Gibbs Free Energy

[Ossih]

Hi guys

I've looked on line a lot and I still don't understand what Gibbs free energy IS. I get that G = H - TS and delta G = delta H - T delta S. Ive also read that its the maximum non-expansion work.

First question, what is non expansion work? What kindsfof work count as non expansion?

Second, how can I get from

Stotal = Ssystem + Ssurroundings

to

delta G = delta H - T delta S?

Any answers would be greatly appreciated

[Emmi]

Expansion work is work done against an opposing pressure and/or volume. So non-expansion work is work done when it's not against an opposing pressure or volume. A few examples of non-expansion work is electrical work, mechanical work, and the formation of chemical bonds.

 

I found a derivation online (here: http://chemistry.tutorvista.com/physical-chemistry/gibbs-free-energy.html ) but I'll explain it out:

 

If a system is not isolated, then you can view the change in entropy as

ΔS(Total) = ΔS(system) + ΔS(surroundings)

 

And if the changes occur under constant heat and pressure, the only place for the heat to go is to the surroundings. This is given by the expression

ΔS(surroundings) = −qp/T = −ΔH/T

Where q is heat and p is pressure (which equal the enthalpy of reaction), and T is the temperature

 

Now we can rearrange the equation as

ΔS(Total) = ΔS(system) − ΔH/T

 

Multiply through by T and you get

 

TΔS(Total) = TΔS(system) − ΔH or -TΔS(Total) = Î”H - TΔS(system)

 

And since Î”G = -TΔS, we get the relation we want, which is:

 

ΔG = Î”H - TΔS(system)

 

Obviously this isn't required to know at the IB level at all, but it's interesting and is used a lot in thermodynamics.

Edited August 25, 2014 by Emmi

[Ossih]

That's awesome, explained everything so well. Thank you!