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Gibbs free energy in standard state vs. equilibrium


Unit of the equilibrium constant: contradiction of Bridgman's theorem?What kind of equilibrium constant we use for Gibbs free energy and Van't Hoff equation?Units for dissociation constant and relationship to Gibbs Free EnergySpontaneous Reaction and Gibbs Free EnergyUsing equilibrium constant in gibbs equationIs the Gibbs standard free energy always constant?reconciling free energy equationsUnderstanding Gibbs free energy and enthalpyWhy does the standard enthalpy of formation diverge so far from the standard Gibbs free energy of formation for some substances?Is the equilibrium constant in the expression based on pressure or concentration?How to derive the relation between gibbs energy and equilibrium constant?













1












$begingroup$


I have a problem with the definition of the standard Gibbs energy and its connection to the equilibrium constants.



I think, that I've basically understood what the different equation mean but there is one thing, I'm unable to understand:



On the one hand:



One may describe a chemical reaction with $Delta G=Delta G^circ + RTlnQ$. In equilibrium $Delta G = 0$ and the equation reads $Delta G^circ = -RT lnK$.



On the other hand:



The definition of standard state is very clear: pressure = 1 bar and all reactants and products must have activity = 1.



If I consider these two aspects separately, everything seems to be fine. But these two concepts have to be valid at the same time, what leads to $Delta G^circ = 0$ (always), since $K=1$ (all activities are per definition = 1).



Therefore, $Delta G^circ$ would be always zero. I know that this isn't true, but I don't understand why.



Can anyone explain this to me?



Thanks!










share|improve this question







New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 2




    $begingroup$
    "since $K=1$" not necessarily true; it is $Q = 1$. Nobody said that at standard state the system must be in equilibrium.
    $endgroup$
    – orthocresol
    9 hours ago











  • $begingroup$
    ok, but the formulae say: At standard state $Delta G^circ = -RTlnK$ and K is the ratio of the activities of reactants and products in equilibrium, due to the standard state definition K = 1, because it says: each $a=1$. Doesn't this definition disagree with your comment? I find this all really confusing.
    $endgroup$
    – user76122
    8 hours ago










  • $begingroup$
    I find that terribly confusing and wrong if it claims $K = 1$.
    $endgroup$
    – orthocresol
    8 hours ago










  • $begingroup$
    I know it is wrong, but I don't get why :( Did you understand my problem, that is the pure formula seems to contradict the general understanding...
    $endgroup$
    – user76122
    7 hours ago










  • $begingroup$
    @user76122 Orthocresol is right. Your definition of standard state in the context of $Delta G^0$ is wrong. The standard state of a pure material entails that its activity is 1. But in the context of the equation for $Delta G$ you deal conceptually with mixtures and thus not pure materials. If you follow my derivation of the formula (see here) you can see which assumptions go into $Delta G^0$. It is true that it is defined for standard pressure/concentration, but activity being equal to 1 is not presumed.
    $endgroup$
    – Philipp
    6 hours ago
















1












$begingroup$


I have a problem with the definition of the standard Gibbs energy and its connection to the equilibrium constants.



I think, that I've basically understood what the different equation mean but there is one thing, I'm unable to understand:



On the one hand:



One may describe a chemical reaction with $Delta G=Delta G^circ + RTlnQ$. In equilibrium $Delta G = 0$ and the equation reads $Delta G^circ = -RT lnK$.



On the other hand:



The definition of standard state is very clear: pressure = 1 bar and all reactants and products must have activity = 1.



If I consider these two aspects separately, everything seems to be fine. But these two concepts have to be valid at the same time, what leads to $Delta G^circ = 0$ (always), since $K=1$ (all activities are per definition = 1).



Therefore, $Delta G^circ$ would be always zero. I know that this isn't true, but I don't understand why.



Can anyone explain this to me?



Thanks!










share|improve this question







New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$







  • 2




    $begingroup$
    "since $K=1$" not necessarily true; it is $Q = 1$. Nobody said that at standard state the system must be in equilibrium.
    $endgroup$
    – orthocresol
    9 hours ago











  • $begingroup$
    ok, but the formulae say: At standard state $Delta G^circ = -RTlnK$ and K is the ratio of the activities of reactants and products in equilibrium, due to the standard state definition K = 1, because it says: each $a=1$. Doesn't this definition disagree with your comment? I find this all really confusing.
    $endgroup$
    – user76122
    8 hours ago










  • $begingroup$
    I find that terribly confusing and wrong if it claims $K = 1$.
    $endgroup$
    – orthocresol
    8 hours ago










  • $begingroup$
    I know it is wrong, but I don't get why :( Did you understand my problem, that is the pure formula seems to contradict the general understanding...
    $endgroup$
    – user76122
    7 hours ago










  • $begingroup$
    @user76122 Orthocresol is right. Your definition of standard state in the context of $Delta G^0$ is wrong. The standard state of a pure material entails that its activity is 1. But in the context of the equation for $Delta G$ you deal conceptually with mixtures and thus not pure materials. If you follow my derivation of the formula (see here) you can see which assumptions go into $Delta G^0$. It is true that it is defined for standard pressure/concentration, but activity being equal to 1 is not presumed.
    $endgroup$
    – Philipp
    6 hours ago














1












1








1





$begingroup$


I have a problem with the definition of the standard Gibbs energy and its connection to the equilibrium constants.



I think, that I've basically understood what the different equation mean but there is one thing, I'm unable to understand:



On the one hand:



One may describe a chemical reaction with $Delta G=Delta G^circ + RTlnQ$. In equilibrium $Delta G = 0$ and the equation reads $Delta G^circ = -RT lnK$.



On the other hand:



The definition of standard state is very clear: pressure = 1 bar and all reactants and products must have activity = 1.



If I consider these two aspects separately, everything seems to be fine. But these two concepts have to be valid at the same time, what leads to $Delta G^circ = 0$ (always), since $K=1$ (all activities are per definition = 1).



Therefore, $Delta G^circ$ would be always zero. I know that this isn't true, but I don't understand why.



Can anyone explain this to me?



Thanks!










share|improve this question







New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




I have a problem with the definition of the standard Gibbs energy and its connection to the equilibrium constants.



I think, that I've basically understood what the different equation mean but there is one thing, I'm unable to understand:



On the one hand:



One may describe a chemical reaction with $Delta G=Delta G^circ + RTlnQ$. In equilibrium $Delta G = 0$ and the equation reads $Delta G^circ = -RT lnK$.



On the other hand:



The definition of standard state is very clear: pressure = 1 bar and all reactants and products must have activity = 1.



If I consider these two aspects separately, everything seems to be fine. But these two concepts have to be valid at the same time, what leads to $Delta G^circ = 0$ (always), since $K=1$ (all activities are per definition = 1).



Therefore, $Delta G^circ$ would be always zero. I know that this isn't true, but I don't understand why.



Can anyone explain this to me?



Thanks!







physical-chemistry reaction-mechanism equilibrium free-energy






share|improve this question







New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question







New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question






New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 9 hours ago









user76122user76122

91




91




New contributor




user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






user76122 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







  • 2




    $begingroup$
    "since $K=1$" not necessarily true; it is $Q = 1$. Nobody said that at standard state the system must be in equilibrium.
    $endgroup$
    – orthocresol
    9 hours ago











  • $begingroup$
    ok, but the formulae say: At standard state $Delta G^circ = -RTlnK$ and K is the ratio of the activities of reactants and products in equilibrium, due to the standard state definition K = 1, because it says: each $a=1$. Doesn't this definition disagree with your comment? I find this all really confusing.
    $endgroup$
    – user76122
    8 hours ago










  • $begingroup$
    I find that terribly confusing and wrong if it claims $K = 1$.
    $endgroup$
    – orthocresol
    8 hours ago










  • $begingroup$
    I know it is wrong, but I don't get why :( Did you understand my problem, that is the pure formula seems to contradict the general understanding...
    $endgroup$
    – user76122
    7 hours ago










  • $begingroup$
    @user76122 Orthocresol is right. Your definition of standard state in the context of $Delta G^0$ is wrong. The standard state of a pure material entails that its activity is 1. But in the context of the equation for $Delta G$ you deal conceptually with mixtures and thus not pure materials. If you follow my derivation of the formula (see here) you can see which assumptions go into $Delta G^0$. It is true that it is defined for standard pressure/concentration, but activity being equal to 1 is not presumed.
    $endgroup$
    – Philipp
    6 hours ago













  • 2




    $begingroup$
    "since $K=1$" not necessarily true; it is $Q = 1$. Nobody said that at standard state the system must be in equilibrium.
    $endgroup$
    – orthocresol
    9 hours ago











  • $begingroup$
    ok, but the formulae say: At standard state $Delta G^circ = -RTlnK$ and K is the ratio of the activities of reactants and products in equilibrium, due to the standard state definition K = 1, because it says: each $a=1$. Doesn't this definition disagree with your comment? I find this all really confusing.
    $endgroup$
    – user76122
    8 hours ago










  • $begingroup$
    I find that terribly confusing and wrong if it claims $K = 1$.
    $endgroup$
    – orthocresol
    8 hours ago










  • $begingroup$
    I know it is wrong, but I don't get why :( Did you understand my problem, that is the pure formula seems to contradict the general understanding...
    $endgroup$
    – user76122
    7 hours ago










  • $begingroup$
    @user76122 Orthocresol is right. Your definition of standard state in the context of $Delta G^0$ is wrong. The standard state of a pure material entails that its activity is 1. But in the context of the equation for $Delta G$ you deal conceptually with mixtures and thus not pure materials. If you follow my derivation of the formula (see here) you can see which assumptions go into $Delta G^0$. It is true that it is defined for standard pressure/concentration, but activity being equal to 1 is not presumed.
    $endgroup$
    – Philipp
    6 hours ago








2




2




$begingroup$
"since $K=1$" not necessarily true; it is $Q = 1$. Nobody said that at standard state the system must be in equilibrium.
$endgroup$
– orthocresol
9 hours ago





$begingroup$
"since $K=1$" not necessarily true; it is $Q = 1$. Nobody said that at standard state the system must be in equilibrium.
$endgroup$
– orthocresol
9 hours ago













$begingroup$
ok, but the formulae say: At standard state $Delta G^circ = -RTlnK$ and K is the ratio of the activities of reactants and products in equilibrium, due to the standard state definition K = 1, because it says: each $a=1$. Doesn't this definition disagree with your comment? I find this all really confusing.
$endgroup$
– user76122
8 hours ago




$begingroup$
ok, but the formulae say: At standard state $Delta G^circ = -RTlnK$ and K is the ratio of the activities of reactants and products in equilibrium, due to the standard state definition K = 1, because it says: each $a=1$. Doesn't this definition disagree with your comment? I find this all really confusing.
$endgroup$
– user76122
8 hours ago












$begingroup$
I find that terribly confusing and wrong if it claims $K = 1$.
$endgroup$
– orthocresol
8 hours ago




$begingroup$
I find that terribly confusing and wrong if it claims $K = 1$.
$endgroup$
– orthocresol
8 hours ago












$begingroup$
I know it is wrong, but I don't get why :( Did you understand my problem, that is the pure formula seems to contradict the general understanding...
$endgroup$
– user76122
7 hours ago




$begingroup$
I know it is wrong, but I don't get why :( Did you understand my problem, that is the pure formula seems to contradict the general understanding...
$endgroup$
– user76122
7 hours ago












$begingroup$
@user76122 Orthocresol is right. Your definition of standard state in the context of $Delta G^0$ is wrong. The standard state of a pure material entails that its activity is 1. But in the context of the equation for $Delta G$ you deal conceptually with mixtures and thus not pure materials. If you follow my derivation of the formula (see here) you can see which assumptions go into $Delta G^0$. It is true that it is defined for standard pressure/concentration, but activity being equal to 1 is not presumed.
$endgroup$
– Philipp
6 hours ago





$begingroup$
@user76122 Orthocresol is right. Your definition of standard state in the context of $Delta G^0$ is wrong. The standard state of a pure material entails that its activity is 1. But in the context of the equation for $Delta G$ you deal conceptually with mixtures and thus not pure materials. If you follow my derivation of the formula (see here) you can see which assumptions go into $Delta G^0$. It is true that it is defined for standard pressure/concentration, but activity being equal to 1 is not presumed.
$endgroup$
– Philipp
6 hours ago











2 Answers
2






active

oldest

votes


















4












$begingroup$

As explained in the comments, the standard state conditions lead to $Q=1$ and therefore $$Delta G=Delta G^circ+ RTln1=Delta G^circ$$ On the other hand at equilibrium $Q=K$ and so $$Delta G=Delta G^circ + RTlnK$$ This of course leads to $Delta G^circ = -RTlnK$ since at equilibrium $Delta G=0$.



So you might want to think of it as three statements:



  1. For the conversion of reactants to products in their standard states $Q=1$

  2. At equilibrium $Delta G=0$

  3. At equilibrium $Q=K$

The first statement is consistent with the definition of standard states.
The second statement follows from combination of the first and second laws of thermodynamics.
The third statement is a definition of $K$.






share|improve this answer









$endgroup$




















    1












    $begingroup$

    What you enter into $K$ are not the activities of the pure reactants and pure products at standard state (if you did then, yes, $K$ would be 1). Rather, it is their activities at equilibrium (raised, of course, to the power of their respective stochiometric coefficients). And, at equilibrium, these activities are generally not equal to one.






    share|improve this answer











    $endgroup$












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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      4












      $begingroup$

      As explained in the comments, the standard state conditions lead to $Q=1$ and therefore $$Delta G=Delta G^circ+ RTln1=Delta G^circ$$ On the other hand at equilibrium $Q=K$ and so $$Delta G=Delta G^circ + RTlnK$$ This of course leads to $Delta G^circ = -RTlnK$ since at equilibrium $Delta G=0$.



      So you might want to think of it as three statements:



      1. For the conversion of reactants to products in their standard states $Q=1$

      2. At equilibrium $Delta G=0$

      3. At equilibrium $Q=K$

      The first statement is consistent with the definition of standard states.
      The second statement follows from combination of the first and second laws of thermodynamics.
      The third statement is a definition of $K$.






      share|improve this answer









      $endgroup$

















        4












        $begingroup$

        As explained in the comments, the standard state conditions lead to $Q=1$ and therefore $$Delta G=Delta G^circ+ RTln1=Delta G^circ$$ On the other hand at equilibrium $Q=K$ and so $$Delta G=Delta G^circ + RTlnK$$ This of course leads to $Delta G^circ = -RTlnK$ since at equilibrium $Delta G=0$.



        So you might want to think of it as three statements:



        1. For the conversion of reactants to products in their standard states $Q=1$

        2. At equilibrium $Delta G=0$

        3. At equilibrium $Q=K$

        The first statement is consistent with the definition of standard states.
        The second statement follows from combination of the first and second laws of thermodynamics.
        The third statement is a definition of $K$.






        share|improve this answer









        $endgroup$















          4












          4








          4





          $begingroup$

          As explained in the comments, the standard state conditions lead to $Q=1$ and therefore $$Delta G=Delta G^circ+ RTln1=Delta G^circ$$ On the other hand at equilibrium $Q=K$ and so $$Delta G=Delta G^circ + RTlnK$$ This of course leads to $Delta G^circ = -RTlnK$ since at equilibrium $Delta G=0$.



          So you might want to think of it as three statements:



          1. For the conversion of reactants to products in their standard states $Q=1$

          2. At equilibrium $Delta G=0$

          3. At equilibrium $Q=K$

          The first statement is consistent with the definition of standard states.
          The second statement follows from combination of the first and second laws of thermodynamics.
          The third statement is a definition of $K$.






          share|improve this answer









          $endgroup$



          As explained in the comments, the standard state conditions lead to $Q=1$ and therefore $$Delta G=Delta G^circ+ RTln1=Delta G^circ$$ On the other hand at equilibrium $Q=K$ and so $$Delta G=Delta G^circ + RTlnK$$ This of course leads to $Delta G^circ = -RTlnK$ since at equilibrium $Delta G=0$.



          So you might want to think of it as three statements:



          1. For the conversion of reactants to products in their standard states $Q=1$

          2. At equilibrium $Delta G=0$

          3. At equilibrium $Q=K$

          The first statement is consistent with the definition of standard states.
          The second statement follows from combination of the first and second laws of thermodynamics.
          The third statement is a definition of $K$.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 5 hours ago









          Night WriterNight Writer

          2,453223




          2,453223





















              1












              $begingroup$

              What you enter into $K$ are not the activities of the pure reactants and pure products at standard state (if you did then, yes, $K$ would be 1). Rather, it is their activities at equilibrium (raised, of course, to the power of their respective stochiometric coefficients). And, at equilibrium, these activities are generally not equal to one.






              share|improve this answer











              $endgroup$

















                1












                $begingroup$

                What you enter into $K$ are not the activities of the pure reactants and pure products at standard state (if you did then, yes, $K$ would be 1). Rather, it is their activities at equilibrium (raised, of course, to the power of their respective stochiometric coefficients). And, at equilibrium, these activities are generally not equal to one.






                share|improve this answer











                $endgroup$















                  1












                  1








                  1





                  $begingroup$

                  What you enter into $K$ are not the activities of the pure reactants and pure products at standard state (if you did then, yes, $K$ would be 1). Rather, it is their activities at equilibrium (raised, of course, to the power of their respective stochiometric coefficients). And, at equilibrium, these activities are generally not equal to one.






                  share|improve this answer











                  $endgroup$



                  What you enter into $K$ are not the activities of the pure reactants and pure products at standard state (if you did then, yes, $K$ would be 1). Rather, it is their activities at equilibrium (raised, of course, to the power of their respective stochiometric coefficients). And, at equilibrium, these activities are generally not equal to one.







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 4 hours ago

























                  answered 4 hours ago









                  theoristtheorist

                  2288




                  2288




















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