  A grid of evolutionary sequences of stars in the mass range $1.2$-$7$
M$_{\odot}$, with solar-like initial composition is presented. We focus on this
mass range in order to estimate the masses and calculate the CNO surface
abundances of a sample of observed red giants. The stellar models are
calculated from the zero-age main sequence till the early asymptotic giant
branch (AGB) phase. Stars of M $\leqslant$ $2.2$M$_{\odot}$ are evolved through
the core helium flash. In this work, an approach is adopted that improves the
mass determination of an observed sample of 21 RGB and early AGB stars. This
approach is based on comparing the observationally derived effective
temperatures and absolute magnitudes with the calculated values based on our
evolutionary tracks in the Hertzsprung-Russell diagram. A more reliable
determination of the stellar masses is achieved by using evolutionary tracks
extended to the range of observation. In addition, the predicted CNO surface
abundances are compared to the observationally inferred values in order to show
how far standard evolutionary calculation can be used to interpret available
observations and to illustrate the role of convective mixing. We find that
extra mixing beyond the convective boundary determined by the Schwarzschild
criterion is needed to explain the observational oxygen isotopic ratios in low
mass stars. The effect of recent determinations of proton capture reactions and
their uncertainties on the $^{16}$O$/^{17}$O and $^{14} $N$/^{15}$N ratios is
also shown. It is found that the $^{14}$N$($ p$,\gamma)^{15}$O reaction is
important for predicting the $^{14}$N$/^{15}$N ratio in red giants.
