Doing this and then rearranging this leads to the expression of the free energy activation (
  
    
      
        Δ
        
          G
          
            †
          
        
      
    
    {\displaystyle \Delta G^{\dagger }}
  ) in terms of the overall free energy of the reaction (
  
    
      
        Δ
        
          G
          
            0
          
        
      
    
    {\displaystyle \Delta G^{0}}
  ).
A Li-ion battery is a kind of flow battery which can be seen in the image on the right. Furthermore, a Li-ion battery is an example of a secondary cell since it is rechargeable. It can both act as a galvanic or electrolytic cell. Li-ion batteries use lithium ions as the solute in the electrolyte which are dissolved in an organic solvent. Lithium electrodes were first studied by G.N. Lewis and F.G. Keyes in 1913. In the following century these electrodes were used to create and study the first Li-ion batteries. Li-ion batteries are very popular due to their great performance. Applications include mobile phones and electric cars. Due to their popularity, much research is being done to reduce the cost and increase the safety of Li-ion batteries. An integral part of the Li-ion batteries are their anodes and cathodes, therefore much research is being done into increasing the efficiency, safety and reducing the costs of these electrodes specifically. Cathodes
In Li-ion batteries the cathode consists of a intercalated lithium compound (a layered material consisting of layers of molecules composed of lithium and other elements). A common element which makes up part of the molecules in the compound is cobalt. Another frequently used element is manganese. The best choice of compound usually depends on the application of the battery. Advantages for cobalt-based compounds over manganese-based compounds are their high specific heat capacity, high volumetric heat capacity, low self-discharge rate, high discharge voltage and high cycle durability.