In the ideal gas model of statistical mechanics one very often assumes the gas is dilute so the average separation between particles is large and hence their mutual interaction is correspondingly small.
In addition, if the gas is sufficiently dilute, the average separation between its particles is much larger than de Broglie wavelength of a particle. In this case, quantum-mechanical effects are of negligible importance and it is permissible to treat the molecules as distinguishable particles moving along classical trajectories (classical approximation).
I am confused about the shaded statement, why we judge the quantum-mechanical effect in terms of the wavelength? I mean if the observable processes are of no disturbance then the particle's dynamics is governed by classical mechanics, so here is there anything I am missing?