[orthoformate]

Hello,

I have learned that Gibbs Free Energy can be derived from The Clausius Inequality.

dS_surr+dS_system≥0 for processes that are spontaneous or in equilibrium.

dS_surr=-q/T

dS_system-q/T≥0

TdS_system-q≥0

assuming constant pressure q=H and assuming H does not vary with temperature

0≥ H-TdS_sys or ΔG=ΔH-TΔS

Based on the Clausius inequality derivation the T in ΔG=ΔH-TΔS is the Temperature of the surroundings.

Do the temperature of the surroundings and the temperature of the system have to be in equilibrium for this definition to hold?

For example. A reaction with a ΔH: -500Kj/mol occurs in a reaction flask at 298K. The heat generated in transferred to the surroundings keeping the temperature constant. The temperature of the surroundings is 315K (it's really hot in the lab) and does not change with the addition of this heat.

ΔS_sys:-1.68 Kj/K*mol
ΔS_surr:1.59 Kj/K*mol

ΔS_universe:-0.09 Kj/K*mol

ΔG=-500Kj-315K(-500kJ/298K)= 29.2Kj

Am I doing this correctly?

[mjc123]

Congratulations, you have just discovered why heat does not flow from a cold body to a hot one! Did you really think heat generated in the reaction is transferred to the (warmer) surroundings? How?
Why doesn't the flask warm up to lab temp? Is it in a constant temperature bath at 298K? Then that is the "temperature of surroundings".
Your calculation of entropy is wrong. There will be an entropy change of reaction; the difference between the entropy of products and reactants. In the isothermal case, this is equal to ΔS_sys. ΔH is lost to/gained from the surroundings, and makes no contribution to S_sys. It comes from the chemical potential energy of the reagents, and goes to the surroundings; it doesn't contribute to the thermal energy of the system.
T in ΔG = ΔH - TΔS is the temperature of the system. The whole point, in a sense, is to express "ΔS_universe > 0" in terms of quantities of the system, so it is equivalent to "ΔG_system < 0". But that equivalency only holds for isothermal processes in thermal equilibrium with the surroundings. In other cases ΔG is not so useful. See this thread (which I notice you contributed to) for an example where ΔG > 0 for a spontaneous non-isothermal process: http://www.chemicalforums.com/index.php?topic=81854.msg297962#msg297962

[orthoformate]

Hi mjc123,

Thanks for the response, and pointing me back to that old thread. It is reassuring to know that thermal equilibrium is a requirement for the validity of a Gibbs free energy calculation. That makes sense to me.

In retrospect, the question I posed is ridiculous. The reaction vessel would of course just heat up. I am just trying to develop a deeper understanding of Entropy.