the 13" Macbook Core 2 Duo was updated to the Santa Rosa chipset in Nov 2007. this model is aka MacBook 13-inch Late 2007.
According to Mactracker, the machine ID for this model is: "MacBook3,1"
this machine ID is unique to the particular version of a model, unlike the generic model number A1181 which spans several generations of this machine
you can find the machine ID for your MacBook by going under the Apple menu and select "About this Mac..." then click on "More info..." - this will launch System Profiler. your machine ID is listed.
if your Machine ID is "MacBook2,1" then you don't have the Santa Rosa chipset and you can only use up to 3GB RAM. if your Machine ID is "MacBook3,1" or higher you have a Santa Rosa machine and can use 4.0GB RAM as specified by Apple (actually, 6.0GB will work)
edit: you mentioned your machine is 2.4GHz - then it looks like your machine ID should be: "MacBook4,1" - this would be a "MacBook 13-inch Early 2008" version