Organic chemistry question

Its the OH part of sodium hydroxide that would react here if anything (as a nucleophile) but you can't do SN2 reactions on alkene carbons (sp2 centre) like you can on alkanes (sp3 centre)

Ok SN2 just means nucleophilic substitution (2 molecules in the fast step), sp2 and sp3 describe the electronics of the carbons, here you have chloroethene each carbon has two single bonds and one double bond this is called sp2 when a carbon has 4 single bonds (such as in cholorethane) is called sp3. You're right in that that maybe the Na+ would be attracted to the electron rich double bond, but Na doesnt form covalent bonds with carbons. But consider the anion OH - in chloroethane, it would attack (SN2) the partially positive C in the C-Cl bond because Cl is more electronegative and pulls electrons away from the carbon. But in chloroethene the carbon isn't so electrophilic and will not undergo nucleophilic substitution

electrophiles have to be able to accept a PAIR of electrons. In the case of Na+ this would form a Na- ion, which just does not exist!