  Using the trace anomaly and low energy relations, as well as Witten-Veneziano
formula for the mass of the $\eta'$ meson, the chiral topology of the QCD
nonperturbative instanton vacuum has been numerically evaluated. Our formalism
makes it possible to express the topological susceptibility and the mass of the
$\eta'$ meson as a functions of the instanton number density in the chiral
limit. We have explicitly shown that the topological susceptibility in this
case is approximately one fours and one half of its phenomenological value at
instanton number densities in the chiral limit, 0.5 fm^{-4} and 1.0 fm^{-4},
respectively. Thus the instanton contributions substantially underestimate the
mass of the $\eta'$ meson which still remains large in the chiral limit. With
the help of the above-mentioned Witten-Veneziano formula, we derived an
absolute lower bounds for the pion decay constant and the mass of the $\eta'$
meson in the chiral limit.
