[disillusioned19]

Greetings everyone,

My lecturer told me that Gibbs Free Energy is just a label of convenience to the quantity:

dH - TdS

i.e. we just call the result of this expression the 'Gibbs Free energy'. Whilst I can understand that, why is this particular expression useful for analysing a chemical reaction, and why not, say dH+dS or any other alternative seemingly arbitrary expression.

I notice this question is fairly philosophical, but I'm a reductionist by nature.

Thanks in advance.

[Jorriss]

It's not a philosophical question, the expression shows up enough to warrant its own special title, 'the gibbs free energy.' Have you seen the derivation of Gibbs free energy as the amount of non-pv work a system can do? That may be enlightening.

BTW, it can't be dH + dS, wrong units.

[juanrga]

Greetings everyone,

My lecturer told me that Gibbs Free Energy is just a label of convenience to the quantity:

dH - TdS

i.e. we just call the result of this expression the 'Gibbs Free energy'. Whilst I can understand that, why is this particular expression useful for analysing a chemical reaction, and why not, say dH+dS or any other alternative seemingly arbitrary expression.

I notice this question is fairly philosophical, but I'm a reductionist by nature.

Thanks in advance.

I suppose that you mean dH+TdS.

Well, consider a simple mechanical example, think of the expression 1/2 mv². This expression appears so often in mechanical equations that we give it a name, which surely you know. Why this expression and not other as 3/5 mc³/v? Because so far as I know this hypothetical term nowhere appears in the equations of mechanics. Why would you name and use something useless?

Return to thermo. The fundamental expression for internal energy U is a function of composition, entropy, volume... U=U(S,V,N)

Now for typical chemical systems volume is not an adequate variable, and at lab we lack entropymeters, but we have good thermometers. Therefore, we can do a Legendre transformation of variables (S,V) (T,p) {*}

U  U + pV - TS

or what is the same because H=U+pV

U  H - TS

This new function G(T,p,N) = U + pV - TS is so important in chemistry that we call it «Gibbs energy» and use it very often.

As in the mechanical case of the hypothetical 3/5 mc³/v, your hypothetical dH+TdS nowhere appears in the fundamental equations of thermodynamics and, therefore, it does not receive any special name, neither is studied.

{*} The Legendre transformation is a way to transform a function in a given set of variables into an equivalent function in other set of variables.