How can I find the molecular formula of a gas from experimental data?

A mixture of cyclopropane gas and oxygen is used in an anaesthetic. Cyclopropane contains 85.7% C, and 14.3% H by mass. At 50.0 C and 0.984 atm pressure 1.56g cyclopropane has a volume of 1 L. What is the empirical and molecular formula of the cyclopropane?
Heather

First, use the element mass percents to obtain the empirical formula of the cyclopropane.

1. Write the mass percent as a mass Mass percent is just mass per 100 g sample. So you have 85.7 g C and 14.3 g H in a hundred-gram sample of cyclopropane.
2. Convert these masses to moles.

   85.7 g C ×	(	1 mol C 12.011 g C	)	= 7.1351261 mol
   14.3 g H ×	(	1 mol H 1.00797 g H	)	= 14.18693 mol

   Notice that I haven't rounded off the mole amounts to the correct number of significant digits (the nonsignificant figures are written as subscripts). These are intermediate results, so don't round them.
3. Find the simplest mole ratios. Divide moles of each element by the smallest molar amount. In this case, C is present in the smallar molari amount so the ratios are 1 for carbon and 14.1₈₆₉₃ ÷ 7.13₅₁₂₆₁ = 1.98₈₃₂₂₃ for hydrogen.
4. Round the mole ratios to the nearest whole number (or simple fraction). These are the subscripts in the empirical formula. They should be whole numbers. 1.98₈₃₂₂₃ rounds to 2, so the empirical formula of cyclopropane is C₁H₂ or CH₂.

You're halfway done. To find the molecular formula, you need to find the molecular weight of the compound. The ideal gas law will be useful here.

1. Calculate the number of moles of gas from the given pressure, volume, and temperature.

   n = PV/RT
   n = (0.984 atm)×(1 L)/(0.08206 L atm mol^-1 K^-1 × 323 K)
   n = 0.0371245 mol.

2. The molecular weight of the gas is grams of gas (1.56 g) divided by moles of gas: 1.56 g ÷ 0.0371245 mol = 42.020768 g/mol.

Finally, to find the molecular formula:

1. Find the empirical formula weight by adding up the weights of the atoms in the empirical formula. For CH₂, the formula weight is 12.011 + 2 × 1.00797 = 14.02694 g/mol.
2. Divide the molecular weight by the formula weight. This number tells you how many times the empirical formula is repeated to make the molecular formula. In this case, the molecular formula weight divided by the empirical formula weight is 42.020768/14.02694 = 3. so the molecular formula of cyclopropane is C₃H₆.

Author: Fred Senese senese@antoine.frostburg.edu

Copyright © 1997-2010 by Fred Senese
Comments & questions to fsenese@frostburg.edu
Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/gases/faq/molecular-formula-cyclopropane.shtml