determination of ionic mobilities and dissociation constants of monovalent acids and bases by...

Journal of Chromatography, 390 (1987) 17-26 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

CHROM. 19 318

DETERMINATION OF IONIC MOBILITIES AND DISSOCIATION CON- STANTS OF MONOVALENT ACIDS AND BASES BY MICROPREPARATIVE CAPILLARY ISOTACHOPHORESIS WITH OFF-LINE MEASUREMENT OF THE pH OF ZONES

JAN POSPfCHAL, MIRKO DEML and PETR BmEK*

Institute of Analytical Chemistry, Czechoslovak Academy of Sciences, CS-6il 42 Brno (Czechoslovakia)

SUMMARY

A method of determining the ionic mobilities and dissociation constants of weak acids and bases by means of capillary isotachophoresis is described which in- volves on-line measurement of the relative effective mobility and off-line measurement of pH in the zones. An isotachophoretic column was constructed, equipped with a potential gradient detector and micropreparative device which, after switching off the driving current, makes it possible to purge the analyzed zone from the column for a subsequent measurement of pH. A procedure based on the linearization of the dependence of the effective mobility on pH is proposed for calculation of the results. The accuracy of the method, adapted for the measurement of monovalent acids and bases, has been established by comparing measured and tabulated data for substances with known mobilities and dissociation constants. The mobilities and dissociation constants of zwitterionic substances of the Good’s buffer type have also been measured, with an error in the mobility not exceeding 3% and in pK* of 0.05 units.

INTRODUCTION

A knowledge of ionic mobilities and dissociation constants is a prerequisite for theoretical prediction of the behaviour of migrating substances in all electromigration methods. In isotachophoresis, such knowledge facilitates the prediction of effective mobilities’, separability2, migration order3 and calibration constants for substances4 in a given electrolyte system.

There are, unfortunately, important substances such as, e.g., zwitterionic Good’s buffers where the values of the ionic mobilities are not yet known or with insufficient precision. This lack of data has led several authors to elaborate methods for the evaluation of ionic mobilities and dissociation constants from isotachopho- retie experiments in combination with the results of computer simulationss-l l. These simulation methods are based on a computation of the conductivity of isotachopho- retie zones in the steady state, by comparing the computed data with experimental values of the conductivity or the potential gradient in the zones. If agreement between the simulated and experimental data for pK and ui of the analyzed substance can be

0021-9673/87/$03.50 0 1987 Elsevier Science Publishers B.V.

18 J. POSPiCHAL, M. DEML, P. BOCEK

achieved, the initial data used for the simulation, i.e., pK and Ui, are then considered to be valid.

The advantages of these methods stem from the principle of capillary isotachophoresis, i.e., the possibility of measuring several substances in a mixture in a single experiment, the high speed of measurement, the small amount of sample needed, and the possibility of routine analysis.

However, these methods are only indirect, because an electrical quantity (conductivity or potential gradient) is measured which is proportional to the effective mobility, whereas the other chemical quantity, the pH, which is necessary for the calculation of h and pK, is again calculated on the basis of this electrical quantity and the composition of the leading electrolyte. So it is evident that the precision of the resulting data is, a priori, influenced by the precision of the data for the leading electrolyte.

The aim of this paper is to elaborate a method of measuring the mobility and dissociation constants on the basis of two independent measurements, namely, of an electrical quantity, i.e., the potential gradient which is directly related to the effective mobility of a substance, and of a chemical quantity, the pH, which is the result of the protolytic equilibria of the participating substances. The development of the corresponding instrumentation and the mobility measurement for a series of important zwitterionic substances forms an integral part of this work.

THEORETICAL

For mobility curves of monovalent acids (Fig. la) and bases (Fig. lb), eqn. 1 or eqn. 2 is valid

KA U,f = Ui ’

KA + [H+l

IX+1 Z&f = 24) ’

KBH + W+l (2)

where Ui is the ionic mobility and KA, KBH are the dissociation constants. By rear- ranging these relationships we obtain

J&(1 +y

‘=$l +s) Uef

(3)

where the mobility curve has been transformed into a linear form (see Fig. 2a, b). Significant points on a mobility curve in its linear form can easily be deter-

mined by a linear extrapolation of the experimentally measured part (in the figures

IONIC MOBILITIES AND DISSOCIATION CONSTANTS 19

2 3 4 5

-b

PH

Ufr 4 (b)

loo-

25.

02. 2 3 4 5

+ PH

Fig. 1. Mobility curves of (a) a monovalent weak acid with ui = - 100 10m9 m* V-’ s-l, pK = 4, and (b) of a monovalent weak base with ui = + 100 lo-’ mz V-’ S-I, pK = 4.

this is limited by points A and C). For an acid, by extrapolation of [H+] to 0, we obtain l/u,r = l/ui, and for I/u,~ = 2/Ui we obtain & = [H+]; see Results (Fig. 6) for details. For bases, we extrapolate l/[H+] to 0 and so obtain l/u,r = I/ui, and for l/u,f = 2/q we obtain l/&n = l/[H+].

To measure the effective mobility, it is advantageous to use a gradient detec- torr2 the response of which is directly proportional to the intensity of the electric field, E. At a constant driving current13:

uefl E2 -_=-

uef2 & (5)

20 J. POSPICHAL, M. DEML, P. BOCEK

Fig. 2. Linearized form of the mobility curve of (a) a weak acid and (b) a weak base.

However, detection of the potential gradient is interfered with by the polarization voltage originating on the electrodes, which is superposed on the signal measured. This voltage, in principle, may attain values of the order of 1 V. To eliminate polarization effects, we can make correction14 by use of standard substances. A question to be solved is whether the constant correction determined in this way is valid for other substances.

Another approach is to choose the working conditions so that the polarization voltage is negligible in comparison to the voltage measured between the detection


electrodes1 5,1 6. This seems to have utility for exact physico-chemical measurements where the detection electrodes are at such separations that the measured value of the electric field intensity is large compared with the polarization voltage (e.g., when the distance between the detection electrodes is more than 1 cm, the measured voltages are expected to be more than 100 V, and the polarization effects may be neglected).

To define the temperature to which the determined mobilities correspond, we have to consider the influence of the Joule heat. A numerical correction is one so- lution; an extrapolation of the measured mobility to zero driving current17*18 or measurement of the actual temperature in the zones and a recalculation of mobility at the required temperature5*i9 are others, as well as minimizing the influence of Joule heat on the measured mobility by effective thermostating of the whole column. This influence was discussed in a previous paperI where it was shown that, to keep the temperature of measurement constant, one should maintain a constant electric power in the zone which is present in the detection cell. The measurement of this constant temperature might still present problems.

As has already been shown, the maintenance of a constant electric potential gradient in the detection cell is generally found to be optimum. The stabilized temperature in the measured zones decreases from the leading electrolyte to the termi- nator and approaches the thermostating temperature. The temperature differences between the measured zones are less than with a constant driving current method. The precision of the measurement is also increased, since mobilities are evaluated by measuring the ratios of electric currents, which can be done with great precision.

When measuring unknown ionic mobilities of substances, we eventually need to consider the accuracy of the determined values. In our case the accuracy is discussed and based on calculating model cases in which the quantities measured are charged with defined errors corresponding to the probability error of a real measurement.

From the chosen values of the ionic mobility and dissociation constants, the “ideal” magnitudes of the effective mobility were calculated for two pH values. These ideal magnitudes were charged with a presupposed error of a real measurement and, from the values obtained in this way, the ionic mobility, UT, and dissociation constant, pK*, were again calculated. By this procedure, four results (corresponding to four combinations of error in two measured quantities, i.e., the pH and effective mobility) were obtained. Only that representing the greatest deviation from the initial quantities was included in the estimation of accuracy.

Fig. 3, shows. the relationship between the relative error of the mobility determination, luf -u;l/uf , and the difference between the average measured pH values and the pK. The width of the measured pH region is taken as the parameter. These dependences have been calculated for a probability error in measurement of & 0.025 units of pH and of & 0.5% in the effective mobility. It is evident from Fig. 3 that, by linear extrapolation, the ionic mobility can be determined with reasonable precision (better than 3%). Also a greater width of the pH region of measurement is advantageous for a lower error in determination, and it is more advantageous to choose the region nearer to full ionization of the measured compound.

Fig. 4 depicts the dependence of the error in determining the dissociation constant, lpK* - pKJ, on the difference between the centre of the pH region and pK, with the parameter of the width of the region for the precisions of the measurement

22

A”, ‘PI 15.

IO.

f-

J. POSPfCHAL, M. DEML, P. B&EK

Fig. 3. Calculated dependence of the relative error of the ionic mobility of a cation on the experimental pH region. The pH and uef were subject to a bias of f 0.025 units and f 0.5% respectively.

quoted above, It is evident that the accuracy of the evaluated data is so much greater the greater is the width of the region and, simultaneously, the nearer is the centre of the region (at the given width) to the optimum value. The latter approximates to pK if the precision of pH measurement is increased.

EXPERIMENTAL

Isotachophoretic separations were performed on a vertical column as depicted

-1 l

0 P’-&+P~ 2 -PK

Fig. 4. Calculated dependence of the absolute error of pK of a cation on the experimental pH region. Other conditions as in Fig. 3.


in Fig. 5. The column is comprised of a separation capillary (400 mm x 2 mm I.D.) equipped with a septum and electrodes belonging to an auxiliary potential gradient detector. After separation, the sample zone enters the measuring cell of the potential gradient detector. This cell is unusually long: the distance between the measuring electrodes is 130 mm, to maintain a sufficiently high voltage between the electrodes compared with the polarization voltage of the metallic sensing electrodes. The voltage between the measuring electrodes was measured by a floating voltmeter, range O-400 V and input resistance 1012 Sz. The sensitivity of such a detector is very low. So, to ensure that no other zone has entered the measuring cell, an auxiliary potential gradient detector was placed in front of the measuring cell. k The separation capillary and measuring cell were enclosed in a kerosene cool-

in$ bath the temperature of which was controlled by a flow ultrathermostat. The temperature resistance of the measuring cell was measured as described2* and was 28K cm W-l. A thin capillary for gas inlet was introduced at the beginning of the measuring cell to facilitate removal of the contents of the cell via the septum of the micropreparative output.

The working electric current was measured and recorded as a voltage drop on a known resistance by means of a TZ 2442 line recorder (Laboratory Instruments, Prague, Czechoslovakia). Simultaneously, the signal of the auxiliary potential gradient detector was recorded. The high voltage supply Described earlier13- was adapted to a constant electric current adjustable within the range O-1500 PA.

Both electrodes were equipped with separating membranes. The terminating

-AIR INPUT

-SAMPLE INPUT

Fig. 5. The micropreparative isotachophoretic column. HV = High-voltage source; FV = floating potential gradient detector; KA = recorder; LE = leading electrolyte chafnber; TE = terminating electrolyte chamber; PGD = potential gradient detector.

24 J. POSPiCHAL, M. DEML, P. BOCEK

electrode was washed by the leading electrolyte during separation, thereby preventing any penetration of H+ or OH- through the membrane into the column.

Procedure After filling the column with electrolytes, a sample of volume 40 ~1 was in-

jected, and the washing of the electrolyte space by the leading electrolyte (250 ml/h- ‘1 and the current supply were switched on. The magnitude of the electric current varies within the range 500-1000 PA depending on the conductivity of the leading electrolyte. By changing the current, the desired electric potential gradient was applied to the measuring detector (corresponding voltage 307 V) between the sensing electrodes. When the migrating zone had filled the whole measuring capillary, the voltage was reduced by changing the current and again set to 307 V. After stabilizing the temperature and conductivity (2 min), this value had to be reset. The electric current was then switched off and the upper part of the capillary was closed by a valve. The sample was forced out of the column by a stream of air (sample volume ca. 200 ~1).

Samples of the zones were preserved in a freezer at -20°C before measurement. The pH measurement was performed by means of a thermostated capillary microelectrode OP 7433 (Radelkis, Budapest, Hungary). The pH meter OP 208 (Ra- delkis) was calibrated by standard buffers (phthalate, pH 4.008; phosphate, 6.865; borate, 9.180; f 0.005 at 25°C).

RESULTS

To demonstrate the accuracy of the method, the mobilities and dissociation constants of weak monovalent acids (acetate, formate and benzoate) were measured under conditions of incomplete dissociation in the measured zone (A) or for more than 99% dissociation (B). The data obtained are been compared with previous val- ueszl (C), in Table I. The agreement indicates the suitability of the proposed method and instrumentation.

Further, the unknown ionic mobilities of some Good’s buffers have been measured by this method. These values as well as the pK values are given in Table II.

^__^_ They correspond to a temperature ot 23°C and <he ionic strengt& quoted (Ui for 0.01 M Cl-, -74.54 . lo-’ m2 V-l s-l for 0.01 M K+, +71.7 . lo-’ m2 V-l s-l).

TABLE I

COMPARISON OF EXPERIMENTAL AND TABULATED RELATIVE IONIC MOBILITIES AND pK VALUES

A, Data measured by the method described; B, data measured by isotachophoresis at full ionization of a substance in its own zone; C, tabulated dataZ1.

Acetate Formate Benzoate

A

&?I

0.5202 0.7178 0.4172

PK

4.736 3.705 4.179

B

U,d

0.5335 0.7198 0.4169

C

%d

0.5342 0.7132 0.4229

PK

4.75 3.75 4.20


TABLE II

MOBILITIES AND pK VALUES OF SOME GOOD’s BUFFERS

The values correspond to a temperature of 25°C and the ionic strength, Z, quoted (see text). MES = 2- (N-morpholino)ethanesulfonic acid, MOPS0 = 3-@J-morpholino)-2-hydroxypropanesulfonic acid, ACES = N-(2-acetamido)-2-aminoethanesulfonicacid,BES = 2-[bis(2-hydroxyethyl)amino]-ethanesulfonic acid, MOPS = 3-(N-morpholino)propanesulfonic acid, TES = N-tris(hydroxymethyl)methyl-2-ami- noethanesulfonic acid, HEPES = N-2-hydroxyethylpiperazine-N’-2-ethanesulfonic acid, DEB = 5,.5’-die- thylbarbituric acid, HEPPSO = N-2-hydroxyethylpiperazine-N’-2-hydroxypropanesulfonic acid.

Substance No. of Mobility Relative PK I. 103 measure (IO9 m2 V-’ s-‘) standard men0 deviation

MES MOPS0 ACES BES MOPS TES HEPES DEB HEPPSO Creatinine Histidine

4 3 3 3 3 3 3 3 3 3 3

-26.8 1.7 6.13 5.00 -23.8 1.7 6.79 6.20 -31.3 0.5 6.84 5.05 - 24.0 1.2 7.16 6.02 -24.4 0.7 7.16 6.00 -22.4 2.9 7.43 5.66 -21.8 3.8 7.51 5.45 -26.2 2.9 7.91 6.02 -22.0 3.2 7.99 5.20 +33.1 1.6 4.89 6.75 + 26.7 0.2 6.13 6.24

An example of the determination of ui and pK is shown in Fig. 6 for 3-(N- morpholino)propanesulphonic acid (MOPS). The straight line was determined by the least-squares method, while each point is an average of eight measurements. The standard deviation of the line (&,x) is 2.365 - IO-’ and the relative standard deviation of the y-intercept is 0.75%.

i

l 1 3 5 K

n mo1 WI

--i- Fig. 6. Example of the evaluation of ui and pK of MOPS from experimental data. Relative standard deviation of u,: 0.75%. Standard deviation of the straight line: 2.365 . IO-*.

26 J. POSPfCHAL, M. DEML, P. BOCEK

The method proposed, based on a direct measurement of the potential gradient and pH in the isotachophoretic zones, makes it possible to determine the ionic mobilities and pK of substances to an accuracy of < 3% and 0.05 units, respectively.

REFERENCES

1 F. M. Everaerts and R. J. Routs, J. Chromatogr., 58 (1971) 181. 2 P. BoEek and P. Gebauer, Electrophoresis, 5 (1984) 338. 3 P. Gebauer and P. BoEek, J. Chromatogr., 267 (1983) 49. 4 T. Hirokawa and Y. Kiso, J. Chromatogr., 260 (1983) 225. 5 Y. Kiso and T. Hirokawa, Chem. L&t., (1980) 323. 6 J. L. Beckers, J. Chromatogr., 320 (1985) 147. 7 V. Zadraiil and J. Vacik, in P. B&k (Editor), 4th International Symposium on ZTP, ITP 84, Hradec

Krcilovh, 1984, Abstracts, p. 90. 8 T. Hirokawa, M. Nishino and Y. Kiso, J. Chromatogr., 252 (1982) 49. 9 T. Hirokawa, S. Kobayashi and Y. Kiso, J. Chromatogr., 318 (1985) 195.

10 V. KaHBka, J. Vacik and Z. Prusik, J. Chromatogr., 320 (1985) 33. 11 T. Hirokawa and Y. Kiso, J. Chromatugr., 252 (1982) 33. 12 T. Haruki and J. Akiyama, Anal. Lett., 6 (1973) 985. 13 M. Deml, P. Bocek and J. JanLk, J. Chromatogr., 109 (1975) 49. 14 T. Hirokawa, M. Nishino, V. Aoki, Y. Kiso, Y. Sawamoto, T. Yagi and J.-I. Akiyama, J. Chromatogr.,

271 (1983) DI. 15 H. J. van der Wiel, J. Chromafogr., 64 (1972) 196. 16 J. Pospichal, M. Deml, Z. Zemlova and P. BoEek, J. Chromatogr., 320 (1985) 139. 17 P. BoEek, Z. RySlavy, M. Deml and J. Janik, J. Chromatogr., 191 (1980) 271. 18 F. M. Everaerts, J. L. Beckers and Th. P. E. M. Verheggen, Zsotachophoresis-Theory, Instrumentation

and Applications (Journal of Chromatography Library, Vol. 6), Elsevier, Amsterdam, Oxford, New York, 1976.

19 Y. Kiso and T. Hirokawa, Chem. Lett., (1979) 891. 20 Z. Ryllajr, P. Bo&ek, M. Deml and J. Jan&k, J. Chromatogr., 144 (1977) 17. 21 Landolt-Bornstein. Zahlenwerte und Funktionen, Part 7, Springer, Berlin, Giittingen, Heidelberg, 1960.

determination of ionic mobilities and dissociation constants of monovalent acids and bases by...

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