Step 1: Understanding the Concept:
In the Hall-Heroult process, pure alumina (\( \text{Al}_2\text{O}_3 \)) is mixed with cryolite (\( \text{Na}_3\text{AlF}_6 \)) to facilitate electrolysis.
Step 2: Detailed Explanation:
1. Assertion (A): Alumina has a very high melting point (\( \sim 2300 \, \text{K} \)) and is a poor conductor in the solid state. Cryolite is added to lower the melting point to approximately \( 1173 \, \text{K} \) and increase electrical conductivity. Thus, the assertion is correct.
2. Reason (R): Cryolite is \( \text{Na}_3\text{AlF}_6 \). Calculating oxidation state: \( 3(+1) + x + 6(-1) = 0 \implies x = +3 \). The oxidation state of Al is indeed +3. Thus, the reason is also a correct statement.
3. Logical Link: The reason for adding cryolite is to act as a flux and a solvent. The fact that Al has a +3 oxidation state in it is not the explanation for why it is used in the extraction of Al from alumina.
Step 3: Final Answer:
Both statements are true individually, but the reason does not explain the assertion.