recommended by Majors (17) and Kirkland (11) was omitted. Such adjustments can take 2-3 hours for inexperienced workers. The most important factor for slurry packing is the relationship between the rate of size segregation due to different settling velocities and the time required for column packing. Because of the long length of tubing used to hold the slurry and the short time required for packing. small changes in the density of the slurry are not importanr. The use of a ball valve for introduction of the slurry is time saving and also facilitates the purging of air trapped in the line. Since water is not used in this procedure. it is not necessary to wash the column with a large series of solvents of different elutropic strength to remove
the adsorbed water (11). One of the most important features of this packing technique is that the experimental parameters of the packing procedure can be better controlled than those for dry-packing procedures. This means t h a t column reproducibility for one person or from one person to another will be much better for the balanced density technique. Received for review March 26, 1973. Accepted October 18, 1973. This work was supported by funds provided by a Public Health Research Grant (Project No. 602-7-141) of the National Health Grants Program and by the National Research Council of Canada.
Potentiometric Titration of Monofunctional Bases in ion Exchanger-Aqueous Solution Medium-An investigation of Multiple Equilibria Frederick F. Cantwell' and Donald J. Pietrzyk2 Department of Chemistry, The University of
lowa, Iowa City, lowa 52242
Potentiometric titration functions are derived, which describe the behavior of a base B or A - titrated with HCI in a medium containing a strong acid cation exchange resin (Li-form) and an aqueous electrolyte (LiCI) solution. All equilibrium steps are considered and the significance of each term is established. The titration functions are verified by potentiometric titration of weak bases in the presence of resin. Minor deviations from predicted behavior are found to result from the presence of weak acid (COOH) and weak base (COO-) groups in the strong acid resin (SO3-). Major alterations in titration curve shape are obtained in the resin containing-medium. This makes possible differentiating titrations of mixtures of bases with similar basicity but different charge type. The proposed model may be extended to investigations of indicator-resin interactions and to more complex naturally occurring weak acid exchanger systems.
T h e shape of a potentiometric acid-base titration curve is determined not only by the strength and concentration of t h e sample but also by the nature of the titration mediu n i . S d v c n t rnodifications. such as mixed solvents. nona q u w \ i , wlvents, high concentration of electrolyte, or suhatances which complex or form ion pairs with the neutralization products, are often used t o advantage analytically. Hence, greater success is obtained in the titration of weak acids or bases and in differential titrations of their ni is t u re b . .I s e c o r d and less used technique of altering the shapes d acid- base titration curves involves heterogeneous titration media. For example, a weak base may be titrated in water which is equilibrated, after each addition of titrant, with a second phase while the p H of the aqueous phase is
monitored. The shape of the resulting titration curve will differ from the curve for the titration of the base in water alone because of the perturbing effect (LeChatelier principle) of the phase distribution equilibria upon the acidbase equilibria in the aqueous phase. If a species, which is a product in the acid-base equilibrium, is distributed into the second phase, then the net result is a shift of the acidbase equilibrium toward the product side, and the compound titrates as though it were a stronger acid or base. On the other hand, if a reactant in the acid-base equilibrium is involved in a phase distribution equilibrium, the net effect will be the opposite and the compound will titrate as though it were a weaker acid or base. This phenomenon does not involve a change in pK, or pKb, but only an apparent change during the titration. Several heterogeneous potentiometric titrations in aqueous solvents have been reported in which solids and liquids are the second phase. Titrations involving a solid include those where an acid or base precipitates (1-3) or where a soluble acid or base is adsorbed from solution onto a solid ( 4 ) . The shapes of such titration curves can be described in terms of heterogeneous equilibria competing with the acid-base equilibria. Potentiometric acid-base titrations, where the second phase is a n organic solvent, have been used to evaluate t h e distribution coefficients of acids and bases ( 5 ) . Also, the titration function for acids of the charge type BHz2+ titrated in aqueous-organic heterogeneous medium has been derived and tested experimentally ( 6 ) , and expressions have been presented to describe the differentiating
Present address, E n d o Laboratories, I n c . . 1000 S t e w a r t A v e nue. G a r d e n C i t y , N.Y., 11530. A u t h o r t o whom r e p r i n t requests s h o u l d be sent.
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C. F. Hiskey and F. F. Cantwell, J. Pharm. Sci., 57, 2105 (1968). I. Setnikar. J . Pharm. Sci., 55, 1190 (1966). D. Ratajewics and Z. Ratajewics, Chem. Anal. (Warsaw), 16, 913 (1971). A . E. Mans and G . J. Vervelde, Red. Trav. Chim. Pays-Bas, 71, 977 ( 1952). J. A . Christiansen, Acta Chem. Scand., 16, 2363 (1963). D. Ratajewics and Z. Ratajewics, Chem. Anal. (Warsaw). 16, 1299 (1971),
effect resulting from phase distribution when titrating a mixture of two acids of the charge type HA in a n aqueousorganic solvent system ( 7 ) .. In the present work, a study has been conducted on the influence of a cation exchange resin on the titration of monofunctional bases B and A - in aqueous solution. This system is of interest because it involves different types of phase distribution equilibria and is a more general system than any heretofore investigated. Ion exchange, electrolyte sorption, and non-electrolyte sorption are included in a model t h a t describes these heterogeneous titrations. In addition to providing a detailed study of the equilibria present in this system. it was possible to develop an aqueous titration procedure of analytical utility for the determination of mixtures of weak bases.
Table I. Equilibrium Constant and Distribution Coefficient Expressions for Bases of Type B and A-"
B
A-
EXPERIMENTAL A p p a r a t u s . A Fisher hlodel 210 p H meter was used with a Corning glass electrode (No. 476021) and a fiber junction saturated calomel electrode and standardized with p H 4.01 potassium hydrogen phthalate 10.0500F) buffer and p H 6.45 phosphate buffer (Radiometer Co., Type S1001).T h e accuracy of p H values reported is *0.05 to 0.10 p H unit. Experimental p H values for 0.1FLiCl solutions of NaOH, HC1, and p-nitrophenol)p-nitrophenolate buffers differed slightly (generally lower) than calculated values for these solutions considering ionic strength and activity coefficients (8). This slight discrepancy is due to a residual liquid junction potential (9) and incomplete selectivity of the glass membrane for hydronium ion ( I O ) . Consequently. a nomograph was constructed from d a t a for known O.lk' LiCl solutions of strong acid. base, and buffer and the value of p H to be added t o a given observed p H reading during a titration in 0.1F LiCl was read from t h e nomograph. The p H correction was less t h a n 0.05 unit between p H 3.5 to 8.0 and increased nearly linearly from 0.07 at pH 9 t o 0.22 a t p H 11.5. A 1-ml l l a n o s t a t Model M B 2000 micrometer buret, equipped with a 15-cm thin-walled polyethylene tube as an extension of the buret tip was used. Calibration of the buret was checked by cumulatively weighing 0.1000-m! increments of doubly distilled water. Reagents. ( ' h e m i c a i . Practical grade 2-methylpyridine ( M a theson. Coleman. and Hell) was purified ( 1 1 ) and the 128.6 to 128.9 "C fraction obtained by fractional distillation a t ambient pressure (7?6 m m i was used. F'ractical grade benzylamine ( M C B ) was dried over NaOH and fractionally distilled from N a O H under nitrogen at ambient pressure (747 m m ) . T h e 182 "C fraction was used. m-Nitrophenol (96.0-97.B"C) a n d p-nitrophenol (112.1-114.5 "C) were recrystallized from 95°C ethanol and dried over PzO5. Sodium nitrophenolate solutions were prepared by exact neutralization of the phenol with 0.11' NaOH (potentiometric end point). All water used was laboratory distilled, ion exchanged water which was redistilled from alkaline permanganate. Strong acid and base titrants were prepared and standardized by established techniques. Resina. A strongly acidic sulfonic acid type resin (Dowex SOWX8. 200 to 400 mesh. H - form) was used and was taken from the same lot (Baker Lot 20541). T h e resin was pretreated by decanting the fines and washing it in a column alternately with HCI, water, a n d NaOH until t h e effluent was free of UV-absorbing m a terial. Particles that would not pass through a U.S. Standard sieve of 80 mesh were removed. Subsequently. the resin was converted back to t h e H form with 61' HC1, washed with water, converted t o the Li form with excess LiOH, washed free of excess alkali with O.OO5,k' LiC1, and filtered on a sintered glass funnel. Interstitial water was sucked off and the resin was stored in a screw cap bottle. This resin had a moisture content of 5 6 . 7 7 ~(drying t o constant weight over P z O ~in a vacuum oven) and by isopiestic measurements. it was shown to lose only about 37c of its moisture content when suspended in 0.100F LiCI. The total exchange capacity was 2.18 mequiv gram of moist resin and the free acid content was 3 (7) M . P. Komar. Ind. Lab. ( U . S . S . R . ) .34,617 (1968). (8) J . Kielland, J Amer. Chem. SOC..59, 1675 (1937). (9) I . Feldman, Ana/. Chem.. 28, 1859 (1956). (10) R. G. Bates, "Determination of pH." Wiley, New York, N.Y.. 1964. (11) D. P. Biddescornbe. E. H . Coulson. R. Handley. and E. F. G . Herington. J. Chem. SOC . Londor;. 1954, 1957.
Symbols defined in List of Symbols.
X 10-4 mequiv/gram of moist resin. The acid content was determined by titrating a resin sample with standard NaOH in 0.10F LiCl using potentiometry for end-point detection. After several months of standing, t h e free acid content increased t o 8 x mequiv/gram of moist resin. T h e original lithium form resin is referred to as Li-1 and t h e other as Li-2. Procedures. Distribution Coefficients. Ion exchange ( K I F . " ) , nonelectrolyte sorption ( K D ) ,a n d electrolyte sorption distribution coefficients were determined by batch equilibration experiments. For example, several ,grams of Li form resin were equilibrated (25 f 1 "C) with 0.10F LiCl solution containing a known concentration of t h e base. In one sample, the p H was a d justed with HC1 or N a O H to 2.5 to 5.0 (retention of B H + or H A ) , while in a second it was adjusted t o 8.5 to 11.3 (retention of B or A - ) . T h e actual p H depended on t h e base. After equilibration, the p H was measured a n d the concentration of t h e base remaining in solution was determined by UV spectrophotometry. T h e amount of the base on t h e resin is found by difference. The n u m ber of moles of base initially used was always less than 10% of the number of moles of LiCl (swamping electrolyte) and less than 3% of the total exchange capacity of the resin. T h e observed distribution coefficient is given by
K ~ M
F,,,,;,,- Fa, ml aq phase F.,Q g resin
(1)
where F,,,,,, and Fag are t h e formal concentration of base started with a n d formal concentration remaining. Since Kobrd is measured a t two p H values, and K , (acidity constant of B H + ) is known, these d a t a can be substituted into two equations of the form, and solved simultaneously to give K D , and ~ K[E.I(H. A similar expression was used for base A-. Values of K,c,H for hydronium ion and K c , O H for hydroxide ion were determined by a similar procedure using a known amount of HCl or N a O H without a n initial p H adjustment. Analyses (after equilibration) were completed by potentiometric titration of an aliquot of the supernatant with standard acid or base titrant. T h e equilibrium concentrations in t h e determination of KII(,HH and KiE," ranged from 1 to 7 x lO-*M a n d for KD.Band KD.HA from 1 to 4 x 10-3M. Titration Procedure. Potentiometric ( p H ) titrations were performed i n 100-ml beakers fitted with a rubber stopper t h a t contained a 6-cm long sleeve of rigid polyethylene through its center. A glass shaft with a Teflon blade was passed through this sleeve and connected to a stirrer motor. Additional holes in the stopper provided access for glass and calomel electrodes, a nitrogen purge tube, and the polyethylene tip of t h e microburet. During a titration, t h e beaker was suspended in a water bath a t 25 f 1 "C. Potentiometric titrations were usually carried out with 60 ml of aqueous phase and 15 grams of resin. T h e amount of each base titrated was 0.5 mequiv a n d the titrant concentration was 1F.After the addition of an increment of titrant and a brief period of equil-
A N A L Y T I C A L C H E M I S T R Y , VOL. 46, NO. 3, M A R C H 1974
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i b r a t i o n (1-2 m i n ) , t h e s t i r r e r was s h u t o f f a n d t h e resin allowed t o settle below t h e f i b e r j u n c t i o n o f t h e SCE. Hence, pH errors res u l t i n g f r o m t h e "suspension effect" were avoided ( 1 2 ) .T h i s pH value did not d i f f e r by m o r e t h a n 0.2 unit f r o m t h a t measured in t h e suspension. Since t h e a m o u n t o f a d d e d t i t r a n t was generally between 0.5 a n d 1.5 ml, v o l u m e changes d u r i n g t h e t i t r a t i o n were never greater t h a n 3% a n d were neglected.
Under these experimental conditions, the ion exchange, electrolyte sorption, and nonelectrolyte sorption distribution equilibria may be represented by distribution coefficients. These distribution coefficients have been shown to be nearly independent of concentration of a trace species on sulfonated polystyrene-divinylbenzene cation exchange resin (15-18) and will remain constant during a titration (13, 14). Previous studies (19, 20) have also demonstrated t h a t water uptake by such resins, which contain greater than about 6% divinylbenzene, is nearly independent of aqueous phase ionic strength between 0 and 0.W. A quantitative titration function describing the titration of a weak base, B or A- in the presence of the resin must include the influence of all of the pertinent equilibria in Equations 3 to 5. The homogeneous equilibrium constants and heterogeneous distribution coefficient expressions for these equilibria under the imposed experimental conditions are listed in Table I. If charge and mass balance relationships are written for both phases, these equations can be combined with the appropriate equilibrium expressions in Table I to yield the potentiometric titration function for that system (21). Hence, for the titration of nB moles of base B, with strong acid HC1, in dilute aqueous solution of salt LiCl, in the presence of a strongly acidic cation exchange resin in the Li form, the titration function is the following:
RESULTS AND DISCUSSION Proposed Model. When a solution of weak base of the
B charge type is in contact with a strongly acidic cation exchange resin in the Li form, the existing equilibria are summarized by Equations 3 and 4. (All symbols are identified at the end of the text.)
B,,
K'i, H
+ H?O,,
+ OH,,-
S BHA:
+
/lKi) 5
(R-Li)R
(3)
BR (R-BH)R 2H,O,,,
K
+ Li,,'
eH,O,,,+ + /I
(R-H
+
OH,,-
( 0 ) ~(LiOH)R
Li.,,+ If the solution in contact with the resin contains a weak base of the A - charge type, then the existing equilibria are summarized by Equations 4 and 5 .
Aaq-
+
K'h A
H20nq
HA,,
+
For the corresponding titration of nA moles of base A - , the titration function is as follows:
OH,,-
n\
=
n4
- (V!, + K,,W,)
[KW(~,,
x
nAKL+ K S A W R ) K'bAaH+.,,(V,,
I+
+ KDH~WR)
(LiAh Heterogeneous equilibrium constants (which are thermodynamically valid) may be written for the equilibria in Equations 3 t o 5 provided t h a t both phases are homogeneous and the system is a t equilibrium (13, 14). However, since one of the present purposes is to describe the influence of an ion exchange resin on acid-base titrations in an analytically useful form, it is desirable to minimize variables such as activity coefficients. The presence of these variables would require iterative methods for solving the titration equation and would also increase the number of physicochemical properties of the system that must be determined by independent experiments. A simplifying experimental condition is imposed on the system by having both the total number of moles of inert electrolyte (LiC1) in the aqueous phase and the total ion exchange capacity of the resin much larger than the number of moles of base being titrated. Also, the resin counterion is the same as for the "swamping electrolyte" ( L i f ) . Hence, the activity coefficients of all chemical species in the aqueous phase are constant during a titration.
These titration functions may be evaluated directly, once the values of the distribution coefficients KIE,K D & and Ks and the basicity constant Klb have been experimentally determined. Predicted Titration Behavior. The right side of Equation 6 contains three terms. The first of these terms accounts for the Contribution of the basic properties of base B to the titration curve and is often called the proton binding curve of the base. The second and third terms on the right account for the contribution of the titration medium ( i e . , solvent plus resin) to the titration curve. Four different distribution coefficients are included in the overall titration function. To illustrate their influence and the
(12) H. Jenny, I . R . Nielson, and D. E. Williams, Science, 112, 164 (1950). (13) F. Helfferich, "Ion Exchange," McGraw-Hill. New York. N.Y., 1962, Chap. 5. (14) 0. Samuelson. "Ion Exchange Separations in Analytical Chemistry." Wiley, New York. N.Y., 1962, p 74.
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(15) E. R . Tompkins and S. W. Mayer, J. Amer. Chem. SOC., 69, 2859 (1947). (16) K. W. Pepper, D. Reichenberg, and D. K. Hale. J. Chem. SOC.. London, 1952,3129. (17) H. P. Gregor and M. H. Gottlieb, J. Amer. Chem. Soc.. 75, 3539 (1953). (18) D. Reichenberg and W. F. Wall, J . Chem. SOC., London, 1956, 3364. (19) H. P. Gregor. F. Gutoff, and J. I . Bregman. J. Colloid Sci., 6, 245 (1956). (20) E. W. Baumann and W. J. Argersinger, Jr., J. Amer. Chem. SOC., 78, 1130 (1951). (21) F. F. Cantwell, Ph.D. Thesis, The University of Iowa, December, 1972.
3r
I‘
6
a
I
a IO
12
14J 0
2
3
n,.x
io4
I
5
4
Figure 1. Calculated theoretical proton binding curves for base B in a cation exchange resin-aqueous solution medium. Effect of KIE,BH and KD,B
mole; Vaq(liter) =
n~ = 5.00 X K ’ ~ , B= (curve 1). = 0.0125 (curves 2-9) ~~
Curve No.
KIE.BH KD.B
=0
ncl- x io4 Figure 2. Calculated theoretical blank titration curves for the addition of HCI to a cation exchange resin-aqueous solution medium. Effect of KIE,H
~
1
2
3
.. 1 io .. . o o .
0.05; WR(kg)
4
5
6
102
103
o
o
o
1
7
o
io
8
9
o
o
io2
103
YH+
=
1;
V,,(liter) = 0.05;W,(kg)
= 0 (curve l ) , = 0.0125 (curves
2-5) ~~~~
contributions of the base and medium, each are treated separately in Figures 1, 2, and 3 for the titration of a hypothetical base B with a PK’b,B = 5.00. In Figure 1 the contribution of the first term in Equation 6 is shown by plotting p H as a function of the number of moles of added titrant for several values of KIE,BH and K D . ~As . KIE,gH increases, the proton binding curve shifts in the same way t h a t it would if the strength of the base (K’b,B) were increased. Conversely, as KD,B increases the proton binding curve resembles t h a t for a weaker base. In Figure 2 the contribution of the second term in Equation 6 is demonstrated by varying the value of KIE,H. In Figure 3, the contribution of the third term in Equation 6 is demonstrated by varying the value of the parameter K b , O H . From Figures 2 and 3, it is seen t h a t as the values of K I ~ , and H K b . 0 ~increase, the useful p H range over which titrations can be performed is reduced. In other words, the “leveling” properties of the titration medium are increased over those of the aqueous solvent alone (curve 1, Figures 2 and 3 ) . The overall titration curve, corresponding to the complete titration function for base B, may be obtained by combining the values of n x from Figures 1, 2, and 3 which correspond to the same p H values. Only portions of the resulting combined curve are used where the net value of nx is positive. When considering a base of charge type A - , the first two terms on the right in Equation 7 represent the contribution of the basic properties of A - to the titration curve (proton binding curve). The third and fourth terms are identical to the second and third terms in Equation 6 and follow Figures 2 and 3. Proton binding curves for a hypothetical base A - with PK’b,A of 5.00 are identical to those presented in Figure 1 if the symbols K’b,A, KD,HAand K S , Aare substituted for the symbols K’b,B, KIE,BH,and KD,B, respectively. It is apparent t h a t an increase in K D , H A causes the base A - to titrate as though it were stronger while an increase in has the opposite effect. It should be noted that the values of Kb,OHand Kb,Ain Figures 3 and 1 are unrealistically high for illustrative
~
Curve No.
1
2
3
4
5
KIE.H
...
1
10
102
103
r
a 7------
3
//i
c
I I4 -02
-01
n,-x
00
io4
Figure 3. Calculated blank theoretical titration curves for the addition of HCI to a cation exchange resin-aqueous solution medium. Effect of K s . 0 ~ .Minus values of n x correspond to the addition of strong base, M O H
= lo-’*; ?OH- = 1 ; V,,(Iiter) 0.0125 (curves 2-5) Kw
= 005; W,(kg)
= 0 (curve 11, =
Curve No.
1
2
3
4
5
KS,OH
...
1
10
102
103
~
~~
purposes. The phenomenon of co-ion exclusion would prevent electrolyte sorption coefficients from being much larger than zero, except a t very high aqueous phase ionic strength (13).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 3, M A R C H 1974
347
small ions in 0.1F electrolyte are approximately IO2 to IO3, while values of K D , H and &,HA are often less than 20 and is usually less than 1. Hence, base B would experience a n apparent strengthening significantly greater than t h a t experienced by base A - . If the two bases have ionization constants that are close, it is reasonable to expect t h a t their apparent ionization constants might be sufficiently separated so as to produce a sizeable p H “break” a t the first end point in a titration of their mixture. Deviation from the Proposed Model. Oxidation is possible in the synthesis of sulfonated cation resins, which can produce carboxylic acid groups accounting for u p to 5% of the total exchange capacity (19, 22). These groups, even in small amounts, will produce deviations from the proposed model since it accounts only for strong acid groups in the resin. In the present study, very small amounts of weak acid IO and base (
