mined in the 3000-800 cm-l region, through comparison with the IUPAC values ( 1 4 ) for peaks of indene and polystyrene. The measurement was repeated 9 times and the means of the peak positions obtained for each measurement are shown in Table 111. Since the scanning speed affects the peak position, the standard scanning speed of 8 min for full range was chosen. A comparison of Table 11 and Table 111 shows that the observed peak position in the spectrum of indene measured a t higher scanning speed is shifted to lower wavenumber. For standard runs this accuracy was within 2 cm-‘. Further, a reproducibility of 0.2 cm-’ was obtained for the peak position in the spectrum of indene, which has more sharp peaks than polystyrene. In general, wavenumber reproducibility of sharp peaks is higher than that of broad peaks. The measurement precision of the spectrophotometer with on-line system is excellent. This system can perform routine analytical application. Furthermore, if the transmittance scale were calibrated appropriately, the corrected digital data could be used for quantitative analysis and band shape analysis,
including the evaluation of thermodynamic data for chemical equilibria and reaction kinetics.
LITERATURE CITED (1) R. N. Jones, Kagaku No Ryoiki, 21, 609 (1967). (2) R. N. Jones, Pure Appi. Chem., 18, 303 (1969). (3) K. Tanabe, S. Saeki, and M. Mlzuno, Jpn. Anal., 18, 1347 (1969). (4) B. R. Kowalski, P. C. Jurs, T. L. Isenhour, and C. N. Reilley, Anal. Chem., 41, 1945 (1969). (5) R . W. Liddle I11 and P. C. Jurs, Appl. Spectrosc., 27, 371 (1973). (6) H. 6. Woodruff, S. R. Lowry, G. L. Ritter, and T. L. Isenhour, Anal. Chem., 47, 2027 (1975). (7) E. C. Elwin, D.A. Padowski, and J. B. b u c k , Anal. Chem., 46, 955 (1974). (8) K. Tanabe and S . Saekl, Anal. Chem., 47, 118 (1975). (9) R . C. FOX. Anal. Chem., 48, 717 (1976). (10) B. G. M. Vandeglnste and L. De Galan, Anal. Chem., 47, 2124 (1975). (1 1) S. Mlnaml and F. Zenltanl, “Informatlon Chemistry”, H. B. Mark, Jr., and S. Fujiwara, Ed., University of Tokyo Press, Tokyo, Japan, 1975, p 143. (12) S . Sasakl, Ref. 11, p 227. (13) A . Savltzky and M. J. E. Golay, Anal. Chem., 36, 1627 (1864). (14) “Tables of Wavenumbers for the Calibration of Infrared Spectrophotometers”, Butterworths, London, 1961,
RECEIVED for review March 21,1977. Accepted July 19,1977.
Precision Titration Mini-Calorimeter Dale Ensor, Lennart Kullberg, and Gregory Choppln” Department of Chemistry, The Florida State University, Tallahassee, Florida 32306
Calorimetry provides the most accurate way to obtain heat data for reactions in solution. Extensive use has been made of the thermometric titration procedure both as an analytical tool for end-point or equivalence determination and for determining heats of reaction, heats of solution, heats of dilution, etc. ( I ) . Previously in this laboratory we have designed and used a Peltier cooling calorimeter which has a sensitivity of 1 x “C (2). The calorimeter has rapid response and equilibration, which makes it possible to perform a titration series consisting of 10-15 additions usually within a couple of hours. However, as most other calorimeters, ours requires fairly large solution volumes (>40 mL). For many chemical systems it is desirable or even necessary to use smaller solution samples for heat measurements without loss of precision. From our experience with the Peltier calorimeter, we felt that a small volume calorimeter of high precision and simple design was possible. In this paper we describe the design and test of a reaction calorimeter operating with solution sample volumes in the range 3-5 mL.
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DESCRIPTION O F THE CALORIMETRIC SYSTEM Calorimeter Vessel. The 5.0-mL vessel was constructed of thin walled (0.5 mm) Pyrex glass and gold painted (Hanovia Gold Paint) to within 1cm of the top. The gold surface was then heavily electroplated with copper. A Peltier heatingcooling device (Borg-Warner Thermoelectrics No. 837-8) was soldered to the bottom of the vessel utilizing an indium alloy solder. T h e copper plating provided a path by which the Peltier device could quickly change the temperature of the vessel’s contents. The calorimeter was sealed in a machined brass housing equipped with a copper heat dissipator in contact with the Peltier device. T h e calorimeter had contained a glass stirrer driven a t 240 rpm, a thermistor, a titrant inlet line, and a calibration heater (Figure 1). All the above were sealed to the superstructure using machined Teflon sleeves. T h e vessel was attached to superstructure with bolts and an O-ring seal.
m a
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VOL. 49, NO. 12, OCTOBER 1 9 7 7
Temperature Sensing Circuit. The temperature sensing circuit was similar to that previously described by Orebaugh and Choppin ( 2 ) . A 100-kR glass bead thermistor (Fenwal Electronics GA 5151) was incorporated as one leg of a Wheatstone bridge. The bridge imbalance was amplified by a Keithley 150B 1V ammeter and the signal recorded by a Sargent Model recorder. An electrical heating circuit was used to calibrate the resistance change of the thermistor. The heater was constructed of epoxy coated Manganin alloy wire loosely coiled around but not touching the stirrer shaft. The voltage drop across the calibrated heater and a precision 1.00000-R resistor were measured with a Fluke Digital Voltmeter. The power dissipated by the heater in 10.00 s was used to provide accurate calibration. Titrant Addition. The titrant was added using a Gilmont 2.0-mL precision buret driven by a 6 rpm motor with a clutch brake mounted on the calorimeter stand. The buret was submerged in the 25.0 OC water bath alongside the vessel. A timer was attached to the buret motor to monitor the addition of titrant. TESTING O F THE CALORIMETER Reproducibility of the System. T h e reproducibility of the calorimeter was determined by several series of electrical calibrations, in which no more than 0.08 J were added to the calorimeter which held 3-4 mL of water. The standard deviations of the calibration constants were typically 0.44.6%. This corresponds in absolute values to an uncertainty of 0.0004 J and to a precision in the measured temperature of -1 X 10-5 “C. In the titration experiments, additions of 0.1-0.2 mL are generally made. Therefore even small absolute volumetric errors may significantly reduce the precision of the measurements. The buret was calibrated by weighing the amounts of distilled water delivered over several time intervals. The mL/s. rate of delivery was found to be (5.13 f 0.03) X Accuracy of the Calorimeter. In order to check the accuracy and the overall performance of the calorimeter, the
t
I Figure 1.
C
I 32
The calorimeter head to scale showing the thermistor (A),
34
36 Total volume ( m
t h e tirant inlet line (B), t h e stirrer (C), and the heater (D)
I
Titration data (series No. 1) for the Hg2'-Br- system; the mercury concentration is obtained from the interception of the two straight lines Figure 2.
Table I. Heat of Protonation of THAM uHCl> mL Q x l o 2 ,J - A H , k J m o l - ' First series 17.07 46.90 0.0364 73.14 47.52 0.1539 72.76 47.28 0.1539 73.43 47.87 0.1534 73.35 47.82 0.1534 85.02 47.63 0.1785 Second series 72.30 47.29 0.1529 48.21 0.1543 74.39 74.81 48.14 0.1554 73.01 47.60 0.1534 Av. 47.63 -c 0.38 enthalpy changes for two standard reactions have been determined: (i) the reaction of tris(hydroxymethy1)aminomethane, THAM, with hydrochloric acid; (ii) the reaction between mercury(I1) and bromide ions. Four mononuclear complexes are formed in the mercury(I1)-bromide system (3). EXPERIMENTAL Chemicals. All chemicals used were of reagent grade. In the THAM experiments, a buffer of the composition 0.0095 M THAM, 0.0040 M THAMH+,and 0.0040 M C1- was titrated with 0.01000 M HC1. The pH of the THAM buffer was about 8. For the Hg(II)-Br- system, a Hg2+solution of approximately 0.004 M was titrated with a 0.0500 M NaBr solution. In order to suppress the hydrolysis of the metal ion, HC104was added to the mercury(I1) solution as well as to the bromide solution (C, = 0.1 M). The ionic strength was kept constant at 0.5 M by addition of NaC104 as a supplementary electrolyte. All experiments were performed as titrations with the calorimeter initially charged with 3.00 mL of solution. RESULTS Enthalpy of Protonation of THAM. Table I summarizes results from two series of experiments. The heat of dilution of hydrochloric acid was found to be negligible. The average value of the protonation enthalpy of THAM, -47.63 f 0.38 k J mol-' (the error given is three standard deviations of the mean), is in good agreement with previously reported values. Grenthe et al. ( 4 ) obtained a value of -47.44 3~0.05kJ mol-' for the protonation enthalpy of THAM a t I = 0.01-0.02 M. Further,,AH" values are reported by Nelander ( 5 ) (-47.53 kJ mol-'), Ojelund and Wadso (6)(-47.48 k J mol-') and Hansen and Lewis (7) (-47.36 k J mol-'). The Mercury(I1)-Bromide System. Three different titration series were performed. Each series consisted of 13-16 additions. During the titration series the total mercury(I1) and bromide concentrations varied in the ranges 4.G2.4 mM and 0-20 mM, respectively. The mercury concentration of the initial solution was determined from the calorimetric
Table 11. Stepwise Enthalpy Changes in the Formation of Mercury(I1)-Bromide Complexes
[ ( I = 0.5 M (NaC10,); T = 25.0 "C)]
-aHIa
AH,^
AH^^
AH,^
Series 1 2 3 Average Ref. 9 Ref. 10 Stability
42.7 45.0 16.1 17.1 47.3 10.9 42.7 10.9 42.7 46.9 11.7 15.1 42.7 i 0.4b 46.4 i 0.8 12.6 i 2.0 14.4 i 2.5 42.3 44.8 12!,6 17.2 ... ... 42.7 46.0 constants used: log p , = 9.00 log o 2 = 17.30 logp, = 19.4 log p, = 21.1 a In kJ mol-'. The uncertainty listed is obtained from the uncertainty (unlisted) in each A H value; S a v 2 = d 1 2 + 6,2
t
s,2.
titration curves which show a break after the formation of the second complex (Figure 2). The precision of the concentration determination was better than 1%. The enthalpy changes for each of the four consecutive reaction steps have been calculated by using the graphical method described in Ref. 8. The stability constants needed for the calculations were taken from Ref. 3. Table I1 shows that the results obtained in this investigation agree very well with those previously reported for the same medium (0.5 M NaC104) and the same temperature ( 2 5 O C ) . CONCLUSIONS Both the precision and the accuracy of the calorimeter are satisfactory. I t has been shown that the calorimeter can be used for small and dilute samples both as an analytical tool and for precise determination of reaction heats. LITERATURE CITED (1) F. Barthel, "Thermometric Titrations", Wiley-Interscience, New York, N.Y., 1975. (2) E. Orebaugh and G. R. Choppin. J , Coord. Chem., 5, 123 (1976). (3) R. Arnek, Ark. Kemi, 2 4 , 531 (1965). (4) I. Grenths, H. Ots. and 0. Ginstrup, Acta. C k m . Scand., 24, 1067 (1970). (5) L. Nelander. Acta. Chem. Scand., 18, 973 (1964). (6) G. Ojelund and I. Wadso. Acfa. Chem. Scand., 22, 2691 (1968). (7) L. D. Hansen and E. A . Lewis, J . Chem. Thermodyn., 3, 35 (1971). (8) S. Ahrland and L. Kullberg. Acta. Chem. Scand., 25, 3471 (1971). (9) M. BjZlrkman and L. G. Sill6n. Trans. Roy. Znsf. Techno/. Stockholm. 1962, No. 199. (10) J. J. Christensen. R. M. Izatt, L. D. Hansen, and J. D. Hale, Znorg. Chem., 3, 130 (1964).
RECEIVED for review April 15, 1977. Accepted July 11, 1977. This research was supported by Contract. No. E-40-1-1797 with the USERDA. ANALYTICAL CHEMISTRY, VOL. 49, NO. 12, OCTOBER 1977
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