The product description for the compressor you purchased doesn't list the cfm rating or duty cycle. However, based upon the physical size and characteristics of the unit, I would seriously doubt that it could power air tools even with a tank.
I have a 1/3 hp, 100% duty cycle, 1.45 cfm @ 40psi (1.85cfm @ 15 psi), 12v Thomas compressor (model TA4101-DC) hard wired into my jeep with a 2.5 gal. tank. That is a greater cfm rating than the biggest Viair with a similar 100% duty cycle (model 450, 1.3cfm @ 40psi) and similar portable 12v compressors by other manufacturers. (Note: most portable and small hard mount 12v compressors only have a 33% duty cycle, and will overheat if you try to run air tools or fill large tires one after the other without a break.) Even the Thomas compressor won't power air tools more than a few seconds with a 2.5 gal tank, barely enough time to break loose stubborn or highly torqued bolts/nuts. The recovery time makes it hardly worth the effort.
In my experience, the only systems adequate for running air tools use engine driven compressors. (There is one system that uses a modified starter motor to spin a York A/C compressor, but it is pricey and there are better alternatives.) The best use a York air conditioning compressor in place of or in tandem with the stock A/C. (Using custom fabricated brackets as the only company I know of that marketed tandem brackets closed almost 10 years ago.) You can also use a Sanden A/C compressor, but these don't have the same cfm rating and have oiling issues that Yorks don't have.
Go to
www.onboardair.com. Brad Kilby, the owner, knows more about onboard air systems than anyone else in the business, and he has put together a website that goes into great detail about how to design and wire a system and the pros and cons of each type of compressor.
For more information regarding the installation of a Thomas compressor, see this site:
http://george4wd.taskled.com/compressor.html