A sample of a halogen gas has a mass of 0.538 g

Question

A sample of a halogen gas has a mass of 0.538 g and exerts a pressure of 600.0 torr at 14.0 oC

in a 100.0 mL flask. Calculate the molar mass of the halogen gas. Is the halogen gas F2, Cl2,

Br2 or I2? R = 0.0821 L atm/mole K 1 atm = 760 torr

Answer 1

Molar mass = grams / moles

We know the grams (0.538 g), so we need to find the moles. For this, we use the ideal gas law:

PV = nRT

P = pressure = 600.0 torr x 1 atm / 760 torr = 0.789 atm

V = volume in liters = 100.0 ml x 1 L / 1000 ml = 0.100 L

n = moles = ?

R = gas constant = 0.0821 Latm/Kmol

T = temperature in Kelvin = 14C + 273 = 287K

Solving for n (moles)

n = PV/RT = (0.789)(0.1) / (0.0821)(287)

n = 0.0033485 moles

Molar mass = 0.538 g / 0.0033485 mols

Molar mass = 160.7 g / mol

The halogen gas would thus be Br₂ which has a molar mass of 159.8 g / mole (it is diatomic)