Question

What is this equation and what does it mean?

Answer 1

I came across this equation in a lecture, I /think/ it's Fick's second law? (or some variation thereof) I know what some of the symbols mean, but not others:

For example hv and gm are Enthalpy of vacancy formation and Activation energy for diffusion,

e is the base exponent,

k is boltzman's constant

t is temperature in Kelvin

but what is A and v? what does the equation equal to?

\[A *\nu* e^{(\Delta hv + \Delta gm)/kt } = ?\]

Thanks in advance!

Answer 2

Well, let's think about it:
hv = energy (E)
and
gm = work (w)

So you have a combination of the arrhenius equation with the addition of other factors.
Not sure why there is ∆gm
But, since this IS a chemistry question, we can disregard newtonian physics and simply think in terms of quantum physics.

A is the number of collisions (leading to a reaction or not) per second occurring with the proper orientation to reaction.
v, since we're talking about collisions here, i'm going to assume it's referring to velocity.
But the arrhenius equation is dealing more with statistical probability.

Am I safe in assuming that this is for your physical chemistry course?

Answer 3

@thadyoung

Hmm, that clears up a few things, it makes sense that A would be collisions per second.

I don't think v is velocity but I could be wrong. I think their needs to be some, pre-exponent factor there somewhere.

One thing I /do/ know is that this equation can be applied to vacancy diffusion, so, there's that.

It's for the Solid State course on edx. c:

Answer 4

In that case, it could be vibrational frequency.
I, personally, have never used this particular equation before. But, it's interesting that this would be in a solid-state course. I'd think they would be more interested in electromagnetic and optical properties rather than kinetics.