# Finding Gibbs energy at different temperatures just given Gibbs energy at one temperature

How would it be found the Gibbs energy at a certain temperature, if they just give you another Gibbs energy at a temperature? For example: Given $$\Delta G = -230 Kcal/mol$$ at $$773K$$ for the reaction $$4/3Al + O_2 > 2/3Al_2O_3$$, find the Gibbs energy at $$573K$$

With that data I can only think of doing $$(-230*573)/773$$, but as far as I know the Gibbs energy is not only related to the temperature.

You have to know the entropy change of the reaction $$\Delta S$$, because the variation of $$\Delta G$$ with temperature is equal to -$$\Delta S$$. So when you know $$\Delta S$$, you multiply it by the $$\Delta T$$, here $$200 K$$, and subtract the result from your original value of $$\Delta G$$. This calculation is a first approach. To be more precise, you would have to take into account the change of heat capacity of the three substances ($$\ce{Al, O2, Al2O3}$$) when $$T$$ goes from $$773 K$$ to $$573 K$$. Usually this change is small and can be neglected.
• Yeah I know how the $\Delta G$ varies, the problem is the exercise, just determining the $\Delta G$ at two different temperatures. But as you say, maybe I could assume the change of the heat capacity and entropy can be neglected. – brt88 Jan 20 at 10:55
• No. You should know the entropy of your substances, calculate the difference product minus reagent, multiply by $\Delta T$ and substance it to $\Delta G$. This is sufficient. And do ignore the changes of heat capacity, which is much smaller than the effect of$\Delta S$. – Maurice Jan 20 at 11:20