Sodium is produced by electrolysis of molten sodium chloride. what are the products at the anode and cathode, respectively?

Answer is: chlorine and sodium.

Molten sodium chloride is separeted::

2NaCl (l) → 2Na (l) + Cl₂ (g),

but first ionic bonds in this salt are separeted because of heat:

NaCl (l) → Na⁺ (l) + Cl⁻ (l).

Reaction of reduction at cathode (-) : Na⁺ (l) + e⁻ → Na⁰ (l) / * 2.

2Na⁺ (l) + 2e⁻ → 2Na (l)

Reaction of oxidation at anode (+) : 2Cl⁻ (l) → Cl₂ (g) + 2e⁻.

The anode is positive and the cathode is negative.