# How to calculate Gibbs energy of formation at a temp T using standard state data?

1. May 15, 2012

### pa5tabear

I hope this isn't deemed school related. It is something I learned in school, but I'm now trying to figure out a reaction model for my work.

In the process of calculating the reaction constant, usually you first determine the Gibbs energy of formation of each species, find the difference between the reactants and products to find the energy of reaction, then use relationship:

ln K = (-grxn)/(R*T)

where K is your equilibrium constant, T is your temperature, and R is the gas constant with appropriate units.

If I have data for the standard state, and want to calculate the energy of formation for a different temperature, how do I do this?

I know I can adjust the equilibrium constant for temperature, but I'm wondering if it is possible to also calculate the energy of formation at a non standard temperature.

2. May 17, 2012

### jfizzix

I was looking at this one day when I was preparing to TA my thermodynamics section. What I think you want to use is the Gibbs-Helmholtz equation.

http://en.wikipedia.org/wiki/Gibbs–Helmholtz_equation

This should allow you to calculate Gibbs free energies of reactions at other temperatures than STP.

-James

3. May 18, 2012

### pa5tabear

Thanks!

I think this is exactly what I needed. I just didn't know such a derivation existed. I was trying to think of ways to do it using the definition ΔG=ΔH-T*ΔS but I wasn't sure how to calculate the T*ΔS term.

I do have one question. In the wikipedia article, it says to treat ΔH as independent of temperature. I'm guessing they say this for ease of calculation. The reaction I'm looking at (silicon epitaxy) occurs at around 1150 °C... very far from 298 K. Do you think it would be worthwhile to calculate a ΔH value at 1150 °C using heat capacity data, and switch that in? I think doing so would only give a more accurate value, and I see no issue.