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  • Basic equation of chemical equilibrium

    • //////////////// Basic equation of chemical equilibrium/////////////////////////

      We consider the following reactions


      Chemical species A, B, ... react to,

      Chemical species X, Y, ... are produced.

      In addition,

      Chemical species A reacts in the ratio a moles, B reacts in the ratio b moles,,,

      Chemical species X reacts in the ratio of x moles, Y reacts in the ratio of y moles, and so on.

       

      This is described by the reaction equation,

                  　　【Original form】                   【Product form】


              　　　　    aA  +  bB  +  …　　  ⇆         xX  +  yY  + …
       

      The system before the reaction is called the "original form" and the system after the reaction is called the "product form".

       

      　When the reaction rate to produce X, Y, ... from A, B, ... is equal to the reaction rate to produce A, B, ... from X, Y, ..., this reaction is said to be in equilibrium.


      In equilibrium, the following relationship is established by the law of mass action.

       

      （Concentration product of product form）／（Concentration product of the original form）＝　K

       

      In other words,

                   


      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.

       

      　This K is called the solubility equilibrium constant or solubility product for dissolution reactions of solids, or the acid dissociation constant for reactions that dissociate hydrogen ions (H+) or hydroxide ions (OH-) when dissolved in water.

      Here, 

      Sum of standard Gibbs energy of formation for each substance comprising the original form：ΣGf0original form

      Sum of standard Gibbs energy of formation for each substance comprising the product form：ΣGf0product 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,


      ⊿∑Gf0product form－original form ＝ ΣGf0product form － ΣGf0original form

       

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

       

                 ⊿∑Gf0product form－priginal form ＝ －R・T・lnK                        （A）
       

              Gas constant R = 8.314, T is absolute temperature

      (The "ln" stands for loge.)

       


      K is the same as the equilibrium constant due to the law of mass action,


                  K = 【Product of the activity of the product form】／【Product of the activity of the original form】


      　In the previous explanation, I wrote [product of concentration], but it is precisely [product of activity]. Again, since it is a constant (K) at equilibrium, the [product of activity] is the product of the activity at equilibrium. 

      The K obtained from the thermodynamic constant (standard Gibbs energy of formation) is called the thermodynamic equilibrium constant.


      The handling of activity shall be in accordance with the following.

      ・　The molar concentration a (mol/L) of the ideal solution is the activity a.

      ・　The partial pressure b (atm) of the ideal gas is the activity b.

      ・　The electron activity is set to 1.

      ・　When water molecules are involved in the reaction in aqueous solution, the water activity is set to 1.

      ・　When a solid is present in a gas or liquid phase reaction, the activity of the solid is set to 1.

      ・　When a liquid is produced in a gas phase reaction, the activity of the liquid is set to 1.

       

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    • Supplement

      　The equilibrium constant determined by the thermodynamic constant (standard Gibbs energy of formation) and the activity is called the thermodynamic equilibrium constant. To distinguish it from the concentration equilibrium constant described next, the thermodynamic equilibrium constant is often written as K°.

                    K° = 【Product of activity of product form】／【Product of activity of original form】

      In contrast, the concentration equilibrium constant is expressed as the ratio of the concentration product of the original form and the product form,

                    K = 【Concentration product of product form】／【Concentration product of original form】

                    K° = K・（Product of activity coefficients of product form）／（Product of activity coefficients of original form）.

      Activity and activity coefficients in solution chemistry will be discussed in the next course.

       

      In this class, K° and K will be explained without distinction.

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      　When they explain it this way, I have no idea what they are talking about or what it is used for. Let's solve a few examples using these formulas and get used to them, for now.