Question

Helium gas has a density of 0.166 g/L at 20 degrees Celsius while radon gas has a density of 9.23 g/L ya the same temperature. What can we infer about the relative sizes of the two types of atoms.

Answer 1

Apply Ideal Gas Law,

PV = nRT

where

P = absolute pressure; V = total volume of gas

n = moles of gas

T = absolute Temperature; R = ideal gas constant

D = mass / volume and Molar volume = n/V

MW = molar weight of sample

Then,

PV = nRT; get molar volume

n/V = P/(RT)

get mass -> n = mass/MW

mass/(MW*V) = P/(RT)

D = mass/V

D/MW = P/(RT)

D = P*MW/(RT)

note that

if P, T and R are constant

D = x*MW directly proportional

Then, we can relate to:

Density of ]Helium < Density of Radon

Molar mass of Helium < Molar mass of Radon

Size of Helium < Size of Radon