  We study the 't Hooft coupling $g_{t}$ and the mass splitting of the
ground-state baryons in a chiral quark model inspired by the large $N_{c}$ QCD.
Depending on $g_{t}$ the Hartree wavefunction of light quark in baryons is used
to map the mass hyperfine splittings for the octet and decuplet baryons. The 't
Hooft coupling $g_{t}$ that reproduces the data of baryon masses is determined
to be around $1.57$, which is small in the sense that $g_{t}^{2}/(4\pi
N_{c})\ll $$1$.
