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I don't think there is a lowest value that G can be. And in many instances G is negative. If you look at the table of Gibbs Free Energy of formation in the back of the textbook, many of the values are below 0.
Yes, I'm not sure if G can have a lowest value, but if I'm remembering correctly, Lavelle said that measuring G alone is very difficult, therefore we always measure the change in G. If you meant to ask about DeltaG, DeltaG can't have a lowest value, and if it does, then it definitely wouldn't be 0! Remember, if DeltaG is positive, then it is an endergonic reaction that requires energy, and if DeltaG is negative, then it is an exergonic reaction that releases energy. This point alone proves that the "lowest" value for DeltaG cannot be 0! Hope this helps! (:
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