re: So how many kW does a 2 ton ac use?

I got you. Well the 12,000 watt gen set in 230 volt mode is in theory going to be handle about 50 amps (12,000 divided 230) but in a practical sense maybe 80% of or 40 amps. That’s likely enough to “run” your 2 ton unit.

The problem is the starting or in-rush amps, which is much higher, even for a brief second, when the compressor kicks on. That will be more in line with the LRA (locked rotor amps) on the outdoor compressor tag. A hard start capacitor or soft start capacitor installed in the outdoor condensing unit can help with that. Remember my example above of my unit, 4-ton with a rated load amps (RLA) of 18.3 but a LRA of 109. A 12000 watt generator can “run” my unit but not start it.

Now that others know what you are trying to do, they can weigh in with better information, knowledge and experience than me - I’m curious myself what the answer is but it will help if you go outside and get the RLA and LRA information off the condensing unit tag - it will be there, and add that info to your OP. Thats really the important info needed to answer your question.