My daughter is a full time university student living 8 hours away. she rents an apartment close to campus and I pay the rent. can I claim this rent?

If your daughter is a resident of Ontario, and the apartment is also in Ontario, your daughter would be able to claim the rent.  Unfortunately you are not able to claim the rent on your return.

http://www.cra-arc.gc.ca/bnfts/rltd_prgrms/ntr-eng.html#ptc