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If the value for delta G is negative then energy needs to be added in order to form the compound so therefore it would not be stable, as it doesn't occur spontaneously. However, a negative delta G for a compound means the compound can form without any stimulus or added energy and is therefore a stable compound.
In order for decomposition of compounds into their elements to be stable, ∆G of decomposition would have to be (+) aka it won't spontaneously break down. Since decomposition is the opposite of formation, ∆Gf would have to be (-). In other words, the formation is spontaneous and the decomposition is not spontaneous (and thus stable).
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