Ask A Scientist Chemistry Archive

name         William
status       student
age          18

Question -   To whom it may concern:
I need a straight forward definition of exactly what the GIBB's Free
Energy is of a system.  I know that this is a thermodynamic state
function, what exactly is it?  Thank you for whom ever responds to this
plaguing question.
------------------------------------------------
This is a very perceptive and respectable question, that deserves a clear
response.  I WILL respond to it, but I do not want to do it "off the cuff"
sitting in front of my computer monitor. Bear with me and give me a couple
of days.

Vince Calder
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There is a "short" answer, and a "longer" answer to your question: "What
exactly is the Gibbs free energy?" The operative word is --EXACTLY. The
"short answer" level response that follows, will tell you what it is at the
operational and application level. But if by EXACTLY you mean, "Where does
it come from?", that is the "longer" answer. The longer answer requires a
very careful explanation, which I will put together, but it will take longer
to find the time to do it so that it is intelligible give the format
limitations of this site. The need for care is that the thermodynamic
derivation is not intuitively "obvious" and some terms need careful and
precise definition. Unfortunately, this need for careful definition and
logic is often dismissed in a lot of texts and in a lot of lectures. The
Gibbs free energy derives from the second law of thermodynamics, as a
special case where the temperature and pressure are constant, but that is
all I will say about the second law in this, the "short answer".

The Gibbs free energy (difference), like all energies except E=mc^2, is a
difference in energy. It is commonly denoted (dG, the "d" indicating a
difference. In some of the earlier literature you will find this as dF
instead of dG). This is in contrast to the Helmholtz free energy, denoted
dA, and the "internal energy" dE, which I will not consider further here.

The Gibbs free energy difference is a thermodynamic function (thermodynamic
function = a function that depends only on the initial and final state of
some process, and not the path by which one goes from the initial to the
final state.). The Gibbs free energy predicts whether a process (e.g. a
chemical reaction) carried out at constant temperature (T (kelvins)), and
constant applied pressure (P (atm)) can occur, or cannot occur under the
prescribed conditions of temperature and pressure. These are the conditions
that most chemical reactions are done. That is why these limitations are
applied.

The Gibbs free energy difference is defined in terms of two other
thermodynamic properties, the enthalpy change denoted "dH" and the entropy
change "dS". The definition is: dG = dH - T*dS. If dG<0 the process/reaction
is allowed, or in the jargon is "spontaneous". If dG>0, the process/reaction
will not occur. If dG=0, the process/reaction is at equilibrium.

The enthalpy change (dH) is the heat given off, or absorbed at constant
(T,P). The convention is dH<0 for exothermic processes/reactions and dH>0
for endothermic processes/reactions. The entropy change dS is a measure of
the relative number of microscopic states available to the final state
compared to the initial state. If there are more microscopic states
available to the products, dS>0; if there are fewer microscopic states
available, dS<0. This term is sometimes referred to as the relative amount
of "randomness", but I personally do not like that characterization.

The dH term takes care of the general observation that processes/reactions
that give off heat (exothermic) tend to occur, while processes/reactions
that absorb heat tend not to occur. This of course is not always true since
some substances like ammonium chloride readily dissolve in water even though
the dissolution is endothermic (the solution gets cold as the ammonium
chloride dissolves), and other processes such as the expansion of the air in
a balloon when you pop it always happens even though there is no heat
absorbed or given off.

These processes occur, because the entropy term, dS, is positive so that the
term,
T*dS is greater than the dH term and consequently dG<0.

You need to understand the term "spontaneous" as it is used in
thermodynamics, which is different than the definition of the term in common
usage. In thermodynamics, the term "spontaneous" means the process is
"allowed", is possible, in contrast to "is not allowed" or "will not likely
occur". It does not mean that the rate is fast or slow. Fast or slow has
nothing to do with "spontaneous". "Spontaneous" only has to do with the
ultimate possibility or impossibility of a process/reaction. For example, if
I have two vessels connected by a valve, where one contains a gas at some
pressure, and the other is evacuated, and I open the valve -- the gas will
spontaneously and quickly expand until the pressure in the two vessels is
the same. The reverse process, where the gas molecules at equal pressure
would move in just such a way that all the gas ends up in one vessel, and
the other vessel is evacuated could happen, but the probability that all the
molecules would individually have the correct trajectory so that it would
happen is so remote that we say the process in not allowed. An example of a
process which is "spontaneous" but slow is a lump of charcoal resting on a
plate. That lump of charcoal is unstable with respect to its burning in air
to produce CO2. That is still a "spontaneous" process/reaction in the
thermodynamic sense, even though it is exceedingly slow at room temperature
and pressure.

There are compilations of dH's and dS's (or quantities from which those can
be computed) for thousands of substances and chemical reactions. So that it
is possible to calculate whether some chemical reaction is possible without
having to actually try the reaction. Or it is possible to say whether one
form a molecule is more or less stable than some other form of the compound
(for example, diamond vs. graphite at room temperature and ambient pressure;
or diamond vs. graphite at 1000 K and 1000 atm pressure).  Obviously this is
tremendously useful, especially when the "answer" is not obvious.

So here is the "short" (not so short) explanation of what the Gibbs free
energy difference is. I hope you find it "straight forward". Thermodynamics
is not a simple subject by its very nature, so the explanations are not
trivial, even the "straight forward" explanations.

I will respond shortly about where the Gibbs free energy comes from, but
this  requires an even more delicate explanation.

Vince Calder
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