A chemistry student found the density of Freon-11 (CFCl3) to be 5.58 g/L under her experimental conditions. Her measurements showed that the density of an unknown gas was 4.38 g/L under the same conditions. What is the molar mass of the unknown?

52.56 g/mol

Explanation:

Given:

density of CFCL3=5.58 g/mol

density of unknown gas=4.38 g/mol

From ideal gas law PV=nRT

N=number of moles=mass/molar mass

P=pressure

R=gas constant

T=Temperature

Therefore PV = (mass/molar mass) RT ...1

Making molar mass the subject of the equation

Molar mass = (mass/V) RT/P ...2

Since density ƥ=mass/volume. Substitute in equation 2 above

Molar mass = ƥ * RT/P ... 3

Since the conditions applied does not change as stated in the question. let k=RT/P

Substituting in equation 3, molar mass = ƥ * k ... 4

For FREON-11 (CFCL3)

Atomic weights are

C=12

F=19

CL3=3*12=36

Molar mass of CFCL3=12+19+36=67

Substitute in equation 4

67=5.58 * k

K=12 L/mol

Applying equation 4 for the unknown gas with 4.38g/mol density

Molar mass=4.38 * 12=52.56 g/mol