Calculate Free Energy for Formation

[mrlucky0]

I realize that this is a chem prob, but I'm stuck with what I thought was a straightforward problem while studying for my physical chemistry exam.

Homework Statement

The standard molar enthalpy of combustion of solid phenol (C6H5OH) is -3054 kJ/mol at 298k and it's standard molar entropy is 144.0 J/(K*mol). Calculate the standard free energy of formation of phentol at 298k.

Homework Equations

G = H - TS

The Attempt at a Solution

G = (-3054.0 * 10^3 J/mol) - (298 K) (144.0 J/k/mol)


From what I know about the determination of G, I simply plugged in those numbers but my solution was way off. The solution should be -50.42 kJ/mol but help with deriving it from first principle is what I'm after.

 

[gaea]

energy of formation of C6H5OH

you have to calculate the standard reaction entropy first and the reaction enthalpies.

G = rxn enthalpies - (Temp x rxn entropy)

The reaction entropy is: entropy of products - entropy of reactants
the reaction enthalpy is: enthalpy of products - entropy of reactants

 

[Moetasim]

As a scientist, it is important to approach problems systematically and accurately. The first step in solving this problem is to ensure that all units are consistent. In this case, the standard molar entropy of phenol is given in J/(K*mol), while the standard molar enthalpy of combustion is given in kJ/mol. Therefore, we need to convert the enthalpy to J/mol by multiplying by 1000. This gives us a value of -3054000 J/mol.

Next, we can use the equation G = H - TS to calculate the standard free energy of formation. Plugging in the values, we get:

G = (-3054000 J/mol) - (298 K) (144.0 J/(K*mol))
G = -3054000 J/mol - 42832.8 J/mol
G = -3096832.8 J/mol

To convert this to kJ/mol, we divide by 1000, giving us a value of -3096.8328 kJ/mol. However, this is still not the correct answer.

The reason for this is that the standard free energy of formation is typically given in units of kJ/mol, not J/mol. Therefore, we need to divide our answer by 1000 again to get the correct units. This gives us a final answer of -3.0968328 kJ/mol, which is much closer to the expected solution of -50.42 kJ/mol.

In summary, when solving problems like this, it is important to pay attention to units and make sure they are consistent. It is also helpful to double-check calculations and convert to the correct units at the end to ensure accuracy.