or following (SR, AR) the diffusion process. By allowing sufficient time for adsorption equilibrium of the oxidized form to be achieved, the potential for its reduction is as least as cathodic as the main process. At very low concentrations, complete constancy of io7 with varying current density is observed and the system approaches the behavior of transferred film reduction in which there is no diffusion contribution. The above conclusions are in good agreement Kith the results reported by Takemori (19) who obtained a value of 0.84 X 10-lo mole cm.? for the oxidized form in 1.0 x 10-4M FMK with 0.1M citric acid as the supporting electrolyte. His calculations were made on the basis of the SR, AR mechanism. In the polarographic case, the variation of half-wave potential with scan direction and the extent of solution reduction is a clear indication of a mixed potential process. The electrode potential is affected not only by the main faradaic process but also by the adsorption phenomena associated with it. Lacking detailed information regarding the adsorption isotherms, molar free energies of adsorption, adsorptiondesorption rates of the individual species and their influence on each other, it is not possible a t present to quantitatively justify the polarographic potential shifts observed. This representation of the adsorption process as one involving only the oxidized and reduced forms has neglected the possible influence of the semiquinone. At present little is known about the adsorption behavior of this intermediate form which could prove important in view of its significant concentration in solution during
electrolysis. Calculations from molecular models indicate a surface coverage for the oxidized form of 1.5 X mole cm.+ assuming a planar orientation of the electrode and the isoalloxazine ring system. In the leuco form, however, the entire ring system cannot be coplanar owing to the quinoid structure of the middle ring. Under such conditions the reduction of an adsorbed layer would also imply reorientation. The observed slow adsorption of the oxidized form suggests the possibility of a preferred electroactive orientation resulting from the reorientation of initially adsorbed material. Such a process would account for the shift of the prepeak to more negative potentials and the creation of an electroactive film sufficiently stable to survive film transfer in the latter studies. It is possible that the initial approach of FMN occurs “edge on” with the plane of the rings normal to the electrode surface to produce a weakly bound unstable state which slowly reorients t o a stable film in which the ring system is coplanar with the electrode. The existence of a polarographic prewave even for a reversible electron transfer does not prove the predominant influence of the reduced form on an equilibrium basis. To correctly evaluate the overall adsorption process, isotherms for the individual forms must be known. The prewave alone cannot be used as a basis for deciding on the mechanism of film electrolysis since the mechanism can change as the experimental parameters are varied. The combination of several electrochemical methods has facilitated the formulation of a consistent picture of FMN adsorption.
LITERATURE CITED
( 1 ) Biegler, T., Laitinen, H. A., J . Phys. Chem. 68, 2374 (1964). (2) Brdicka, R., Collection Czech. Chem. Commun. 12, 522 (1947). (3) Breyer, B., Biegler, T., Zbid., 25, 3348 (1960). ( 4 ) DeMars, R. D Shain, I., ANAL. CHEM.29,1825 (19k7). ( 5 ) Enke, C. G., Bsxter, R. A., J. Chem. Educ. 41,202 (1964). (6) Hartley, A. M., Wilson, G. S., unpublished results, 1966. ( 7 ) Ke, B., Arch. Biochem. Biophys. 68, 332 (1957). (8) Koryta, J., Collection Czech. Chem. Commun. 18,206 (1953). ( 9 ) Laitinen, H. A., Chambers, L. M., ANAL.CHEM. 36, 5 (1964). (10) hfalmstadt, H. V., Enke, C. G., Toren, E. C., “Electronics for Scientists,” p. 370, W. A. Benjamin, New York, 1962. (11) Michaelis, L., Schubert, &I P., . Smythe, C. V., J. Biol. Chem. 116, 587 (1936). (12) Muller, 0. H., Ann. N . Y . Acad. Sci. 40,91(1940). (13) Murray, R. W., J . Electroanal. Chem. 7. 242 (1964). (14) Nicholson, R. S., Shain, I., ANAL. CHEM. 36,706 (1964). (15) Osteryoung, R . A,, Ibid., 37, 429 (1965). (16) Randles, J. E. B., Trans. Faraday SOC.44.327 11948). (17) Senda, hi., Senda, M., Tachi, I., Rev. Polarog. (Kyoto) 10, 142 (1962). (18) Sevcik, A., Collection Czech. Chem. Commun. 13, 349 (1948). (19) Takemori, Y., Rev. Polarog. (Kyoto) 12,63 (1964). (20) Tatwawadi, S. V., Bard, A. J. ANAL.CHEM.36, 2 (1964). (21) Weir, W. D., Enke, C. G., Rev. Sci. Instr. 35, 833 (1964). (22) Wilson, G. S., Ph.D. Thesis, University of Illinois, 1965. ~
RECEIVED for review Jan. 7, 1966. Accepted February 25,1966. This work was supported by the National Institutes of Health Grant USPH GM 12009.
Cryoscopic Titrations Principles of a N e w Method of End-Point Detection STAN LEY BRUCKENSTEIN and NICHOLAS E. VAN DERBORGH School of Chemistry, University of Minnesota, Minneapolis, Minn.
b An experimental apparatus for continuously recording the variation in the freezing point depression during the course of a titration is described and applied to several model aqueous systems. Close approach to equilibrium conditions is attained in the titration of a strong and a weak acid and their mixture with strong base, and in the titration of chloride ion with silver ion. A number of bases were also titrated in benzene as a solvent using trifluoroacetic, trichloroacetic, and acetic acids as titrant. The analytical accuracy was approximately 1 yoin all titrations, and the experimental titration curves agreed with the theoretical predictions.
A
55455
solution parameters have been successfully investigated using a variety of colligative properties. For example, the association of carboxylic acids, nitrogen bases, and their adducts has been studied by cryoscopic (2,S, 7‘) and ebuillioscopic (1, 8) methods. More recently, studies have demonstrated the utility of the differential vapor pressure method for the investigating acid-base reactions in the solvent benzene (4) as well as solute association in several other solvents (6). In nonaqueous acidbase studies using cryoscopy, it w&s desirable to continuously monitor the equilibrium freezing temperature as the QUEOUS AND NONAQUEOUS
mole ratio of acid to base was varied. Experimentally, this was accomplished by adding acid from a motorized buret to a rapidly stirred mixture of the solvent plus base in the presence of finely divided frozen solvent, while the temperature was measured continuously using a thermistor bridge, This paper reports the resulte of the initial investigations of this technique with both water and benzene as solvents. The measurement of equilibrium freezing temperature of a two-phase (solid-liquid) mixture permits determination of the total number of solute particles in the liquid phase. This measurement offers a universal end-
point detection technique, provided that the number of particles produced by adding titrant is different before and after the equivalence point. A titration curve constructed from such data would have the appearance of a conductance titration in which each species has the same equivalent conductance. In the solvent benzene, experimental and theoretical curves similar in shape to the cryoscopic titration curves, but obtained by a manual differential vapor pressure technique, have been described previously (4). In addition t o the problems of rapid mixing of titrant and solution and of maintaining thermal equilibrium between the solid and liquid phases, the problem exists of minimizing heat exchange with the surroundings. Ideally, adiabatic conditions should be maintained and heat effects caused by the addition of titrant (heat of solution, heat of reaction, and heat gain caused by the temperature difference between titrant and solution) should be minimized to eliminate changes in the relative amounts of liquid and solid phases. However, the heat of fusion of most solvents is large compared to the heat capacity of the liquid, so that heat effects caused by using a microburet to deliver a concentrated solution are tolerable. For example, in an unfavorable situation, adding 1 ml. of 5M NaOH a t 25' C. to a mixture of 25 ml. of water and 25 grams of ice containing 2 mmoles of hydrochloric acid has the net effect of melting only approximately 2 grams of ice. The dilution of the sodium chloride solution produced by these extraneous heat effects results in only a minor distortion of the titration curve in this particular example. EXPERIMENTAL
Apparatus. The apparatus used in this investigation was of simple design. It consisted of a Dewar flask (10-oz., wide-mouth Thermos replacement filler) in which a three-hole rubber stopper was positioned. The thermistor and delivery buret were inserted into this stopper and, when necessary, a transfer pipet was inserted for delivery of the solute. Optimum titration conditions occur when the thermistor and delivery buret are placed opposite one another and about 5 mm. from the side of the vessel. Stirring was effected by a magnetic stirrer with a 1-inch Teflon-covered stirring bar operating a t the maximum possible stirring rate. The titrant was delivered via a Gilmont 1.0-ml. Ultramicro buret. The delivery tip of this buret was modified by extending it with a piece of capillary tubing (1-mm. bore) which terminated in a tip extending below the surface of the liquid. The buret was coupled t o a variable-speed synchronous motor which allowed eight titrant delivery rates varying from 0.0061 to 0.64 ml. per minute. 688
ANALYTICAL CHEMISTRY
The thermistor used in these studies was a Veco 32A30 glass-covered bead thermistor (nominal resistance a t 25' C. = 2000 ohms). This thermistor was immersed in the solution as far as possible without interfering with the stirring. The equilibrium temperature was monitored by following the resistance of the thermistor which made up one arm of a conventional Wheatstone bridge. This bridge was powered by two Mallory Rh'142R batteries; the output of these batteries was applied to a 10-kilohm voltage divider which allowed varying the bridge voltage from 0 t o 2.7 volts. Each arm of the bridge had a nominal resistance of 20 kilohms. Inserted in the same arm as the thermistor was a variable resistance (0 to 20 kilohms) and opposite to this was another variable resistance (0 to 20 kilohms) in series with a balancing resistance substitution box (Leeds and Northrup). By adjustment of the two variable resistances it was possible to make the bridge approximately equiarmed. The off-balance voltage from the bridge was fed directly to a Texas Instrument, 1.0-mv. stripchart r e corder equipped with a variable chart speed of 0.50 to 8.0 inches per minute. Temperature sensitivity of the apparatus was adjusted by varying the applied thermistor bridge voltage. In the experiments conducted in potassium chloride aqueous solutions, a small constant d.c. signal (millivolt level) was inserted in series with the recorder. This was done so that the thermistor bridge could be used a t the lower temperature of these solutions without changing the bridge resistor settings. Calibration and Sensitivity. The thermistor was calibrated a t several different bridge voltages. Initially the Wheatstone bridge sensitivity (millivolt recorder deflection per ohm change) was determined by replacing the thermistor by a resistance substitution box and noting the millivoltper-ohm change. For an applied voltage of 0.8 volt, a sensitivity of 0.022 mv. per ohm was found. Then the thermistor was calibrated in absolute temperature units by comparing recorder deflections with temperature readings taken with a Beckmann thermometer. At an applied bridge voltage of 0.802 volt the bridge tempoerature sensitivity was 4.63 mv. per C. Under our conditions (recorder reading error of 5 pv.) the smallest discernible change in the number of particles (mmoles) is given by ~ r = n 1.1
x
10-3 V I K , ~
where K j is the mold freezing point constant, d is the density and V is the volume of the liquid phase. For water ( K , = 1-86),Am is equal to 2.3 X mmoles while for benzene ( K , = 5.12) a change of 9.6 X 10-3 mmoles can be detected when V is equal to 40 ml. The temperature measurement is not the limiting factor because increasing the applied bridge voltage proportionally increases the measured unbalance e.m.f. However, the sensitivity is limited by rapid, random temperature fluctuations
which produced oorly defined curves. This effect, whicg became the limiting factor in more dilute solutions, was probably caused by relatively large pieces of solid phase coming in direct contact with the thermistor. Determination of the Volume of Liquid Phase. To estimate dimerization constants of the organic acids in benzene solutions, i t was necessary to determine the volume during the course of the experiment. This was done by adding 1.00 ml. of 1 . O O M naphthalene in benzene solution. Since naphthalene is monomeric in the solvent benzene, the total volume is readily calculated from the observed temperature change. Chemicals. The water used for the solvent was distilled and then frozen in polyethylene ice cube trays. All of the other chemicals used in the aqueous studies were reagent grade. The acids, bases, silver nitrate, and sodium chloride were standardized using conventional techniques. Mallinckrodt or Merck A.R. benzene, thiophene-free, was first shaken with aqueous sulfuric acid solution (1 : I), washed with distilled water, and then shaken with Alcoa activated alumina for 4 to 6 hours. (About 100 grams of alumina were used per liter of benzene.) The solvent was then filtered through a sintered glass funnel and stored in glassstoppered bottles until used. The water content of benzene treated in this way was determined (Karl Fischer) to be approximately 5 X 10-3X. n-Dodecylamine was donated by the General Mills Research Laboratory. All other organic bases were reagent grade and used as received. The purity of all these bases was determined by the titration of the various benzene solutions in glacial acetic acid as the solvent with perchloric acid as the titrant and crystal violet as indicator. Reagent grade trifluoroacetic acid (TFAA), trichloroacetic acid (TCAA), and acetic acid (HOAc) were standardized by withdrawing an aliquot of the acid (in benzene solution) and titrating, after extraction in water, with potassium hydroxide as the titrant to a phenolphthalein end point. The naphthalene used in this study was practical grade and was recrystallized from benzene before use. Experimental Procedure. An aliquot of dissolved solute was placed in the Dewar flask containing the twophase (liquid-solid) solvent mixture; as the titrant was added using the motorized buret, a voltage proportional to the change in the equilibrium freezing temperature was recorded. The concentration of the titrant solution was high enough to assure that only a small volume change - would ensue from its addition. Typically, in the aqueous studies, 25 ml. of prechilled water (about 4' C.) was added to a Dewar flask containing 25 grams of finely divided ice. The thermistor was inserted and the thermistor bridge unbalance was adjusted to approximately zero. The contents of the Dewar flask were vigorously stirred, the solute was added (via pipet),
the delivery tip of the buret was positioned opposite the thermistor, and the bridge rebalanced if necessary. The addition of the titrant was commenced (recorder running) and the equilibrium freezing temperature was recorded. The procedure for the benzene titrations was similar. Three glass-stoppered extraction tubes were each filled with 20 ml. of dry benzene and cooled in a water bath t o 3' C. A few benzene crystals were introduced to circumvent the superccoling problem. When the mixture had solidified, the tubes were removed and the solid phase was broken into a solid-liquid slush by vigorous shaking. This slush was then poured into the titration vessel, the solute was added, and the titration was carried out in a manner similar to the aqueous titrations. During the initial nonaqueous investigations, the equilibrium temperature of the associated carboxylic acidamine base adduct (at the equivalence point) was frequently higher than that of the two-phase mixture. This result is most easily explained by assuming the incorporation of some dissolved impurity into the highly associated acidbase aggregate. Treatment of the solvent with aqueous sulfuric acid, followed by drying with activated alumina, was successful in maintaining the equilibrium temperature throughout the titration a t a value lower than that of the pure solvent. This unknown impurity, present in millimolar concentration, was established not t o be water since titrations performed in a solvent previously shaken with water (water concentration of 10-2M) did not exhibit the anomalous temperature behavior. RESULTS AND DISCUSSION
Equilibrium and Heat Gain Studies. This end-point detection method depends upon rapid attainment of thermal equilibrium. Experimentally the necessary conditions were established by adding titrant initially a t a rapid rate, and then a t successively slower rates until no improvement in the titration curve was found. Although adiabatic conditions were approximated, measurable heat transfer between the contents of the Dewar flask and the surroundings occurred. This gain in heat increased the total solvent volume which, in turn, decreased the concentration of the solute, thus producing a temperature rise. This decrease in the freezing point depression was used to determine the rate of heat exchange. A solution (approximately 0.5M) of either sodium chloride in water or naphthalene in benzene was introduced into the two-phase mixture and the slope of the temperature-time curve measured. A known volume of chilled liquid phase was then added, the temperature increase determined, and the rate of melting calculated. Heat gain into the Dewar occurred a t a rate of approximately 5 cal. per minute when the
Curve BI 7
6
6
Minutes from beglnning o f titratlon IO
I5
IS
II
14
I6
1
I
4
I
a
I
6
Curve A:
Figure 1.
I
IO
I
12
I
I
14
I6
I I6
1
20
.
Minutes from beginning of titration
Typical aqueous titration curves
A.
Titration of 1 .OO mmoie of acetic acid and 1 .OO mmoie of hydrochloric acid with J.OOM NaOH. Titrant added at a rate of 0.0244 ml./minute. Point I is the equivalence point for HCi; point II is the equivalence point for acetic acid. E. Precipitation titration of 2.50 mmoles AgNO3 with 5.00M NaCI. Titrant added at o rate of 0.0487 ml./minute. Point 111 is the equivalence point for AgNOa.
buret tip was not inserted, and approximately 9 cal. per minute when the buret tip was submerged in the liquid phase. To determine the origin of this heat gain, a similar experiment was carried out with the Dewar flask immersed in an ice-water bath for 5 minutes previous to the addition of the solute. Under these conditions heat transfer was decreased by 40%. However, in the experimcnts reported below this refinement was unnecessary because, in all cases, the amount of solid phase present wm enough to allow a t least 30 minutes before the solid phase melted completely, more than sufficient time to complete a titration. Aqueous Titrations. To test the applicability and limitations of this method, the first experiments performed were studies of model aqueous reactions. All the data obtained are shown in Table I. I n each case 5.OM titrant was added to the Dewar flask containing approximately 2.5 mmoles of
Table 1.
solute in approximately 40 ml. of liquid phase. Figure 1 (curve A ) illustrates a typical titration of an equimolar mixture of hydrochloric acid and acetic acid with sodium hydroxide and an attempt has been made to reproduce the actual titration curves by tracing. The equivalence points are clearly defined by the intersection of two straight lines drawn through that portion of the curve immediately before and after the change of slope. The ratio of the slopes of the straight-line portions (after correcting for dilution) and the ratio of the values of the temperature changes are 0 :1:2 as predicted by theory. The second equivalence point (that of acetic acid) is slightly rounded but still clearly defined. Following this last slope change, the equilibrium freezing temperature decreases as more titrant is added. The rate of this temperature decrease depends upon the volume of the liquid phase and the rate at which the
Aqueous Cryoscopic Titrations
Buret rateb 0.09748 0.04874
Solute taken, mmolesc
Solute Titrant" HCld NaOH 2.500 HCld NaOH 2.500 HOAcd NaOH 0.02440 2.500 HOAcds NaOH 0.04874 0.998 HCl 1.000 HOAcd.6 NaOH 0.02440 0.998 HCl 1.000 AgNOad NaCl 0.04874 2.500 Titrant concentration = 5 M . Titrant delivery rate in milliliters per minute. Average volume of liquid phase = 35 =k 5 ml. Average result of three determinations. * Mixture of acetic and hydrochloric acids.
Precision,
%
Accuracy, %
1.5 0.2
-0.25 -1.2
1.1
0.4 -0.9
0.5 0.6
0.8
1.0
1.0
0.6 0.1
0.5 0.2
0
VOL 38, NO. 6, MAY 1966
689
!
! 0
100
I
200
300
Y. TITRATED
Figure 2. Cryoscopic titrations in benzene. Titration of DMBA, DBA, and DDA with trichloroacetic acid
Figure 3. Cryoscopic titrations in benzene. DMBA, piperidine, and DDA with acetic acid
Normalized curves are plotted CIS a function of i (described in text) VI. per cent titrated (to the HX-B equivalence p3int). A. The slope which would b e found in the DDA titration if no further reaction occurred upon addition of acid after the equivalence point. Initial freezing point lowering, (caused b y oddition of the three amines) were: DMBA, 0.1 17' C.; DBA, 0.1 3 0 ' C.; DDA, 0.1 13' C. m of equation 3 a t equivalence point: DMBA, m = 1.4; DBA, in = 2.3; DDA m N 3 0
Normalized curves are plotted as a function of i VI. per cent titrated (to the HX-B equivalence point). Initial freezing point lowerings (caused b y addition of the amine to the two-phase mixture): DMBA, 0.1 81 ' C.; piperidine, 0.1 24' C.; DDA, 0.1 3 8 ' C. Acetic acid (4.32M) added at a rate of 0.0244 ml./minute. m of equation 3 at equivalence point: DMBA, m = 1.1 ; piperidine, m = 5.3; DDA, m N 30.
titrant is added. For this particular titration in Figure 1, the titrant was added a t a rate of 0.122 mmoles per minute (0.0244 ml. per minute). The rate of temperature decrease is 0.00775 degree per minute, indicating that the terminal volume (Kf= 1.86) was approximately 55 ml. (25 ml. of water initially, 5 ml. of HC1, 5 ml. of acetic acid, 1 ml. of NaOH added as titrant, and 19 grams of ice melted from the various heat gains which occurred principally before the start of the titration). The second curve shown in Figure 1 is that obtained from a precipitation titration. The experiment involved adding 5.00M sodium chloride to the Dewar flask which contained 2.5 mmoles of silver nitrate in the ice-water mixture. Again, the equivalence point is clearly defined. The slight, rapid increase in freezing point lowering found immediately after the equivalence point was a reproducible phenomenon. However the end point defined by the intersection of the two lines on either side of the point of inflection corresponded within usual experimental error with the equivalence point. The slope of the portion of the curve past the end point (corrected for dilution) is 0.1254 mv. per minute which is equivalent to 0.0214' C. per minute. Since NaCl is being added a t a rate of 0.244 mmoles per minute the terminal volume of the liquid phase is approximately 42 ml. The experimental freezing lowering correlated well with that predicted from usual cryoscopic considerations in all the aqueous titrations studied. Several experiments were conducted 690
e
ANALYTICAL CHEMISTRY
in concentrated salt solutions to simulate behavior which might be observed in solutions containing extraneous electrolytes or required buffers. The medium used in these experiments was either a 0.1 or 1.OM potassium chloride solution. The freezing point of these salt solutions increased measurably during the time required for a titration; this temperature increase is caused by dilution from ice melting as heat is gained from the surroundings. However, a titration of hydrochloric acid (with 5.0M NaOH) in 1.OM KCl gave a clearly discernible end point which coincided with the equivalence point within the experimental error. Thus, it appears feasible to conduct cryoscopic titrations in solutions containing a significant concentration of other solutes. In all the aqueous titrations, the precision and accuracy were better than 1% and were limited by the ability to read the recorder time axis. Benzene Titrations. Benzene was the second solvent investigated. This solvent was selected since it has a convenient freezing point and a recent study had been conducted in this laboratory which provided information about acid-base reactions in benzene. This earlier differential vapor pressure study was conducted a t 25' and 40' C. and showed that acid-base adducts were significantly associated in benzene and that this association was quite temperature dependent. Therefore it was of interest to examine such reactions at a considerably lower temperature using the cryoscopic technique. In addition a simple, practical endpoint detection technique for acid-base
Titration of
titrations in this solvent would be of considerable importance. To interpret the titrations described below, the extent of association of the pure solutions of acids and bases had to be estimated. Freezing point depressions of the base solutions indicated that the bases were essentially monomeric in this solvent at 5.5' C. (Base concentrations were approximately 0.02°M.) Carboxylic acids were extensively dimerized. Estimation of the equilibrium constant, K , for the reaction
(RCO0H)Z
~
2 RCOOH
(1)
were obtained by monitoring the temperature change as concentrated acid was added with the motorized buret to the two-phase benzene mixture in the Dewar flask. (The slope of the temperature vs. time curve was corrected for dilution effects.) The volume of the liquid phase was determined both before and after the addition of acid and the volume used to determine the equilibrium constant ( K in Equation 1) was that a t the midpoint of the acid addition curve. (The volume was measured by noting the temperature change caused by adding 1 mmole of naphthalene.) The value for K (Equation l) for TCAA thus determined was 7 . 0 X lop3 while that for HOAc was 1.9 X Examination of the literature indicated no previously determined values for these two constants a t the freezing point of benzene. A previous cryoscopic study (3) in p-chlorotoluene (m.p. = 6.9' C.) of the dimerization of mono-, di-, and trichloroacetic acid found each acid to be completely di-
L
X
TITRATED
Usually the second ion-aggregate is less associated than the first-Le., the value of n is less than that of m. Further addition of acid, past that point where two equivalents of acid per equivalent of base have been added, results in a slope slightly less than that corresponding to excess unreacted dimerized acid. This lower value of the slope indicates the formation of acid-base adducts with a stoichiometry B . 3HX. Figure 2 is a composite graph showing the titration of three representative bases, dodecylamine (DD-4) , dibenzylamine (DBA), and N,X-dimethplbenzylamine (DMBA) , with trichloroacetic acid. Figure 3 summarizes the titration of a primary, a secondary, and a tertiary amine with acetic acid. In both these figures, especially with the primary amines, there is evidence for a species with stoichiometry of B2"X when the base is in excess-Le., in the initial part of the titration. In each case, a clearly discernible change of slope a t the BH+X- equivalence point is evident. The primary amine-acid adduct is the most strongly associated while the tertiary amine-acid adduct is the least strongly associated. The curves are similar in shape to those found vvhen the differential vapor pressure technique is used ( 4 ) , but differ significantly in the greater extent of association a t this lower temperature.
I
I BOTH BASES 1
Figure 4. Cryoscopic titration of a mixture of DDA and DMBA in benzene with TCAA l e f t side of curve shows freezing point lowering caused by addition of two amines to two-phose mixture. 0.595 mmoles of DDA and 1.064 mmoles of DMBA titrated with 5.096M TCAA
merized-Le., the value of K was so small to be unmeasurable. A comparison of the benzene data with the p-chlorotoluene data indicates interaction between the pi electrons in benzene and the monomeric acid species; this interaction serves to stabilize the monomeric species. The basicity of benzene is also illustrated by the high solubilities of Lewis acids, like SnCl,, in this solvent. Also, unpublished differential vapor pressure work done in this laboratory has shown that, at 25" C., complete dimerization of these carboxylic acids occurs in n-hexane where monomer-solvent stabilization Kould be minimal. The relative magnitude of the equilibrium constants for TCAA and HOAc (Reaction 1) is in agreement with observations of Barton and Kraus (2) who noted the strongest acid in water is the least associated in the nonaqueous solvent. Table I1 summarizes the data obtained in benzene. In each titration studied, a clearly defined change in slope occurred when equivalent amounts of acid (HX) had been added to base (B) in the Dewar flask. The products of the acid-base reaction can be elucidated from Figures 2 and 3. The curves in these figures are plotted as a function of i us. per cent titrated (to the BH+Xend point). We define the value of i as the freezing point lowering found for base B (at a concentration of 2 moles per liter) divided by the freezing point lowering found for naphthalene a t an identical concentration (4). The initial reaction that occurs upon addition of acid to the two-phase mixture containing the amine can be written as (4): B
+ H X e BH+X-
base reacts with the monomeric acid species.) This acid-base adduct is highly associated : BH+X+
=
'/,,, (RH+X-),
(3)
The value of rn is given under Figures 2 and 3 for each titration. If no further reaction occurs beyond the BH+Xequivalence point, the freezing temperature us. time curve will have a slope corresponding to the addition of dimerized acid. This, however, is not the case as the data show that a second molecule of acid adds to the BH+X- adduct:
Table II.
Cryoscopic Titrations of Acids and Amine Bases in the Solvent Benzene
Amine Benzyl Dodecyl Dodecyl
Acid TFAA TFAA TCAA
Hexyl Benzyl
TCAA TCAA
Cyclohexyl
TCAA
Piperidine Dibenzyl N ,N-dimethylbenzyl
TCAA TCAA TCAA HOAc HOAc HOAc HOAc TCAA
Dodecyl and N,N-Dimethylbenzyld
TCAA
(M) 4.95b 4.95b 2.9P 2.95b 5.10b 5.10" 2.95* 2.95b 2.95c 2.95b 2.95c 5.1OC 5.1OC 2.95b 2.95" 4.32< 4.32c 4.32" 4.32O 5.1OC
Solute taken, mmoles@
1.10 1.49 0.497 0.994 1.19 ~. 1.19 0.953 1.10 1.10 0.939 0.939 0.962 1.00 1.06 1.05 1.21 0.953 0.962 1.05 0.595 0.501 (total) 1,096 ~ 5 . 1 0 ~ 0.595 1,045 (total) 1.640 ~
a
Average volume of liquid phase
d
Buret delivery rate of 0.02440 ml. of titrant per minute. Mixture of two bases.
= 40
Precision,
Accuracy,
0.7 1.0 -
-0.9 2.6 1.3 -0.7 0 -2.2 +0.7 -0.9 0 -1.6 -0.6 -1.4 0 -0.9 -0.7 -0.3 -0.7 0.5 0
70
1.0 0.4
-
0.7 0.1
-
1.o 1.o 1.3
-
4.4 3.0 0.7
76
-
-1.3 -5.2 3.9
0.5
5 ml.
* Buret delivery rate of 0.04874 ml. of titrant per minute,
(2)
(We arbitrarily assume here that the VOL. 38, NO. 6, MAY 1 9 6 6
8
691
Several years ago Copenhafer and Kraus (6) studied the association of ionic compounds (tetrasubstituted ammonium halides) in benzene with a cryoscopic technique. They concluded that the association of such species is governed by both the dipole moment of the ion pair and by the size and symmetry of the ions. The present work suggests that similar conclusions are valid for ion pairs formed from these proton acid-amine base adducts. The value for m found by these earlier workers was as high as 21 for the systems then under investigation. As in that study, the highly associated ionic aggregates showed no evidence of precipitation. As noted earlier (4) the degree of association is clearly influenced by acid and base strength-i.e., the stronger acid, TCAA, forms an ion pair with N,N-dimethylbenzylamine which is considerably more associated than that formed by HOAc with the same base. (For TCAA, m has a value of approximately 1.5 while for HOAc, m is approximately 1.) The geometry of the acid-base adduct is also a factor as is evidenced by considerably more association of the cyclic secondary amine, piperidine, with HOAc than with another secondary amine, dibenzylamine, and TCAA. Figure 4 illustrates a titration curve for the reaction of TCAA with a mixture of two bases, dodecylamine, a primary amine, and N,N-dimethylbenzylamine, a tertiary amine. The curve is plotted as a function of millivolt recorder deflection (from that recorder reading
taken before the solutes were added)
us. per cent titrated (to the composite B-HX end point). The freezing point lowering caused by addition of 0.595 moles of dodecylamine followed by the addition of 1.06 mmoles of N,Ndimethylbenzylamine is shown on the left side of the figure. The first point of inflection (dotted lines) corresponds to the equivalence point of the primary amine, DDA, and, as in the titration of this amine alone with TCAA, the adduct is very highly associated with a value of m of approximately 25. Upon further addition of acid, the tertiary amine reacts. As a practical matter only the sum of the total amount of both bases can be determined accurately. Because of the complicated equilibria occurring in these benzene solutions, and the resulting nonlinear titration curves, the accuracy of the cryoscopic method in benzene is not as good as that found for the model aqueous systemsLe., the accuracy is about 1 or 2%.
CONCLUSIONS
The method of cryoscopic titrations can detect the end point for any reaction which has a net change in the rate of production of solute particles before and after the end point. Potential analytical applications include the study of reactions where the customary electrometric, optical, and indicator techniques fail. Supercooling phenomena do not interfere, since the solid solvent phase is always present; the
possibility of solid solution formation is minimal since the total change in the amount of solid-solvent phase during a titration is small. Useful, quantitative information can be obtained from the experimental titration curves which help elucidate the chemical species present during the titration; these curves are interpreted in a way similar to differential vapor pressure data (4). The cryoscopic method complements the differential vapor pressure method in those cases where precipitation occurs or volatile solutes are involved. ACKNOWLEDGMENT
We thank Mr. James Landmark for performing the aqueous titrations. LITERATURE CITED
(1) Allen, G., Caldin, E. F., Trans. Faraday SOC.49, 895 (1953). (2) Barton, B. C., Kraus, C. A., J . Am. Chem. SOC. 73, 4557 (1951). (3) Bell, R. P., J . Chem. SOC.1934, p. 1969. (4) Bruckenstein, S., Saito, A., J . Am. Chem. SOC.87, 698 (1965). (5) Coetzee, J. F., Lok, R. M., J . Phys. Chem. 69, 2690 (1965). (6) Copenhafer, D. T., Kraus, C. A., J . Am. Chem. SOC.73,4557 (1951). (7) Mukherjee, L. M., Bruckenstein, S., Badawi, F. A. K., J . Phys. Chem. 69, 2537 (1965). (8) Wolf, K. L., Metzger, G., Ann. Chem. 563, 157 (1949).
RECEIVED for review January 21, 1966. Accepted March 4, 1966. Work supported by the National Science Foundation.
Further Study of the Iodide-Iodine Couple at Platinum Electrodes by Thin Layer Electrochemistry ARTHUR T. HUBBARD, ROBERT A. OSTERYOUNG,' and FRED C. ANSON Gates and Crellin laboratories of Chemisfry, California lnstifute of Technology, Pasadena, Calif. Thin layer electrochemical experiments were employed to study the adsorption of iodide and iodine a t platinum electrodes. About 2 X mo1e/cm.2 of iodide ion or 2 X l o w g mole/cm.2 of iodine were shown to b e adsorbed in a nonelectroactive state. An additional 1 X 10-9 mole/cm.2 of iodine, but no iodide, is adsorbed in an electroactive state. Some implications of these results on the mechanism of the iodide-iodine electrode reaction are discussed.
I
a recent series of papers (9, 10, 11) the electrochemical behavior of iodine and iodide ion a t platinum electrodes has been treated in some detail. Extensive adsorption of both iodide and N
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ANALYTICAL CHEMISTRY
iodine was shown to occur and it was demonstrated that although the adsorbed iodine is electroactive-Le., can be reduced near the reversible iodideiodine potential-the adsorbed iodide ion was not. Among the data presented (10) wasa brief set of experiments involving the technique of chronopotentiometry in thin layers of solution ( 4 , 5 ) . The simplicity of this experimental technique coupled with its considerable elucidative powers, especially for studies involving adsorbed reactants, prompted us to perform the additional experiments described in this paper. These experiments led to the discovery of considerable amounts of previously undetected nonelectroactive iodine adsorbed on platinum electrodes.
EXPERIMENTAL
The theory, practice, and circuitry of thin layer chronopotentiometry have been described (4, 5 , 6). For several of the experiments constant-potential, instead of constantcurrent electrolysis, was employed. In these cases the integral of the current was obtained by means of solid-state operational amplifiers (Geo. Philbrick Researches, Inc., Type P-65 and P-75) and the charge-time variations were recorded. The constant-potential experiments have two advantages: a blank is readily obtained and there is no arbitrariness about how to measure 1 Permanent address: North American Aviation Science Center, Thousand Oaks, Calif.
