  The problem of formulating a thermodynamically-consistent finite internal
partition function (IPF) in nonideal hydrogen plasma systems is investigated
and analyzed within the chemical picture revealing inaccuracies and
inconsistencies buried in widely used formulations in the literature. The
analysis carried out here, though performed for the simplest case of pure
nonideal hydrogen plasma, it shows all specific features of the problem and is
extendable to the general case of a complex multi-component plasma mixture. A
criterion for the separability of the configurational component of the free
energy is presented and an accurate and consistent formulation of the problem
is introduced. The presented criterion and the introduced consistent
formulation of the problem clear ambiguities in other formulations in the
literature and provide a better understanding of the problem. An illustrative
example is worked out showing simplicity and effectiveness of the proposed
consistent formulation and the importance of terms, essential for thermodynamic
consistency, which are commonly neglected by other authors in the literature.
