How can you tell if a reaction is spontaneous?

In order to tell if a reaction is spontaneous you must ask one simple question:

"Does the entropy of the system increase?"

All processes seek to have an entropy INCREASE, therefore if there is an entropy decrease the theoretical process cannot happen in the real universe (although I've been told theres some "odd" physicist acceptions, but these really arent applicable here)

Mathematically however this is expressed as:

[tex]\Delta G = \Delta H - T\Delta S [/tex]

Where:
[tex]\Delta G[/tex] - The gibbs free energy, this is a measure of the overall energy change for the reaction (and therefore entropy), a negative gibbs free energy corresponds to an increase in the entropy of the system and therefore a spontaneous reaction
[tex]\Delta H[/tex] - The enthalpy change for the process in question, be it a reaction enthalpy or otherwise. This is the energy released to/absorbed by the reaction and is a gauge of the overall entropy change of the system, if energy is released to the surroundings it can be said that the entropy of the surroundings is increasing.
[tex]T\Delta S[/tex] - The entropy change of the process in question.

A sometimes convinient way of viewing this equation (even though its a gauge of free energy) is:

[tex]\Delta S_{Total} = \Delta S_{Surroundings} + \Delta S_{System}[/tex]

 

This is confusing in the extreme. You've got things bass ackwards. Let's do some rearranging:

In order to tell if a reaction is spontaneous you must ask one simple question:

"Does the entropy of the universe increase?"

[tex]\Delta S_{Total} = \Delta S_{Surroundings} + \Delta S_{System} > 0[/tex]?

"The entropy of the universe strives toward a maximum"; therefore,if there is a decrease in the entropy of the universe, the process cannot happen.

Is there a state function of the system that can tell us whether a process
can occur spontaneously? There are, in fact, several. If the process occurs at constant temperature and volume, the Helmholz free energy should be used;
if the conditions are constant temperature and pressure, then the Gibbs free energy may be used. For the latter case,

[tex]\Delta G = \Delta H - T\Delta S [/tex],

where G, H, T and S are properties of the system. If the change in the
Gibbs free energy is negative, then the process in question can occur
spontaneously.

Not necessarily. The entropy of the system can in fact decrease as long
as the enthalpy change compensates for this---that is what the equation says! In many exothermic chemical reactions, the change in the enthalpy is huge in comparison with the entropy term. If all of this energy were released as heat, then there would be a massive increase in the entropy of the universe. Instead of letting the energy be released as heat, one can harness the process to produce useful work. The change in the free energy function tells us how much useful work can be extracted from the process.

 

KISS


Calculate the change in gibbs free energy for the reaction that you want to examine. You should have tables of Gibbs energies in the back of your textbook.


If it is negative then it is spontaneous. Simple as that.

 

A process is spontaneous if the Gibbs free energy is negative.

 

A process is spontaneous if the Gibbs free energy variation is negative.

 

a negative gibbs free energy change corresponds to an increase in the entropy of the system

Is a correct statement, because the enthalpy releases energy to the surroundings that then become "The system" in order to compensate for the fact that the "universe" is a closed system in itself. I guess the wording whas slightly off i'm not seeing why I had my post rehashed and shot down when the content was basically exactly the same, but the general math was put in front of the qualitative entropy stuff, because he's probably asking it for a homework Q.

 

"Shooting down" your post was not at all my intention. After all, you did
mention the criterion for a spontaneous reaction, but why did you
put it at the very end and then in the form of a footnote, as it were? I
did, however, intend to strongly criticise your post because 1)
there are fundamental errors in it and 2)several things in it
are very confusing, at least to me. If you feel hurt by my wording, I
apologise for that but I do not wish to retract my criticism.

The first error is your main statement:

This is not
the relevant question but rather "Does the entropy of the universe
increase?". Quoting from Atkins, "The only criterion of
spontaneous change in thermodynamics is the increase in total entropy of
the universe" By universe is meant the system plus the surroundings. The
entropy of the system in a spontaneous process may increase or
decrease (The existence of the birds and the bees and the flowers and the
trees bears witness to this).

This criterion fully answers the question posed in the original post. And
it is not "qualitative entropy stuff"; it can be made quantitative and
precise and the Gibbs free energy criterion and other criteria can be
derived from it. You correctly give the Gibbs free energy change in terms
of the enthalpy H and entropy S, state functions of the system.
You failed to mention, however, that the particular criterion for
spontaneous change, a decrease in the Gibbs free energy change, only
applies to reactions which occur under the restraint of constant
temperature and pressure. You are in excellent company, for Andy_Resnick
and Lightarrow also leave out this important qualifier. They thereby
ascribe to the Gibbs free energy criterion a generality that it does not
possess: for reactions restrained to occur at constant temperature and
volume, for example, it is the Helmholz free energy that one must use.
Granted, most chemical reactions are carried out under conditions of
constant temperature and pressure, but not all by any means. So why appeal
to a criterion that only applies some of the time when a general criterion
is available? Why negotiate with the monkey when the organ grinder is
present?

Now to the confusion. Why do you insist that

? You could say that an increase in the entropy contributes
to decrease in G. True, but G could still increase if the enthalpy
increased sufficiently. And conversely, G could decrease even if S
decreased, as long as H decreased sufficiently. So although G depends on
S, it does not correspond to it. This misunderstanding certainly
leads to a lot of confusion.

Thermodynamics is exquisitely precise but one must be precise in talking
about it. Consider this:

What
does this mean? You have to be quite clear about what is the system and
what are the surroundings; you cannot willy nilly change them about. In
talking about the enthalpy you say

. Since when is the enthalpy a gauge of the overall
entropy change of the system? This is just plain wrong. Also, you mean
"the energy released to/absorbed by the system". Consider the
following in your remarks about the free energy change:

. What precisely is "overall energy change"? And why do
you add "(and therefore entropy)"? Are energy and entropy being equated
here or what? Again "...an increase in the entropy of the system and
therefore a spontaneous reaction." Incorrect. There is, however, a true
statement hiding in all this: "a negative gibbs free energy (change)
corresponds to...a spontaneous reaction", at least at constant temperature
and pressure!

I'm sorry but I am hopelessly confused by such statements. You probably
want to throw bricks at me, and I understand that, but I think that a
reply to a question should be as clear as possible.

 

That's correct. We are too much used to constant T and P processes and we can easily forget the others.
I assume that, e.g., for an enginer working on spark ignition internal combustion engines, thinking about constant volume processes is more usual.

 

But for a reaction to be spontaneous in human terms we need something more than just universe entropy increasing or Gibbs free energy (for constant T and P) decreasing. There ar e a number of termodynamically spontaneous reactions that will not happen un human time scales. As an example, you won't see a diamond burning at 20º even when this reaction should be spontaneous.

 

Certainly, but you know that spontaneity in chemical physics is a different concept from kinetics.

 

I wasnt offended or anything, it just seemed you went a little overly harsh to somone attempting to contribute to a purely educational forum. As for system/surroundings, some people seem to use the convention that the "system" includes the "Surroundings" this is used to debunk stupid things like creationists claiming that DNA cant evolve because the entropy of the system decreases so nananananah scientists must be wrong. I do aploigize however for making my posts in this confusing.

However I do personally use the system/surroundings convention, just I see gibbs free energy as a measure of the total entropy change of a reaction, and it constitutes both the entropy change of the reaction and the entropy change of the surroundings, but I do agree that it's better to explain it in terms of the universe, just I am used to trying to explain it to people who are convinced that AHMAHGAHD it must be a change in the system! you cant talk about the surroundings! its a closed system! etc etc.

Also I wasnt aware of the helmholtz being its own equation , for constant volume but varying pressure I just tended to use the [tex]\Delta H = \Delta U + p\Delta v[/tex] relationship but it's nice to know theres a name for the constant volume case. Thanks for the clarification of the matter Pkleinod and I'll try not to do it again, after all I'm here to learn as much as the next guy :).

 

This is exactly what I was trying to point out.

Thermodynamics (Gibbs, Helmholtz, universe entropy criteria, ...) will tell you what can be spontaneous and what won't. But even when is thermodynamically established that a reaction is spontaneous it might be that on human time scale the reaction does not evolve at all. If a reaction is thermodynamically established to not to be spontaneous, it cannot be spontaneous independently of time scale.

 

A quotation from Atkins might help again: "The word 'spontaneous' is another of those common words that has been captured by science and dressed in a more precise meaning. In thermodynamics spontaneous means not needing to be driven by doing work of some kind. Broadly speaking, 'spontaneous' is a synonym of 'natural'. Unlike in everyday language, spontaneous in thermodynamics has no connotation of speed: it does not mean fast. Spontaneous in thermodynamics refers to the tendency for a change to occur. Although some spontaneous processes are fast (the free expansion of a gas for instance) some may be immeasurably slow (the conversion of diamond into graphite, for instance). Spontaneity is a thermodynamic term that refers to a tendency, not necessarily to its actualization. Thermodynamics is silent on rates."

 

Doh! right. Thanks.