Experimental Determination of the Sublimation Pressure of Iodine. A = log I 0

Transcription

1 CH353L Wet Lab 1 / p.1 Experimental Determination of the Sublimation Preure of Iodine The determination of the vapor preure of olid iodine at temperature from 25 to 65 C in tep of about 1 C i accomplihed throuh pectrophotometric meaurement of the aborbance A of the iodine vapor in equilibrium with the olid at the aborption maximum (52 nm. You hould alo verify that at 7 nm, where the molar aborption coefficient of iodine vapor i o mall a to be neliible, the aborbance read eentially zero. (On the hort-wavelenth ide of the maximum there i no acceible wavelenth at which the aborption i neliible; hence the baeline can be taken only from the lon-wavelenth ide. The aborbance i indicated directly on the pectrophotometer; at every wavelenth it i related to the incident beam intenity I and the tranmitted beam intenity I by the equation A = lo I I (34 The tet tube containin iodine in the olid and vapor tate mut alo contain air or nitroen at about 1 atm to provide preure broadenin of the extremely harp and intene aborption line of the rotational fine tructure (which can be individually reolved only by pecial technique of laer pectrocopy. The reaon lie in the loarithmic form of Eq. (34. Within the lit width or reolution width of the kind of pectrophotometer that may be ued in thi experiment, lowpreure I 2 ( exhibit many very harp line eparated by very low backround aborption. The intrument effectively averae tranmitted intenity I, not aborbance A, over the harp peak and backround within the reolution width, but the loarithm of an averae i not the averae of the loarithm. If the extremely harp line are o optically "black" that varyin the concentration ha little effect on the amount of liht tranmitted in them, the aborbance i controlled mainly by the backround between the line, and the contribution of the line to the aborbance i larely lot. Increain the concentration of a molecule increae the number of molecular colliion and thu decreae the time between them. Thi can reatly broaden the line and lower their peak aborbance, cauin them to overlap and mooth out the pectrum over the reolution width o that the aborbance readin are meaninful averae over that rane. Thi effect i readily demontrated experimentally by comparion of pectra taken of I 2 vapor with and without air preent. Fiure 1, how the aborption pectrum of I 2 vapor over the rane of interet at the vapor preure of iodine at 27 C, at moderate reolution and at low reolution. A low-reolution pectrum, obtained with wide lit uch a thoe in your pectrophotometer, illutrate how the vibrational tructure i averaed out, facilitatin the determination of the aborbance at 52 nm. For each temperature that you will require, there will be a thermotated water bath to hold the tet tube that contain the iodine ample. A the vapor preure depend tronly on the temperature, keepin the ample equilibrated at the deired temperature i a primary concern in thi lab. There can be ome coolin of the tet tube in the fraction of a minute that it take to brin the tube from the water bath to your pectrophotometer, o you hould move the tube and take your aborbance meaurement a quickly a poible. You hould record the initial (hihet value of the aborbance. To help low the coolin of the iodine, la bead have been placed at the bottom of the tube to act a heat reervoir. When you are done with your

2 CH353L Wet Lab 1 / p.2 meaurement, you hould replace the tube back in their oriinal water bath, ince temperature equilibration of the ytem, includin la bead, can take everal minute. In your lab write up, you hould etimate the manitude of the uncertainty introduced by coolin. Fiure 1. A Aborbance of I 2 (, in equilibrium with the olid at 26 C and in the preence of air at about 1 atm, for wavelenth ranin from 47 to 7 nm. The top curve i at moderately hih reolution. The bottom curve i at relatively low reolution, about the hihet uitable for thi experiment. λ (nm t, C ε, L mol -1 cm Table I. Molar aborption coefficient of iodine vapor at = 52 nm (Baed on an equation derived in Ref. 13

3 CH353L Wet Lab 1 / p.3 CALCULATIONS For each temperature, determine the net aborbance a the difference between the aborbance at 52 and 7 nm: A = A 52 A 7 (35 The net aborbance i related to the concentration c and the preure p of iodine vapor in the cell a follow (aumin the perfect-a law: A = dc = d RT p (36 where c i the concentration of I 2 vapor, p i the partial preure of I 2 vapor, d i the optical path lenth inide the inner aborption cell, and ε i the molar aborption coefficient for I 2 vapor at 52 nm and temperature T. The value of the molar aborption coefficient ε at each temperature can be found from Table 1 by interpolation. Then p may be calculated with Eq. (36. In the calculation of thi experiment, coniderable care mut be taken with unit. It i deirable to obtain p in pacal for the tatitical mechanical calculation; accordinly, ε hould be converted into unit of m 2 mol -1, d hould be in m, and R hould be in unit of J K -1 mol -1. To determine H ub from the approximate Clauiu-Clapeyron equation [ee the firt pae of the dry lab], plot ln p aaint 1/T and determine the lope of the bet traiht-line fit to the data by raphic or leat-quare method. The value of p and T can now be ued for the tatitical mechanical calculation. In order to calculate the rotational characteritic temperature Θ rot with Eq. (2, ue the literature value for the rotational contant B = cm -1 [or calculate B from the internuclear ditance in the molecule, r =.2667 nm, with Eq. (17 to (19]. From the literature value of the molecular vibrational frequency in the a phae, = cm -1, calculate the vibration characteritic temperature Θ vib with Eq. (22. From the phonon frequencie iven in the dry lab handout, calculate the 12 vibration characteritic temperature Θ j. Calculate E from Eq. (33 at each temperature uin the Excel/Mathematica/Mathcad preadheet you developed for the dry lab. Do the value obtained for E aree atifactorily? If not, check the calculation and/or conider poible ytematic error. We can alo rewrite Eq. (33 in a form that more cloely matche the Clauiu-Clapeyron equation: ln p ln T 7 / 2 12 (1 e Θ j / T 1 / 2 j=1 (1 e Θ vib / T = ln 2 mk h 2 3/2 k Θ rot RT E (37

4 CH353L Wet Lab 1 / p.4 Plot the LHS of Eq. (37 aaint l/t, and determine both E and the contant term raphically or by leat quare. Doe thi value of E aree with the averae of the value obtained by direct application of Eq. (37? Doe the contant term aree with the theoretical value? Entropy and Enthalpy of Sublimation. Since we have a ytem of only one component, the chemical potential for I 2 in crytalline and aeou form, iven in Eq. (32 and (25, repectively, are equivalent to the molar Gibb free enerie G and G, aide from an additive contant. The entropie of the two phae can be obtained by differentiatin with repect to temperature. The expreion obtained are S = R 2 12 G T j =1 p = T p Θ j / T e Θ j / T 1 ln(1 e Θ j / T (38 S G T = E T The heat of ublimation at temperature T i p T p R + R Θ vib / T e Θ vib / T 1 (39 H ub = T S ub = T( S S (4 Calculate the molar entropie S and S of the crytalline and vapor form of I 2 at 32 K with Eq. (38 and (39, and obtain the molar heat of ublimation H ub with Eq. (4. Compare it with the value obtained by the Clauiu-Clapeyron method and with any literature value that you can find. DISCUSSION Of the two method of determinin E with Eq. (33 and (37, which do you jude ive the more precie value? Which ive the more accurate value? Which provide the better tet of the overall tatitical mechanical approach? Compare thi approach with the purely thermodynamic method uin the interated Clauiu-Clapeyron equation, takin into account the approximation involved in the latter. State the averae temperature correpondin to your Clapeyron value of H ub.

5 CH353L Wet Lab 1 / p.5 Comment on the choice of repreentative value of J for the 12 vibrational mode of the crytal. How much would reaonable chane (ay, 1 to 2 percent in thee value affect the reult of the calculation? If poible, comment on the effect of uin the Debye approximation (different crytal vibrational frequencie for the acoutic lattice mode intead of the Eintein approximation (all the ame vibrational frequency. REFERENCES Thi lab i modified for CSM ue from Ch. 48 of Experiment in Phyical Chemitry, 6 th edition by D. P. Shoemaker, C. W. Garland, and J. W. Nibler ( N. Levine, Phyical Chemitry, 4th ed., pp , McGraw-Hill, New York ( P. W. Atkin, Phyical Chemitry, 5th ed., pp , Freeman, New York ( Ibid., pp Adapted from R. P. Huber and G. Herzber, Molecular Spectra and Molecular Structure IV: Contant of Diatomic Molecule, p. 332, Van Notrand Reinhold, New York ( P. W. Atkin, op. cit., pp C. Kittel, Introduction to Solid State Phyic, 5th. ed., Wiley, New York ( N. W. Ahcroft and N. D. Mermin, Solid State Phyic, Saunder, Philadelphia ( F. van Bolhui, P. B. Koter, and T. Mihelen, Acta Crytallor. 23, 9 ( a. H. G. Smith, M. Nielen, and C. B. Clark, Chem. Phy. Lett. 33, (1975; b. H. G. Smith, C. B. Clark, and M. Nielen, in J. Lacombe (ed., Dynamic of Molecular Crytal, pp , ep. fi. 2, Elevier, Amterdam ( C. Kittel, op. cit., pp N. W. Ahcroft and N. D. Mermin, op. cit., pp G. E. Bacon, Neutron Diffraction, 3d ed., chap. 9, Oxford Univerity Pre, Oxford ( P. Sulzer and H. Wieland, Helv. Phy. Acta 25, 653 ( J. G. Calvert and J. N. Pitt, Jr., Photochemitry, p. 184, ref. 424 in chap. 5, Wiley, New York ( D. A. Shirley and W. F. Giauque, J. Am. Chem. Soc. 31, 4778 ( G. Henderon and R. A. Robart, Jr., Am. J. Phy. 46, 1139 ( F. Stafford, J. Chem. Educ. 4, 249 (1963. GENERAL READING N. W. Ahcroft and N. D. Mermin, op. cit., chap. 4, 5, 7, N. Davidon, Statitical Mechanic, chap. 6-8, McGraw-Hill, New York (1962. C. Kittel, op. cit., chap. 4.