molecular and empirical formula

Question

Hydrocarbons are organic compounds that are made up of only carbon and hydrogen atoms. A hydrocarbon was found to contain 84.63% of carbon by mass. Determine the empirical and the molecular formula of this hydrocarbon if 0.471 g of its vapour occupies a volume of 268 cm3 at 18 °C and 101 kPa​

Answer 1

When faced with a problem like this, a good idea is to assume you have 100 g of the unknown. Then the % of each element simply becomes the grams of that element, and we can then find the moles of each element. The % H will be 100% - 84.63% = 15.37% H

84.63% C = 84.63 g C x 1 mol C / 12 g = 7.053 moles C

15.37% H = 15.37 g H x 1 mol H / 1 g = 15.37 moles H

Divide both by 7.053 in an attempt to get whole numbers:

7.053/7.053 = 1 mol C

15.37/7.053 = 2.1 (close to 2)

So empirical formula = CH₂

Molar mass of the empirical formula = 12 + 2 = 14 g/mol

Now, in order to find the molecular formula, we must first figure out how many moles of the unknown we have. Once we find that, we can find the molar mass of the unknown and the we can find the molecular formula.

moles of unknown gas:

Use ideal gas law PV = nRT and solve for n (moles)

P = pressure =101 kPa

V = volume in L = 0.268 L

R = gas constant = 8.314 LkPa/Kmol (note the value has kPa as the unit of pressure)

T = temperature in Kelvin = 18ºC + 273 = 291K

n = PV/RT = (101)(0.268) / (8.314)(291)

n = 0.0112 moles of unknown gas

molar mass of unknown gas = grams / moles = 0.471 g / 0.0112 moles

molar mass of unknown = 42.1 g/mol

Molecular formula of unknown = molar mass / molar mass of empirical formula = 42.1 / 14 = 3

Molecular formula = CH₂ x 3 = C₃H₆