[Big-Daddy]

I know this is more Maths than chemistry but can someone explain how it is actually done? I would like to apply to N_A, that is why I ask in a chemistry forum ... (not the best reason but I'm sure you guys know)

[curiouscat]

I would like to apply to NA

That does't make much sense, sorry.

[Big-Daddy]

I would like to apply to NA

That does't make much sense, sorry.

Ah sorry, I meant N_A!. I meant I would like to apply Stirling's approximation to the factorial of Avogadro's number.

But in general, I'd like how to see how n! goes down in Stirling's approximation, assuming n is very large.

[curiouscat]

ln(n!) = n ln(n) - n

[Big-Daddy]

Thanks.

The common use of this calculation as far as I know (in chemistry) is to do with entropy and the number of possible microstates, but for all normal values of entropy this results in a number between ω=10¹⁰²⁰ and ω=10¹⁰²⁶. Yet N_A!=10^4.6957·1046. This isn't anywhere near the right ballpark ... if we had ω=10^4.6957·1046 microstates the entropy of our system would be roughly 5·10²⁴ J·K^-1·mol^-1 which is obviously ludicrous. What am I doing wrong? Is it perhaps not N_A!, but rather something else, that is meant to be here?

[Borek]

Google for "calculating number of microstates".

[Corribus]

I have no idea what you're trying to do.  Maybe you could try explaining where you came up with this need.

[Borek]

IMHO he tries to calculate the entropy of a mole of ideal gas using S=k×ln(W) and assuming W=N_A!

[Big-Daddy]

IMHO he tries to calculate the entropy of a mole of ideal gas using S=k×ln(W) and assuming W=N_A!

Yes but W≠N_A! according to my Internet search (and also basic logic) ... I will have to dig deeper to find out what it is exactly.

[Corribus]

W is a partition function and significantly more difficult to figure out than simply taking factorial of the number of particles in the system.  Stirling's approximation is involved in the determination, but as you see here:

http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture_6/node2.html

There is a lot more to it.  This is really the subject of graduate level statistical mechanics. 

[Big-Daddy]

W is a partition function and significantly more difficult to figure out than simply taking factorial of the number of particles in the system.  Stirling's approximation is involved in the determination, but as you see here:

http://www.nyu.edu/classes/tuckerman/stat.mech/lectures/lecture_6/node2.html

There is a lot more to it.  This is really the subject of graduate level statistical mechanics.

Haha I looked at the third equation on the page and realized instantly where this was going  Anyway, thanks for clearing up Stirling's approximation. At least now I know that W≠N_A! as I used to think.