Why does Gibbs free energy have to be negative?

Answer 1

The system's and its surroundings' overall entropy must rise for a reaction to occur on its own:

#DeltaS_(overall)=DeltaS_(sur)+DeltaS_(sys)>0#
The entropy of the system changes by #(DeltaH_(sys))/T#, and because #DeltaH_(sys)=-DeltaH_(sur)#, entropy change of the surroundings can be calculated from the equation
#DeltaS_(sur)=-(DeltaH)/T#
Substituting this for #DeltaS_(sur)# gives
#DeltaS_(overall)=(-DeltaH)/T+DeltaS_(sys)>0#
Multiplying through by #-T# gives
#DeltaG=-TDeltaS_(overall)=DeltaH-TDeltaS_(sys)<0#
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Answer 2

For a spontaneous reaction to occur, the Gibbs free energy change (∆G) must be negative, indicating that the system moves towards a lower energy state. This is in accordance with the second law of thermodynamics, ensuring the system's tendency to increase overall entropy and stability.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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