# Boltzmann Distribution (Chemistry/ Physics)

1. Jan 8, 2013

### Klestine

1. The problem statement, all variables and given/known data
Okay i want to ask 2 questions.
Question 1
Hyperstoichiometric compound Al3O has a vibrational energy spacing of 3.08x 10^-21J
how many molecules are present in the ground state at 300k and 3000K

Question 2
Calirimetric data for protein unfolding yielded following thermodynamic parameters
Parameter
ΔH (Tr) 220kJ/mol
ΔS (Tr) 0.68 kJ/mol/K
ΔCp 2.5 kJ/mol/K
how many protein molecules unfolded at 300K
2. Relevant equations
For question 1
Shown below is the boltzmann equation
nj/ni = e-(Ej-Ei)/KT

Grond state equation is
nj/n0 = e-(Ej)/KT (this I found in a text book)

For question 2

ΔG=ΔH-TΔS

3. The attempt at a solution

Okay for question the equation given in lecture notes is different to the equation i found in text books and the internet and it is

n0 = n(1-e-(ΔE)/KT

Two equations are confusing me, the this is if i use the equation given under relevant equations I get a weird answer,obviously wrong. Using the equation given in lecture notes it is easy and straight forward, but i doubt if it correct!

and for question 2 i have no clue what so ever to be honest. I do not know how i can use ΔCp

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Jan 8, 2013
2. Jan 9, 2013

### Staff: Mentor

With the Boltzmann equation, you would have to consider all states (and add their relative probabilities), as this just gives a relative probability. Your equation at (3.) did take this into account, you can use it.

Question 2: No idea.

3. Jan 10, 2013

### Mandelbroth

Question 2 looks like fun!

Think about what the link between ΔS and CP ($\Delta S = nC_p ln\frac{T}{T_0}$) means for the system.

4. Jan 11, 2013

### Klestine

thanx guys, question 2 is fun and an absolute killer