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I've just managed to understand a bit the meaning of having the notation of 0.5 in a molecular formula, when I found a set of multiple notations for the same discharge process that started to confuse me.

One can find this set of notation for the discharge reaction of a LiCoO$_2$ cathode:

  1. $CoO_2 + Li^{+} + e^{-} \rightarrow LiCoO_2$ (see here)
  2. $LiCoO_2 - Li^{+} - e^{-} \rightarrow Li_{0.5}CoO_2$ (see here)
  3. $Li_{1-x}CoO_2 + xLi^+ + xe^- → LiCoO_2$ (see here)
  4. $2Li_{0.5}CoO_2+Li^{+}+e^-\rightarrow 2LiCoO_2$ (see here)
  5. $Li_{0.5}+0.5Li^+ + 0.5e^-\rightarrow LiCoO_2$ (see here)

and the list can continue...

Why are there so many notations for the same thing? It's so confusing for someone who is trying to understand this. Aren't they representing the same discharge process? What changes? And why do we have to have so many notations?

Sorry if this is too puerile, but notations were always a source of confusion for people trying to learn something from different sources.

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