Elementary particles are atomic or sub-atomic particles that make up all kinds of matter. They are classified into two main groups, namely: bosons and fermions. In other words, bosons and fermions are found in all states of matter, viz: solids, liquids and gases. Fermions are constituents of matter while bosons are force carriers. Bosons are particles that transmit interactions or the constituents of radiation. The main objective of this paper is to derive and integrate the intermolecular partition function into the general partition function of the elementary gases. The application of the partition function so formulated in the determination of the thermodynamic states of the elementary particles and its validity can eventually be addressed. The partition function of a system is the ratio of the total number of particles in the system to the number of particles in the lowest energy state of that system. Thus, it is dimensionless. Partition function is very important in the analyses of thermodynamic systems. Once an expression for the partition function of a system is known, then the thermodynamic functions appertaining to the system; entropy, specific heat capacity, Helmholtz free energy, internal energy, etc can be determined. Many have been neglecting the effects of intermolecular interactions while calculating the overall partition function of interacting systems. This article considered the common way of determining partition function, z without considering intermolecular interaction effects and compared it with z determined by taking cognizance of the effects of intermolecular interactions. A comparison of the two was made, and the result analyzed. An overview of the various z’s in the old way was presented and a new one called inter-particle interaction partition function was derived using the Schrodinger equation. . To validate the work, the entropies and specific heats of hydrogen were compared with published data by two-way ANOVA. It was determined that the values were significantly different as expected. This work has established that intermolecular interaction