  We investigate the semiclassical limit and quantum corrections to the metric
in a unitary quantum gravity formulation of the CGHS 2d dilaton gravity model.
A new method for calculating the back-reaction effects has been introduced, as
an expansion of the effective metric in powers of the matter energy-momentum
tensor. In the semiclassical limit the quantum corrections can be neglected,
and we show that physical states exists which contain the Hawking radiation.
The first order back-reaction effect is entirely due to the Hawking radiation.
It causes the black-hole mass to monotonically decrease, and it makes it
unbounded from bellow as the horizon is approched. The second order quantum
corrections have been estimated. Since the matter is propagating freely in this
unitary theory, we expect that the higher order corrections will stabilize the
mass, and the black hole will completely evaporate leaving a nearly flat space.
