Vibrational Stretching Frequencies of some Diatomics

[DDTea]

For an assignment (not really homework, but not really exciting either), I'm trying to calculate the total entropy for the reaction:

Na₂ + X₂ $$\rightarrow$$ 2 NaX

Where X = F, Cl, and Br . ( I told you this isn't exciting). Also, in this theoretical reaction, everything involved is an ideal gas. As part of my calculation, I need to find the stretching frequency (in cm^-1, but I can always convert units to that) of the following molecules (ideal gasses, again): Na₂, F₂, Cl₂, Br₂, NaF, NaCl, and NaBr.

What is the best way to go about calculating these?? I was thinking that I'd simply look at the infrared spectra, but I cannot find any... Can I calculate the "force constant" of the bond somehow (modeling it in a sort of classical way) and then, from that, calculate the stretching frequency/IR absorption?

 

[DDTea]

Well, apparently it was staring me right in the face.$$\omega_{e}$$ is the vibrational stretching frequency I was looking for (I'm just not familiar with spectroscopic notations...doh!).

 

[Trave11er]

Here is NaCl spectrum.

 

[Trave11er]

If you take reaction Na2+X2=2NaX then entropy change of the system is 0 if you take everything as ideal gases then number of moles and volume doesn't change. Total entropy change will be equal to the entropy change of the surroundings which is (ejected heat)/(temperature of the surroundings).
There may be plenty of useful data for you here: http://webbook.nist.gov/chemistry/

 

[DDTea]

See, I would expect a very small *decrease* in entropy due to the removal of symmetry. That is, Na₂ and X₂ both have symmetry numbers of 2 while NaX has a symmetry number of 1.

I'm trying to calculate this from statistical mechanical principles, with a bit of the quantum harmonic oscillator thrown in (when it comes to calculating bond strengths from IR spectra, at least). Specifically, I'm trying to recreate data from JANAF tables.

I'll throw in the equations I'm using here; they're taken from Ch. 2 of Sydney Benson's "Thermochemical Kinetics."

$$S^{o}_{total} = S^{o}_{tran}+S^{o}_{vib}+S^{o}_{rot}+S^{o}_{symm}+S^{o}_{elec}$$

I expect the translational, vibrational, and rotational contributions to form the bulk of the total entropy. The symmetry term is a correction factor to the rotational term. The electronic term is expected to be miniscule and I'm not considering it in my calculation.

Continuing,

$$S^{o}_{tran}=37.0 + \frac{3}{2}Rln(\frac{M}{40})+\frac{3}{2}Rln(\frac{T}{298})+Rln(n)$$

Where R = ideal gas constant, M = molar mass of compound, T = absolute temperature, n = number of optical isomers the compound has.

$$S^{o}_{vib} = Rln(\frac{k_{B}T}{h\nu})+R$$

nu = energy of photon that causes a vibrational transition.

$$S^{o}_{rot} = 6.9+Rln(\frac{I}{\sigma_e})+Rln(\frac{T}{298})$$

where sigma_e = external symmetry number of the molecule.

$$S^{o}_{symm} = -Rln\sigma$$

And sigma= total symmetry number of the molecule (combination of external and internal symmetry).

Unfortunately, I have no idea how these equations were derived!

 

[alxm]

What is the best way to go about calculating these?? I was thinking that I'd simply look at the infrared spectra, but I cannot find any...

That'd be because most of the species you mention are homonuclear, so they're not IR active. (you'd need IR-Raman spectrum) Otherwise you can look at the http://www.nist.gov/pml/data/msd-di/index.cfm"

And there are tables of Morse potential parameters for diatomics out there, (which includes the force constant)

Can I calculate the "force constant" of the bond somehow (modeling it in a sort of classical way) and then, from that, calculate the stretching frequency/IR absorption?

That'd be the second derivative of the energy with respect to the coordinate distance, hence it's explicitly dependent on the energy, and the wave function, and a complete description of all the electrons. You can't calculate that classically; there's no property of a chemical bond you can calculate classically.

You're trying to create a (semi-)classical model of a chemical bond, which is to assume an effective potential that's a harmonic oscillator or Morse potential. But the only way to determine the parameters for that model is to fit them to experimental data, or to do an explicit quantum-mechanical calculation. Most QC programs will automatically, on doing a frequency calculation, do the entire calculation of the partition function and thermodynamic properties. So I'd assume you're intended to find some experimental values.

Calculating the IR frequencies given a harmonic-oscillator or Morse potential model is covered in every phys-chem textbook, really.