It's easier to use dry ice. You can get it for like $4 at most grocery stores. You place the rat in a container, like a 10 gallon tank, and hold a container (something plastic that won't crack, and can hold a bit of water) with a bit of dry ice over the tank, and pour hot water into it slowly so that the tank fills up slowly with CO2. It's not perfect science like a CO2 tank can be, but you can just do it slowly until the rat passes out, then crank it up and just flood the tank with CO2 to kill him. It's a lot less messy than vinegar and baking soda, which foams up and it tough to measure.

You can move the dry-ice back and forth over the container (so the CO2 is falling into the tank, and not) so that you can control the amount of CO2 flowing in at first.