The Four ΔH/ΔS Sign Combinations
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State
A reaction with ΔH negative and ΔS positive is spontaneous at every temperature; positive ΔH and negative ΔS is nonspontaneous at every temperature; the other two combinations flip.
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Hydrogen peroxide's decomposition to water and oxygen is exothermic and increases gas moles, so it is spontaneous at every temperature.
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A negative ΔH alone does not guarantee spontaneity; unfavorable ΔS can push ΔG positive.