This is an old thread, but if I found it, others can.
The exhaust of an A/C is laden with moisture. That's hard on a carbon filter.
I suggest you blow your exhaust air into a container with Ona gel, then on out into the world. Make your own Ona gel - buy Ona liquid off Amazon for about $38 a...
Growing in an apartment is extremely risky.. riskier. I reckon if you're going to do a cabinet grow for personal use, cool. If you're growing any amount, I'd switch over to running moonshine. You can get a small still that runs off electricity, roll off some shine, sell that, and use the money...