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[tex]\Delta G = \Delta H - T \Delta S [/tex]

I don't understand this equation satisfactorily.

I have learned so far that endothermic reaction having a positive [tex]\Delta S_{system}[/tex] is spontaneous at higher temperature because [tex]T\Delta S[/tex] out-compete the enthalpy term and make the free energy change negative.

But I don't understand why [tex]T\Delta S _{sorrounding}[/tex] should not increase with temperature as [tex]T\Delta S _{system}[/tex] does.

Clearly [tex]\Delta H[/tex] =[tex]-T\Delta S _{sorrounding}[/tex]

so we can rewrite the gibbs free energy equation

[tex]\Delta G= -T\Delta S _{sorrounding} - T\Delta S _{system}[/tex]

[tex]\Delta G = -T ( \Delta S _{sorrounding} + \Delta S _{system})[/tex]

if [tex]\Delta S _{sorrounding}[/tex] and [tex]\Delta S _{system}[/tex] both are constant then the sign of [tex]\Delta G[/tex] is independent of temperature. If [tex]\Delta G[/tex] is positive increasing temperature just make it more positive and If [tex]\Delta G[/tex] is negative increasing temperature just make it more negative. Temperature cannot change the sign.

I know I must be missing something. Please help!!

A[tex]^{ }_{A}[/tex]

I don't understand this equation satisfactorily.

I have learned so far that endothermic reaction having a positive [tex]\Delta S_{system}[/tex] is spontaneous at higher temperature because [tex]T\Delta S[/tex] out-compete the enthalpy term and make the free energy change negative.

But I don't understand why [tex]T\Delta S _{sorrounding}[/tex] should not increase with temperature as [tex]T\Delta S _{system}[/tex] does.

Clearly [tex]\Delta H[/tex] =[tex]-T\Delta S _{sorrounding}[/tex]

so we can rewrite the gibbs free energy equation

[tex]\Delta G= -T\Delta S _{sorrounding} - T\Delta S _{system}[/tex]

[tex]\Delta G = -T ( \Delta S _{sorrounding} + \Delta S _{system})[/tex]

if [tex]\Delta S _{sorrounding}[/tex] and [tex]\Delta S _{system}[/tex] both are constant then the sign of [tex]\Delta G[/tex] is independent of temperature. If [tex]\Delta G[/tex] is positive increasing temperature just make it more positive and If [tex]\Delta G[/tex] is negative increasing temperature just make it more negative. Temperature cannot change the sign.

I know I must be missing something. Please help!!

A[tex]^{ }_{A}[/tex]

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