  Analyzing the equations for the unary distribution functions of the
Bogolubov-Born-Green-Kirkwood-Yvon chain of equations for the equilibrium
two-phase system consisting of binary mixture of simple liquids and gas mixture
with plane interface, we derived the analytical expression for the mono-atomic
potentials in liquid and gas phases. Using the asymptotic values of mono-atomic
potentials in liquid and in gas far away from interface, for each component of
the mixture was obtained expression for the atom work function from liquid into
gas. The interrelation between the general equation of state for liquid mixture
and the atom work functions from mixture into vacuum was established. The
stability criterion for each component of the mixture in limiting points of the
first type (using I.Z. Fishers classification) was formulated in terms of the
atom work function from liquid mixture into vacuum. As it turned out, the
stability criteria correspond to atomization conditions of the mixture
components.
