Quantum-mechanical characteristics have been embedded inevitably into macroscopic thermodynamic quantities. However, concerning chemical potential, the connection from a quantum nature has not been analyzed so far. The purpose of this paper is to redefine chemical potential by incorporating quantum consideration. The relationship, between the quantum-mechanical nature and the chemical potential of a classical ideal monatomic gas, is given. The present paper focuses on a simple specified model which is based on the Helmholtz free energy. Thermal average of the position-momentum Heisenberg uncertainty product is introduced to find the link between the chemical potential and the quantum nature. The chemical potential of a classical ideal monatomic gas can be expressed as a function of the value of the thermal average of this uncertainty product. Consequently, it turned out that the quantum characteristic is embedded into the chemical potential of the classical ideal monatomic gas.