What is a laboratory set-up for the synthesis of ethanol from ethene?
You should try bubbling the ethene gas through dilute sulfuric acid. It should form ethyl sulfate and get hydrated with water forming ethanol. As the gas will bubble through the solution, you should have an ample amount of liquid so that most of the gas can maximally react with the sulfuric acid before bubbling out as gas. You should do the reaction in a fume, hood too. Then I think that you could separate the ethanol from the water by distillation of the ethanol from the mixture, or you could separate it by exploiting the great difference in the freezing points of ethanol and water.

If you could connect tubes in such a way with special chemistry glassware, then maybe you could make some kind of reflux apparatus like an acid reflux apparatus where the gas funnels back into the bottom of the liquid and cycles through several times then you could increase your yield. Just if you use some cyclic mechanism, don't release the gas too quickly or you could break your apparatus. 

I'm not exactly sure what the experimental design is. But due to the concentration of gas in the reaction chamber, it's important to have an escape valve for the gas for safety purposes of equalizing pressure. If you know what you want, an experienced glass-blower can make your apparatus.