(14) "TTL Applications Handbook", Fairchild Semiconductor, Mountain View, Calif., 1973,p 9-23. (15) T. W. Rosanske and D. H. Evans, J. Electroanal. Chem., 72,277 (1976). (16) I. M. Kolthoff and J. F. Coetzee, J. Am. Chem. SOC.,7Q,870 (1957). (17)J. H. Christie,J. Osteryoung,and R. A. Osteryoung, Anal. Chsm., 45,210 (1973). (18) M. E. Peover and B. S. White, J. Electroanal. Chem., 13, 93 (1967). (19)N. Klein and Ch. Yarnitzky, J. Electroanal. Chem., 61, 1 (1975). (20)J. Bacon and R. N. Adams, Anal. Chem., 42,524 (1970). (21)E. P. Parry and R. A. Osteryoung, Anal. Chem., 37, 1634 (1965). (22) D. E. Smith in "ElectroanalyticalChemistry",A. J. Bard, Ed., Marcel Dekker, New York, N.Y.. Vol. 1, 1966,pp 1-155.
(23)J. A. Richards, P. E. Whitson, and D. H. Evans, J. Electroanal. Chem., 63, 311 (1975). (24)H. D. McBride and D. H. Evans, Anal. Chem., 45,446(1973).
RECEIVEDfor review June 14,1976. Accepted September 13, 1976. This research was supported by the National Science Foundation, Grant No. CHE75-04930. Presented in part at the 2d annual FACSS Meeting, Indianapolis, Ind., October 1975.
Dilatometric Titrations with Pressure Transducing Instrumentation S. J. Swarin,' J. L. Driscoll,2 and D. J. Curran" Department of Chemistry, University of Massachusetts, Amherst, Mass. 0 1002
A method has been devised to use pressure transducer instrumentation in dilatometric titrations. The titration reaction is carried out in a closed system containing gas and solution phases separated by a layer of silicone fluid placed on top of the solution. This layer prevents interaction between the phases but transmits to the gas phase any expansion or contraction of the solution produced by chemical reactionstaking place in the latter phase. Millimole amounts of materials were titrated, producing pressure changes In the system of 0 to 0.3 Torr (measrired differentially vs. a closed system at atmospheric pressure) which corresponded to volume changes in the microliter region. Examples are presented of neutralization and precipitation titrations among which are: fluoride, oxalate, or phosphate anions titrated with neodymium(lll), and a mixture of hydrochloric and acetic acids tltrated wlth sodium hydroxide. Precision and accuracy were a few ppt in many cases.
the signals corresponded to much larger volume changes than those which could be predicted and an arbitrariness in the interpretation of the data was necessary because the output of the transducer system continued to change slowly after a fairly abrupt initial change (21). I t was believed that most of the slow response was due to heat effects with other more minor contributions from interactions between the gas and solution phases present. This problem has been overcome and we report a study of precipitation and acid-base reactions. The determination of a mixture of acids, both with and without the presence of a large concentration of electrolyte, is presented. Examples using neodymium(II1) as a titrant for precipitation reactions are included. Precision and accuracy of a few ppt have been found in a number of cases and the volume changes observed correspond well with those calculated from literature data.
EXPERIMENTAL Although the study of volume changes produced in solution by chemical reactions has been of interest for many years, dilatometric titrations appear to have been first reported in a communication by Jahr, Gegner, Wiese, and Fuchs (1). Their note was based on the dissertation by Gegner (2) and an apparatus designed by Wiese in which the volume change was measured by a side-arm capillary manometer ( 3 ) .A second communication appeared in 1967 ( 4 )and the first full report was authored by Jahr, Wiese, and Uttech ( 5 ) .The work has since been carried out by Wiese and coworkers (6-19). The amounts of material involved are typically a few millimoles and the volumes of solutions ranged from a few milliliters to tens of milliliters. These figures correspond to typical volumetric buret work and the precision and accuracy found were also comparable in many cases. In our work on hydrogenation reactions with pressuremetric end-point detection, it was found that non-ideal solute-solvent behavior could be observed upon addition of an unsaturated organic to a solvent system (20). This led to attempts to follow the course of a titration and Driscoll successfully obtained titration curves but
Present address, Chemistry Department, Research Laboratories, General Motors Corp., Technical Center, Warren Mich. 48090. Present address, Clinical Laboratories, Rhode Island Hospital, Providence. R.I. 02980. 2180
Reagents and Solutions.Reagent grade or primary standard grade chemicals were used unless otherwise stated. All aqueous solutions were prepared with laboratory distilled water which had been redistilled from alkaline permanganate and were standardized by established methods. Neodymium chloride (Alpha Inorganics) had a rare earth purity of 99.9% based on neodymium oxide. Dow Corning Silicone Fluid 200 (viscosity a t 25 OC = 350 centistokes) was obtained from Contour Chemical. Apparatus. Dilatometric Titrations.Figure 1consists of a top view of the working and reference chambers and a cross-sectional view of the working chamber. This unit was constructed from a 4.5 X 4% X 3.5 inch block of aluminum. The internal volume of each chamber is the unshaded area extending from the socket joints, I and J, which provide connection to the pressure transducing system, to K, a three-way stopcock, which provides connections among reference chamber, working chamber, and outside atmosphere. The stopcock can be turned to connect any two of these together, or all three, or to isolate all three. The internal volume is also bounded by ball and socket joints, D and E, which connect to the working and compensating microburets (type S-3100, Roger Gilmont Industries, Inc., Great Neck, N.Y.). Buret A was used to deliver titrant and buret B to compensate for the volume change caused by the process of titrant delivery. The glass stems of these microburets are sealed to the inner section of their respective ball joints and the corresponding socket section is epoxied into the aluminum block. Epoxy seals a t L enclose part of the buret stems within the ball joint. Water can circulate completely around the glass stems of the burets through holes, C, when the apparatus is submerged. All other glass to aluminum connections were made with epoxy to ensure water and pressure tightness and were varnished. Titrations were performed in a 20-mm 0.d. glass vial, M, 52 mm high or a similar plastic vial. A 0.5-inch Teflon-coated
ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976
stirring bar, N, was used. As shown by the top view, the reference chamber is the mirror image of the working vessel except it contains ball joint stoppers, F and G, instead of microburets. All glass joints and stopcocks are greased with Dow Corning High Vacuum Silicone stopcock lubricant and are fastened together with spring loaded pinch clamps. Pressure measurements were made with a Barocel Modular Pressure Transducing System (Datametrics Inc., Wilmington, Mass. 01887) which has been described by Curran and Driscoll, (22), and Curran (23).A Datametrics Series 511-10 Pressure Sensor with a nominal differential pressure range of 0 to 10 Torr was used. A range selector switch provides a 5.000-volt full scale output for pressure inputs corresponding to X1, X0.3, XO.l, X0.03, XO.01, X0.003, and XO.001 of the nominal pressure range. The sensor was contained in a Lucite watertight box which had a %-inch thick aluminum lid fastened with 8 bolts. Stopcock grease and a rubber gasket between the lid and the box produced a watertight seal. The pressure sensor was mounted on the lid to provide good heat transfer between it and the bath. The output of the transducer system was monitored with a servorecorder and the voltage at equilibrium was measured with a Fluke Model 8300A DVM. The aluminum block, submersible magnetic stirring motors, and the pressure sensor in its watertight box were mounted on a ring stand which was submerged in a constant temperature bath up to the metal parts of the microburets. The bath was regulated at 26.300 0.001 "C by a Tronac Temperature Controller, Model PTC-1000. Temperature Studies. The temperature in the chambers was measured with the apparatus in the same configuration as that used for dilatometric titrations. However, the ball portion of joint D in Figure 1 was replaced by a 2-hole number 5 rubber stopper for the glass stem of the microburet and for a ten junction iron/constantan thermopile (Thermo Electric Model CTP, Saddle Brook, N.J.). The reference chamber stopper was replaced by a 1-hole number 5 rubber stopper which held another thermopile. These thermopiles have a temperature sensitivity of 0.5152 mV per "C. The potential difference between the two thermopiles was measured with a Keithley Model 149 Milli-Microvoltmeter. The dc output of the Model 149 was used to drive a Honeywell Electronik Model 194 recorder. Titration Procedures. The pressure transducer system is mechanically and electrically zeroed, adjusted for zero pressure differential, and full scale readout is set to 5.000 V. The ring stand is placed in the bath so the water level reaches almost to the top of the aluminum block. The compensating microburet, containing just a little water at the plunger to provide a good pressure seal, and the corresponding reference chamber cap are well greased, fastened in place, and clamped. Then 2.5 ml of water is poured into each chamber cavity. A titration vial containing a stirring bar, 4.991 ml of sample solution, any other necessary solutions, and 5.0 ml of Silicone Fluid is placed in each cavity and forced down so water in the block forms a thin film between the outer wall of the glass vials and the inner wall of the aluminum block. The working microburet, filled with titrant previously brought to the bath temperature, and the cap of the reference side are set in place and clamped. After setting the three-way stopcock to connect the reference and working chambers together, the ring stand is lowered to its final depth in the bath. Stirring is begun on the working and reference sides a t motor controller speed settings of 1 and 3, respectively. The system is allowed to reach thermal equilibrium as indicated by a steady baseline on the recorder when the three-way stopcock is adjusted to seal the reference and working chambers from each other and the atmosphere. The equilibration time for the first titration in a series is usually 1 t o 1.5 h. Subsequent titrations require only about 0.5 h for equilibration since the apparatus is not removed from the bath. The titration is performed by adding a volume of titrant from one buret and compensating for the compression of the system by turning the other buret back by the same volume. Four points are obtained before the end point and a t least four more after the end point. The time between addition of titrant and the voltage measurement is usually 4 min. A t the end of the titration, the three-way stopcock is turned so the working and reference sides are open to each other. After again sealing off the chambers, a 10.00-plvolume of glass is added to the system using the compensating buret and the output voltage change is measured with the DVM. Compensation is then achieved by withdrawing the plunger of the working buret from the system. This addition and compensation process is repeated three more times, and the average voltmeter reading is calculated. In this way, a calibration factor in mV/pl is obtained for each titration which can be used to convert the output voltage into volume change data more easily. A plot of output signal (in mV or pl) vs. the volume of titrant added yields a linear-segmented titration curve from which the end point is obtained.
I
Flgure 1. Dilatometric titration reactor A. Titrant delivery micrometer buret, 0.25-ml capacity: B. Volume compensating micrometer buret, 0.25-ml capacity;C. Holes for water circulation;D. 8 35/25 bail and socket joints, working side; E. 8 1819 ball and socket joints, working side;F. 9 35/25 ball and socket joints, reference side; G. 9 1819 ball and socket joints, reference side; H. Aluminum metal remaining after machining; I. 1215 socket joint for connection to working side of transducer, P,; J. 1215 socket joint for connection to reference side of transducer,P p ; K. T 2 three-way stopcock; L. Epoxy seals; M. Titration vessel; N. Teflon coated magnetic stlrring bar
RESULTS AND DISCUSSION Volume Change Measurements with Pressure Transducers. Consider a closed system consisting of a gas and a liquid phase. T o make measurements of t h e volume change in the liquid phase with pressure transducing instrumentation, three problems m u s t be addressed: all interactions between t h e phases must b e eliminated except for t h e contraction or expansion of t h e liquid phase, a method of adding reagents (titrant) is needed which is convenient and which does not change t h e internal volume of t h e system, and an experimental arrangement which avoids t h e nonlinearity of the inverse relationship between pressure and volume is necessary. T h e first problem was solved by adding t h e Silicone oil t o t h e system. Such a phase should have t h e following chemical and physical properties: very low vapor pressure, low thermal conductivity, very poor solvent characteristics, fairly low viscosity, water immiscibility, and a density less than that of aqueous solutions. Silicone oils come in a range of densities and satisfy all of these requirements. Dow Corning Silicone Fluid 200 was chosen primarily o n the basis of its viscosity and density (24, 25). It proved a n effective barrier t o mass transport between the gas and solution phases and no evidence was obtained that i t interacted with either of these phases. A method for adding t i t r a n t t o a closed system without changing t h e internal volume h a d been developed in our earlier work with pressuremetric titrations and it was used here as shown in Figure 1 (21,26).T h e validity of this volume compensation technique was established in t h e following manner. T h e a p p a r a t u s was assembled in t h e constant t e m perature b a t h with water in t h e sample vial a n d in t h e titrant buret. Twelve 2 0 . 0 0 - ~ lincrements were delivered a n d compensation was performed for each increment. T h e entire process was repeated three times. T h e average change of t h e output from t h e initial value after addition a n d compensation was k25.3 mV, which corresponded t o a pressure signal of
ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976
2181
I
Figure 2. Recorder tracings for temperature monitored titrations of HCI with NaOH Lower tracing: without water jacket and silicone fluid layer. Upper tracing: with water jacket and silicone layer. Sample: 4.991 rnl of 0.20M HCi. Titrant: 9.67 M NaOH
61.57 X Torr and a volume error of f0.074 pl. This result is within the buret manufacturer's specified accuracy of 0.05 to 0.1 pl and better than the worst possible case since the individual buret errors could add. The output signal of the transducer system is a dc voltage which may be expressed as:
E = uAP
+b
(2)
where P is the pressure on the working side. Noting that the total system volume, Vt is constant and equal to the sum of V , and the liquid phase volume, VL, Equation 2 may be written:
Thus, the relationship between the transducer system output and the volume of the solution phase is linear if the change in the gas phase volume, ( Vt - VL), is negligible. Typically this change is 10 gl or less in a gas volume of 10 to 15 ml. Using the X0.03 range of the transducer system, the constant, u , in Equation 2 is 5.000 V10.3 Torr and the magnitude of the slope is 1267 V/ml at atmospheric pressure for a gas volume of 10 ml. This is only an estimate of the sensitivity of the measurement because of the uncertainty in the volume of the gas and a loss of sensitivity due to the deflection of the transducer diaphragm. Blanchette has presented a quantitative treatment of the latter (27). Experimental values were in the vicinity of 330.0 mVfK1. Temperature Effects. Figure 2 shows the stripchart tracings for two temperature-monitored titrations carried out under different experimental conditions. The lower tracing was obtained when the glass vial containing a 0.20 M HC1 solution was placed in the sample cavity and titrated with slow stirring. The large rise in the temperature signals the addition of an increment of titrant. It took approximately 20 min for the temperature to return to the baseline. The upper tracing was obtained when the air space between the outer wall of the vial and the inner walls of the aluminum block was filled by a thin film of water. In addition, 5 ml of Silicone oil was placed on top of the sample solution. Here, the heat of reaction was dissipated in 4 min or less and the magnitude of the temperature change was somewhat less. These results indicate that pressure readings taken 4 min after the addition of titrant should be unaffected by the heats of reaction or dilution. It 2182
$v = 4VO
(1)
where a is the appropriate conversion factor in volts per Torr, A P is the pressure difference between the two chambers, and b is a constant representing the initial pressure difference. If ideal gas behavior is assumed and the pressure on the reference side is constant, it is readily shown that the change in output voltage with change in gas phase volume, V,, is: dEfdV, = -uP/V,
should be noted that the Silicone layer also eliminates carbon dioxide uptake during acid-base titrations. Operating on the X0.03 range setting, the noise observed on the recorder strip-chart was 6 mV peak-to-peak which Torr. Assuming this noise is due corresponds to f3.6 X only to temperature variations between the working and reference chambers, a temperature fluctuation of f0.00013 OC is estimated from a temperature sensitivity of about 2.8 TorrPC. This is an order of magnitude better than the specifications for the bath controller and probably reflects the differential nature of the measurement and some success in smoothing out the temperature fluctuations within the bath by means of the aluminum block. In addition to short term fluctuations in the base line, a longer term drift was observed in some, but not all cases. The drift rate was constant and less than +5 mVlmin on the X0.03 range setting. The source of this drift is not known but when present, its rate was measured and the data were corrected by subtracting the signal due to drift from the measured signal. Calculation of Volume Changes from Literature Data. The apparent molar volumes of electrolytes exhibit a concentration dependence which has been described by Masson's empirical relationship (28),
+k
(C)1'2
(4)
where $V is the apparent molar volume at concentration C; $v0 is the apparent molar volume a t infinite dilution (equal to the partial molar volume); and h is the experimental slope of a plot of 4~ vs. C112. The latter has been found to vary for each electrolyte. Redlich and Rosenfeld (29,30)applied the Debye-Huckel theory in considering the concentration dependence of 4~ and derived a limiting law for the concentration dependence of the apparent molar volume of electrolytes:
$v = +"O
+ S(C)1/2
(5)
where S, the limiting slope, is a constant for all electrolytes of the same charge type ( S = 1.868 a t 25 "C for 1:l electrolytes). Although Equations 4 and 5 are of the same form, they do not have the same meaning and for many years workers incorrectly used the Masson equation to extrapolate molar volume data to infinite dilution. This is discussed in reviews by Redlich and Meyers ( 3 1 )and by Millero (32).T o extend the limiting law to higher concentrations, the following equation has been proposed (29,31):
+
+
+v = $vo S(C)'12 b(C) (6) where b is a deviation constant which must be experimentally determined. Owen and Brinkley (33) derived a still more complex equation based on the extended Debye-Huckel theory. Their equation and Equations 4-6 are discussed by Millero ( 3 4 ) .In terms of the present work, very few studies in the literature have made use of the Owen-Brinkley equation. More information is available concerning the deviation constant, b , and a tabulation has been made by Millero ( 3 4 ) . However, the great bulk of the data available is in the form of the Masson equation. Fortunately, this equation is appropriate for use here. Thus, many of the literature data used in the calculations were taken from the tabulation of Harned and Owen (35) and the remainder taken from Millero (34). The calculations employ the principle of additivity which has been discussed by Millero (34)and Harned and Owen (35). The molar volume change, in mlfmol, due to a chemical reaction may be written: (A4v)rx = z ( 4 v ) p r o d u c t s - z ( 4 v ) r e a L t a n t s
(7)
Using the Masson equation or the extended limiting law equation, the molar volumes of the reactants are calculated
ANALYTICAL CHEMISTRY, VOL. 48, NO. 14, DECEMBER 1976
Table I. Data and Results for Precipitation Titrations
Samplen
Titrant
Expected end-point volume, y l b
End-point volume found, plc
105.8 83.9 166.9 105.1 98.3
106.0 f 0.8
0.1599 M KCl 0.1310 M KBr 0.1297 M KCl 0.1921 M NaF 0.08989 M Na2C204 0.05054 M KHzPO4
7.543 M AgN03 7.796 M AgN03 3.042 M NdC13 3.042 M NdC13 2.18 M NdC13
1 6 7 . 0 i 0.31 104.5 f 0.5 97.7f 0.4 97.9 f 4.lf
115.2
Calculated AV, pld After Before +1.81
-4.41
-1.09 +1.39
-3.66
e e
e
.. . e e e
Observed AV, yld Before
After
+1.78 f 0.10
