Non-Adiabatic Thermometric Titrations Involving Operational Amplifier Compensation of Exchanged Heat Masaki Nakanishi and Shuko Fujieda Department of Chemistry, Ochanomizu University, Bunkyo-ku, T o k y o , Japan
An improved technique of thermometric titration is described, in which heat is allowed to be exchanged freely between the reaction vessel and the environment and the temperature change observed is treated with an adequate analog computation circuit using an operational amplifier. The temperature vs. titrant volume curve thus formed was such as could be obtained in a perfectly adiabatic process. In practice, thermal equilibrium was established more quickly and the temperature change was more reproducible than in ordinary adiabatic processes. Calculation of the heat effect, as well as location of the end point, could be easily performed with precision. The method was applied to titrations of hydrochloric acid and of phenol with sodium hydroxide. The AHO values were estimated to be -13.46 & 0.06 kcal/mole for hydrochloric acid and -7.80 f 0.10 kcal/mole for phenol at the infinite dilution.
THERMOMETRIC TITRATIONS have so far been carried out in an adiabatic or a quasi-adiabatic fashion (1-3). In such processes, however, a considerably long wait is usually required for the establishment of thermal equilibrium before starting titration and the perfectly adiabatic condition can hardly be maintained throughout the entire course of titration. Sometimes the temperature difference, even if it is slight, between the titrant and the solution being titrated is also a source of problems. These difficulties are more serious when quantitative tracing of the temperature change is needed in addition to locating the end point of titration. This paper describes a non-adiabatic type of thermometric titration in which heat is allowed to be exchanged freely between the reaction vessel, as well as a reference vessel, and the environment and then the temperature difference between the two vessels is fed to an operational amplifier circuit to obtain an idealized adiabatic type of titration curve. In principle, the non-adiabatic titration equipment used in this work essentially resembles the simple twin calorimeter described by Borchardt and Daniels (4) and also by Lueck, Beste, and Hall (5) in their investigations of reaction kinetics, though the present one is the more improved version. Thus, a pair of glass vessels, one serving as a reaction calorimeter and the other as a reference calorimeter, together with the tubing through which titrant was delivered, were simply immersed in a bath of water to assure free exchange of heat between the vessels and the environment. Since in this process the temperature of the titrand as well as the titrant could be equilibrated with that of the surrounding water in a shorter time than in an adiabatic process, thermal equilibrium in the whole system could be reached much more quickly before the start of titration. (1) J. Jordan, J. Chem. Educ., 40, A5 (1963). (2) H. J. V. Tyrrell and A. E. Beezer, “Thermometric Titrimetry,” Chapman and Hall, Ltd., London, 1968. (3) L. S. Bark and S. M. Bark, “Thermometric Titrimetry,” Pergamon Press, Oxford, 1969. (4) H. J. Borchardt and F. Daniels, J . Amcr. Chem. SOC., 79, 41 (1957). ( 5 ) C. H. Lueck, L. F. Beste, and H. K. Hall, Jr., J. Phys. Chem., 67, 972 (1963). 574
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
For the same reason, the temperature change, as a result of chemical reaction during titration, was of a lesser extent than in an adiabatic process. Thus, the slower the titration proceeded, the more the temperature difference between the solution and the titrant could be reduced. Therefore, the thermal equilibrium in the whole system was more closely approximated throughout the course of titration. Although the temperature difference changed in a very stable and reproducible way so long as the titrant was added at a sufficiently low speed, the curve showing the temperature difference as a function of titrant volume added could not be readily analyzed in a graphical manner. In some cases, the end point could not even be located directly on the curve. However, this difficulty was overcome by introducing the analog computation technique. Thus, the temperature difference actually measured in this non-adiabatic process was treated by an adequate operational amplifier circuit to convert it into the temperature change which could be expected if the process was carried out in a perfectly adiabatic condition. The titration curve finally obtained by the operational amplifier circuitry consisted of three intersecting straight lines in most types of chemical reactions which should appear in a perfectly adiabatic thermometric titration and be readily interpreted. The proposed method was applied to titrations of hydrochloric acid and phenol with sodium hydroxide to illustrate the accuracy and precision of the method. GENERAL CONSIDERATIONS
It was assumed throughout this work that the mixing of titrant was instantaneous and that the temperatures were uniform in each of the glass vessels and in the surrounding water. Since the concentration of titrant was high enough, the increase in volume of the solution being titrated was ignored for the sake of simplicity. When heat is evolved in the reaction vessel at the rate q which is expressed, for example, in calories per sec, the actual temperature, Ts, in degree centigrade of the sample solution in the vessel can be expressed by the equation, dTs/dt
=
q/W
- a(Ts - Tw)
(1)
where t is time in sec, W is the effective heat capacity in calories per degree centigrade, LY is a constant in reciprocal time related to the heat transfer, and Tmis the temperature of the surrounding water which need not be constant but may vary with time. The variation of temperature, e,, of the sample solution indicated by the temperature sensing device, in this case by a thermistor, can be expressed as follows: where p, in reciprocal time, is a constant related to the delay of response. Integrating Equation 1 followed by substitution of Equation 2 gives the expression,
where T,, and Os, are the actual and the indicated temperatures, respectively, at t = 0 of the sample solution in the vessel. Similar relations are valid for the reference solution in 0 by definition. Thus, which q = I
dTr/dt = -a(Tr - Tw)
(4)
dO,/dt = P(Tr - 8,)
(5)
t
to
TIME
where T, and 8, stand for the actual and the indicated temperatures, respectively, of the reference solution. Equations 4 and 5 are combined to give the expression,
where T,, and e,, are the actual and the indicated temperatures, respectively, at t = 0 of the reference solution. These relations are valid for q and Twwhich vary with time. If T,, and Os, can be made equal to T,, and Or*, respectively, and the difference of 8, from 8, is designated as 8, the following equation results by subtracting Equation 6 from Equation 3,
Figure 1. Variation of temperature as a function of time for constant q and T, A. (l/W).f'qdt, B. T,, C. 0,
CI
Figure 2. Analog computation circuit for (l/W).f'qdt in Equation 7
(7) The left side of Equation 7 is equal to the temperature change of the sample solution which could be expected when no transfer of heat occurs to and from the solution, or in other words when the process is carried out in a perfectly adiabatic condition. This quantity can be calculated from the observed value 8 in accordance with Equation 7. The analog computation technique was employed for the on-line calculation. Figure 1 shows three different temperatures, T,, e,, and (l/W)Sqdt, as functions of time when heat is evolved in the period to to te at a constant rate either by titration involving a constant delivery rate of titrant or by electrical heating using a constant current through a resistor. The curves are arranged with their initial temperature on the same level. They are graphical presentation of solutions of Equations 1 and 2, when a constant value of Twis assumed. Discrepancy between the curves for T, and 0, is somewhat exaggerated for the purpose of illustration. Under the conditions given, variation of 8 is parallel to that of e,, so that the curve C in Figure 1 also shows the variation of 8 when the initial value is zero. In the operational amplifier circuit shown in Figure 2, the output voltage, E,, is expressed by a function of the input voltage, Et, as follows: E,
=
-
"{ -
Ri
R1Cl dEi - f dt
If, in Equations 7 and 8, Ei
=
k'8
(9)
the following relation is valid, k E, = - - f q d t W
where k = (R2/Rl)k'. Therefore, if a voltage which is proportional to the experimentally obtained value 8 is applied as Et to the input of the operational amplifier circuit and the time constants of the parallel combination of R1and C1and the series combination of RZand C2are adequately selected so as to be reciprocally equal to P and a, respectively, of the titration apparatus, the output of the amplifier varies in accordance with Equation 12, giving the calculated change of temperature of the solution being titrated which should be expected if the perfectly adiabatic process was followed throughout the course of titration. EXPERIMENTAL
Reagents and Apparatus. AI1 reagents used were of reagent grade, and deionized water which was boiled immediately before use to expel dissolved carbon dioxide was used for preparing solutions, Hydrochloric acid solutions were standardized by the iodometric method using a thiosulfate solution which was standardized against a weighed amount of purified potassium iodate. The concentration of sodium hydroxide solutions was determined by carefully titrating with the hydrochloric acid solutions using phenolphthalein as indicator. The concentration of phenol solutions was determined by the usual bromate-bromide method. ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
575
Figure 3. Reaction vessel (1) Rubber stopper, (2) Buret tip, (3) Thermistor, (4) Heater, (5) Ground glass joint, (6) Sample solution, (7) Magnetic stirrer, ( A ) To Wheatstone bridge, ( B ) To power source, (c)To buret
Titrations took place in a 100-ml glass vessel shown in Figure 3. Holes were drilled in the rubber stopper to accommodate a buret tip, a thermistor, a heater element, and an empty tubing (not shown in the figure) to release pressure if any. The buret tip was a capillary which was connected by Teflon (Du Pont) tubing with a Metrohm piston buret, Model E274. By combining the buret with a gear arrangement and a synchronous motor, the buret could be operated at a constant delivery rate selected from 2,4, and 6 min/ml. This buret was also provided with output terminals to record the position of the piston. The thermistor (TOA Electronics, Tokyo, 6PA) had an approximate resistance of 2500 ohms at 25 OC; a temperature coefficient, -2.59x/deg and a nominal time constant, 0.3 sec in water. The heater element was a l/r-watt carbon resistor, of which the body and the leads were coated with epoxy resin and fixed at the end of a glass stem. In most cases a 100-ohm resistor was used, but the value of resistance was not critical. This element was heated by a current supplied from a regulated dc power source (Metronix Corp., Tokyo, Model 543). The energy dissipated by the electrical heating was calculated as usual with a high-wattage reference resistor in series with the heater, a digital voltmeter (Takeda Riken Industry Co., Tokyo, Model -TR-6834), and an electric stop clock (Japan Servo Co., Tokyo). Another glass vessel of identical configuration equipped with the same attachments except the buret tip was used as reference. Both vessels were immersed in a large bath of water. Each of the solutions inside them was stirred with a rod which was operated magnetically by a motor placed outside the bath, while the bath water was vigorously stirred with a motor-driven agitator. The bath was covered on all sides with 2-cm thick Styrofoam boards. The two thermistors, one in the sample solution and the other in the reference solution, were incorporated in two arms of a Wheatstone bridge, and the unbalanced voltage of the bridge was fed into a preamplifier (TOA Electronics, Model PM 17A). The output voltage was treated by an operational amplifier (Philbrick/Nexus Research, SA-3a) circuit in the configuration shown in Figure 2. Variable resistors were incorporated in the resistances R1 and RZ so that the time constants could be adjusted to be equal to the reciprocals of CY and p, as Equations 10 and 11 postulate. The capacitor C2was a 100-pF tantalum electrolytic capacitor 576
of the etched type (Nippon Chemical Condenser Co., Model TFK 15-100BP). The output of the operational amplifier was recorded either with a potentiometric recorder (TOA Electronics, Model EPR-3T) or an X-Y recorder (Riken Denshi Co., Model F3B). Procedure. A 50-ml aqueous solution containing the substance to be titrated was placed in the reaction vessel, The front of the titrant in the buret tip was withdrawn from the tip end by operating the buret, so that an empty space was left ahead of the titrant front. The reaction vessel with all its attachments was immersed and fixed in the water bath. Another vessel containing 50 ml of water as reference was placed side by side in the same bath. The temperature of the water was adjusted approximately to within 0.2 "C of the desired temperature and the bath was covered with Styrofoam boards. Magnetic stirrers and the mechanical stirrer were started to agitate the solutions in the vessels and the surrounding water. The temperature of the water was then brought to within 0.1 "C of the desired temperature either with a low-wattage heater or by adding a small amount of ice water. Usually stirring for not more than 10 minutes sufficed before thermal equilibrium, or balancing of the bridge, was established. When equilibrium was reached, the output voltage of the bridge was brought to null by adjusting the zero adjuster voltage and the capacitor CZ in the feed-back circuit was discharged by being short-circuited for a moment. An arbitrary quantity of heat was evolved in the reaction vessel by electrical heating, while the output voltage of the operational amplifier was being recorded as a function of time. If the plot on the recorder chart was not straight and parallel to the time axis after the current was switched off, the value of resistance RZwas changed. This was repeated until a linear plot was obtained in the final period. In this way, the experimental constant CY could be reciprocally reproduced by the time constant RsCZ. If roundings of the plot occurred at the start and especially at the termination of heating, the resistance R1 was varied so that sharp breaks of the thermogram resulted, and the entire thermogram was composed of three intersecting straight lines similar to those which appear as titration curves in an ordinary adiabatic type of thermometric titrations. After the resistances R1 and R2 were set to appropriate values, a known quantity of heat was produced for the purpose of calibration, while the output voltage was being recorded. The thermal energy produced should amount to the approximate heat which was expected in the actual titration. When thermal equilibrium was attained again, perhaps in several minutes, a small unbalanced voltage of the bridge, if any, was compensated by the zero adjuster voltage so that a zero input was applied to the preamplifier before and at the start of titration. The condenser CSwas short-circuited to discharge. Then the automatic buret was started while the output of the operational amplifier was being recorded as a function of time or the titrant volume. Another thermogram was prepared for calibration using electrical heating. Finally, determination of the substance titrated and estimation of the heat of reaction involved were performed in the usual way.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
RESULTS AND DISCUSSION
For the sake of simplicity, the following discussion refers to exothermic reactions unless otherwise stated. The advantages of free exchange of heat between the reacting solution and the environment involved in the proposed technique were fourfold. (a) Thermal equilibrium or balancing of the Wheatstone bridge before the start of titration could be established so rapidly that it usually took less
than 10 minutes depending on circumstances. (b) The temperature change of the solutions followed the Newtonian behavior expressed by Equations 1 and 4 so strictly that the whole thermal phenomena could be treated by the mathematical manner. (c) Since there occurred less accumulation of heat in the reaction vessel than in an adiabatic process, the temperature rose far less during the course of titration. This effect became the more significant for the slower rate and the larger total amount of heat evolution. For example, when heat was evolved in neutralization titrations at the rate 0.135 cal/sec for 15, 75, and 160 sec, the actual temperature rises in the reaction vessel approximately amounted to O.Ql, 0.03, and 0.05 "C, respectively, while the same heatings would have resulted in an adiabatic process in the approximate temperature rises 0.04, 0.2, and 0.4 "C, respectively. In addition, the heat loss through wires which is probable in an adiabatic process could also be reduced markedly. (d) The temperature difference between the titrant and the solution being titrated, which caused difficulty in an adiabatic process as pointed out by Christensen and Izatt (6), could be reduced to a lesser extent as far as the heat was evolved at a sufficiently low rate. In making the time constants, RICl and R2C2, equal to the reciprocals of experimental constants, /3 and a,respectively, the numerical values of the latter could be estimated by a mathematical treatment of the curve (in the shape of Curve C in Figure l), but a trial-and-error method as described above is preferred. As is evident from Equation 8, the time constant R2C2, of which the reciprocal is the coefficient of the integral term, is the most dominant factor to decide the slope of titration curve (or thermogram) after the heat evolution is completed. Figure 4 shows how the time constant affects the thermogram. Curves in Figure 4 were produced for three different values of the time constant when approximately the same quantity of heat was evolved by electrical heating at a constant rate and the time constant RIClwas kept at the correct value which is exactly reciprocal to p as postulated in Equation 10. Curve 11, a perfect adiabatic type curve, was obtained at a time constant R G of 57 sec, while Curves I and I11 were produced for the larger and the smaller time constants, respectively. In conclusion, the correct value of the time conZ be attained when a linear final period plot stant R ~ C could was obtained. This could be performed precisely within 0.5 %. Likewise, the portion of the thermogram where heat is being evolved is a straight line for the correct value of R2C2, while it is upward convex and upward concave in accordance with the larger and the smaller values of the time constant, respectively, as is readily anticipated from Equation 8. On the other hand, the constant p is primarily concerned with those portions of a thermogram which are related to sudden change of temperature or, in other words, to the close vicinity of the starting and the end points of heat evolution. Thermograms obtained on a recorder chart for three different values of RICI are shown in Figure 5, where heat was evolved by electrical heating in the same manner as in Figure 4 and the time constant RzC2was kept at the correct value. Curve I1 was obtained when the time constant RICl was adjusted to the correct value, while Curves I and 111 obtained for a larger and a smaller time constant, respectively, were different in appearance from Curve JI, particularly at the end point of heat evolution. The correct value of the time (6) J. J. Christensen and R. M. Izatt, J. Phys. Chem., 66, 1030 (1962).
P-
TIME
Figure 4. Thermograms for different values of RzC2 (I) 70 sec, (11) 57 sec, (111) 40 sec. RICl: 3.6 sec
R&:
TIME
___)
Figure 5. Thermograms for different values of RlCl RICI:(I) 6.0 sec, (11) 3.6 sec, (111) 1.5 sec. R&:
57 sec
constant RICl could be determined by adjusting the resistance R1 so that the thermogram obtained for electrical heating assumed the shape of Curve 11. The time constant thus determined was precise to several per cent. Strictly speaking, heat evolved at the electrical heater is transferred rather slowly to the solution, while a chemical reaction liberates heat in the solution itself. Therefore, the time constant RICI determined using electrical heating does not necessarily apply to the constant 0 in the actual titration. However, the discrepancy may be ignored in most cases so long as heat is evolved at the sufficiently low rate. The constants a and /3 depend on the characteristics and geometry of the apparatus and the experimental conditions, so that whenever they are changed the time constants of the operational amplifier circuit should be checked for satisfactory agreement with a and p. The thermograms, or temperature us. time curves, described above involve a constant rate of heat evolution or absorption where q in Equation 1 is a constant, as is usually the case with most titrations. However, the principle of the present technique is not restricted to a constant value of q, but may be applied to any process in which q is variable with respect to time, as is evident from the mathematical considerations. Further, this technique can also be applied
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
577
Taken, mmole
Table I. Titration of Hydrochloric Acid with Sodium Hydroxide at 25.0 f 0.1 O C - A H . , kcalhole . Hydrochloric acid Standard Found, mmole Error, Mean deviation
1.6416 1.6400 1.6400 1.6396
1.644 1.642 1.646 1.644
0.1 0.1 0.4 0.2
13.40 13.39 13.42 13.40
13.40
0.01
0.18
0.8234 0.8223 0.8222 0.8219
0.824 0.829 0.824 0.824
0.1 0.8 0.2 0.2
13.37 13.47 13.43 13.43
13.43
0.04
0.13
0.1658 0.1654 0.1649 0.1647 0.1644
0.1668 0.1652 0.1650 0.1650 0.1641
0.6 -0.1 0.2 0.2 -0.2
13.50 13.37 13.45 13.42 13.42
13.43
0.05
0.06
to any kind of thermal phenomena other than titration, especially when perfectly adiabatic data as a function of time are required. The effective heat capacity, W in Equation 1, of the reaction vessel was supposed to be constant in the mathematical treatment of the phenomena. Actually it changed gradually in the course of titration owing to the increase of the liquid phase, though the increase was kept small by using a very concentrated solution as titrant. As could be presumed from Equation 7, the effect of increased W on the shape of titration curves could nearly, but not completely, be cancelled by the slight decrease of the CY value which also resulted from the increase in volume of the liquid phase. Therefore, the volume change exerted far less influence on the heat of reaction estimated by the present method than by ordinary calorimetric methods. The cell constant of the reaction vessel was measured for the purpose of calibration both before and after each titration run, the two values differing from each other, for example, by a few per cent as a result of the volume increase of 1 ml. From the two values the cell constant at the equivalence point was estimated and used to calculate the heat of reaction. It is desired, of course, that the two thermistors have the same temperature-resistance characteristics in the temperature range in which the titration is carried out. This requirement has been virtually satisfied in ordinary titration procedures by use of a selected pair of commercially available thermistors, so long as the temperature change remained within approximately 0.1 "C. The present method is more favored in this respect than ordinary adiabatic processes, since actual temperature changes are less in the former. The temperature of the surrounding water that chiefly determined the temperature of the whole system, varied for two reasons: one was the thermal effect inside the system such as, for example, evolution (absorption) of heat by the chemical change under consideration and the heat from the stirrers, and the other was the heat exchange with the environment. To minimize the temperature variation of the surrounding water, a large amount, usually 15 liters or more, of water was placed in the bath. Simply enclosing the bath with an insulating material such as Styrofoam remarkably improved the results, since a steady shift of the bath temperature, if any, revealed deviated characteristics of one thermistor from those of the other. In general, simple insulation of the bath, instead of hermetically isolating it from 578
Ccl/B
ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
the environment, was sufficient to maintain the temperature within 0.1 "C variation for a period of several minutes. For longer observation, however, a more elaborate equipment would be necessary to maintain the temperature within the limit. The heater element was a simplified version of that described previously (7). The epoxy resin coating over the surface of the resistor was satisfactorily chemically inactive as well as electrically insulating, so that the heater might be powered in a conductive solution which contained electrolytes. The element was kept immersed in the solution, so that the effective heat capacity of the vessel apparently remained the same throughout a run. Titration of Hydrochloric Acid. The present technique was applied to titrations of hydrochloric acid with sodium hydroxide in an aqueous solution at 25.0 f 0.1 "C, for which wellinvestigated literature values were available. Determination of the acid and estimation of the heat of reaction involved were carried out from a single titration curve in order to illustrate the accuracy and the precision of the present method. Figure 6 is a photographic reproduction of actual thermometric titration curves of hydrochloric acid (Curve A ) and phenol (Curve B ) with sodium hydroxide. The points b's and c's correspond to the starting and the equivalence points of titrations, respectively. The acid was determined from the horizontal distance between b and c of Curve A combined with the knowledge of the delivery rate of sodium hydroxide in moles per second, while the molar heat of reaction was obtained from the vertical distance between the lines ab and cd divided by the total quantity reacted in moles. Different quantities of hydrochloric acid were titrated and the results obtained are shown in Table I. The heat effect due to dilution could be corrected by the extrapolation method proposed by Jordan and Alleman (8), but this effect was usually very small. Quantities of hydrochloric acid taken were calculated from the weight of the sample solutions to reduce the error originating in the sampling procedure. In most runs, satisfactory results could be obtained and the relative errors that appear in the third column of Table I were generally very small, since errors in the order of a few tenths of 1 % are reasonably considered inevitable in the present method which involves graphical measurement.
(7) M. J. Stern, R. Withnell, and R. J. Raffa, ANAL.CHEM., 38, 1275 (1966). (8) J. Jordan and T. G. Alleman, ibid.,29,9 (1957).
R
I w
0
0.4
0.2
I-
oi a
Figure 8. Variation with ionic strength of the heat of neutralization of phenol with sodium hydroxide at 25.0 f 0.1 "C
b
TIME
Figure 6. Thermometric titration curves of ( A ) hydrochloric acid and ( B ) phenol with sodium hydroxide
Table 11. Titration of Phenol with Sodium Hydroxide at 25.0 =t= 0.1 "C Phenol Taken, Found, Error, -A,H(kcal/mole) ii a mmole mmole Z
,
1.0704 0.8028 0.7905 0.5356 0.2676 0.1070
0
0.2
01
P Figure 7. Variation with ionic strength of the heat of neutralization of hydrochloric acid with sodium hydroxide at 25.0 f 0.1 "C The heat of neutralization was evaluated for individual runs from the height above b of extrapolated line cd and the quantity of hydrochloric acid taken. In case of an unknown sample, the heat should of course be calculated using the found value instead of ,that taken. The A H values thus calculated are shown in the fourth column, of which the means for samples of similar quantities and the precision expressed in terms of standard deviation are in the fifth and the sixth columns, respectively. Plot of the mean values as a function of p l i Z ,where p is the ionic strength of the solution before and at the equivalence point, gives Figure 7. The heat of neutralization at the infinite dilution, A H " , is obtained by extrapolating the linear plot of A H us. p 1 ' 2 to p = 0. Considering the precision of each of the mean values, AH" is determined to be -13.46 f 0.06 kcal/mole or -56.32 f 0.25 kJ/mole at 25.0 f 0.1 "C, where f indicates the estimate of the maximum uncertainty. There exist two sets of values for the heat of neutralization of a strong acid with a strong base at the infinite dilution. In general, electrometric methods gave higher values ranging from - 13.48 to -13.52 kcal/mole (9-11), while calorimetric methods gave mostly lower values ranging from -13.31 to (9) D. H. Everett and W. F. K. Wynne-Jones, Trans. Faraday Soc., 35, 1380 (1939). (10) H. S. Harned and R. A. Robinson, ibid., 36, 973 (1940). (11) T. Ackermann, 2.Elektrochem., 62, 411 (1958).
1.074 0.802 0.787 0.539 0.267 0.1077
0.3 -0.1
-0.4 0.6 -0.2 0.7
7.64 7.52 mean 7.71) 7.62 7.55 7.78 7.88
0.23 0.14 0.40 0.082 0.052
- 13.38 kcal/mole (12, 13), except - 13.50 kcal/mole by Papee, Canady, and Laidler (14). The value, -13.46 kcal/mole, by the present method is much higher than those by most calorimetric methods, but is close to values by electrometric methods and also to that of Papee and others. The present method, though it is calorimetric, is quite different in nature from ordinary calorimetric methods, and does not substantially suffer from troubles due to loss of heat which is inherent to them. Further investigations along these lines are desired. Titration of Phenol. As is generally recognized, thermometric titrations are more advantageous in titrating weak acids with a strong base than other titration methods. Thus, moderately weak acids such as, for example, acetic could be titrated with more accuracy. For an extremely weak acid, however, a curvature appears on the titration curve at the equivalence point owing to the incomplete dissociation of the acid, as illustrated in detail by Tyrrell (15). The end point can be obtained as the intersection of two straight lines which are an extrapolation of the straight portions of the titration curve, as seen with Curve B in Figure 6. Phenol is so weak an acid that the pK, is about 10 and it is almost impossible to titrate phenol in an aqueous solution by conventional titration methods other than thermometric. Using Curve B, the end point c could be obtained as intersection of the two broken lines. In order to be accurate in locating the end point by extrapolating the straight portions of the titration curve, the curve (12) J. D. Hale, R. M. Izatt, and J. J. Christensen,J . Amer. Chem. SOC.,67, 2605 (1963). (13) C . E. Vanderzee and J. A. Swanson, ibid., p 2608. (14) H. M. Papee, W. J. Canady, and K. J. Laidler, Can. J . Chem., 34, 1677 (1956). (15) H. J. V. Tyrrell, Talanta, 14, 843 (1967). ANALYTICAL CHEMISTRY, VOL. 44, NO. 3, MARCH 1972
579
itself should exactly represent the stoichiometry of the reaction. It seemed this was accomplished by the present method and the curve could readily be smoothed so as to permit precise extrapolation. Table I1 shows results of titration of phenol with sodium hydroxide at 25.0 =k 0.1"C. The extremely weak acid, phenol, could be determined with sufficient accuracy, but errors in the third column are slightly larger than those in Table I in general, as phenol requires additional extrapolation procedure. The values of - A H in the fourth column are shown as a function of I.C"~ in Figure 8. Linear extrapolation of the plot of p = 0 gave the AH" value, -7.80 kcal/mole, for the neutralization reaction. The uncertainty in the value was approximately 10.10 kcal/mole. The heat of proton dissociation of phenol could be calculated from the AH" for the neutralization reactions with sodium hydroxide of hydrochloric acid and of phenol.
- (-13.46) = 5.66 kcal/mole. The estimated uncertainty in this value will be approximately of the order +0.15 kcal/mole. Previous data for the heat of proton dissociation of phenol obtained by calorimetric methods are found in the literature, that is 5.650 i. 0.100 (16), 5.7 (In, and 6.1 0.2 (18) kcal/mole. The present value agrees satisfactorily with the former two. From all these results, it may be concluded the titration curves produced by this technique offer useful and reliable information concerning the reaction involved. Thus, -7.80
*
RECEIVED for review May 14, 1971. Accepted November 4, 1971. (16) L. P. Fernandez and L. G. Hepler, J. Amer. Chem. Soc., 81, 1783 (1959). (17) R. M . Milburn, ibid., 89, 54 (1967). (18) A. G. Desai and R. M. Milburn, ibid., 91, 1958 (1969).
Unit Sheet Weights of Asphalt Fractions Determined by Structural Analysis Graeme A. Haley School of Highway Engineering, University of New South Wales, Box 1, P.O., Kensington, 2033, N.S. W . Australia Two asphalt short residues, one Kuwait and the other Arabian, were fractionated by gel permeation chromatography and the fractions obtained were examined by nuclear magnetic resonance and infrared spectrometry. Fraction mean molecular weight and elemental composition were also measured. The proportions of the different types of carbon linkage present were determined by the solution of a series of simultaneous equati.ons derived from the experimental data. A unit sheet weight calculated from the molecular structural analysis was found to be equivalent to the weight calculated by NMR, thus eliminating the estimation of values of the nonaromatic carbon to hydrogen ratio. The relative error was 7.6%.
APPLICATION OF GEL PERMEATION CHROMATOGRAPHY (GPC) to the separation of petroleum residues has enabled relatively narrow structural and molecular size fractions to be obtained for further analysis. The examination of these fractions by nuclear magnetic resonance (NMR) and infrared (IR) spectrometry and their characterization by vapor pressure osmometry (VPO) molecular weight measurements and elemental analysis, provides suitable information for the determination of asphalt unit sheet weights and the development of structural models. The association of individual unit sheet weights in the formation of asphalt molecules was proposed by Dickie and Yen ( I ) from X-ray and molecular weight measurements. Ramsey, McDonald, and Peterson ( 2 ) modified the NMR equations of Brown and Ladner (3) to obtain a value for the average unit sheet weight for a number of alumina column chromatography asphalt fractions. Their method was applied to a GPC fractionated asphalt by Dickson, Davis, and Wirkkala
( 4 ) and an attempt was made to correlate the unit sheet weight
with VPO molecular weights. The presence of a condensed naphthenic structure closely associated with the aromatic nucleus, as suggested by Dickie, Haller, and Yen (5) from electron microscopic investigations, justifies the use of lower values for the hydrogen to carbon ratio of the non-aromatic groups, x . A correlation between the VPO molecular weights and their respective unit sheet weights, for a GPC fractionated asphalt was found when lower values of x were tried (6). Later work by Dickson et al. (7) also suggested use of a lower x value. However, as the value for x varies for asphalts from different sources containing different amounts of naphthenic carbon, an alternate method requiring further analytical data, but giving a better indication of structural types present in the fractions, has been developed. Crude oil and asphaltic fractions are complicated by the multitude of individual components which are present even at low molecular weights. It becomes increasingly difficult to define and resolve the components into a particular structural formula as the molecular weight increases, and although individual formulas would give a more complete picture of the basic units, the use of mean structural types becomes more reasonable and necessary for the interpretation of the properties of the higher molecular weight mixtures. Vlugter, Waterman, and Van Westen (8, 9) investigating low molecular
(1) J. P. Dickie and T. F. Yen, ANAL.CHEM., 39, 1849 (1967). (2) T. W. Ramsey, F. R. McDonald, and J. C . Petersen, Znd. Eng. Chern., Prod. Res. Defielop., 6 , 231 (1967). (3) J. K. Brown and W. R. Ladner, Fuel, 39,87 (1960).
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(4) F. E. Dickson, B. E. Davis, and R. A . Wirkkala, ANAL.CHEM., 41, 1335 (1969). (5) J. P. Dickie, M. N. Haller, and T. F. Yen, J . Colloid Zizferface Sci., 29, 475 (1969). (6) G . A. Haley, ANAL.CHEM., 43, 371 (1971). (7) F. E. Dickson, R. A. Wirkkala, and B. E. Davis, Separ. Sci., 5 , 811 (1970). (8) J. C. Vlugter, H. I. Waterman, and H. A. Van Westen, J . Inst. Petrol. Techno/.,18,735 (1932). (9) Zbid., 21, 661 (1935).
