Thermometric Titration Determination of AH”, A G O , and ASo of Dissociation of Ephedrinium and Pseudoephedrinium Ions Richard J. Raffa,’ Marvin J. Stern,2 and Louis Malspeis3 College of Pharmaceutical Sciences, Columbia Unicersity, New York, N . Y., and Belfer Graduate School of Science, Yeshica Unicersity, New York, N. Y. Thermometric titration with NaOH titrant at 2 5 O C has been used to determine the enthalpy (AH), free energy (AG), and entropy (AS) changes in the acid dissociations of the diastereoisomeric ephedrinium H?O + Eph H30+. The measured ions, EphHt diastereoisomeric differences (pseudoephedrinium minus ephedrinium) from thermometric titrations alone were 200 & 38 cal/mole for AH’, 199 f 72 cal/mole for A G O , and 0.00 i 0.27 eu for ASo, where the error limits are estimated standard deviations. The corresponding difference for A G O from potentiometric measurements was 197 i 13 cal/mole, which combines with the above AHo difference to yield a aso difference of 0.01 i 0.13 eu. All of these values are in excellent agreement with the respective values of Everett and Hyne, which were based solely on potentiometric measurements over a range of temperatures. The individual diastereoisomer thermometric titration values of AHo (-11,000 cal/mole) were also in excellent agreement with Everett and Hyne’s potentiometric values, while the individual thermometric titration A G O values (-13,000 cal/mole) were about 2% lower than the corresponding potentiometric values. The results indicate that even with relatively simple apparatus and interpretive methods, thermometric titration at a single temperature provides a means of measuring statistically valid small differences in thermodynamic functions of similar compounds such as diastereoisomeric pairs.
+
+
THERMOMETRIC TITRATIONS (1-3) are finding widespread applicability as analytical tools. However, relatively little work on the use of such titrations for the determination of the thermodynamic functions of fast reactions has been reported, except, perhaps, for enthalpy determinations. As it is theoretically possible to determine the enthalpy (AH), free energy (AG), and entropy (AS) changes of a reaction from a single thermometric titration curve (enthalpogram) ( 4 , 5), the use of thermometric titrations for this purpose should become quite important. The present study was initiated to determine if, with a relatively simple thermometric titration apparatus and utilizing simple interpretive methods, it would be possible to measure, with statistical validity, the small differences in thermodynamic Present address, Analytical Research Section, Quality Control Department, Chas. Pfizer and Co., Inc., Brooklyn, N. Y. 11206. * Present address, Belfer Graduate School of Science, Yeshiva University, New York, N. Y. 10033. Present address, College of Pharmacy, The Ohio State University, Columbus, Ohio 43210. (1) S. T.Zenchelsky, ANAL.CHEM., 32, 289R (1960). (2) J. Jordan and G. J. Ewing, “Handbook of Analytical Chemistry,” L. Meites, Ed., Sect. 8, p. 3f, McGraw-Hill, New York, 1963. (3) W. W. Wendlandt, “Chemical Analysis,” P. J. Elving and I. M. Kolthoff, Eds., Vol. 19, Chap. 8, p. 271f, Interscience. New York, 1964. (4) J. Jordan, J. Chem. Educ., 40, A5 (1963). (5) J. J. Christensen, R . M. Izatt, L. D. Hansen, and J. A. Partridge, J. Pliys. Chem., 70, 2003 (1966).
70
ANALYTICAL CHEMISTRY
properties of diastereoisomers. The reactions chosen for investigation were the acid dissociations, in aqueous solution at 25 O C, of the diastereoisometric ephedrinium (erythro)and pseudoephedrinium (threo) ions. These reactions were chosen because their thermodynamic functions have been previously evaluated by Everett and Hyne (6) with the use of potentiometric measurements carried out over a range of temperatures. The reactions investigated are shown in Figure 1, where the Newman projections depict the most probable (6) conformations in aqueous solution. (See reference 6 for a discussion of the evidence suggesting these conformations.) Everett and Hyne have interpreted their observed difference in AGO for these reactions (pseudoephedrinium - ephedrinium = 225 cal/mole) as being due to a difference between the energies of the conformer rotations rather than due to a difference between the energies of the proton dissociation processes per se. (Throughout this report, the superscript will be used to refer to infinite dilution; the standard state employed is that of a hypothetical unit molar solution, at unit atmosphere pressure and 25” C, acting in an environment of infinite dilution.) In a recent paper, Malspeis, Turner, and Lachman (7) estimated that the rotation energy difference to which Everett and Hyne’s AGO difference data were attributed represented about one half of the total barrier to internal rotation in either isomer. Thus, on this basis, a total barrier to internal rotation of only -500 cal/mole would be predicted for either isomer. Applying similar reasoning to their own electrocapillary measurements, Malspeis et al. (7) estimated a (more reasonable) value of -2-3 kcal/mole for the total barrier in either diastereoisomer. Additional problems concerning the above interpretations become apparent when one considers that there is evidence that the most stable conformations of the ephedrine and pseudoephedrine bases in nonaqueous solvents are not those shown in Figure 1. Kanzawa (8, 9 ) concluded from the infrared spectra of these bases in several nonaqueous solvents that both isomers exhibit intramolecular hydrogen bonding between the hydroxyl and methylamino groups. Such bonding would tend to favor a gauche or nearly gauche relationship in both isomers. Hyne (10) found that the nuclear magnetic resonance spectra for ephedrine and pseudoephedrine in chloroform were consistent with “off-staggered” arrangements in which the carbon-hydroxy and carbonmethylamino dihedral angle was 80-90” in ephedrine and 30-40” in pseudoephedrine. Hyne also pointed out that his data were consistent with a population distribution among several “pure-staggered” conformations, but he felt that the latter interpretation was less plausible than his interpretation O
(6) D. H. Everett and J. B. Hyne, J. Chem. SOC.,1958, p. 1636. (7) L. Malspeis, J. W. Turner, and L. Lachman, J. Pharm. Sci., 54, 253 (1965). (8) T. Kanzawa, Bull. Chem. SOC.Japan, 29, 398 (1956). (9) Ibid., p. 479. (10) J. B. Hyne, Can. J . Chem., 39, 2536 (1961).
Ephedrine H
A+cH3+ H,O+
no
HZO
H,CNH,
+
H3CNH
H
Pseudoephedrine
HEATER
-
-THERMISTOR
Figure 1. Probable conformations for diastereoisomeric ephedrines and ephedrinium ions in aqueous solution
TITRANT LIVERY TIP
'Q)
based on a preferred residence in off-staggered conformations. If the conformations shown in Figure 1 are not preferred residence arrangements for the diastereoisomeric ephedrines and ephedrinium ions in aqueous solution, then the theoretical interpretations of both Everett and Hyne (6)and Malspeis, Turner, and Lachman (7) are subject to question. Despite any discrepancies or uncertainties concerning Everett and Hyne's interpretations, the fact remains that they have measured apparently significant differences in AHo and AGO for the acid dissociations of the diastereoisomeric ephe.. . . . . .. . arinium ions. I neir porenriomerric measurement resuits can be checked by, or, alternatively, can serve to check, the thermometric titration results of the present investigation.
-.
:
~
Figure 2. Thermometric titration cell head
._~
(Merck & Co., -mc.,Materials. - . (-)-Ephedrine ., was arreahydrochloride Kanway, unoer vacuum * \
~~
> ~ : ~ >
ar ruum w r i -
perature for 24 hours. Its melting point was 218.5-19" C (uncorrected) . ...[lit. .(11) 216-20". C]. . . Its .optical . ". rotation -.~ (5 grams in 100 ml aqueous solution) was ~ a ] , ,= ~a -34.bx" [lit, (11) - 33 to -35.5" (+)-Pseudoephedrine hydrochloride (kindly supplied by Burroughs Wellcome & Co., Tuckahoe, N. Y.) was dried at 100" C for 3 hours. Its melting point was 184-5" C (uncorrected) [lit. (12) 181-2" a. Its optical rotation (0.8 gram in 100 ml aqueous solution) was [ a ] P = f62.25" [lit. (12) +62" Throughout this report, ephedrine or ephedrinium refers to the (-) enantiomorph, while pseudoephedrine or pseudoephedrinium refers t o the (+) enantiomorph. All titrate solutions were prepared with recently boiled deionized (Barnstead mixed resin bed) water which was stored in a borosilicate glass carboy equipped with a NaOH pellet trap. Titrate solutions were used only on the day of their preparation. 1.OM NaOH and 1.OM HCI titrant solutions were purchased as certified volumetric solutions (Fisher Scientific Co.). Thermometric Titration Apparatus. Adequate external temperature control was achieved by mounting the titration . . syringe . .... . ~ . ~. , cel.l,. .titrant . . pump, a n a titranr reservoir (viae injra, in a Plexiglas box, and by careful thermostat setting of a room air conditioner and three strategically placed, small, electric, fan-forced room heaters. The Plexiglas box was
a.
a.
..
._..- m e . . . -iodex," . 7th ed., p. 403, Merck MercK N.
(11)
(12)
\
& Co., Rahway,
-
-
~~
EXPERIMENTAL N. J.,
constructed of 1-cm thick material and was 52 cm in height and 43 cm in width and depth. The entire front of this box served as a door; the doorway was surrounded with rubber weatherstripping. The box had a wooden base which was attached to the laboratory bench. With this arrangement, the room temperature could be maintained at 25.0 + O S 0 C, while the temperature inside the box was maintained at 7C 0 I n".*1 0 F A i s r i n n a h.n+or.+i+rrtinn ~".~"I..ll l ) n i i - n r(nido ~ infm\ &.,." ,..,. The titration vessel was a modified Dewar flask of a design by Christensen, Izatt, and Hansen (13) with a titrate capacity of 100 ml. The titration cell head, a modification of that of Christensen et al. (13), is shown in Figure 2. It consisted of a Teflon-fabricated 29/42 standard-taper male joint, with a 35-mm extension at the narrow end, press-fitted above the wide end into a 20-mm thick, 125-mm diameter, Plexiglas disk. The disk was suspended from the top of the Plexiglas box with three . threaded ... aluminum . rods. ';ted of a stainless I ne cenrraiiy posirionea stirrer consi! steel shank, 23 cm long and 7.5 mm in diameter, into the bottom of which was fitted a 7.9-cm Iong, 5-mm diameter, Teflon shaft containing four quadrantal p,addles, each 8 mm in width, 11 mm in height, and 4 mm in thickness. The stirrer was positioned in its shaftway so t hat only the Teflon part was exposed. Around and in clos'e proximity to the stirrer were positioned the heater, the t.itrant delivery tip, and the thermistor probe. The stirrer IO tated in a direction such that liquid near the delivery tip hadI to make almost a complete loop around in the flask, past the heater, before reaching the thermistor probe. The bottoins ofthe thermistor and heater were positioned 5 mm above th,e top of the stirring blades, while the bottom of the delivery tip was positioned 4 mm above the blades. When the titrati on vessel contained 100 ml of titrate, the stirrer was submei-ged to a depth of -5 cm, the heater, thermistor, the delivery tip were submerged to a depth of -3.5 cm, and the b,ottom of the Teflon joint extension was -2.5 cm above the: liquid level. The n the titration cell titration flask was held firmly in place oN
"
..
-.
L-.>~~~:.L
- ..*.+..,-....-.."..
_I...
, . . L
\"..._
..I
.
> .,--.:-.---A-
ncau wiin grass IIUULS ail" a a u c
UIIIIU~.
The heater and its power supply have been described (14). The t i t i m t deliwrv tin consisted of a 22-cm length of 4-mm (13) J. J. Christensen, R. M. Izatt, and L. D. Hansen. Rev. Sei. Insfr., 36, 779 (1965). (14) M. J. Stern, R. Withnell, and R. J. RafFa, ANAL. CHEM.,38, 1275 (1966). VOL 40, NO. 1, JA NUARY 1968
71
_.._.-.."..
..~."...
..-. I . l . _ _ l
V1YCC Y L L l l r L"&,
"I
Lllr
ucrrvcry
tip with tape and sealed to the bottom of the tip with epoxy cement (6 parts by weight of hardener No. 3404 to 100 parts adhesive No. 4307, Hysol Corp., Olean, N. Y.). The end of the delivery tip was cut with a glass-grinding wheel so that the solid epoxy plug was only 2 mm thick. The thermistor probe was prepared by sealing the tip of a 2000-ohm bead-inglass-probe thermistor (No. 32A1, Victory Engineering Corp., Springfield, N. J.) into a borosilicate tube (4.5-mm o.d., 22 cm long) with epoxy cement so that only the glass-coated bead was exposed. The stirrer was powered with a Synchro-Tork stirring motor (General Laboratory Supply Co., Patterson, N. J.) which was mounted with aluminum rods on the top of the Plexiglas box. The stirrer shaft protruded through a small opening in the top of the box. Titrant was delivered with a 2.5-ml gas-tight syringe (No. 1002, Hamilton Co.) powered by a constant-speed syringe pump (Model 234-2, Sage Instruments, Inc., White Plains, N. Y.) housed in the Plexiglas box. The heavy weight of the Teflon-tipped stainless steel syringe plunger caused it t o acquire an off-horizontal position, especially when fully extended. This situation, which could cause nonuniform delivery rates, was rectified by grinding a flat surface on the plunger flange and allowing it t o rest on a Plexiglas lip attached to the driving carriage of the pump. The pump was operated t o produce a delivery rate of approximately 0.6 mllminute with reproducibility and uniformity of &O.l%. The pump could be operated with a switch outside of the Plexiglas box. The titrant was stored, in the Plexiglas box, in a 500-ml capacity polyethylene bottle which contained a screw cap through which was sealed a polyethylene-coated 2000-ohm thermistor. This thermistor could be used t o check titranttitrate temperature equality. A 0.044-inch bore Teflon syringe needle (No. KF16LTF, Hamilton Co.) was sealed through the side of the polyethylene bottle with epoxy cement. This needle, as well as the delivery tip needle, led to a threeway Teflon valve (No. 3MLF3, Hamilton Co.) on the syringe. All electrical connections to the components in the Plexiglas box were made through adapters sealed into €he sides of the box. With the door of the box closed, the only free air communication between the inside and outside of the box was through the small gap between the stirring shaft and the sides of the hole through which it protruded. The thermistor bridge used was a modified version of that described by Jordan and Alleman (15)). The titration (15) J. Jordan and T. G. Alleman, ANAL.CHEM.,29.9 (1957).
72
ANALYTICAL CHEMISTRY
.---.....I._.-. ..I... """SC. 1 I l r .III"'zI(LIICC potential of the bridge was recorded with a 1-mV Dynamaster recorder (The Bristol Co., Waterbury, Conn.) at a chart speed of 2.25 inch/minute. For absolute titrate temperature measurement, the bridge was operated as a null instrument with balancing resistor settings converted to temperature readings by means of a previously prepared calibration curve. For occasional checks on titrant-titrate temperature equality, the bridge was again operated as a null instrument, with the titrant thermistor replacing one of the fixed-resistor arms of the bridge. Figure 3 shows the entire thermometric titration apparatus, except for the recorder. Thermometric Titration Procedure. The titrant syringe was filled to capacity and the titrant level was withdrawn to the top of the delivery tip in order to prevent thc first few drops of titrant from being heated during the subsequent operation of the heater. Exactly 100 ml of titrate solution was placed in the titration flask and the flask was positioned on the titration cell head. The stirrer, bridge, and recorder were activated; thermal equilibrium was established within 2 minutes. The temperature of the titrate was then measured and, if necessary, the heater was operated to raise the temperature so that the average of the temperatures before and after the heater-titration sequence (oide infra) was 25.0" C. (The maximum temperature span from the beginning t o the end of such a sequence was -0.1' C.) After establishment of thermal equilibrium and obtainment of a base line on the recorder, the heater was activated and allowed t o operate for about the same period of time that would be necessary for the subsequent titration. The heater setting (14) was chosen to produce a heater curve which resembled the titration curve as closely as possible. After thermal equilibrium had been re-established, the recorder zero point was readjusted and a new base line obtained. The titration was initiated by starting the syringe pump. Titrant delivery was allowed to continue until well after the end point had been reached in order to produce a sizable excess reagent branch (portion of curve after the end point) on the enthalpogram. During a heater-titration sequence, the bridge and recorder were never turned off, nor were any instrumental adjustments made other than the repositioning of the recorder zero point. Because of the incorporation of a heater calibration with each titration, instrumental variations were almost completely eliminated and the necessity for scrupulous drying of the titration cell between titrations was avoided. Potentiometric Measurements. All p H measurements were made with a Becknian Model G pH meter equipped with a calomel reference electrode and a glass indicating electrode I .
I -..I
"I
L..U
(Type E2; No. 40495, Beckman Instruments, Inc., Fullerton, Calif.). The measurements were made on half-neutralized (with NaOH) solutions of ephedrine hydrochloride or pseudoephedrine hydrochloride immersed in a water bath main0.01" C. tained a t 25.00 Treatment of Data. Figure 4 shows a simulated enthalpogram on which the measurements necessary for enthalpy and free energy determinations are indicated. It is assumed that Figure 4 represents a n exothermic reaction and that the usual convention of recording an increase in temperature as a positive change in voltage is followed. Points a and c represent the start of the titration and the end point, respectively. The factors contributing t o the various portions of the curve have been discussed (2-4). The curvature in the vicinity of point d is due t o the incompleteness of the titration reaction a t the end point. The vertical distance ab can be shown t o be a direct measure of the heat evolved from the titration reaction itself. Height ub was compared to the corresponding heater curve height, in a straightforward manner, to yield a n absolute value of the heat change due to the titration reaction. In such comparisons, the uncertainty of the heater calibration was not considered as this uncertainty probably represented the experimental error in the calibration measurements rather than irreproducibility of the heater output (14). Such a procedure may slightly underestimate the errors in the absolute values of the enthalpies of reaction but does not underestimate the significance of the error in the diastereoisomeric difference in enthalpy of reaction. As the same errors in measurements that occurred in the heater calibration appear again when the heater is used with a titration, consideration of the uncertainty in the absolute calibration of the heater would overestimate the significance of the error in the diastereoisomeric enthalpy difference. I n determining the difference between the enthalpies of acid dissociation of the diastereoisomeric ephedrinium ions,
*
must consider the reaction of the base with water (reverse of Reaction 3) (often referred to as hydrolysis). The untitrated titrate consists of a n equilibrium mixture containing Eph, EphH+, and OH-. Thus, the heat evolved in the titration with H 3 0 + results from both the protonation of Eph and the neutralization of OH-. In order to correct the measured heats for the heat of the OH- neutralization reaction, one can use the straightforwardly derived equation cal due to protonation
=
measured cal
- 13,335 [OH-],V,
(6)
(1)
where [OH-], is the equilibrium hydroxyl ion concentration in the original titrate solution, and V , is the titrate volume. [OH-], and [Eph], can be determined from the equilibrium constant for Reaction 3. Similar considerations applied t o neutralization titrations of ephedrinium (or pseudoephedrinium) ion with base, according to Reaction 3, lead t o a correction for the dissociation equilibrium (Reaction 1) of the same form as Equation 6, but with [HyOS],, the hydronium ion concentration in the original titrate solution, replacing [OH-],. For the titrations with NaOH titrant discussed in this report, this correction was always well within the experimental error and was, therefore, neglected. The vertical distance cd in Figure 4 can be taken as a direct measure of the amount of unreacted reactant and (height cd)/ (height ab) as the fraction of unreacted reactant (F)a t the equivalence point. As AG," is about 13 kcal/mole (pK, i= 9.6), the end point of an ephedrine (or pseudoephedrine)strong acid titration is too sharp to allow precise F measurements, while the end point of a n ephedrinium (or pseudoephedrinium) ion-strong base titration is sufficiently curved. For the titration of ephedrinium (or pseudoephedrinium) ion with hydroxyl ion (Reaction 3), the classical (Le., based on concentrations rather than on activities) neutralization equilibrium constant is
one has a choice of studying the protonation reaction by titration with strong acid titrant,
(7)
EphH+
Eph
+ Hz0
+
+
+
Eph
+
EphH+
(AHB"),
+ H20
(AH,'),
(2)
or the neutralization reaction by titration with strong base titrant,
+
+
EphH+ OH- + Eph HzO (AH,'). (3) The enthalpies of Reactions 1-3 are related according to AH,"
=
-AH,"
(4)
where C, is the initial (analytic) concentration of acid (Le., ephedrinium or pseudoephedrinium), V , is the titrate volume, and u is the volume of titrant added at the equivalence point. AGO of the acid dissociation can then be calculated with
and
AG,'
and AH,"
=
13,335 cal/mole
+ AH,"
(5)
=
-RT In K,"
(9)
where K, is the classical dissociation equilibrium constant, R is the gas constant, T is the absolute temperature, and K, is the ion product of water at the ionic strength of the equivalence point. The use of a modified Debye-Huckel equation allows one to calculate K, at 25' C as
where the constant in Equation 5 is the enthalpy of ionization of water at 25" C (16, 17). Since AH," is about 11 kcal/mole, it is evident that a small percentage difference in AH," between diastereoisomers will be reflected as a large percentage difference in AH,". Thus, one would expect that measurement of heats of neutralization of the diastereoisomeric ephedrinium ions would be a more sensitive method of determining a small difference in enthalpy of acid dissociation than would be direct measurement of heats of protonation. In using Equation 5 , the small uncertainty in the constant (probable error = 10 cal/mole) was not considered, again to avoid overestimating the significance of the error in determining the diastereoisomeric enthalpy difference, In analyzing the results of titrations of ephedrine (or pseudoephedrine) with acid, according to Reaction 2, one
where p is the ionic strength at the equivalence point. The precision of the present apparatus did not warrant the use of more sophisticated methods (5, 18, 1Y) of analyzing thermometric titration curves. For the p H measurements of half-neutralized solutions of
(16) J. D. Hale, R. h4. Izatt, and J . J. Christensen, J . Pliys. Cliern., 67, 2605 (1963). (17) C . E. Vanderzee and J. A. Swanson, Ibid., p. 2608.
(18) J. Barthel, F. Becker, and N. G. Schrnahl, 2. Physik. Cliern. ( N e w Folge), 29, 58 (1961). (19) F. Becker, J. Barthel, and N. G. Schrnahl, Ibid.,37, 33 (1963).
pK,
=
13.997 - 1.018 1
1/11
+ di
VOL. 40, NO. 1 , JANUARY 1968
73
9-1
2.5c
2.0
TIME,
1
L.-:-LI-1
m)
10
00
MOLES X IO4
Figure 5. Enthalpogram for titration of 0.01M ephedrine hydrochloride with 1.OM NaOH ephedrine (or pseudoephedrine) hydrochloride, semiclassical K. values were calculated according to (20)
Figure 6. Apparent heats of neutralization, Qn,of ephedrine hydrochloride (0)and pseudoephedrine hydrochloride (0). Lines shown are least-squares fits
Figure 5 is a typical enthalpogram for the titration of ephedrine hydrochloride with NaOH ; a corresponding enthalpogram for pseudoephedrine hydrochloride has almost an identical appearance. Table I contains a summary of the measured apparent heats of neutralization, Q,, of the diastereoisomeric ephedrine hydrochlorides with 1.OM NaOH. Plots of Q,(cal) cs. moles of titrate, shown in Figure 6, are quite linear but intersect the ordinate slightly above the origin, indicating that a nearly constant error, manifested as an increased value of the measured heat evolution, was involved in each titration. Although it was not possible t o determine unambiguously the source of this error, a slight distortion observed in the initial rising portions of most of the enthalpograms indicated that the error derived from some extraneous source of heat. There are two probable ways for extraneous heat to be introduced. Because the titrate solution was stirred for some time before the actual titration was performed, and because the titration cell was not completely air-tight, a small amount of C o n from the atmosphere could have dissolved in the
solution. As a C02-NaOH titration is exothermic, dissolved COZwould serve t o increase the measured value of the heat evolved in the titration. The second possible source of extraneous heat derives from the fact that the titrate was heated by the calibration heater just prior to the titration. Although the titrant level in the delivery tip was kept well above the titrate level during the heating operation, it is possible that the first portion of titrant entering the titrate solution was heated slightly by the epoxy seal in the delivery tip. An alternate explanation for the plots in Figure 6 not intersecting the origin is the possibility that even at the low titrate concentrations employed, an ionic strength effect on the heat of neutralization was operative. However, plots of apparent AH,( = Q,/moles of titrate) cs. titrate molarity and cs. (titrate molarity)1'2 failed t o exhibit even reasonable linearity, nor did they allow reasonable extrapolations to zero ionic strength. These facts, coupled with the excellent linearity of the plots in Figure 6, lead t o the conclusion that ionic strength effects were within the experimental errors. The datum points in Figure 6 were fit t o linear equations by a least-squares procedure, with each point weighted as the inverse square of its error limit shown in Table I. The AH,' were taken as the slopes of the least-squares lines. The results of these analyses are included in Table I. Application of the statistical t-test (21) t o the least-squares parameters indicated almost a 99.9 % probability that the two slopes (AH," values) were not derived from the same population (i.e,, are different) but about a 99% probability that the two intercepts were derived from the same population (Le., are identical). (The authors beg the forgiveness of statisticians for the nonrigorous but convenient interpretations of t-tests used in this report.) As mentioned under Treatment of Data, direct determination of AH," by titrations of free ephedrine (or pseudoephedrine) base with HCI requires a correction for the "hydrolysis" of the base. One way of possibly circumventing this problem is to carry out titrations of solutions of the free base containing an excess of NaOH. The excess hydroxyl ions will react with the acid titrant prior t o the reaction of the free ephedrine base. Thus, an enthalpogram with a change in slope in the titration branch will be obtained. A measure of the heat evolved in the reaction of the free base itself can be taken as the vertical distance from the first end point
(20) J. J. Lingane, "Electroanalytical Chemistry," 2nd ed., Interscience, New York, 1958, p. 101.
(21) W. C. Hamilton, "Statistics in Physical Science," Ronald Press, New York, 1964.
where p H is in terms of hydronium ion activity (assuming that the glass electrode is a reasonable indicator of activity), C, is the initial (analytic) concentration of the hydrochloride salt, and [H,O+] and [OH-] are the concentrations of hydronium and hydroxyl ions, respectively. (For the cases considered here, [H30c] was always negligible compared to the other terms, and negligible error was introduced by taking [OH-] equal to the hydroxyl ion activity.) AG," was again calculated with Equation 9. With both AH," and AG," determined, the entropy of the dissociation reaction, ASa", was calculated with the standard thermodynamic relationship AS,"
=
AH,"
- AGa" T
(1 3)
and the propagated estimated standard deviation of the entropy, s(AS.."), was taken as
RESULTS AND DISCUSSION
74
ANALYTICAL CHEMISTRY
Concn, M X lo3 1.491 3.504 5.056 7.512 10.012
Table I. Heats of Neutralization of Diastereoisomeric Ephedrinium Ions at 25” C Pseudoeohedrine hydrochloride Eohedrine hvdrochloride Concn, M X lo3 Titrations, no. Q,, -caP Titrations, no. Q n , -ala 8 0.4436 f 0.0045 1.496 8 0.4059 f 0.0035 9 0.9538 f 0.0055 3.506 8 0.8751 f 0.0083 9b 1.3119 f 0,0044 5.008 9 1.2249 f 0.0039 8 1.9338 f 0.0064 7.508 9 1.7779 f 0.0084 8 2.6045 f 0.0092 10.026 96 2.3617 f 0.0084
RESULTS OF LEAST-SQUARES ANALYSES Ephedrine hydrochloride Pseudoephedrine hydrochloride AH,” = -2498 f 35 al/mole AH,” = -2298 f 15 cal/mole (AH.” = 11,037 f 15 cal/mole) (AHB’ = 10,837 f 35 cal/mole) Intercept = -0.066 f 0.007 cal Intercept = -0.066 f 0.018 cal Appended error limits are estimated standard deviations of the means. b One value eliminated from average by Chauvenet’s Criterion. CAppendederror limits are estimated standard deviations.
(change in slope) t o the extrapolated excess reagent branch (similar t o the measurement shown in Figure 4). Since the excess OH- initially present suppresses “hydrolysis” of the free ephedrine base prior t o the titration, within the limitations of the extrapolation method for determining end points (Le,, extrapolating the linear segments on either side of the end point to their intersection), no “hydrolysis” correction need be applied. Figure 7 shows an enthalpogram for the titration of ephedrine with HCI titrant, while Figure 8 shows an enthalpogram for the titration of an ephedrine plus excess OH- solution with HCI titrant. Similar curves are obtained for the corresponding titrations of pseudoephedrine. A careful examination of Figure 8 reveals that there is indeed a slight change in slope in the titration branch, but the exact location of the first end point is impossible t o determine accurately. Table I1 lists the results of titrations with 1.OM HCl of free base solutions and of free base plus excess OH- solutions. The free base titrations yield values of AH,” which are in the same order but numerically lower than the values calculated from the heats of neutralization (cf. Table I). The “hydrolysis” corrections only serve to increase the discrepancies between the two sets. The reason for the low values of AH,” here is probably associated with excessive COz absorption by the basic solution prior t o the titration. The values in Table I1 of AH,” from free base plus excess OH- titrations are not only lower than the values calculated from the heats of
Figure 7. Enthalpogram for titration of 0.0075M ephedrine with 1.OM HCI
Table 11. Direct Measurement of Enthalpies of Dissociation of the Diastereoisomeric Ephedrinium Ions at 25 ” C Titrations, AH, ’, cal/moleb Titrateo No. Uncorrected Correcte& 0.0075MEph. 8 10,658 f 19 10,459 f 21 10,768 f 12 0.0075M $-Eph. 9 10,976 f 11 0.0075MEph. 0,0025M OH9 10,734 f 114 ... 0.0075M $-Eph. 0.0025M OH9d 10,533 f 86 ... Eph. = Ephedrine; li.-Eph. = Pseudoephedrine. * Appended error limits are estimated standard deviations of the means. Corrected for reaction of free base with water. Two values eliminated from average by Chauvenet’s Criterion.
+
+
neutralization, but are also in the reverse ordering of magnitude; Le., here AH,” for ephedrinium is larger than for pseudoephedrinium. These discrepancies cannot be attributed t o Con absorption, as absorbed COz would react with the excess OH- rather than with the ephedrine or pseudoephedrine. These rather strange results are probably due t o the error involved in locating the NaOH end point. I n view of all the difficulties mentioned above, as well as the inherent difficulties in trying t o determine small differences between large
Figure 8. Enthalpogram for titration of 0.0075M ephedrine plus 0.0025M OH- with 1.OM HCI VOL 40, NO. 1, JANUARY 1968
75
~~
~
Table 111. Classical pK, Values for Diastereoisomeric Ephedrinium Ions from Thermometric Titrations at 25 O C Concn, M X IO8
Titrations, No.
1.491 3.504 5.056 7.512 10.012
Ionic strength" EPHEDRINE HYDROCHLORIDE
pKwa
0.0017 0.0038 0.0054 0.0079 0.0104
8
9 9
8c 8
pKah
13.957 13.938 13.928 13.914 13.903
9.390 f 0.037 9.414 f 0.027 9.349 f 0.004 9.353 0.019 9.394 f 0.041 A v . 9.380 ~ & 0.013
13.956 13.938 13.926 13.914 13.903
9.638 f 0.033 9.583 f 0.009 9.934 f 0.0326 9.415 f 0.035 9.468 f 0.026 AV.d9.526 f 0.051
*
PSEUDOEPHEDRINE HYDROCHLORIDE 1.496 3.506 5.008 7,508 10.026
8 8c 9 9
0.0017 0.0039 0.0056 0.0079 0.0105
9e
Ionic strength and pK, at equivalence point. standard deviations of the means. e One value eliminated from average by Chauvenet's Criterion. d Unweighted arithmetic average; see text. Eliminated from overall average by Chauvenet's Criterion. o
* Appended error limits are estimated 6
Table IV. Semiclassical pK, Values for Diastereoisomeric Ephedrinium Ions from Potentiometric Measurements at 25 O Co Ephedrine hydrochloride PHb PK. 9.547 f 0.004 9.572 f 0.004 9.580 f O.OO4 9.567 f 0.004 9.580 f 0.000 9.589 f 0.m 9.580 f 0.000 9.587 f O.oo(J 9.613 f 0.004 9.618 f 0.004 9.617 f 0.004 9.621 f O.O4
Concn.. M X lo3 2.500 5.000 7.500 10.000 15.000 20.000
RESULTS OF LEAST-SQUARES Ephedrine hydrochloride pK," = 9.565 f 0.005 Slope = 3.0 & 0.4M-1 a
b
Pseudoephedrine hydrochloride PHb PKS 9.673 f 0.009 9.706 f 0.009 9.7% f 0.000 9.718 f 0.000 9.723 f 0.004 9.735 f 0.004 9.737 f 0.004 9.747 f 0.004 9.743 f 0.009 9.749 f 0.009 9.747 f 0.004 9.752 f 0.004 ANALYSESC
Pseudoephedrine hydrochloride PK." = 9.709 f 0.008 Slope = 2.6 f 0.7M-1
Each pH and pK, value is the average from three determinations. The appended error limits are average deviations. pH at half-neutralization. Appended error limits are estimated standard deviations.
Table V. Thermodynamic Functions for Dissociations of the Diastereoisomeric Ephedrinium Ions at 25 O Co AH,", cal/moleb Ephedrine hydrochloride Pseudoephedrine hydrochloride Pseudoeph. HCI - Eph. HCI
10,837 f 35 10,830 f 40 11,037 f 15 11,030 f 40 200 f 38 200 f. 57
AG,". - , cal/molec . T.T. P.M. 12,797 f 18 12,996 f 70 199 f 72
13,049 f 7 13,020 f 8 13,246 f 11 13,245 j=5 197 f 13 225 f 9
AS,'-. . eud T.T.
-6.57 f 0.13 -6.57 f 0.24 0.00 f 0.27
P.M. -7.42 -7.35 -7.41 -7.42
f 0.12 f 0.25 f 0.06 f 0.25 0.01 f 0.13 -0.07 f 0.35
Source This work Ref. 6 This work Ref. 6 This work Ref. 6
Appended error limits for this work are estimated standard deviations of the least-squares parameters, except for the limits on the AG." thermometric titration values, which are estimated standard deviations of the means (cf. Table I11 and text). Error limits on Everett and Hyne's values (ref. 6 ) are one half the values quoted by them as "approximately twice the standard deviations of the means." Thus, all of the error limits shown have approximately the same statistical significance. Deviations for the differences (last two rows) were taken as the square roots of the sums of the squares of the individual deviations. This work values from thermometric titrations of hydrochloride salts (Table I). Ref. 6 values from potentiometric measurements. T.T. = from thermometric titrations. P.M. = from potentiometric measurements. T.T. = derived from AH," and AG," thermometric titration values, P.M. = derived from AH," thermometric titration value and AG." potentiometric measurement value for this work; from potentiometric measurements for ref. 6.
76
ANALYTICAL CHEMISTRY
I
1
9.5
I
I 4
I
I' I I I I 8 12 16 CONCENTRATION ( M x i 0 3 1
I
I
20
Figure 9. Semi-classical pK, values of ephedrine hydrochloride (0) and pseudoephedrine hydrochloride ( 0 ) . Lines shown are least-squares fits
values, the results shown in Table I1 must be deemed unreliable. They will not be considered further. Table I11 is a compilation of the classical pK, values obtained from the same thermometric titration curves that were used for the enthalpy analyses. The scatter between the points in each set was considered t o o great t o allow meaningful ionic strength relationships t o be derived from them. Thus, no attempt was made t o fit the data t o a least-squares equation, but instead, each average pK, value shown in the table was considered t o be a single determination and the unweighted averages of the values for each compound were taken. Weighted averages were not taken because the apparent error limits of the individual values are much smaller than the scatter between the values. Within the approximation of the Debye-Huckel limiting law, these classical pK, values should be ionic-strength independent, as K, contains a singly-charged positive ion concentration in both numerator and denominator, and a neutral molecule concentration. The classical pK, values are related t o the corresponding semiclassical values obtained from the potentiometric measurements (cideinfra) by
where Y ~ is the ~ activity ~ + coefficient of H30i. Considerations of the results of the potentiometric measurements and of approximate values of yHaO+ lead to the conclusion that the error in the individual classical pK, values arising from the disregard of ionic strength effects should be no greater than about 0.01-0.02 pK,, unit (for the highest concentration; less for the lower concentrations). Two sources of error may be involved in the values in Table 111. The first possible source of error is the obvious one involved in the measurements of the heights cd (Figure 4) which never were more than a few millimeters. The second source of error is associated with the previously discussed uncertainty in the actual titration heights, ab, which caused the nonzero intercepts in the plots shown in Figure 6. The F values in Equations 7 and 11 were not corrected for the errors in the heights ab as it was not certain whether the heights cd were also affected by the undetermined source of
error. (Initial attempts at such corrections led to obvious overadjustments and were, therefore, abandoned.) The results of semiclassical pK,, determinations from pH measurements are shown in Table I V and Figure 9. The data were fit to a least-squares equation, pK,, = m M + pK,,",where the slope, n7, reflects the ionic strength dependence of yR:l,l,/ yl,;l,~,,,+. The points were all given equal weights in the leastsquares analyses because the observed average deviations were less than 0.01 pH unit, the maximum precision of the instrument. The thermodynamic functions, AH,", AG,', and AS,", for the acid dissociations of the diastereoisomeric ephedrinium ions are shown in Table V along with the corresponding values obtained by Everett and Hyne (6). Application of the t-test of significance t o the values in Table V for the results of the present investigation indicated the following approximate probabilities that the thermodynamic function differences found between diastereoisomers were not due to chance but t o actual differences: AH,", 0.99; AG,"(T.T.), 0.97; AG,"(P.M.), 1.00; AS,"(T.T.), -0; AS,"(P.M.), 0.06. The agreements between the values obtained in this investigation and Everett and Hyne's values are excellent. Even the thermometric titration AG," values, which are about 2 lower than the corresponding potentiometric measurement values, yield a diastereoisomeric difference in excellent agreement with the potentiometric measurement values. The striking agreement of the AH," values is particularly interesting in view of the fact that the two sets of data were obtained by completely different experimental methods: in this work by thermometric titration at 25.0°C, and in the previous work by consideration of the temperature dependences of pK, values obtained from potentiometric measurements. It is apparent from Table V that, even with the relatively simple apparatus and interpretive methods described in this report, thermometric titration provides a means of measuring statistically valid small differences in thermodynamic functions of similar compounds such as diastereoisomers. Differences of similar relative magnitude would be expected between other types of compound pairs, such as members of a homologous series or some isotopically substituted compounds. ACKNOWLEDGMENT
The authors wish to express their appreciation t o Ragy Boshra Hanna for carrying out the potentiometric measurements, and t o Walter C. Hamilton for helpful discussions on statistical methods. RECEIVED for review August 31, 1967. Accepted October 17, 1967. Division of Analytical Chemistry, 153rd National Meeting, Miami Beach, Fla., April 1967. Paper based on a thesis presented t o the College of Pharmaceutical Sciences, Columbia University, by R. J. R. in partial fulfillment of the requirements for the degree of Master of Science. Research at Columbia University supported in part by the Ciba Pharmaceutical Co., Summit, N . J. Research at Yeshiva University supported in part by U. S. Atomic Energy Commission Contract AT(30-1)-3663.
VOL. 40,
NO. 1, JANUARY 1968
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