The Gibb's free energy equation is used to determine the spontaneity of a reaction and is written as follows: .

is Gibb's free energy,  is enthalpy, and  is entropy. In order for a reaction to be spontaneous, Gibb's free energy must have a negative value. Based on the equation, we can see that a positive enthalpy in combination with a negative entropy will always result in a positive value for Gibb's free energy.

This means these are the conditions that will always result in a nonspontaneous reaction. 

A galvanic cell results in a positive cell potential from a spontaneous reaction. Spontaneous reactions always have a negative Gibb's free energy.

An equilibrium constant greater than one would indicate that the equilibrium concentration of products is greater than the equilibrium concentration of reactants, consistent with a spontaneous reaction.

You can find the Gibb's free energy of a galvanic cell by using the following equation:

 is the number of moles of electrons that are transferred in the reaction,  is Faraday's constant, and  is the potential of the cell.

We are given the constant value and the cell potential. The moles of electrons transferred is equal to the change in charge on the atoms in the reaction. In this reaction, copper is reduced from a charge of to zero, requiring that is gained two moles of electrons.

Using these values, we can find Gibb's free energy for the cell.

Notice that the value is negative. Galvanic cells are spontaneous, and will have negative Gibb's free energies at standard conditions.

If Q is less than K, then the reaction has not yet reached the equilibrium state. It will proceed spontaneously in the forward direction. Since it is proceeding spontaneously in the forward direction, this must mean that the ΔG (Gibbs free energy) must be negative, or less than zero.

Enthalpy and temperature are necessary when mathematically evaluating Gibbs free energy, but the reaction quotient and equilibrium constant provide enough information to qualitatively determine that the reaction is proceeding spontaneously.

Based on Gibbs Free Energy, ∆G = ∆H – T∆S, we find that ∆H– will contribute to spontaneity (∆G<0). Since we are looking at temperatures, in order for ∆S to make an nonspontaneous reaction spontaneous at only high temperatures, ∆H will be positive, and ∆S will be positive.

Given the equation for free energy, (delta)G = (delta)H-T(delta)S, we can determine that the reaction is nonspontaneous at all temperatures if H is positive and S is negative. This combination would always lead to a positive G value, meaning that free energy is required for the reaction to take place and it is therefore nonspontaneous. 

Change in free energy must always be negative for a spontaneous process. Additionally, Q must be less than K so that the reaction will proceed in the forward reaction, toward equilibrium.

A reaction being favorable or unfavorable is largely determined by the thermochemistry of the reaction.  More specifically it is determined by the change in gibbs free energy which is determined by the change in enthalpy, the change in entropy, and the temperature of the reaction.  Here we are told that the reaction has a favorable enthalpy change (- means energy is released).  Qualitatively we can see that the reaction will have an unfavorable change in entropy because the product, being a solid, is more ordered than the reactants which are both solid and gaseous.  Thus we can conclude that the reaction is favorable because of the favorable change in enthalpy, which helps to overcome the unfavorable change in entropy.  

A reaction is spontaneous if the change of Gibb's free energy (G) is less than zero. Recall that (G) is related to H and S by the equation below.

For this particular reaction,  S is negative because the total number of moles of gas decreases from reactants to products. Since the reaction is spontaneous at lower temperatures, then G must be negative when T is small. Since the -TS term would be positive for all values of T, the only way G can be negative is if H is negative. At higher temperatures, the positve -TS term would outweigh the negative H term, resulting in a positive G and a non-spontaneous reaction.

We know that , so

There is a net decrease in free energy, so the reaction is more spontaneous at 500 K.