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A cell diagram is just shorthand notation for the overall reaction that occurs in a cell. Because stochiometric coefficients can easily be determined from this shorthand notation, it is not necessary for them to just be included.
You add platinum (s) or carbon (gr) when the anode and/or the cathode have no solid conductors in the cell diagram (they either have nonmetals or metals in an aqueous phase). As far as I know, platinum and carbon can be used interchangeably, but platinum is more common.
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