About 1860 Maxwell sowed that the viscosity of a gas is given by η=ρνι where ρ iπs density ν mean velocity and ι mean free path.The latter quantity he had earlier shown to be ι = 1/(square root of 2)(π)(Ng)(d2)where d is diameter of a molecule.Loshmidt(1865)used the measured value of η,p(gas) and p(solid) together with Joules calculation of ν to determine Ng the number of molecules per cm3 in a gas at STP(1atm 0°C).He assumed the molecules to be hard spheres tightly ppacked ina solid.Given η = 2*10^-4 cm^-1 s^-1 for air at STP ρ(liquid)≈ 1 g cm^-3 p(gas)≈1*10^-3 g cm-3 ,and ν≈ 500 m/s-1. Calculate Ng(number of molecules)
in the problem has a sentence that said "Loshmidt(1865)used the measured value of η,p(gas) and p(solid) together with Joules calculation of ν to determine Ng the number of molecules per cm3 in a gas at STP(1atm 0°C)".
So your problem is to find d, and clearly that has something to do with the densities given, which are for air. Would the answer be different for H2 instead of air?
Notice that the density given includes mass (g) in the dimensions, but mass doesn't appear anywhere else in the equations. This needs to be resolved somehow with external information.
Also note that there is a typo as presented you (or they) have mixed up the gas density and the liquid density in the problem. Easy to resolve though, use the larger one for liquids, the smaller one for gas.
OK, a 1cm x 1cm x 1cm cube has a volume of 1 cm3. With a density of 2.70 g/cm3, this means there are 2.70 g of Al in the cube. So, how many Al atoms weight 2.70 g? What information do you need to get to solve this problem? Where/how will you get it?
Then, when you find out how many atoms there are. How far apart are they (center to center, since they will be touching each other)? Imagine carefully placing tennis balls inside a big box to get as many as possible inside.
Finally, for the original problem, you will need to know that air is composed of 80% N2 and 20% O2. A N2 molecule weighs twice as much as a N atom.