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How does nucleophilic substitution work in a compound consisting of two leaving groups?

2,2-dichloropropane to acetone

I understand that hydroxide ions will attack the carbon centre (which bears a partial positive charge) and cause a nucleophilic substitution reaction.

What I'm unsure of is whether the reaction proceeds via

  1. The hydroxyl groups replacing the leaving groups one at a time (double $\mathrm{S_N2}$).

  2. After the replacement of the first hydroxyl group, the repulsions between the electron pairs of oxygen and of chlorine cause the chlorine, a better leaving group, to leave, causing formation of a cation. ($\mathrm{S_N2}$ followed by $\mathrm{S_N1}$).

  3. Both bonds forming at once (a transition state with six bonds to the center), although this seems very unlikely.

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    $\begingroup$ I don't think it needs to go through the geminal diol - simply one SN2 followed by oxygen lone pair kicking chloride out is sufficient. $\endgroup$ – orthocresol Aug 29 '17 at 17:53
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    $\begingroup$ But if it does, it will go one by one. $\endgroup$ – Jan Aug 30 '17 at 1:09

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