Gas Density and Molar Mass

Question

To identify a diatomic gas (X2X2), a researcher carried out the following experiment: She weighed an empty 3.1-LL bulb, then filled it with the gas at 2.01 barbar and 20.0  ∘C ∘C and weighed it again. The difference in mass was 7.1 gg . Identify the gas.

Express your answer as a chemical formula.

Answer 1

Ideal gas law: PV = nRT

P = pressure = 2.01 bar 0.987 atm / bar = 1.98 atm

V = volume in liters = 3.1 L

n = moles = ?

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 20C + 273 = 293K

solve for n (moles)

n = PV/RT = (1.98)(3.1 L) / (0.0821)(293) = 0.255 moles

molar mass = g / moles = 7.1 g / 0.255 moles = 27.8 g / mol

Gas appears to be nitrogen (N2) which has a molar mass of 28 g / mol

If you are meant to use density and molar mass, as suggested by the title of the question, then the following will suffice:

Density = mass / volume

mass of gas = 7.1 g

volume = 3.1 L

density of gas = 7.1 g / 3.1 L = 2.29 g / L

If we have 1 L of this gas (2.29 g), under the given conditions, we can use the ideal gas law to find moles

PV = nRT

P = pressure = 2.01 bar 0.987 atm / bar = 1.98 atm

V = volume in liters = 1 liter

n = moles = ?

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 20C + 273 = 293K

Solving for n (moles) we have

n = PV/RT = (1.98)(1) / (0.0821)(293)

n = 0.0825 moles

Molar mass = g / moles = 2.29 g / 0.0825 moles = 27.8 g / mole

Gas appears to nitrogen (N₂)