  Context. The availability of asteroseismic constraints for a large sample of
red giant stars from the CoRoT and Kepler missions paves the way for various
statistical studies of the seismic properties of stellar populations.
  Aims. We use the first detailed spectroscopic study of 19 CoRoT red-giant
stars (Morel et al 2014) to compare theoretical stellar evolution models to
observations of the open cluster NGC 6633 and field stars.
  Methods. In order to explore the effects of rotation-induced mixing and
thermohaline instability, we compare surface abundances of carbon isotopic
ratio and lithium with stellar evolution predictions. These chemicals are
sensitive to extra-mixing on the red-giant branch.
  Results. We estimate mass, radius, and distance for each star using the
seismic constraints. We note that the Hipparcos and seismic distances are
different. However, the uncertainties are such that this may not be
significant. Although the seismic distances for the cluster members are self
consistent they are somewhat larger than the Hipparcos distance. This is an
issue that should be considered elsewhere. Models including thermohaline
instability and rotation-induced mixing, together with the seismically
determined masses can explain the chemical properties of red-giants targets.
However, with this sample of stars we cannot perform stringent tests of the
current stellar models. Tighter constraints on the physics of the models would
require the measurement of the core and surface rotation rates, and of the
period spacing of gravity-dominated mixed modes. A larger number of stars with
longer times series, as provided by Kepler or expected with Plato, would help
for ensemble asteroseismology.
