You can run OS X Mountain Lion with 2 GB of RAM, but you cannot be sure that it will work correctly.
"MacBookPro3,1" belongs to the Late 2007 MacBook Pro, so it is compatible with OS X Mountain Lion. However, you say your MacBook Pro has got an Intel Core Duo processor, when it should have got an Intel Core 2 Duo processor. You can check which processor you have in > About this Mac.
I recommend you to upgrade RAM. You can buy more RAM at OWC or Crucial.
The latest OS X version is Mavericks and it is free, so you may want to install it instead of OS X Mountain Lion. You can download it from the Mac App Store. If you want OS X Mountain Lion, you can buy it in the Apple Online Store > http://store.apple.com/us/product/D6377Z/A/os-x-mountain-lion