CHGN 353 DRY LAB
THE SUBLIMATION ENERGY OF I2
Show that by substituting the expression of Equations (25) and (32) into Equation (2), and doing some
rearranging, you can obtain the following expression:



*
+ 12 
−Θj
/0
2
7 )12
$ %
1 32
2
T
T
1
−
e
j=1
1
2πmk
k




∆E00 = RT ln
+ ln 
 + ln

−Θvib
2
p
h
2Θrot
1−e T
(33)
Where k is the Boltzmann constant, h is the Planck constant, R is the molar gas constant, T is temperature,
m is the molar mass of I2 , Θj =
hcνj
k ,
Θrot =
hcBo
k ,
and Θvib =
hcνo
k .
The quantity
hc
k
= 1.43877 cm K.
For I2 gas B0 = 0.037315 cm−1 , and ν0 = 213.3 cm−1 . For I2 solid the frequencies of the 12 independent
vibrational modes, all in units of cm−1 are 21.0, 26.5, 33.0, 41.0, 49.0, 51.5, 58.0, 59.0, 75.4, 87.4, 180.7, and
189.5.
So we are able to relate the vapor pressure of I2 gas over solid I2 in terms of the quantum mechanically
determined energies of the vibrations, rotations and translations of the molecules of I2 in both the gaseous
and solid states and the experimentally determined value of ∆E00 .
Though this looks complicated, it really is not. What we see is that the energy of sublimation is divided
into three parts, these tell how the energy is partitioned among the translational, vibrational, and rotational
motions of the solid and gas. The first term on the right hand side of the equation, in which the pressure
appears, really tells us nothing more than the pressure arises only from translational motions of the gas.
The probability of translational motions of the solid goes as ln(1), not very likely. The second term on the
right relates the way in which energy is partitioned among the vibrational modes of the solid and gas, while
the third term gives the same information about rotations. Again, as in translation, because a rotation of
the solid requires the cooperative motion of all of the molecules in the crystal it is not very likely and no
energy is found in rotational modes of the solid.
You are now in the position to perform a “computational experiment”, that is to alter the parameters of
Equation (33) and see how this will effect the equilibrium vapor pressure. For instance, what would be the
effect of changing the moment of inertia of I2 on the equilibrium vapor pressure, if the energies of all other
modes in the crystal and gas were held constant. Some possible exercises to explore these relationships are
suggested below.
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1. Rearrange Equation (33) to express pressure as a function of ∆E00 and T . Using the value of ∆E00
measured in wet lab plot the variation in pressure with temperature. How do these results compare
with those you measured in the previous lab? Can you get a better agreement by adjusting ∆E00 slightly?
How sensitive is the pressure to changes in ∆E00 ? Look up the actual sublimation energy of I2 . How
close were you in determining this energy?.
2. Evaluate the second term on the right hand side of the above Equation (33) (note it is a function of T ).
Plot this term versus T for the temperatures between 300 and 350 K. Does this term vary strongly with
T ? If you were to replace this term with a constant equal to its average value over the temperature
range of the experiment (300 to 350 K), how much error will be produced in the calculated values of
pressure? To what do these changes physically correspond.
3. Now examine the effects of changing Θrot on the equilibrium partial pressure of I2 .
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