Boltzmann Distribution (Chemistry/ Physics)

[Klestine]

Homework Statement

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 (T_r) 220kJ/mol
ΔS (T_r) 0.68 kJ/mol/K
ΔC_p 2.5 kJ/mol/K
how many protein molecules unfolded at 300K

Homework Equations

For question 1
Shown below is the Boltzmann equation
n_j/n_i = e^-(Ej-Ei)/KT

Grond state equation is
n_j/n₀ = e^-(Ej)/KT (this I found in a textbook)

For question 2

ΔG=ΔH-TΔS

The Attempt at a Solution

Okay for question the equation given in lecture notes is different to the equation i found in textbooks 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 ΔC_p

Thank you very much in advance for your help

Homework Statement

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[mfb]

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.

 

[Mandelbroth]

Homework Statement

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
Calorimetric data for protein unfolding yielded following thermodynamic parameters
Parameter
ΔH (T_r) 220kJ/mol
ΔS (T_r) 0.68 kJ/mol/K
ΔC_p 2.5 kJ/mol/K
how many protein molecules unfolded at 300K

Homework Equations

For question 1
Shown below is the Boltzmann equation
n_j/n_i = e^-(Ej-Ei)/KT

Grond state equation is
n_j/n₀ = e^-(Ej)/KT (this I found in a textbook)

For question 2

ΔG=ΔH-TΔS

The Attempt at a Solution

Okay for question the equation given in lecture notes is different to the equation i found in textbooks 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 ΔC_p

Thank you very much in advance for your help

Question 2 looks like fun!

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

 

[Klestine]

thanx guys, question 2 is fun and an absolute killer