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From the second law of thermodynamics, we know that the natural progression of a system is to an increase in entropy. Therefore, a reaction in which the total entropy naturally increases is spontaneous. In the equation for Gibbs, deltaG = -T[deltaS(tot)] at constant temperature and pressure. As a result, as the change in total entropy increases, Gibbs becomes more negative. That's why a negative deltaG is associated with spontaneity. Hope that helps!
Spontaneous reactions release free energy, thus the sign of ΔG must be negative. Looking at the Gibbs free energy equation, when ΔH is negative and ΔS is positive, the sign of ΔG will always be negative and therefore the reaction will be spontaneous at all temperatures.
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