### Core Logic Let's resolve both components step by step: 1. **Finding X:** In an acidic medium, the permanganate ion (KMnO_4$KMnO_4$, where Mn$Mn$ is in the +7$+7$ state) is reduced to the divalent manganese cation (Mn^2+$Mn^{2+}$, state +2$+2$): X = 7 - 2 = 5$X = 7 - 2 = 5$ 2. **Finding Y:** During qualitative salt analysis, the acetate ion reacts with neutral ferric chloride to produce a characteristic blood-red coordination solution. Boiling this solution throws down a **brown-red precipitate** of basic ferric acetate, [Fe(OH)_2(CH_3COO)]$[Fe(OH)_2(CH_3COO)]$. In this complex, Iron retains its +3$+3$ oxidation state: Fe^3+ implies [Ar] 3d^5 4s^0 implies textNumber of d-electrons (Y) = 5$Fe^{3+} \implies [Ar] 3d^5 4s^0 \implies \text{Number of d-electrons } (Y) = 5$ Summing the values yields: X + Y = 5 + 5 = 10$X + Y = 5 + 5 = 10$ ### Pattern Recognition This problem elegantly links standard redox transitions with qualitative inorganic salt tests. Remember that throughout the basic ferric acetate precipitation test, Iron remains steadily in its ferric +3$+3$ (d^5$d^5$) core configuration. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: The d- and f-Block Elements Inorganic Qualitative Analysis