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How can you tell if a reaction is spontaneous?

  1. Feb 25, 2008 #1
    How can you tell if a reaction is spontaneous?
  2. jcsd
  3. Feb 25, 2008 #2
    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]

    [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]
    Last edited: Feb 25, 2008
  4. Feb 26, 2008 #3
    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

    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.
  5. Feb 26, 2008 #4

    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.
    Last edited: Feb 26, 2008
  6. Feb 26, 2008 #5

    Andy Resnick

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    A process is spontaneous if the Gibbs free energy is negative.
  7. Feb 26, 2008 #6
    A process is spontaneous if the Gibbs free energy variation is negative.
  8. Feb 26, 2008 #7
    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.
  9. Feb 27, 2008 #8
    "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

    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:
    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.
  10. Feb 27, 2008 #9
    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. :smile:
    Last edited: Feb 27, 2008
  11. Feb 28, 2008 #10
    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.
  12. Feb 29, 2008 #11
    Certainly, but you know that spontaneity in chemical physics is a different concept from kinetics.
  13. Feb 29, 2008 #12
    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 o_O, 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 :).
  14. Feb 29, 2008 #13
    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.
  15. Feb 29, 2008 #14
    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."
  16. Feb 29, 2008 #15

    Andy Resnick

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    Doh! right. Thanks.
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