[lugerard]

Hi all,

I have a question whereby my tutor used ΔG(T2) = ΔG(T1) - (T2-T1)ΔS(T1)
shouldnt it be ΔG(T2) = ΔH(T1) - (T2-T1)ΔS(T1)?

[Yggdrasil]

No.  Here's the derivation.  We'll start with the definition of the Gibbs free energy:

ΔG = ΔH - TΔS

Now at temperatures T1 and T2, we have:

ΔG(T2) = ΔH(T2) - T2ΔS(T2)
ΔG(T1) = ΔH(T1) - T1ΔS(T1)

Let's subtract these two equations from each other:

ΔG(T2) - ΔG(T1) = ΔH(T2) - ΔH(T1) - T2ΔS(T2) + T1ΔS(T1)

Now, we assume that ΔH and ΔS do not change significantly with temperature (that is, ΔH(T1) = ΔH(T2) and ΔS(T1) = ΔS(T2).

ΔG(T2) - ΔG(T1) = ΔH(T1) - ΔH(T1) - T2ΔS(T1) + T1ΔS(T1)

Now, we can simplify the expression to obtain:

ΔG(T2) = ΔG(T1) - (T2-T1)ΔS(T1)

[lugerard]

So when do we actually use ΔG(T1) = ΔH(T1) - (T2-T1)ΔS(T1)

[Yggdrasil]

So when do we actually use ΔG(T1) = ΔH(T1) - (T2-T1)ΔS(T1)

You don't.  That's not a valid expression.

[lugerard]

So all I have to do before attempting any question is to determine the independence of parameters such as pressure or temperature, and then rewrite the equation for gibbs free energy at a higher temperature? Gibbs free energy of a system only revolves around this eqn? What do I have to do if they asked to raise Gibbs free energy from 298 K to 498K? Do I do the same way?

PS: I am having finals later on, its really crazy but I appreciate your *delete me* Thanks!