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Experimental Determination of the Sublimation Pressure of Iodine
The determination of the vapor pressure of solid iodine at temperatures from 25 to 65°C in steps
of about 10°C is accomplished through spectrophotometric measurements of the absorbance A of
the iodine vapor in equilibrium with the solid at the absorption maximum (520 nm). You should
also verify that at 700 nm, where the molar absorption coefficient of iodine vapor is so small as
to be negligible, the absorbance reads essentially zero. (On the short-wavelength side of the
maximum there is no accessible wavelength at which the absorption is negligible; hence the
baseline can be taken only from the long-wavelength side.) The absorbance is indicated directly
on the spectrophotometer; at every wavelength it is related to the incident beam intensity I 0 and
the transmitted beam intensity I by the equation
A
λ
= log
I
0
I
λ
The test tube containing iodine in the solid and vapor states must also contain air or nitrogen at
about 1 atm to provide pressure broadening of the extremely sharp and intense absorption lines
of the rotational fine structure (which can be individually resolved only by special techniques of
laser spectroscopy). The reason lies in the logarithmic form of Eq. (34). Within the slit width or
resolution width of the kinds of spectrophotometers that may be used in this experiment, low-
pressure I 2 (g) exhibits many very sharp lines separated by very low background absorption. The
instrument effectively averages transmitted intensity I , not absorbance A , over the sharp peaks
and background within the resolution width, but the logarithm of an average is not the average of
the logarithm. If the extremely sharp lines are so optically "black" that varying the concentration
has little effect on the amount of light transmitted in them, the absorbance is controlled mainly
by the background between the lines, and the contribution of the lines to the absorbance is
largely lost. Increasing the concentration of gas molecules increases the number of molecular
collisions and thus decreases the time between them. This can greatly broaden the lines and
lower their peak absorbances, causing them to overlap and smooth out the spectrum over the
resolution width so that the absorbance readings are meaningful averages over that range. This
effect is readily demonstrated experimentally by comparison of spectra taken of I 2 vapor with
and without air present.
Figure 1, shows the absorption spectrum of I 2
vapor over the range of interest at the vapor
pressure of iodine at 27°C, at moderate resolution and at low resolution. A low-resolution
spectrum, obtained with wide slits such as those in your spectrophotometer, illustrates how the
vibrational structure is averaged out, facilitating the determination of the absorbance at 520 nm.
For each temperature that you will require, there will be a thermostated water bath to hold the
test tubes that contain the iodine samples. As the vapor pressure depends strongly on the
temperature, keeping the samples equilibrated at the desired temperature is a primary concern
in this lab. There can be some cooling of the test tubes in the fractions of a minute that it takes
to bring the tube from the water bath to your spectrophotometers, so you should move the tubes
and take your absorbance measurements as quickly as possible. You should record the initial
(highest) value of the absorbance. To help slow the cooling of the iodine, glass beads have been
placed at the bottom of the tubes to act as heat reservoirs. When you are done with your
measurement, you should replace the tubes back in their original water baths, since temperature
equilibration of the system, including glass beads, can take several minutes. In your lab write up,
you should estimate the magnitude of the uncertainty introduced by cooling.
A
λ (nm)
t, °C ε, L mol
Figure 1.
Absorbance of I 2 (g), in
equilibrium with the solid at
26°C and in the presence of air
at about 1 atm, for wavelengths
ranging from 470 to 700 nm.
The top curve is at moderately
high resolution. The bottom
curve is at relatively low
resolution, about the highest
suitable for this experiment.
Table I. Molar absorption coefficient
of iodine vapor at λ = 520 nm
(Based on an equation derived in Ref. 13)
ln p − ln
T
7 / 2 ( 1 − e
−Θ j / T
)
1 / 2
j = 1
12
( 1 − e
−Θ vib / T )
= ln
2 π mk
h
2
3 / 2 k
σΘ rot
E
0
0
RT
Plot the LHS of Eq. (37) against l/ T , and determine both Δ
E
0
0 and the constant term graphically
or by least squares. Does this value of Δ
E
0
0 agree with the average of the values obtained by
direct application of Eq. (37)? Does the constant term agree with the theoretical value?
Entropy and Enthalpy of Sublimation. Since we have a system of only one component, the
chemical potentials for I 2 in crystalline and gaseous forms, given in Eqs. (32) and (25),
respectively, are equivalent to the molar Gibbs free energies
G
s
and
G
g
, aside from an additive
constant. The entropies of the two phases can be obtained by differentiating with respect to
temperature. The expressions obtained are
S
s
G
s
∂ T
p
∂μ s
∂ T
p
R
j
/ T
e
Θ (^) j / T − 1
− ln(1− e
− Θ j / T
)
j = 1
1 2
S
g
∂
G
g
∂ T
p
∂μ g
∂ T
p
E
0
0 − μ g
T
R + R
vib
/ T
e
Θ vib / T − 1 (39)
The heat of sublimation at temperature T is
H
sub
= T Δ
S
sub
= T (
S
g
S
s
Calculate the molar entropies
S
s
and
S
g
of the crystalline and vapor forms of I 2 at 320 K with
Eqs. (38) and (39), and obtain the molar heat of sublimation Δ
H
sub
with Eq. (40). Compare it
with the value obtained by the Clausius-Clapeyron method and with any literature values that
you can find.
DISCUSSION
Of the two methods of determining Δ
E
0
0 with Eqs. (33) and (37), which do you judge gives the
more precise value? Which gives the more accurate value? Which provides the better test of the
overall statistical mechanical approach? Compare this approach with the purely thermodynamic
method using the integrated Clausius-Clapeyron equation, taking into account the
approximations involved in the latter. State the average temperature corresponding to your
Clapeyron value of Δ H sub
Comment on the choice of representative values of
ν J
for the 12 vibrational modes of the crystal.
How much would reasonable changes (say, 10 to 20 percent) in these values affect the results of
the calculations? If possible, comment on the effect of using the Debye approximation (different
crystal vibrational frequencies) for the acoustic lattice modes instead of the Einstein
approximation (all the same vibrational frequency).
REFERENCES
This lab is modified for CSM use from Ch. 48 of Experiments in Physical Chemistry, 6
th edition
by D. P. Shoemaker, C. W. Garland, and J. W. Nibler (1996).
- N. Levine, Physical Chemistry , 4th ed., pp. 756-757, McGraw-Hill, New York (1995).
- P. W. Atkins, Physical Chemistry , 5th ed., pp. 674-675, Freeman, New York (1994).
- Ibid ., pp. 694-698.
- Adapted from R. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure IV:
Constants of Diatomic Molecules , p. 332, Van Nostrand Reinhold, New York (1979).
- P. W. Atkins, op. cit. , pp. 698-700.
- C. Kittel, Introduction to Solid State Physics , 5th. ed., Wiley, New York (1976).
- N. W. Ashcroft and N. D. Mermin, Solid State Physics , Saunders, Philadelphia (1976).
- F. van Bolhuis, P. B. Koster, and T. Migghelsen, Acta Crystallogr. 23, 90 (1967).
- a.) H. G. Smith, M. Nielsen, and C. B. Clark, Chem. Phys. Lett. 33 , 75-78 (1975); b.) H. G.
Smith, C. B. Clark, and M. Nielsen, in J. Lascombe (ed.), Dynamics of Molecular Crystals ,
pp. 4411-4446, esp. fig. 2, Elsevier, Amsterdam (1987).
- C. Kittel, op. cit ., pp. 120-121.
- N. W. Ashcroft and N. D. Mermin, op. cit ., pp. 470-474.
- G. E. Bacon, Neutron Diffraction , 3d ed., chap. 9, Oxford University Press, Oxford (1975).
- P. Sulzer and H. Wieland, Helv. Phys. Acta 25 , 653 (1952).
- J. G. Calvert and J. N. Pitts, Jr., Photochemistry , p. 184, ref. 424 in chap. 5, Wiley, New
York (1966).
- D. A. Shirley and W. F. Giauque, J. Am. Chem. Soc. 31 , 4778 (1959).
- G. Henderson and R. A. Robarts, Jr., Am. J. Phys. 46 , 1139 (1978).
- F. Stafford, J. Chem. Educ. 40 , 249 (1963).
GENERAL READING
N. W. Ashcroft and N. D. Mermin, op. cit ., chaps. 4, 5, 7, 22-24.
N. Davidson, Statistical Mechanics , chaps. 6-8, McGraw-Hill, New York (1962).
C. Kittel, op. cit ., chap. 4.
