<p>The equation of state of an <i>l</i>-cluster of Yukawa molecules of charged dust particles immersed in plasma is investigated using the cluster expansion method as a function of particle charging, screening length, and dust molecule size. This paper investigates the use of modified Mayer cluster integrals to model the equation of state (EoS) of particle clusters in dusty plasma environments. Conventional approaches often fail to capture coupling and particle correlations inherent in these systems. By leveraging the screened activity expansion, this study derives virial coefficients from pairwise and triplet particle interactions, thereby revealing the thermodynamic behavior across various plasma conditions. The density of molecules and the mean inter-particle spacing are defined, which can be used to estimate the strength of screening on the dust particles. These variables can express the thermodynamic quantities of dust molecules in terms of the dynamical variables related to the local characteristics of the plasma. It shows that dust particle grains can be formed as spherical shells. The main advantage of the presented theoretical formulations is the viable model of EoS for incorporating particle correlations in a partially ionized plasma with a more accurate thermodynamics description, accounting for high screening and strong coupling effects. The equation of state obtained here shows good agreement with the result obtained by molecular dynamics simulation.</p>