Application of Volume Characteristics of Sulfonated Polystyrene Resins as a Tool in Analytical Chemistry Determination of p H and Dissociation Constants of Acids C4LVIN CALMON Reseurch Laboratory, T h e Permutit Co., Birminghum, 3'. J .
In order to determine the most effective sulfonated polystyrene cation exchanger as an analytical tool by virtue of its volume change characteristics, a study was made of the effect of cross linking of the polymer on the swelling of the dry sulfonated product in water, and the volume relations of these exchangers in hydrochloric acid solutions and when combined with cations of different valences. The cation exchangers containing a divinylbenzene content of 1%or less were found to be the most sensitive to volume changes. A low cross-linked exchanger containing 0.5% divinylbenzene was used to determine the pH of acid solutions and the dissociation constants of some weak acids. Although the method described is limited to pure solutions and to certain concentration ranges, it may become useful as a micromethod, because volume changes of single particles may be measured microscppically.
1. Determination of concentrations of strong electrolyte5 2. As a n indicator of end points of reactions involving a change in valence or concentration of ions 3. Determination of the concentration of a more selective ion having different valence than the ion on the resin 4. Determination of the ratio of ionic solutions containing several valences such as F e + + and Fe""+ 0. Determination of water content in various solvent mixtures 6. Determination of degree of dissociation of electrolytes and dissociation constant of acids and bases 7. Determination of pH of acid solutions 8. Separation of an ion mixture through difference in density of the resin containing ions of the mixture
I n order t o find a resin which would give the greatest volume changes, an investigation was made on the effect of cross linking of the polymer on the volume characteristics of the sulfonated product.
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T
HE application of ion exchangers in many analytical pro-
cedures is primarily due to the ion exchange property of many synthetic and processed natural products ( l a ) . As far back as 1917, Folin and Bell ( 5 ) used a synthetic siliceous cation exchanger for determining ammonia in urine. With the development of new types of ion exchangers containing different active groups-such as the carboxyIic, quaternary amines, etc.-the possibilities of applying these in analytical procedures have greatly increased. The new polystyrene-type ion exchangers ( 3 ) may be applied to analytical procedures because of their ion exchange character and wet volume characteristics (4). I n a previous publication ( J ) , it was shown how the volume characteristics of a sulfonated polystyrene cation exchanger, having a cross linking of 1% divinylbenzene (Permutit QX), may be used for determining the concentration of salts in boiler waters, the concentration of calcium and magnesium in natural waters, and the breakthrough point of hardness in a softening unit. I n this paper, it is shown how the volume characteristics of a low cross-linked polystyrene cation exchanger may be used for determining the dissociation constants of various acids and the pH of acid solutions. The swelling of dry ion exchange granules when placed in water or in a solution is due mainly to osmotic pressure and hydration of the ionic components (6). I n general, the volume of a resin in solution depends on the following factors: 1. Degree of cross linking of polymer matrix 2. Exchange group, whether -S08H, -COOH, -PO(OH)?, etc. 3. Exchangeable ion, valence, size, etc. 4. Concentration of electrolyfe in contact with the exchanger 5 . Degree of dissociation of electrolyte in contact with the exchanger 6. Type and concentration of nonaqueous solvent 7 . Number of exchange groups per unit weight of dry exchanger of a given cross linking It is obvious from the outline of factors influencing the volume of an ion exchanger that factors 3, 4, 5, and 6 lend themselves to application in analytical procedures, especially for the following:
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0.25
0.5
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1.0
2.0
3.5
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I 10
I 15
7. CROSS LINUING IN POLYMER
Figure 1.
Ratio of Swollen Volume to Dry Volume of Sulfonated Polystyrene Exchangers With varied DVB cross linking
Figure I shows the degree of swelling of a polystyrene cation exchanger in water for a given cross linking of divinylbenzene. The volume ratios-Le., wet volume to dry volume-were determined by measuring microscopically the diameters of single spheres in the dry and wet (4,7+,11). The curve gives the average ratio for three or more spheres for a given cross linking. h vide variation has been found from sphere to sphere owing, no doubt, to nonuniform polymerization. .Us0 the method of preparation of the polymer matrix enters as n factor. Three different swelling values were obtained for a 1% divinylbenzene cross-linked exchanger prepared by different methods (cf. samples h and B in Table I and Figure 2 ) . Defining the cross linking of a polystyrene exchanger may be best done by indicating the swelling of the polymer matrix in an organic solvent (1, 10) because the same quantity of divinylhenzene added may yield prod-
490
49 1
V O L U M E 2 5 , NO. 3, M A R C H 1 9 5 3 Table I. Effect of Hydrochloric Acid Concentration on Wet Volumea Ratio of Sulfonated Cross-Linked Polystyrene Resins with Various Degrees of Cross Linkingb .&-of HC1 0 25 0 50 1 O(B)C 1 O ( . l ) C 2 0 3 5 7 0 10 15 0.0 1 0 1 .o 1.0 1.0 0 98 0.005 0.93 0.93 0.96 0.01 0 93 0 . 8 7 0 . 8 9 0 97 0 96 0 Si 0.02 0 . 8 5 0.87 0 95 0.05 0.75 0.76 0.78 0.10 0.67 0 . 6 7 0 . 6 8 0 91 0.25 0,57 0.57 0 84 0 56 0 75 0 . 5 1 0.50 0.19 0.50 0 69 0.43 0.42 0.43 1.0 0 59 0.33 0.35 0.35 2.0 'e 10-nil.column. b DVB as cross-linking agent. 6 Samples (. and -I (B) ) prepared by digwent polymerization conditions.
ucts of different, swelling depending on the method of preparation. Thert,fore, st,nndardization of each batch of material and the use of R column instead of single spheres for measuring volume changes of ion exchangers are recommended for analytical applications. I n this work, since comparisons of volumes were made on the wet resin (the rat,io being unity when the exchanger is in contact with distilled water), an investigation was made on the wet voluine ratios of the various exchangers (Permutit Q type) when in contact with hydrochloric acid solutions ranging from 0.005 to 2.0 .\-. Table I shows that the maximum changes in volume ratios of the exchanger, when measured in a column, take place when the cross linking u.as 1% divinylbenxene or less. There was little difference in the volume ratios for given concentrations of hydrochloric acid in the 1.0, 0.5, and 0.25% divinylbenzene resins. However, in the study on the effect of the valence of the cation on the volume ratio of the sulfonated polystyrene resins (Figure 2 ) , it was found that t,he loq-er the cross linking, the greater the reduction in volume with increasing valence. Therefore, in the case of the sulfonated polystyrene cation exchangers, very low cross-linked resins should be preferred for analytical procedures involving volume ratio changen due to ionic valences.
tact with a solution of a given concentration was made by passing the solution through the column until the minimum volume was obtained. This required about 100 ml. of solution for a 10-ml. column of bed. The properties of the 1.0% (DVB, sample A) cross-linked exchanger were the following: T o t a l exchange capacity, 5.15 meq. per gram Density (dry), 1.15 grams per ml. (pycnometer methqd) Density (wet), 49 grams per liter (back washed a n d drained) Mesh size, 16 40 mesh Degree of swelling (ratio of swollen t o dry form): sulfonated product, 22.6 (in water); polymer, 5.7 (in benzene)
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APPLICATION OF VOLUME CHAKGES
Figure 3 shows the volume ratios of a 10-ml. column of a low cross-linked cation exchanger (I yo DVB, sample A) when in contact with various acid solutions. The acids investigated ITere hydrochloric, sulfuric, phosphoric, and acetic. The most deswelling with concentration was noted with hydrochloric acid and the least with acetic, indicating that the ionic concentration is the determining factor. Therefore, if one assumes that the volume
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EXPER1,MENTAL
A back washed and drained volume of cation exchanger (Hstate) in a small buret was taken as the reference volume. The determination of the nery volunw of the exchanger when in conIO
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WET VOLUME RATIO OF RESIN
Screen size, -16 f 40 mesh; 10-ml. column
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3.5% DV0
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Figure 3. Effect of licid Type and Concentration on Volume Ratio of a Sulfonated Low Cross-Linked Polystyrene Resin (Permutit QX)
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changes are entirely due to the ions, and that the concentration of the ions a t a given volume ratio is the same as the concentration of a very strongly ionized electrolyte of the same volume ratio, then the volume of the cation exchanger in the H-state should indicate the ionic concentration of an acidic solution and it should also make possible the calculation of the dissociation constant of an acid. Table I1 gives the results obtained with 1 solutions of acetic, monochloroacetic, trichloroacetic, formic, oxalic, and phoyphoric
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1.0% ( A ) DVB 112 7 . DVB
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Table 11. Determination of Dissociation Constants of Acids by Volume Ratios of a Sulfonated Polystyrene Cation Exchanger (Permutit QX-0.5Yo DVB) Acid
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I Mgtt(2)
I Cr+tt(3)
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VALENCE OF CATION
Figure 2. Effect of Various Ions on Wet Volume Ratio of Sulfonated Cross-Linked Polystyrene Resins
Acetic Chloroacetic Trichloroacetic Formic Oxalic Phosphoric
H-Resin in .\' HCI for 1 A- Acid, Vol. Same. Vol K Calcd Ratio Ratio from T'ol. Ratio 0.95 0 0035 1 . 3 x 10.6 0.055 3 . 2 X 10-8 0.77 0.55 0.49 6 . 7 X 10-1 0.0053 0.92 3 o x 10-4 0.58 0 25 8 . 3 X 10-2 0.70 0.084 0 8 x 10-2
K from Literature (9)
1 . 7 5 X 10-6 1 . 4 x 10-3 2 . 0 x 10-1 1 . 7 6 X 10-4 6 . 5 x 10-2 1.1
x
10-2
492
ANALYTICAL CHEMISTRY
acids when in contact with a 0.5% divinylbenzene cross-linked polystyrene exchanger. The concentration of ionized acid was read from the curve of the plotted data of Table I and the dissociation constant was calculated by the standard equation in which the concentrations n-ere used in place of activities. A plot of the data (Figure 4) shows a straight line for K values greater than 10-4. The data from the literature ( 9 ) ,m-hen plotted lXIOO
Similarly, the pH of acetic and phosphoric acid solutipns was determined from the volume ratios by reading the p H of hydrochloric acid solution (8) which gives the same volume ratio as the acid solution in question. Table I11 presents these data which are on the average within 0.1 pH unit of the data available in standard handbooks. No doubt single spheres of the polystyrene cation exchangers could be used for the same determinations if more uniform polymerizations could be obtained. Microscopic measurements would be very accurate and could easily be made. Very small samples of solutions would be necessary. Exchange groups other than sulfonic also can be used, as shon-n by Breitenbach and Karlinger (5).
Table 111. Determination of pH of Acid Solutions from Volume Ratios of a Sulfonated Polystyrene Cation Exchanger
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(Permutit QX-0.5% DVB) Acid Acetic .Acetic Phosphoric Phosphoric Phosphoric Phosphoric Phosphoric
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H-Resin. Vol. Ratio 0.95 0.93 0.87 0.83 0.76 0.70 0.63
N HC1 for Same, 1’01. Ratio 0.0035 0,005 0.02 0.028 0.048 0.083 0.16
Measured p H of HC1 p H of Acid Soln. Soh 2.40 , 2.45 2.25 2.21 1.80 1.73 1.60 1.6 L3.5 1.41 1.12 1.21 0.88 0.95
ApH -0.0
+0.05 -0.04 0.07 -0.00 -0.06 -0.09
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-4lthough the volume ratio method yields less accurate results than one can get with other known procedures, and also requires pure solution, as well as specific concentrations, thus limiting the method to special cases, it is presented as a possible new analytical tool because it will find greater application especially when improvements in technique and products are made.
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LITERATURE CITED
(1) Bauman, W.C., paper presented a t 23rd Natl. Colloid Symposium, Minneapolis, hfinn., June 1949. ( 2 ) Bauman, W.C., and Eichhorn, J., J . Am. Chem. Soc.. 69, 2830
ixlo-’ VOLUME RATIO
OF CATION EXCHANGER
Figure 4. Dissociation Constants of Acids Plotted for Various Volume Ratios
against the volume ratio, give the same type of curve as the calculated results. With phosphoric and oxalic acids, the second ionization constant was ignored, since the effect on the volume due to the ions is negligible. As a whole, however, the values for the dissociation constants fall within the range of magnitude as given in the literature. The deviation from a straight line for a K value belox which indicates a very small change in volume, may be due to the failure of the Donnan effect at low concentrations.
(1947). and Karlinger, H., .Monalsh. Chem., 80, 312 (3) Breitenbach, J. W., (1949). (4) Calmon, C., ANAL. CHEM.,24, 1456 (1952). (5) Folin, O., and Bell, R. D., J . Bid. Chem., 29, 329 (191T). (6) Gregor, H. P., J. Am. Chern. Soc., 73, 642 (1961). ( 7 ) Gregor, H. P., Held, K. M., and Bellin. J., . ~ K A L .CHEX,23, 620 (1951 ) . (8) Hodgman, C. D., “Handbook of Chemistry and Physics,” p. 1437, Cleveland, Ohio, Chemical Rubber Publishing Co., 1949. (9) Ibid., p. 1451. (10) Pepper, K. W., Paisley, €1. II., and Young, hI. d.,J . d p p l . Chem., 1,124 (1951). (11) Saunders, L., and Srivastan, R. 3, J . Chem. Soc., 1952, 2111. (12) JTalton, H. F., “Principles and Methods of Chemical .1nalysis,” S e w York, Prentice-Hall, Inc., 1952. RECEIVEDfor review September 15, 1952. Accepted November 19, 1952. Presented before t h e Division of .tnalytical Chemistry a t the 122nd Sleeting Of the A M E R I C A N CHEMICAL SOCIETY .ttlantic City, N. J.
