Physical Chemistry

hazel06

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

The question is attached.

2. Relevant equations

-∆_fS (T - T₀) - (∆_fC_p/T₀)[(T - T₀)²/2] = 0

Please let me know if this doesn't make any sense!

3. The attempt at a solution

Given:

Td: 39.3ºC = 312.45K
∆H: 157 kJ/mol = 152000 J/mol

I calculated ∆S = -∆H/Td -----> ∆S = -486.48 J/mol.K (Entropy)

Now, for the temperature of maximum stability. I know that I have ∆S, Td(T₀), and ∆_fC_p. All is needed is to plug it into the equation I was given. But, I know I would need to derived it to make it more simpler to find T. Or at least that's what I think!

I derived it. And got: -∆_fS-∆_fC_p(T)/T₀+∆_fC_p

Not sure if I did it right! If someone could confirm I did it right or show me the correct way to derive it. That would be great! B/c I plugged the values in and did not get a value of around 260K. Which is given by the instructor to be the approximate answer.

Set up as: -(-486.48 J/mol.K) - (2800 J/mol.K)(T)/312.45K + 2800 J/mol.K = 0

Maybe I calculated it wrong b/c I keep on getting 312.62K. Which is exactly like the 312.45K. Very clueless!

After this could someone give me a hint on how to start finding the cold denaturation temperature? Thanks!

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