ the initial absorbance progressively decreases. Therefore, if KD,Bwere large enough, all of the neutral B species would be sorbed by the resin and the titration curve would nearly coincide with the abscissa. Also, it should be noted in Figure 1 that the titration curve for a base of this strength has 1452
ANALYTICAL CHEMISTRY, VOL. 46, NO. 11, SEPTEMBER 1974
r
084
I
\‘
\ 3
b
n c l -x
n,,-x I O Figure 3. Theoretical photometric titration curves showing one effect of KE,BH %=5 X Kb.6 = lo-’’; KW = 1.00 X mole; &,E = 0; KE,H= 0; K s . 0 ~= 0; CBH = €6 = 100; pathlength = 1.000 cm; YH = YOH = 1; Vas = 0.05 I.; WR(kg) = 0 (curve 1). = 0.01 (curves 2-5); ~ E , B H= 1 (curve 2), = 10 (curve 3). = lo2 (curve 4), = i o 3 (curve 5)
Figure 5. Theoretical photometric titration curves showing the effect of KE.H KW = 1.00 X q=5X mole: KD,B= 0; KE,+ = 0; KS,OH= 0; t g = ~ 0; cE = 100; pathlength = 1,000 cm; Y H = yoH = 1; Vas = 0.05 I.; WR(kg) = 0 (curve I ) , = 0.01 (curves 2-4); &,H = lo3 (curve Z ) , = io4 (curve 3), = 105 (curve 4) K6.g = lo-‘;
4
0
to4
t
\\
04-
00
0
2
4
6
ncl-x
IO
8
1
0
ncl-x t 0
Figure 4. Theoretical photometric titration curves showing a second effect of &E,BH K ~ .= B lo-“; KW = 1.00 X q =5X mole; &,E = 0; I
