Determination of the Heat of Sublimation of Iodine A Physical Chemistry Laboratory Experiment Richard W. Schwenz University of Northern Colorado, Greeley, CO 80639 The determination of either the vapor pressure or total . . pressure of a subsranre as a function of tempernture is eommunlv performed in physiral chemistry laboratory (1-3). The P, 'l'data is h e n ma~hematicallytreated by plob uf In K or in P versus 11T. We have developed an experiment for the physical chemistry laboratory that combines the traditional experiment of the measurement of the vapor pressure versus temperature with the use of a computer interface to collect the data. Such experiments have previously been described for measurements of absolute pressure versus temperature data (3).This experiment automates the measurement of the concentration of vapor phase Ip molecules through their ahsorhance as a function of temperature, so that the absolute pressure need not be measured: Thevisible absorption spectrum of the 1 2 molecule is fairly complex, consisting of a number of vibrational bands arising from transitions from the ground X '2 state to the B 311 excited state (4). , . Other ohvsical chemistrv laboratories using this spectrum include ihe determinatihn of the molecular constants (5. 6 ) or the studv of atomic recombination kinetics following flash photolysis (7). ~
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Experimental The spectrometer used is a Varian Superscan 3 operated with a bandwidth of 0.6 nm. A room temperature spectrum of I*vapor is taken after placing several crystals of Ip in the bottom of a l-cm-path-length cuvette. The experiment begins by taking a spectrum of the vapor from 450 to 650 nm. At this resolution the vibrational bandheads are readily apparent, which can be related to the laboratory on molecular constants. The resolution may be changed for the points with temperature change, although it is not necessary. At this noint.. the students pick a waveleneth near the maximum absorption and vary the temperature. The temperature of the 11-vaoor . formed in eauilibrium above the iodine crystals is controlled by circulating the water from a constant temperature bath throueh a set of tem~erature-controlled hoidrrs ior thedual-hedm ;ipectrophotdmeter. A eonstnnt-temperature bath (I.auda RMS-20) maintains a constant temperature to f0.02 "C after being set to a given temperature (0.1 OC intervals). The temperature is monitored by the computer using a temperature-to-current converter (Analog Devices AD590JF). This device is small enough to fit next to the spectrophotometer cell. A hardware interface was designed so that an output of 0.00 V corresponds to 0 OC and 10.0 V to 100 OC witha precision of better than 1 O C . The output of the spectrophotometer is also scaled so that 0.0 V corresponds to an absorption of 0.0 and 10.0 V corresponds to an absorption of 1.0. An analog-to-digital converter is used to digitize the analog signals and place these signals in the memory of an Apple IIe computer for data collection and analysis (8). Trial runs of the experiment showed that for a temperature of 80 OC an absorption of 0.3 is obtained with a 1.0-cm cell at 510 nm (near the maximum
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absorption). An absorption of 0.01 is obtained a t 25 'C. A 10%error (0.001 absorption unit) is introduced in the digital conversion a t 25 "C by using a 10-bit analog-to-digital converter set un for 1.0 absorotion unit full scale. and essentiallv no error is introduced in the conversion of the temperature (-0.1 "C) with the digitization. One experiment consists of monitoring the temperature and absorotion due to the iodine vapor at a sinele wavelength near the absorption maximumas the temperature of the water bath is raised from 25 OC to 80 "C. The points should be more widely spaced at higher temperatures because of the I I T functional form of the 1: axis. Studentobtained heats of sublimation range from 11500 to 14000 cnl mol-' (seven groups) with the literature value of 13056 cal mol-I (9). This experiment can also be done in a manual mode (no computer), or in real time (computer collecting points continuouslv~ .. and can determine the heat of vaoorization or sublimation of volatile, absorbing compounds. Caution:Stoo~er .. the too of the cells before beeinnine- this experiment, or the inside of your spectrophotometer will become covered with iodine.
Discussion Good data is obtnined at a varietv,of waveleneths near the maximum nhsorptiun hemuse the rcnults are independent of waveleneth. One key feature of this exoeriment is the inde" pendence of the measured heat of sublimation from the molar absorptivity and the absolute vapor pressure of iodine. This independence rises from the form of the plot needed (In P vs. lIT), the Beer-Lambert law and the ideal gas equation, namely that In P transforms t o in (TnIV) + In R to In (Rlcb) In (AT). Thus a plot of in (AT) versus 1IT should be linear with slope -AHH,,bIR. This experiment could be enhanced by having the computer check the absorbance a t different wavelengths while the temperature is changing to prove the wavelength independence of the heat of sublimation. One factor which is evident from looking a t an I2 spectrum taken at 80 OC relative t o one a t 25 "C is the increased intensity of several bands near the intensity maximum, which may be attributed to"hot bands". These may alter the measured heat of sublimation because of the increased population of the lower state with temperature (10). ~
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Llteratvre Cited 1. Shuemsker. D. P.; Garland. C. W.;Steinfeld, J. I.: Nihler, J. W. Erperiments Physical Chemistry, 4th ed.: MeCrsw-Hill: New York,1981: p 197.
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2. Crockford, H. D.: Nowdl, J. W.; Baird, H. W.: Gefzen. F. W. Laboratory Monvol of Physicol Chemistry, 2nd ed.; Wiley: New York. 197b p 134. 3. Waldo, C. 8.; Schuire, C. A,; Battino, R. J . Chem. Edue. 1984,61,530. 4. Huher. K. P.:Her.herg, C.Moleculor speetr. and Moiacuior structure IV. cohstonts ojDiafomk Molecules:Van Nostrand: New York. 1979. 5. McNaught. I. J. J. Chem. Educ. 1980.57,101. 6. CartwrighLH. M. J . Chem. Edue 1983.60.608. 7. Porter.G. A.: and Smith. J. A.Proc. Rgv.Sot. (London1 1961.A261.28. 8. Hallgren. R. C. Inleilace Prprjicta jar the Appls II: Prentice-Hall: Englewood Cliffs.
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9. Weast, R. C., Ed. Handbook of Chemistry ond Physics, 53rd ed.; Chemical Rubber Company: Cleveland, OH, 1973. 10. Preus,D. R.:Cole,J.L.J . Chem. Phys. 1977.66..2994. Volume 64
Number 6 June 1987
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