Explanation:

To distinguish between ethanol and ethanoic acid, we need to understand their chemical properties and reactions with different substances.

a) Na metal:
Sodium (Na) metal reacts violently with ethanol, producing hydrogen gas (H2) and sodium ethoxide. The reaction is as follows:
2C2H5OH + 2Na → 2C2H5ONa + H2

Similarly, sodium metal reacts with ethanoic acid, producing hydrogen gas and sodium ethanoate. The reaction is as follows:
2CH3COOH + 2Na → 2CH3COONa + H2

Since both ethanol and ethanoic acid react with sodium metal in a similar way, this substance cannot be used to distinguish between them.

b) NaHCO3:
Sodium bicarbonate (NaHCO3) reacts differently with ethanol and ethanoic acid. Ethanol does not react with sodium bicarbonate, so no reaction occurs. However, ethanoic acid reacts with sodium bicarbonate to produce carbon dioxide gas (CO2), water (H2O), and sodium acetate. The reaction is as follows:
CH3COOH + NaHCO3 → CH3COONa + CO2 + H2O

Therefore, by observing the production of carbon dioxide gas, we can distinguish between ethanol and ethanoic acid using sodium bicarbonate.

c) Hot alkaline KMnO4 solution:
Hot alkaline potassium permanganate (KMnO4) solution oxidizes ethanol to ethanoic acid. The reaction is as follows:
CH3CH2OH + 2KMnO4 + 3OH- → CH3COOH + 2MnO2 + 2K+ + 2H2O

Since the reaction converts ethanol into ethanoic acid, this substance cannot be used to distinguish between them.

d) Hot acidified K2Cr2O7 solution:
Hot acidified potassium dichromate (K2Cr2O7) solution also oxidizes ethanol to ethanoic acid. The reaction is as follows:
3CH3CH2OH + K2Cr2O7 + 4H2SO4 → 3CH3COOH + Cr2(SO4)3 + K2SO4 + 7H2O

Similarly to the previous substance, this reaction also converts ethanol into ethanoic acid and cannot be used to distinguish between them.

Therefore, the correct answer is option A (Na metal) as it reacts similarly with both ethanol and ethanoic acid.