The discharging half equations of a lithium iron phosphate (LiFePO6) cell with LiFePO6 as the cathode and C6 (graphite) as the anode can be represented as follows:
At the cathode (LiFePO6): LiFePO6 → Li+ + FePO4 + e-
At the anode (C6): C6 + Li+ + e- → LiC6
In the overall reaction, lithium ions (Li+) move from the cathode to the anode through the electrolyte during the discharging process, resulting in the reduction of iron phosphate (FePO4) at the cathode and the formation of lithium-intercalated graphite (LiC6) at the anode.
Now, let's discuss why the reaction is spontaneous. Spontaneity in a reaction is determined by the Gibbs free energy change (∆G) of the system. If ∆G is negative, the reaction is spontaneous.
In the case of a LiFePO6 cell, the reaction is spontaneous due to the difference in the electrochemical potential of the cathode and anode materials. LiFePO6 has a higher electrochemical potential (or voltage) compared to the electrochemical potential of graphite (C6).
During discharging, the lithium ions (Li+) move from the cathode to the anode, driven by the difference in electrochemical potential. This movement of ions allows the system to lower its overall energy. As a result, the reaction proceeds spontaneously to establish equilibrium and release electrical energy.
It's worth noting that the reaction spontaneity also depends on other factors, such as temperature, concentration, and the specific cell design. However, the inherent difference in electrochemical potential between the cathode (LiFePO6) and anode (C6) is the primary driving force for the spontaneous discharge of the LiFePO6 cell.