A process for converting multihydroxylated-aliphatic hydrocarbon compound(s) and/or ester(s) thereof to chlorohydrins and/or esters thereof is disclosed in which one or more of multihydroxylated-aliphatic hydrocarbon compound(s) and/or ester(s) thereof and/or monochlorohydrin(s) and/or ester(s) thereof with at least one chlorinating feed stream comprising at least one chlorinating agent and at least one impurity having a boiling point below the boiling point of the chlorohydrin product having the lowest boiling under hydrochlorination conditions, optionally in the presence of water, one or more catalyst(s), and/or one or more heavy byproduct(s) in a reaction vessel under hydrochlorination conditions, wherein the liquid-phase reaction mixture is maintained at a temperature below the boiling point of the chlorohydrin product having the lowest boiling point under hydrochlorination conditions and greater than the boiling point(s) of the at least one impurity and a vapor phase vent stream comprising the at least one impurity is removed from the liquid phase reaction mixture. An apparatus suitable for carrying out the disclosed process is illustrated in FIG. 1 of the drawings. The process and apparatus improve conversion rates and/or provide for recovery of chlorinating agent for lower operating costs.