An unknown gas contains 85.6% c and 14.4% h. at 0.455 atm and 425 k, the gas has a density of 0.549 g/l. what is the molecular formula for the gas?

We first have to find the empirical formula. 

assuming that we have 100 g of sample, the percentages convert to grams. So, we have 85.6 grams of C and 14.4 grams of H. now we need to convert the grams to moles using the molar mass of the atoms.

85.6 g C (1 mol C/ 12.0 g)= 7.13 mol C

14.4 g H (1 mol H/ 1.01 g)= 14.3 mol H

now we divide both values by the smallest to find the ratios.

Carbon---> 7.13 / 7.13= 1

Hydrogen---> 14.3 / 7.13= 2

the empirical formula= CH₂

molar mass of CH₂= 12.0 + (2 x 1.01)= 14.02 g/mol

now we have to determine the molar mass of the compound using the following formula.

molar mass= (density x gas constant x temperature) / pressure

molar mass= ( 0.549 x 0.0821 x 425 ) / 0.455 = 42.1 g/mol

let's find the ratio between this molar mass and the empirical formula molar mass. 

42.1 / 14.02 = 3

so the molecular formula---> 3 x CH₂ > C₃H₆