Final answer:
The question involves writing a balanced chemical equation for a double displacement reaction between sodium permanganate and iron(III) chloride. Since iron(III) permanganate's solubility is not well-known, the expectancy of the reaction's products and progression is questionable, and further investigation on the actual reaction mechanism is needed.
Step-by-step explanation:
The subject of the question is a double displacement reaction between sodium permanganate and iron(III) chloride in water. According to the question, the likely products would be sodium chloride (NaCl) and iron(III) permanganate (Fe(MnO4)3), assuming iron(III) permanganate is not soluble. However, since iron(III) permanganate is not a common compound and its solubility is not well-known, it's possible that this reaction may not proceed as a typical double displacement reaction. Instead, iron may react with permanganate in a redox reaction, which is beyond the scope of the question. For educational purposes, the balanced equation for the proposed double displacement reaction would look like this:
3 NaMnO4(aq) + FeCl3(aq) → 3 NaCl(aq) + Fe(MnO4)3(s)
However, this is a hypothetical situation as the actual reaction may differ based on redox conditions and the actual solubility of the products formed.