When bromine water is added to cyclohexene, cyclohexene readily reacts with the bromine and opens the double bond as it bonds to the carbon. For cyclohexene to react with bromine water, there are no conditions or catalysts required. Only cyclohexane requires the presence of UV light to react with bromine water.
To forms bromocyclohexanol, or just cyclohexanol from cyclohexene, it is a addition reaction (called hydration). For this reaction, H2O is added in presence of some dilute acid catalyst such as H2SO4 or H3PO4, to form an alcohol. So the cyclohexene double bond is broken, and the hydrogen and the hydroxyl group from the water bonds with the carbon (which had the double bond).
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In terms of dibromohexane, its called a halogenation reaction, which is basically where the double bonds in hexene open, as the Br compounds are bonded to it. It does not require a catalyst.
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Always add less bromine water for alkenes and alkanes (i.e. 3ml of alkane or alkene add about 0.5ml of bromine water). So for 5ml of cyclohexane and cyclohexene, you should add around 1-2ml of bromine water, you don't want to add to much of this as you would not be able to distinguish the colour change (i.e. will not be able to recognise which one is alkene and which one is alkane). You can add it together (no need to add dropwise), and mix if necessary, but there should be some notable change (i.e. the cyclohexane should have no change so stays brown, while the brown colour in the cyclohexene disappears). Also make sure that there is no presence of UV light, in order for the experiment to be valid and accurate.
Sorry but I wasn't really able to understand the question specifically "When bromine water is added to cyclohexene, why and under what conditions does bromocyclohexanol form in addition to dibromohexane?", so wasn't able to answer directly, but I placed relevant info on how those type of bonds are formed.
Hope this helps.
