Chemistry problem related to a dumas bulb experiment

Question

An organic volatile solvent analyzed by a combustion analysis is 85.63% C and 14.37% H. In a Dumas bulb experiment, a 2.174-g sample of that compound’s vapor occupies 1.00-L volume at 120.0oC and 760 Torr. What are: (a) the molar mass, and (b) the molecular formula of the compound? Enter your detailed solution below and answers in the boxes provided with corrected units and sig. figs. (no points without detailed solution entered):

Answer 1

Using the Ideal Gas Law we can find the molar mass of the unknown:

Ideal Gas Law:

PV = nRT and solving for n (moles) we have..

n = PV/RT = (1 atm)(1.00L)/(0.0821 Latm/Kmol)(393K)

n = 0.0310 moles

molar mass = 2.174 g/0.0310 moles = 70.1 g/mole (3 sig. figs.)

From the % composition we can find the empirical formula and then the molecular formula:

14.37 g H x 1 mol/1 g = 14.37 moles H

ratio C:H = 1:2

85.63 g C x 1 mol C/12 g = 7.135 moles C

Empirical formula = CH₂ with a molar mass of 12 + 2 = 14

Molecular formula: 70.1 g/14 g = 5 empirical formulae in 1 molecular formula

Molecular formula = C5H10