The question is attached.
-∆fS (T - T0) - (∆fCp/T0)[(T - T0)2/2] = 0
Please let me know if this doesn't make any sense!
The Attempt at a Solution
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 ∆fCp. 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-∆fCp(T)/T0+∆fCp
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!