In the process of electrolysis of molten NaCl, Cl₂ is obtained at the anode as a by product.

NaCl   →  Na⁺  + Cl^-

Cathode:  Na⁺   ₊ e^-  →   Na

Anode: Cl^-    →  Cl_(g) + e^-

2Cl_(g)  →  Cl_2(g)

The overall reaction is as follows:

If an aqueous NaCl solution is electrolyzed, Cl₂ will be obtained at the anode but at the cathode, H₂ will be obtained and not Na. This is because the standard reduction potential of Na (E°= - 2.71 V) is more negative than that of H₂O (E° = - 0.83 V). Hence, H₂O will get preference to get reduced at the cathode and as a result, H₂ is evolved.

NaCl_(aq)  →  Na⁺_(aq) + Cl^-_(aq)

At cathode:  2 H₂O_(l)  +  2e^-   →   H_2(g) + 2OH^-_(aq)   

At anode: Cl^-    →  Cl_(g) + e^-

2Cl_(g)  →  Cl_2(g)