Let's analyze the reactions one by one in the context of balancing chemical equations and the charges of the involved ions.
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Na3PO4 + 3KOH → 3NaOH + K3PO4: This equation is balanced correctly. The reactants have a total of four charges (3+ from Na and 3- from PO4) and the products also have a total of four charges (3+ from K in K3PO4 and 3- from PO4). K retains its charge of 1+ throughout. Therefore, this equation is correct.
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Na3PO4 + KOH → Na3OH + KPO4: This equation is not balanced. The total charges do not match, and the quantities of sodium (Na) and potassium (K) do not balance properly.
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Na3PO4 + KOH → 3NaOH + K3PO4: Again, this equation is not valid; it repeats the issue of the second equation. The sodium and potassium ions would not balance in terms of their counts and charges.
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Na3PO4 + KOH → Na3OH + KPO4: Similar to point 2, this equation is not balanced, and again it misrepresent the charges. Here, you have not accounted for the stoichiometry correctly.
Given this analysis, the first equation is the only one that is balanced correctly and represents the reaction correctly. It states that:
Na3PO4 + 3KOH → 3NaOH + K3PO4, because K retains the same charge throughout the reaction.
So the correct answer is the first equation.