"To mentor someone during a project" vs. "to mentor someone on a project"

"..., whom I mentored during his final semester's project" vs "..., whom I mentored on his final semester's project"

Which of these two are grammatically correct?

Both are grammatically correct.

Since I am not talking about the final semester but the final semester's project, I am not very sure about during.

The second option is more particular about what you did and hence, it is better. So, you might want to go with the second option - ..whom I mentored on his final semester's project.

Both options are technically correct, although with the first someone may interpret it to mean that you were mentoring him on something besides his final project that just happened to take place at the same time he was working on his final project. I'd also avoid using the wording "final semester's project," as that tends to construe that the final semester is animate and doing the project itself. I'd say "final semester project."

Though (as others have said) both of these are technically correct, they have subtly different meanings.

To mentor someone during a project means, at its most literal level, to mentor someone during the time when they were doing a project. The mentoring does not necessarily relate to the project- the mentoring could have been focused on something else.

To mentor someone on a project specifies that the mentoring was related to the project. This phrasing is more specific, so it should be used if and only if it accurately describes what you did.

Note that both of these wordings imply that the mentoring took place only during the duration of the project. If you mentored the student for a longer period of time that included the student's project, then another wording that better conveys your relationship would be more accurate.

In addition, as Schlockading pointed out, the wording *final semester's project, when taken literally, implies that the final semester is what's doing the project, not the student. "Final semester project" is one alternative, though I would recommend the more concise and equally accurate "final project".