  Using chiral perturbation theory and the large-$N_c$ expansion, we obtain
expressions for the $\eta'$ mass and $\eta - \eta'$ mixing in terms of
low-energy chiral Lagrangian parameters. This is accomplished through an
intermediate step of `matching' the topological susceptibility in the
large-$N_c$ and chiral Lagrangian descriptions. By inserting the values of
well-measured parameters we obtain predictions involving the the second order
parameters $L_6,L_7$ and $L_8$. The prediction for $L_6$ is quite restrictive
even after allowing for $1/ N_c$ corrections.
