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  • Energy balance of half-reactions and standard electrode potentials

    • 　Consider the energy balance of the half-reaction equation, taking into account the energy possessed by the electrons.

      　By the way, where there is an electric charge (such as an electron), an electric field is generated, and that charge has energy corresponding to the potential of the electric field.

      The complicated explanation is not important, so remember the following.

      "A quantity of charge q(C) at a certain potential E(V or J/C) has an energy (J) of q×E."

      "The absolute value of the charge (C) of one mole of electrons (e-) is 96485 (C/mol), which is called Faraday constant (F)."


      This is also complicated, so be sure to memorize only the following equation.

      「Energy possessed by an n-mole electron」＝　－n・F・E

      　F：Faraday constant, 96485 (C/mol)、E：potential (V or J/C)


      　Faraday constant is the absolute value of the amount of charge that one mole of electrons has. Since electrons have a negative charge, they have negative energy. Therefore, in the above equation, the potential is multiplied by the Faraday constant and the negative is attached to it.


      ※Remember that electrons are negatively charged, so the energy equation will have a negative value.


    • Example of finding the standard electrode potential for a half reaction


      　Let E①(V) be the potential generated in the electron 4e- that is transferred in the half reaction ① of organic matter oxidation.

      　The unit of volt (V) can be converted to (J/C), where J (joule) is the unit of energy and C (coulomb) is the unit of charge. The absolute value of the amount of charge that one mole of electrons has is given by Faraday constant (F) 96485 (C/mol).

      　Therefore, the energy possessed by the electron 4e- in the half-reaction equation ① is -4・F・E①(J).

      　The standard Gibbs energy of formation for each substance, including the energy held by this electron, is noted below the half-reaction equation, and the equation is solved to balance the energies on the left and right sides of the half-reaction.

                                                                                                                                   

      Standard electrode potentials for half-reactions of organic matter oxidation

                                （original form）               （productform）

      ①                        CO2  +   4H+   +    4e-   =    CH2O    +     H2O

      Gf0 (kJ/mol)        －385        0                        －129.7      －237.18

      electric energy(J)                       －4FE①

       

      Equation that balances the total energy of the left and right sides：

      －385・103　－4FE①    =   －129.7・103 －237.18・103

       

      Find the unknown number E①.

      E①    =  (－129.7・103 －237.18・103＋ 385・103)／(－4・96485) = －0.05 (V)


      　This means that the total difference (product form - original form) between the standard Gibbs energy of formation of the left side (original form) and the right side (product form) is given to the four electrons. In a redox reaction, the energy given to these electrons is used to recombine chemical bonds.

      　The potential calculated from that energy (E①) is called the standard electrode potential for that half-reaction. Since the standard Gibbs energy of formation is unique to a substance, each half-reaction equation has a unique standard electrode potential.

                                                                                                                                   


    • In oxygen respiration,

      Find the standard electrode potential of the half-reaction equation ② at which oxygen molecules are reduced.

                                                                                                                                   

      Oxygen respiration (oxygen reduction)

      ②          　　　　　 O2 　+ 　4H+ 　　+　4e- 　　= 　　 2H2O    

      Gf0 (kJ/mol)        　　0         0                                 2（－237.18）

      Electric energy (J)                             －4FE②

      Energy balance：－4FE②　＝ 2（－237.18・103）

      E② =  2（－237.18・103）／ (－4・96485) = 1.23 (V)                                             


    • Find the standard electrode potential for the half-reaction of sulfate reduction.

                                                                                                                                   

      Sulfate respiration (sulfate reduction)

      ④                      SO42-   +   10H+   +   8e-   =  H2S   +   4H2O

      Gf0 (kJ/mol) 　　－744.5                  0                      －27.78    4(－237.18)

      Electric energy (J)                             －8FE④

      Energy balance：－744.5・103－8FE④　＝　－27.78・103－4・237.18・103

      E④ =  （－27.78・103－4・237.18・103＋744.5・103）／ (－8・96485) = 0.30 (V)

       

      ※Remember to multiply by 1000 because of the kilo (k) unit of Gibbs energy.