Answer:
An halogen addition reaction, particularly bromine addition, could be used to check if the hydrogenation has completed.
Explanation:
The aim is to find a way to check if the hydrogenation process of an alkene has completed. So the logic should be use a reaction that needs the participation of the double bound of the alkene, and therefore shouldn't take place in the process has finished.
A simple organic reaction is the halogen addition reaction, which occur between the halogen molecule and the double bond of the alkene. Basically, the pi electrons of the double bond attacks a relatively electrophilic halogen atom following a mechanism that leads to the addition of two halogen atoms to the double bond. As a consequence the alkene transforms into an haloalkane.
Also, a commonly used halogen is bromine, as it has a reasonable reactivity and it has red colour, which allows to monitor the progression of the reaction.
Taking all this in account, we can say that using a bromine addition reaction to the alkene it's a good option to check the completion of the hydrogenation.
Note that the bromine will react only if the double bond is present. So, if the hydrogenation has completed, the reaction won't occur. Using bromine will be the best option, as it is red coloured. That means that is we add bromine to an incomplete hydrogenation, as it will react with the alkene, the colour should disappear.
In other words, to check if the hydrogenation reaction has completed, we should add bromine and see what happens to the colour. If it doesn't change, then the hydrogenation reaction has completed.