  Recent theoretical investigations have unveiled a rich structure in the
quantum chromodynamics (QCD) phase diagram which consists of quark gluon plasma
(QGP) and the hadronic phases but also supports the existence of a cross-over
transition ending at a critical end point (CEP). We find a too large variation
in determination of the coordinates of the CEP in the temperature (T), baryon
chemical potential ($\mu_{B}$) plane and, therefore, its identification in the
current heavy-ion experiments becomes debatable. Here we use an equation of
state (EOS) for a deconfined QGP using a thermodynamically consistent
quasiparticle model involving quarks and gluons having thermal masses. We
further use a thermodynamically consistent excluded volume model for the hadron
gas (HG) which was recently proposed by us. Using these equations of state, a
first order deconfining phase transition is constructed using Gibbs' criteria.
This leads to an interesting finding that the phase transition line ends at a
critical point (CEP) beyond which a cross-over region exists. Using our thermal
HG model, we obtain a chemical freeze out curve and we find that the CEP lies
in close proximity to this curve as proposed by some authors. The coordinates
of CEP are found to lie within the reach of RHIC experiment.
