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The salt bridge allows ion transfer between two half reactions by providing an electrical connection within which ions can flow. This keeps both solutions at a neutral state, so electron flow can continue and be measurable through a voltmeter. Salt bridges usually contain an unreactive electrolyte too. Without a salt bridge, electrons produced at the anode will accumulate at the cathode, which will stop the reaction from running.
Salt bridges allow for a circuit so that the cathode doesn't become too saturated with electrons and thus reject electrons. The salt bridge allows a transfer of electrons back to the anode so that the transfer of electrons is continuous.
Since electrons are constantly being gained or lost, the solutions of the cathode and anode may gain a charge. If the solutions have a charge, the transferring of electrons will come to a stop. To allow the electrons to continue to be transferred, the salt bridge needs to maintain the solutions neutral.
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