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

 

[DeeNos]

I would first clarify the equations and parameters being used to ensure accuracy and consistency in my calculations. For question 1, the Boltzmann equation is typically used to calculate the ratio of molecules in different energy states, but it is unclear how it applies to the given information about vibrational energy spacing. I would ask for clarification or further information to properly answer the question.

For question 2, the ΔG equation is correct for determining the change in Gibbs free energy, but I would also consider using the Van't Hoff equation (ΔG = ΔH - TΔS) to calculate the change in Gibbs free energy at different temperatures. To determine the number of unfolded protein molecules at 300K, I would need more information about the system and the conditions of the experiment. Without this information, I cannot provide a proper solution.