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Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: jamesrb on February 09, 2015, 12:31:59 AM

Title: "Statistical Thermodynamics of Iodine Sublimation" data analysis help.
Post by: jamesrb on February 09, 2015, 12:31:59 AM

So for my undergraduate Physical Chemistry II class we used a UV spectrophotometer (Shimadzu UV-2450) to record the absorption spectrum (from 700 to 450 nm) of a sample of I₂ in a solid/gas equilibrium (in a cuvette) at 20, 30, 40, 50, 60, and 70^oC. We recorded the absorbance at 700 and 520 nm at each temperature respectively in order to calculate the net absorbance via the difference:

A = A₅₂₀ - A₇₀₀

That's all well and done and a lot of other calculation have been performed thus far as I worked my way through the calculation laid out for me. I am leaving them out for the sake of brevity. However I have come to a point in the lab manual that leaves me confused. I need to solve the equation below for: [tex]\Delta \widetilde{E}_{0}^{0}[/tex] The energy needed to sublime 1 mold of crystalline I₂ into the ideal gas phase at absolute zero:

Equation (sorry about the thumbnail size, I don't know how to properly insert an image on the forums):
(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fs27.postimg.org%2F946xsxfhb%2FExperiment5_Equation34.jpg&hash=e2e79bf815c75b18024f8d20c506fcd3c8e5adc0) (http://postimg.org/image/946xsxfhb/)

So I need to use the above equation to solve for the energy as I state above. I have my p value, I have my T value, I also have Θ_vib and Θ_rot. The only problem is the Θ_j value inside the summation of the second term. I don't know what that correspond to exactly. The lab manual include a table of "Discrete (representative) phonon frequencies in I₂ crystals*" and I know that has something to do with the calculation.

Table 1:
(https://www.chemicalforums.com/proxy.php?request=http%3A%2F%2Fs16.postimg.org%2Fpztc2qcjl%2FExperiment5_Table1.jpg&hash=412f41d9c237e4afd685d1623a0af3048038a14e) (http://postimg.org/image/pztc2qcjl/)

I know how to handle summations I am just not sure what I am supposed to be summing here. Do I plug in the representative frequency for Θ_j? Θ_rot is the rotational characteristic temperature given by:
[tex]\Theta _{rot}=\frac{hcB_{0}}{k}[/tex]

I solved for it earlier. Additionally Θ_vib is given by:
[tex]\Theta _{vib}=\frac{hc\tilde{v}_{0}}{k}[/tex]
I solved for that too. Since they are both characteristic temperatures I think maybe I am supposed to use the representative frequencies for from Table 1 to calculate the 12 "whatever" characteristic temperatures to be used in the summation? Would I use:

[tex]\Theta _{j}=\frac{hc\tilde{v}_{i}}{k}[/tex]
and plug in the appropriate values from Table 1? And then sum up appropriately in the equation above. I still don't know what Θ_j is.

If anyone could guide me in the right direction I would be grateful. This type of lab report is difficult to write considering statistical mechanics isn't covered until much later in the semester.

*MOD EDIT -- attach image for convenience

Title: Re: "Statistical Thermodynamics of Iodine Sublimation" data analysis help.
Post by: mjc123 on February 09, 2015, 05:17:03 AM

I think that's right. If that's all the data you are given in the lab manual, I don't see anything else you can do.