Hi John Although Rottweilers are big dogs, they're not generally 'high energy' adults, and are inclined to be pretty laid back once mature (of course, each dogs' individual temperament does factor into this).
As puppies they are as energetic and rambunctious as any breed, with the added tendency to be a bit clumsy (due to their rapid growth and that awkward 'teenage' stage).
The biggest issue is not how big their living space is, but whether or not you can provide them with enough exercise, play and stimulation. There's a lot of truth to the saying 'a tired puppy is a good puppy', and as long as your Rottie pup has a safe area to play and get enough exercise, an apartment shouldn't be a huge problem. Once your pup is an adult, the same applies.
One concern with an apartment is finding a safe area for him to play, eliminate, exercise in terms of protection from disease. Rotties are a breed that is very vulnerable to Parvovirus, and a pup needs to be kept away from areas where other, unvaccinated dogs, may have been until he's had all his Canine Vaccinations.
If you can meet the needs for exercise, and for disease prevention, then I think you would be just fine.
Hope this helps, best of luck with whatever dog you choose.
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