Apple has tightened its requirements for this OS upgrade, and some older Macs— even ones that qualified for Lion — won't make the cut for Mountain Lion.
The general system requirements are straightforward:
- OS X v10.6.8 or later
- 2GB of memory
- 8GB of available space
Apple also lists which models support Mountain Lion:
- iMac (Mid 2007 or newer)
- MacBook (Late 2008 Aluminum, or Early 2009 or newer)
- MacBook Pro (Mid/Late 2007 or newer)
- Xserve (Early 2009)
- MacBook Air (Late 2008 or newer)
- Mac mini (Early 2009 or newer)
- Mac Pro (Early 2008 or newer)
So it appears you Cannot run Mountain Lion on that machine.
Hope this helps