A 0.271 g sample of an unknown vapor occupies 294 ml at 140.°c and 847 mmhg. the empirical formula of the compound is ch2. what is the molecular formula of the compound?

When the molar mass M = mass (g) / no. of moles (Mol)

∴ moles = 0.271 g / M

By using the gas equation:

PV = n RT

when P is the pressure = 847 mmHg / 760 = 1.11 atm

V is the volume = 0.294 L

n = 0.271 / M

R is constant = 0.0821

T = 140+273 = 413 K

so by substitution:

when n = PV/RT

∴ 0.271 / M = 1.11 atm * 0.294 L / 0.0821 * 413

∴ M = 28

when the empirical formula of CH2 = 12+2 = 14

∴ the exact no. of moles = 28/14 = 2

∴the molecular formula = 2 (CH2) = C2H4