  We study the consequences of the running Newton's constant on several key
aspects of spherically symmetric charged black holes by performing a
renormalization group improvement of the classical Reissner-Nordstr\"om metric
within the framework of the Einstein-Hilbert truncation in quantum Einstein
gravity. In particular, we determine that the event horizon surfaces are stable
except for the extremal case and we corroborate the appearance of a new
extremality condition at the Planck scale that hints at the existence of a
final stage after the black hole evaporation process. We find explicit
expressions for the area and surface gravity of the event horizon and we show
the existence of an exact form $dS$ with the surface gravity as integrating
factor. This result is a first clue towards finding a generalization of the
first law of black hole dynamics, for improved charged spherically symmetric
spacetimes in contrast to a previous no-go result for axially symmetric ones
with null charge. We finally calculate an explicit formula for the Komar mass
at the event horizon, and we compare it with the total mass at infinity for a
wide domain of values of the black hole parameters M, Q and $\bar{w}$, showing
a loss of mass which can be interpreted as a consequence of the antiscreening
effect of the gravitational field between the event horizon and infinity.
