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We use platinum in a cell diagram when either the cathode or the anode lacks a solid that can be used to conduct electrons from one side of the beaker to the other. This is because platinum is inert and will not react with anything else in the reaction.
Platinum is used when there isn't a conducting solid. So in the textbook, there can be platinum on a side with a solid because that solid isn't a conductor. Platinum is used because it is inert and won't react.
A metal is used as a cathode or anode to conduct electricity so a reaction without a metal would not transfer ions. To make the circuit work for solutions with aq or gas reactants platinum needs to be added as a conductor.
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