Question

A sample of an unknown gas is found to have a density of 2.50 g/L at a pressure of 1.18 atm and a temperature of 38 °C. Assume ideal behavior.

The molar mass of the unknown gas is=   g/mol.

Answer 1

Ideal gas law states that PV = nRT

P = (n/V) RT

n = moles of gas = mass of gas(g) / molar mass of gas(g/mol)

n/V = [mass of gas (g)] ÷ [molar mass of gas (g/mol) × Volume (L)]

n/V = density of gas (g/L) ÷ molar mass of gas (g/mol)

d = density of gas (g/L)

M = Molar mass of gas (g/mol)

n/V = d/M

So P = (d/M) RT

Where P = pressure of gas = 1.18 atm

R = 0.0821 L.atm/(mol.K)

T = temperature of gas = 38^oC = 273.15 + 38 = 311.15 K

d = 2.50 g/L

M = (dRT)/P

= (2.50 g/L × 0.0821 L.atm/mol.K × 311.15 K) ÷ (1.18 atm)

= 54.12 g/mol