Which liability account would hold the balance of rent due but not yet paid?

Rent Payable

A payable account is any account that has a balance due that has not been paid yet. Say you owe $500 for one months rent, but want to record it on the books but not pay it, the journal entry would be:

Rent Expense (debit) $500

Rent Payable (credit) $500

It's the same concept as with such payable accounts like, Income Tax Payable, Salary or Wages Payable, etc.

Though it is very uncommon to record rent as a payable, usually it is recorded as prepaid (an asset) or as it is paid, not before.