Physical Chemistry terminology

[ChopChop]

I'm just having a difficult time trying to differentiate between variables used and terms thrown around in PChem.

First of all, what is the difference between "bond energy" and "bond dissociation energy" in a Morse potential curve? I thought they were interchangeable.

Also, does anyone know what the vibrational constant (v_e) is? I've been searching through my book and the terms "vibrational constant" isn't on there, but for some reason, I keep thinking it's this equation:

ω = (k/m)^1/2

But my book never gives that equation a name! I just assumed it was a vibrational constant because of the force constant, k.

I'm so confused...

 

[zhermes]

"Bond Energy" (BE), and "bond dissociation energy" (BDE) are the same IDEA, at the very least--details can vary a little on context. BDE is literally the amount of energy it would take to break a bond; so this is a well defined number. BE is the 'energy stored in the bond' which is dependent on your reference point; usually BE is a negative number--the zero point referring to the point at which the bond will be broken. E.g. the BE is -151 J/mol, and the BDE is 151 J/mol. If for some reason the BE was being measured relative to something else, then the BE and BDE wouldn't be the same.

"Vibrational constant" (VC) is not a classical term, but I'm guessing you're on the right track. The equation you wrote
$$\omega = \sqrt(k/m)$$
is the angular frequency of oscillation (for a mass m, and spring constant k), the frequency would then be
$$\nu = \omega / 2\pi$$
which might be what they are referring to. Check the units to be sure, if its frequency is should be in Hz (hertz = inverse seconds).

 

[ChopChop]

Thank you for the much needed clarification! :)

Is it possible to estimate bond energy and bond dissociation energy from just looking at the molecule? Here the professor asks:

Estimate the bond energy and bond dissociation energy for ²D⁷⁹Br based on the isotope ¹H⁷⁹Br.

But my book never gives anything on how to solve something like that! I don't know where to start other than the fact that I can calculate the reduced/effective mass.

Do know of any books that would explain in detail each variable for each equation? It's so frustrating to have a useless textbook plus the fact that I have to stay tethered to a computer because I don't have a laptop.

 

[zhermes]

Sorry, I don't know of any good books for it.
My guess about question:
You can get the BE by take the mass of the molecule, and subtracting the mass of its components. E.g.
$$E_{DBr} = E_{D} + E_{Br} + E_{bond}$$
im not sure what that has to do with the other isotope though...

 

[ChopChop]

I'm not sure, either. Maybe it has something to do with bond order?

 

[vela]

You may want to take a gander at Wikipedia.

http://en.wikipedia.org/wiki/Bond_dissociation_energy#BDE_vs_bond_energy

 

[alxm]

I take it you're calculating vibrational energy levels, probably using the harmonic oscillator model?

Given the H.O. model, the vibrational energies can be calculated from the reduced mass and the force constant. Since isotopes have the same chemical properties, the force constant will be the same. They different isotope species will have different vibrational energy levels, including the ground state (zero-point) level.

This difference in zero-point vibrational energy means a difference in bond energy.