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When DH is negative and DS is positive, the Gibbs free energy change DG = DH - T*DS is always negative and thus the reaction is always spontaneous.
When DH is positive and DS is negative, the Gibbs free energy change DG is always positive and thus the reaction is never spontaneous.
When the signs of DH and DS are the same, the entropy and enthalpy parts of the Gibbs free energy oppose each other. When this occurs, the temperature decides when the reaction is spontaneous or not. You can compute this temperature by figuring out the temperature at which DG is zero: this is where it changes sign and thus the reaction changes its spontaneity.
Example: At what temperature does the following reaction become spontaneous?
Solution: We need to compute the parts of DG,
so first look up the thermodynamic data from a table
Next, compute DH and DS