Spock Prime died, presumably, of old age. When Spock Prime died on New Vulcan, he would have been approximately 162 years old.
Sarek, Spock's father, was considered to be middle-aged at 102 (TOS) and very old at 203 (TNG). Using this as a scale, we can assume that 162 for a Vulcan would be roughly 7080-ish for a human. And like humans, not all Vulcans could expect the same lifespan - all manner of criteria, including genetics, would factor into determining their natural lifespan.
Couple this with Spock's half-human biology and we can safely assume that 162 was a pretty good lifespan for him - just a couple of decades shy of the Vulcan norm, in fact.