itouch app issue

I created a new library for my itouch. i have a separate one for my nano. I downloaded an app from the itunes store. When i hook up my itouch to my Mac the app does not download to my itouch. It is in the app folder. All of my songs and music are on my itouch, but I cannot figure out why the app does not appear. I am very new to this. Any help is appreciated.

Thank you. Your help in the past has been invaluable.