Question

A certain type of aerosol particles is composed of organic molecules with an average molecular mass of 224.5 g/mol. The density of the aerosol particles is 1.29 g/cm3. Determine the number organic molecules that make up an aerosol particle of 137.9 nm diameter.

Answer 1

diameter = 137.9 nm
radius = 137.9/2 nm
radius = 68.95 nm
radius = 68.95*10^-7 cm
radius = 6.895*10^-6 cm

Lets find the volume of this particle as it should be a spehere
volume = (4/3)*pi*r^3
= (4/3)*pi*(6.895*10^-6 cm)^3
= 1.373*10^-15 cm^3

density = 1.29 g/cm^3

so,
mass = density * volume
= 1.29 g/cm^3 * 1.373*10^-15 cm^3
= 1.771*10^-15 g

molar mass = 224.5 g/mol
so,
number of mol = mass / molar mass
= (1.771*10^-15 g)/(224.5 g/mol)
= 7.89*10^-18 mol

number of particles = number of mol * Avogadro’s number
= 7.89*10^-18 mol * 6.022*10^23 particles/mol
= 4.75*10^6 particles

Answer: 4.75*10^6 particles