In electrolysis of NaCl. How does CL become 1/2CL2?

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In the electrolysis of sodium chloride (NaCl), chlorine ions (Cl-) undergo oxidation to form diatomic chlorine gas (Cl2). The reaction can be represented as Na+ + Cl- → Na + 1/2 Cl2. Each chlorine atom donates one electron to form a covalent bond with another chlorine atom, resulting in the formation of Cl2, which satisfies the octet rule for both atoms. This process adheres to the law of conservation of mass, as the total number of atoms remains unchanged.

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Na+ + CI- → Na + 1/2C12

How is it Cl becomes Cl2? (what about conservation?) and why does it become diatomic?
 
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I'm not sure about the conservation you're mentioning, but I believe Cl becomes Cl2 because they are each short of an octet by one electron. So, each Cl gives up one electron to form a bond between them and the octets are satisfied.
 

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