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What is the significance of Gibbs free energy?

Calculating change in Gibbs energy! Help figure out please?

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    Compute ΔrxnG0 from the data provided, and multiply by the number of moles in 600.0 mg of bromine. Solution: At 291 K, the Gibbs Free Energy for dissolving bromine in water is ΔrxnG0 = -2600 - (291)(-22.2) = 3860 J/mol For 150.0 mg, the change is (60.0 mg)(3860 J/mol)/(159.808 g/mol)/(1000 mg/g) = 1.449239

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Compute ΔrxnG0 from the data provided, and multiply by the number of moles in 600.0 mg of bromine. Solution: At 291 K, the Gibbs Free Energy for dissolving bromine in water is ΔrxnG0 = -2600 - (291)(-22.2) = 3860 J/mol For 150.0 mg, the change is (60.0 mg)(3860 J/mol)/(159.808 g/mol)/(1000 mg/g) = 1.449239

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