If I submit my 30 day notice, is it state law that I am liable for the rent for the remainder of the lease or until the apartment is re-rented?

That depends. Is there any kind of provision in the lease about early termination?

The general rule is that, if you have a lease and break it, and if there is nothing in the lease about early termination, then you are responsible for the rent until the landlord re-rents or until the end of the term, whichever is earlier. Most states require that the landlord make a good faith effort to re-rent. However some states, notably Florida, do not require the landlord to make any effort to re-rent.

If you're trying to get out of a lease your best bet is to speak to the landlord and work something out, such as forfeiting the security deposit or paying a month or two of rent.