We show that textbook formula for the thermodynamic potential for Grand-Canonical ensemble is not always correct. For an exactly solvable model system, comparison is made between the pressure of the canonical ensemble and that of the grand-canonical ensemble. It turns out that the conventional thermodynamic potential for Grand-canonical ensemble yields a result that is not always consistent with that of the canonical ensemble even for a macroscopic system, for which equivalence between predictions of difference ensembles is well-established. We define a range of application of the conventional thermodynamic potential formula for the Grand-canonical ensemble.