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The salt bridge allows for positive charges to be equalized in the anode half cell and negative charges to be equalized in the cathode half cell. This prevention of charge buildup allows the galvanic cell to continue working.
In a galvanic cell, there are electrons flowing from one beaker (the oxidation reaction) to the second beaker (reduction reaction). This means that there is going to be a building up of negative charge in the reduction reaction and it is gaining electrons and a buildup of positive charge in the oxidation beaker as it is losing electrons. Eventually, the galvanic cell would stop reacting because of this buildup of charge as the electrons would no longer want to go to the negatively charged solution in the reduction beaker. The salt bridge puts ions into both beakers that balance out the charges. This allows the galvanic cell to continue working.
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