modern vacuum pumps permit the pressures down to  p = 4 x 10^ -15 atm to be reached at room temp , assuming that the gas exhasted is nitrogen find the no of molecules per cm3 and the mean distance

 easy

PV=nRT

here n= no. of moles=no.of molecules/avegadro's no.

so

no.of molecules/avegadro's no.=n=PV/RT

no. of molecules/V(IN CUBIC decIMETRE)=

then substitute 1dmcube=1000 cm cube