Applications question

Can you install applications on a hard drive that doesn't have the os on it, because my mac only came with a 20gb hard drive with the os on it and im running out of space to install applications on, so i out a second 120gb hd, but it wont let me install them to that second hard drive

what format is that second hard drive?

Right click on the drive icon and select Get Info

it is mac os journaled extended