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### Topic: "Statistical Thermodynamics of Iodine Sublimation" data analysis help.  (Read 2745 times)

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#### jamesrb

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##### "Statistical Thermodynamics of Iodine Sublimation" data analysis help.
« 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 70oC. 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: $$\Delta \widetilde{E}_{0}^{0}$$ 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):

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 Θvib and Θrot. The only problem is the Θj 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:

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 Θj? Θrot is the rotational characteristic temperature given by:
$$\Theta _{rot}=\frac{hcB_{0}}{k}$$

I solved for it earlier. Additionally Θvib is given by:
$$\Theta _{vib}=\frac{hc\tilde{v}_{0}}{k}$$
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:

$$\Theta _{j}=\frac{hc\tilde{v}_{i}}{k}$$
and plug in the appropriate values from Table 1? And then sum up appropriately in the equation above. I still don't know what Θj 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
« Last Edit: February 09, 2015, 07:23:55 AM by Arkcon »

#### mjc123

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##### Re: "Statistical Thermodynamics of Iodine Sublimation" data analysis help.
« Reply #1 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.