Question

A pure gaseous hydrocarbon has a density of 0.103 lb/cu ft at 14.7 psia and 100 degrees F. Chemical analysis shows that there are two hydrogen atoms for each carbon atom in each molecule. What is the formula of this molecule? Assume that the hydrocarbon acts like an ideal gas. Additional instruction from teacher : calculate the molecular weight of the molecule. Then divide it by the molecular weight of CH2 , which is the simplest molecule that has two hydrogen atoms for each carbon atom, to determine the number of atoms in this molecule and hence its chemical formula.

Answer 1

Solution :-

Given data

Density = 0.103 lb/ft3 = 1.6499 g/L

Pressure = 14.7 psi =1 atm

Temperature = 100 F = 311 K

Molecular formula = ?

Empirical formula = CH2

Lets first calculate the molar mass of the compound

M= dRT/P is the formula to calculate the molar mass

Lets put the values in the formula

M= 1.6499 g/L *0.08206 L atm per mol K * 311 K / 1 atm

     = 42.0 g per mol

Empirical formula mass CH2 = 14 g per mol

N= molar mass / empirical formula mass

    = 42.0 g per mol / 14.0 g per mol

     = 3

Molecular formula = N* empirical formula

                                  = 3*CH2

                                = C3H6