Explanation of Assertion (A):
In aqueous solutions, $\text{Cr}^{2+}$ acts as a reducing agent and is oxidised to $\text{Cr}^{3+}$. This is because $\text{Cr}^{3+}$ has a stable $d^3$ electronic configuration. Conversely, $\text{Mn}^{3+}$ acts as an oxidising agent and is reduced to $\text{Mn}^{2+}$, which has a stable half-filled $d^5$ electronic configuration.
Explanation of Reason (R):
The half-filled electronic configuration provides extra stability due to symmetrical distribution of electrons and exchange energy. This explains why $\text{Cr}^{3+}$ and $\text{Mn}^{2+}$ are more stable compared to their respective other oxidation states.
Conclusion:
Both Assertion (A) and Reason (R) are true. The reason given (R) correctly explains why $\text{Cr}^{2+}$ is reducing and $\text{Mn}^{3+}$ is oxidising, as it is related to the stability of the resulting electronic configurations.
$\mathrm{KMnO}_{4}$ acts as an oxidising agent in acidic medium. ' X ' is the difference between the oxidation states of Mn in reactant and product. ' Y ' is the number of ' d ' electrons present in the brown red precipitate formed at the end of the acetate ion test with neutral ferric chloride. The value of $\mathrm{X}+\mathrm{Y}$ is _______ .
Match List-I with List-II: List-I