Determining the Molar Mass of Gases
David L. Emrick
October 22, 2007
Lab Partner - Enrico Fermi
Instructor – Dr. Robert Goddard
Abstract:
The molar masses of selected gases were determined by comparing the masses of the selected gases to the
mass of an equal volume of oxygen under the same conditions of temperature and pressure. The molar
masses were determined using the experimental ratios and setting the molar volume of oxygen as 32.0 g/mol.
The molar masses of air (28.7 g/mol), nitrogen (27.9 g/mol), butane (53.0 g/mol) and burner gas (55.5 g/mol)
were calculated.
Purpose: The purpose of this experiment was to determine the molar mass of several gases and volatile
liquids
Avogadro’s hypothesis states that under the same conditions of temperature and pressure equal volumes of
gases contain the same number of molecules. The mass of equal volumes of four gases (air, propane,
nitrogen, and burner gas) as well as the mass of an equal volume of oxygen were measured. Setting the
molar mass of oxygen as 32.0 g/mol, the molar masses of the four gases were calculated using ratios and
proportions.
Procedure and Materials: See attachment, “Determining the Molar Mass of Gases” published by Flinn
Scientific, for a list of materials and the procedure that was followed.
Data: The following data was collected during the determination of the molar masses of selected gases.
Mass of Evacuated Syringe
40.726 g
Table 1: Data and Calculated Results– Molar Mass of Gases
Gas
Mass of
Syringe and
Gas (g)
Mass of Gas (g)
Experimental
Molar Mass
(g/mol)
Theoretical
Molar Mass
(g/mol)
Percent Error
Air
Oxygen
Nitrogen
Burner Gas
Sulfur
Hexafluoride
40.782
40.786
40.759
40.808
40.991
0.056
0.060
0.033
0.082
0.265
30
-
18
45
140
28.9
32.0
16.0
44.0
146.1
3.8 %
-
12.5 %
2.3 %
4.2 %
Calculations: The molar mass of the gases was calculated using Avogadro’s hypothesis and ratio and
proportion. Avogadro’s hypothesis states that equal volumes of gases at the same state of pressure and
temperature contain the same number of molecules. By setting up a ratio and proportion between the mass
of the unknown gas to the mass of an equal volume of oxygen to the molar mass of the unknown gas to the
molar volume of oxygen, the molar mass of the unknown gas can be calculated.
Experimental Molar Masses: (See Data Table 1)
Air:
mass of air
molar mass of air
=
molar mass of oxygen (32.0 g/mol)
mass of oxygen
mass of air
mass of oxygen
0.056 g
= 32.0 g/mol x
0.060 g
molar mass of air = 32.0 g/mol x
molar mass of air = 30. g/mol
Burner Gas: Molar Mass = 18 g/mol
Carbon Dioxide: Molar Mass = 45 g/mol
Sulfur Hexafluoride: Molar Mass = 140 g/mol
Theoretical Molar Masses:
Air: 79% N2; 0.79 x 28.0 g/mol
=
20% O2
0.20 x 32.0 g/mol =
1% Ar
0.01 x 40.0 g/mol =
Molar Mass
22.1
6.4
0.4
=
28.9 g.mol
Burner Gas (CH4): 12.0 + 4.04 = 16.0 g/mol
Carbon Dioxide (CO2): 12.0 + 32.0 = 44.0 g/mol
Sulfur hexafluoride (SF6): 32.1 + 114.0 = 146.1 g/mol
Results and Error Analysis: The experimental molar masses were as follows:
 air: 30 g/mol
 burner gas: 18 g/mol
 carbon dioxide: 45 g/mol
 sulfur hexafluoride: 140 g/mol
The errors were quite small except for the molar mass of burner gas.
Percent Error:
Air: % error =
| theoretica l molar mass - experiment al molar mass |
x 100%
theoretica l molar mass
=
| 28.9 g / mol  30 g / mol |
x 100 %
28.9 g / mol
= 3.8 %
Burner Gas: % error = 12.5 %
Carbon Dioxide: % error = 2.3 %
Sulfur Hexafluoride = % error = 4.2 %
A primary source of possible error may have been the purity of the gases used. If the gas contained water
vapor (molar mass of 18.0 g/mol), the calculated molar masses would have been low due to the presence of
the lighter mass water for all gases except burner gas. The burner gas would be slightly more massive. The
burner gas was more massive and sulfur hexafluoride was less massive than expected, but air and carbon
dioxide were more massive than expected. This error was not consistent with all trials. Therefore, the
presence of water vapor may not have been that much of a factor.
The burner gas, with the largest percent error, was assumed to be 100% methane (CH4). Many times
“natural gas” contains gases other than pure methane. Since methane is the lightest of all hydrocarbons, any
hydrocarbon other than methane would add an increase to the molar mass of burner gas. The composition of
the burner gas may have been a mixture of many light mass hydrocarbons. If the supplier could have been
contacted, the composition of the gas may have been acquired.
To eliminate any possible error due to the presence of water vapor, a drying agent could be used to insure
that the gas being studied is a dry gas. To avoid assumptions concerning the composition of burner gas, the
supplier should be contacted to obtain a reliable analysis of the burner gas composition. Also, a larger
syringe could be used to measure larger samples of gas that allow more precise calculations.
Discussion:
By using Avogadro’s hypothesis it was possible to determine the molar masses of several gases. The results
were within limits of reasonable error. The experiment not only supported Avogadro’s hypothesis, but the
use of it allows an investigator a method of determining molar masses.