A model system of charged spherical macroions and oppositely charged point counterions with a macroion-charge to counterion-charge ratio Z(r)=10 was investigated by employing a temperature and density scaling Monte Carlo simulation method. This approach allowed for a determination of the relative free energies among arbitrary number of thermodynamic states over a substantial region of the state space. Here, relative free energies were determined for the macroion volume fraction interval 0.04 < phi (M)<0.24 at different values of the electrostatic coupling parameter Gamma (II)equivalent toZ(I)(2)L(B)/R-M, where Z(I) denotes the counterion charge, L-B the Bjerrum length, and R-M the macroion radius. The binodal curve separating the one-phase system and a gas-liquid two-phase region was determined near the critical point which was determined to phi (cr)(M)=0.15 and Gamma (cr)(II)=2.6.