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Propene + Br2 + hv ==> 3-Bromo-1-propene (free radical halogenation - allylic position is halogenated only)


3-bromo-1-propene + OsO4 ==> 1,2 dihydroxy-3-bromo propane (or, you can also use MCPBA to create the epoxide and open it with mild acid or base, or you can use Br2 and H2O to create the halohydrin... lots of options here)


1,2 dihydroxy-3-bromo propane + NaOH ==> 1,2,3 trihydroxy propane (glycerin aka glycerol)

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