My other answer was more in line with what you had previously posted as a question and I believe it was closed; but really, the question is, what are you trying to achieve? Are you monitoring traffic? Are you cutting off Internet access while talking? Are you trying to proxy web access? Because really you're just asking for all the traffic in the lab to be bottlenecked at a single computer before going out, with no end goal to achieve other than bottlenecking them.
If you want to keep them paying attention, there's the software I mentioned, or if there's a switch for that lab you can pull the uplink cable (which your sysadmins will most likely frown on.)
Or you can set up a proxy system that forwards traffic, like a Squid web proxy. There are turnkey Linux/BSD distros that act as gateway/routers that can then forward traffic on for you (although you'd want this to be uplinked from the single switch if you want to make sure the traffic doesn't bypass the proxy/filter, otherwise all the machines in that lab will need their gateway specified as that router machine and they could conceivably bypass your configured bottleneck.
Anything you do to "segment" off this network this way, by routing it through a special PC, is going to add what is probably an unnecessary layer of complexity for network management, and if you're not the admin for this network doing this will not endear you to them. If you have a direct concern...keeping users from web browsing during a class, speeding up access to sites, etc...you may wish to state your actual end goal rather than coming up with a solution of sorts in your mind already and asking how to achieve your solution. Putting in barriers that could muck up DHCP or other network management within the context of the higher-up network admins taking care of all the systems will ask for trouble. Not to mention someone may ask why, when the teacher computer is taken out for repair or has a disk failure, the entire lab suddenly became useless...