When a Reaction Proceeds from Chemical Equilibrium

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• Basic equations of chemical equilibrium (review)
  • In the Basic Equations of Chemical Equilibrium (Remember This and Be Able to Use It) course, we noted the conditions that lead to chemical equilibrium.

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    //////////////// Basic equation of chemical equilibrium (review) /////////////////////////

    
    

                　　 【Original form】                   【Product form】

    
            　　　　    aA  +  bB  +  …　　  ⇆         xX  +  yY  + …
     

    In equilibrium, the following relationship holds.

                 
    

    
    

    K is called the equilibrium constant, and this relationship is called the law of mass action.

    
    
    

    [A], [B], [X], [Y] are the equilibrium concentrations for this reaction and a, b, ..., x, y, ... are the reaction molar ratios.

     

    Here, 
    

    Sum of standard Gibbs energy of formation for each substance comprising the original form：ΣG_f⁰_{original form}

    Sum of standard Gibbs energy of formation for each substance comprising the product form：ΣG_f⁰_{product form}

    
    

    If we take the total difference in the standard Gibbs energy of formation (of the substances that make up the product form and the original form) before and after the reaction,

    
    

    ⊿∑G_f⁰_{product form－original form} ＝ ΣG_f⁰_{product form} － ΣG_f⁰_{original form}

     

    If this reaction is in equilibrium, the following relationship is satisfied.

    　⊿∑G_f⁰_{product form－priginal form} ＝ －R・T・lnK 

    
    

    Gas constant R = 8.314, T is absolute temperature

    //////////////////////////////////////////////////////////////////////////

    
    

• When not in equilibrium (when the reaction proceeds in either direction)

  This is a lengthy explanation, but scroll down and just remember the parts marked in red.
  

  • 　In a system in which substances A, B, X, and Y are mixed, it is natural that they may not be in equilibrium.

    　In general (not necessarily in equilibrium), the sum of the Gibbs energyof a substance, in its original or product form, is expressed as

    (energy required to synthesize a substance in its standard state: standard Gibbs energy of formation) + (energy required to change a substance from its standard state to an arbitrary state or concentration).

    Energy to change a substance from its standard state to an arbitrary state or concentration = RT・ln (activity product).

    　(Expression derivation will be covered in a later course.)

     

    ΣGoriginal form = ΣG^f_{original form} + RT・ln (activity product of the original form)

    
    

    ΣG_{product form} = ΣG^f_{product form}+ RT・ln (activity product of the product form)

     

    　The total difference in Gibbs energy (⊿∑G_{product form－original form}) between substances constituting the original form and the product form,

     

    ⊿∑G_{product form－original form} = ΣG_{product form}－ ΣG_{original form}

    
    

          = (ΣG^f_{product form}+ RT・ln (activity product of the product form)) － ( ΣG^f_{original form} + RT・ln (activity product of the original form))

    
    

          = ΣG^f_{product form} － ΣG^f_{original form} +  RT・ln (【activity product of the product form】／【activity product of the original form】)

    
    

          ＝ ⊿∑G_f⁰   +    RT・ln (【activity product of the product form】／【activity product of the original form】)

    
    

    　　　（⊿∑G_f⁰  ：Difference between the standard Gibbs energy of formation of substances present in the product and in the original form.）

    
    

    Note 1: The 【activity product of the product form】 and 【activity product of the original form】 described here mean the product of any activity when not necessarily in equilibrium.

    Note 2: Since the term "activity" is unfamiliar to most people, please assume that "activity" = "concentration" for now.
    

    
    

    When in equilibrium, 
    

    ⊿∑G_{product form－original form}= 0

    In other words,

    ⊿∑G_f⁰  =  －RT・ln (【Activity product of the product form】／【activity product of the original form】).

    
    

    When not in equilibrium,
    

    If ⊿∑G_{product form－originl form} <  0, the reaction proceeds from 【original form】 to 【product form】.
    

    If ⊿∑G_{product form－originl form} >  0, the reaction proceeds from 【product form】 to 【original form】.

    
    

  • The conditions under which a reaction proceeds are expressed using the equilibrium constant (K)
    

    ～〜〜Condition when the reaction proceeds from 【original form】 to 【generated form】～～～

    
    

    When ⊿∑G_{product form－original form} < 0, the reaction proceeds from 【original form】original form to 【generated form】.

     

    To rewrite this,
    

    ⊿∑G_{product form－original form}= ⊿∑G_f⁰ + RT・ln (【activity product of the product form】／【activity product of the original form】),

    
    

    When, ⊿∑G_f⁰ + RT・ln (【activity product of the product form】／【activity product of the original form】) < 0 the reaction proceeds from 【original form】original form to 【generated form】.

     

    ⊿∑G_f⁰  = －RT ・ln K, so, 

    
    

    lnK  >  ln (【activity product of the product form】／【activity product of the original form】)

    
    

    In other words, when
    

    
    

    　

    【activity product of the product form】／【activity product of the original form】 < K,

    
    

    the reaction proceeds from original form to product form.

    
    

    On the contrary, when

    　

    【activity product of the product form】／【activity product of the original form】 > K,

    
    

    the reaction proceeds from product form to original form.

    
    

     

    ※　The 【activity】 (or concentration) here is the activity (or concentration) of a substance in a given system when it is not necessarily in equilibrium.　

    ※　【The activity product of the product form in equilibrium】 / 【activity product of the original form in equilibrium】 = K. So, the larger the activity product of the original form in equilibrium, the more the reaction of the original form to the product form progresses, and it should be understood that if the activity product of the product form becomes larger, the reaction proceeds from the product form to the original form.　　　　
    

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