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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.

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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.

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  • $\begingroup$ 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. $\endgroup$ – brt88 Jan 20 at 10:55
  • $\begingroup$ 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$\Delta S$. $\endgroup$ – Maurice Jan 20 at 11:20

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