Spontaneity in terms of Gibbs Free Energy

[Stevin1H]

How do we determine the temperature for when a reaction is at equilibrium in order to use this value to determine the other values of temperature that would be spontaneous with a negative Gibbs Free energy value or non spontaneous with a positive Gibbs Free Energy value?

[Hedi Zappacosta 1E]

You set the gibbs free energy equation delta H - T x delta S equal to 0. In other words, delta G is 0 because this is the value at which the reaction will change from non spontaneous to spontaneous. If a higher value of the resulting temperature gives a negative Delta G, then the reaction will be spontaneous at temperatures higher than the T you found from setting the equation equal to zero. And the opposite works as well for non spontaneous reactions.

[gwynlu1L]

also, if you're given the values for delta H and delta S, you can make a guess as to what T values will make the rxn spontaneous or not spontaneous. For example, if delta H is negative and delta S is positive, the rxn is spontaneous at all temps bc delta G will always be negative. However, if delta H is negative and delta S is negative, then the rxn will be spontaneous at low temps bc you'd have to decrease the value of TdeltaS