Abstract: The dependences of the pressure, the chemical potential and the free-energy density on the number density of particles for a homogeneous system of hard spheres have been compared using the Carnahan–Starling equation of state, the Rusanov equations of state and the 18-coefficient virial expansion. The full and a narrower ranges of the number density of hard spheres have been considered. It is shown that in general the 6th-order Rusanov equations agree better with the virial expansion over the full range of the number density, but this is due to the high-density region. In the low- and medium-density regions, the Carnahan–Starling equation shows slightly better agreement with the 18-coefficient virial expansion. Using the dependences of the chemical potential and the free-energy density on the local number density of particles obtained from the Carnahan–Starling equation of state, the truncated 6th-order Rusanov equation, and the 18-coefficient virial expansion within an integral density functional theory, we have calculated the molecular density profiles in radially nonuniform spherical small droplets and bubbles of an argon-like substance and plotted the surface tension of small droplets and bubbles vs the curvature of their equimolecular surface. It is shown that the choice of the equation of state affects the values of quantities characterizing the two-phase equilibrium,e.g., the value of the chemical potential or the surface tension at a flat interface, and can shift the droplet or bubble size.