Determining the molar mass of a gas
The purpose of this experiment was to determine the molar mass of CO2 experimentally. A simple calculation using the periodic table would provide the correct answer for the molar mass of carbon dioxide, however, one can also conduct an experiment and try to reach the accepted value.
Introduction: The ideal gas law equation(PV = nRT) defines the relationships between pressure (P), volume (V), number of moles (n), and temperature (T) for any ideal gas sample.
R is the ideal gas constant, defines as 0.0821 L atm/K mol. Therefore P must be expressed in atmospheres (atm), V in liters (L), n in moles (mol), and T in Kelvin (K). Almost all experimental conditions correspond with the ideal gas law equation. Only when the gas pressure is several atmospheres or higher does the behaviour deviate from the equation. In order to calculate the molar mass of CO2, one must first be familiar with this equation.
Hypothesis: It was expected that the mass would be approximately 44 g/mol.
- Volumetric flask, 100cm3, dry with stopper
- Scale with accuracy of three decimal places.
- Carbon dioxide generator
- Delivery tube
- Access to barometer
Dependent: Mass of CO2
Fixed: Temperature, pressure and air density
1.The dry volumetric flask was weighed with its stopper to the nearest 0.001 g before the result was entered in Result Table 17a.
2.The stopper was removed and the delivery tube from the carbon dioxide generator was inserted into the bottom of the flask. Thereafter, the valve was opened, releasing CO2 into the flask for approximately one minute before the valve was closed. The flask was kept upright throughout.
3.To avoid releasing CO2, the tube was slowly removed from the flask and the flask was sealed with a stopper.
4.The flask was weighed with its content and stopper to the nearest 0.001 g.
5.Steps 2, 3 and 4 were repeated until there was no further change in the mass (i.e. the carbon dioxide had displaced all the air in the flask).
6.Thereafter, the flask was filled with water before being sealed, using an excess amount of water to ensure that it was completely filled. The flask was dried and weighed to the nearest 0.1g
7.The room temperature and pressure were recorded.
Data: After measuring the mass of the flask with the various contents, it was clear that the wight was not always consistent due to the large number of decimal places. The flask with air became constant at about 48.303 g (ï¿½ 0.01 g) and after inserting and measuring the flask with CO2 three times, it finally stabilised at 48.360 g (ï¿½ 0.01 g). The flask with water weighed 157.2 g (ï¿½ 0.1 g), the temperature was found to be 21ï¿½C (ï¿½ 0.5ï¿½C), and the atmospheric pressure 750 mmHg. By using table 17b (see below) the density of air could be found, and thereafter, table 17a could be filled in.
Mass of flask filled with air
48.303 g ï¿½ 0.01
Mass of flask filled with CO2
48.360 g ï¿½ 0.01
Mass of flask filled with water
157.2 g ï¿½ 0.1
21 ï¿½C ï¿½ 0.5 ï¿½C
Density of air under conditions of experiment
0.00199 g cm-3
Table 17b (Density of air (g cm-3) at different temperatures and pressures)
Analysis: Before the Ideal gas equation was used to calculate the molar mass of CO2, some calculations were done.
1) Calculating the volume of the flask.
From table 17a the mass of the flask with both air and water was read. The mass of the flask with air was subtracted from the mass of the flask with water, leaving only the mass of the water. Knowing the density of water (1 g cm-3), the volume of the flask was deduced.
(Mass of flask + Water ) – Mass of flask = mass of water = volume of flask.
157.222 g – 48.303 g = 108.919 g = 108.919 cm3
2) Calculating the mass of air in the flask.
The mass of air in the flask was calculated by multiplying the density of air and the volume of the flask.
Volume of flask ï¿½ density of air = mass of air in flask.
108.919 cm3 ï¿½ 0.00119 g cm-3 = 0.129613 g
3) Calculating the mass of the empty stoppered flask.
The mass of air was subtracted from the mass of the flask with air, leaving only the mass of the empty flask.
Mass of flask with air – mass of air = mass of flask.
48.303 g – 0.129613 g = 48.173387 g
4) Calculating the mass of carbon dioxide in the flask.
After calculating the mass of the flask, the mass of CO2 was found by subtracting the mass of the flask from the mass of the flask with carbon dioxide.
(Mass of flask + CO2) – Mass of flask = mass if CO2
48.360 g – 48.173387 g = 0.18661 g
5) Calculating the molar mass of carbon dioxide.
Once all the calculations were done, enough information was retrieved to deduce the mass of carbon dioxide through the ideal gas law equation (PV = nRT) – (M= (mRT/PV)). Before inserting the values, the data was converted to the correct unit related to the gas constant(R=0.0821 L ï¿½ atm/K ï¿½ mol). The air pressure (750mmHg) was therefore expressed in atmospheres (atm) (750mmHg = 750/760atm). The volume (108.919 cm3) was converted to litres (108.919 cm3 = 108.919/1000 L = 0.108919 L), and the temperature (21 ï¿½C) to Kelvin( 21+ 273 = 294K).
Molar mass = (mass ï¿½ gas constant ï¿½ temperature)/ (pressure ï¿½ volume)
M = (0.18661 g ï¿½ 0.0821 ï¿½ 294K)/((750/760)atm ï¿½ 0.108919L) = 41.9 g mol-1
1) What value does the experiment give for the relative molecular mass of CO2?
The relative molecular mass of CO2 was 41.9.
2) Calculate the density of CO2 at s.t.p from your results.
Density = mass/volume.
d = 0.18661 g/108.919 cm3 ï¿½ 10-3 = 1.71329 g m-3
3) In step (4) why were you told to remove the delivery tube slowly?
It was to prevent the carbon dioxide escaping from the flask.
4) Why was a less accurate balance adequate for weighing the flask full of water?
It was more adequate because the mass of water is much larger than both CO2 and air, increasing the uncertainty and removing the need for a large number of decimal places.
Errors & improvements
The molecular mass of carbon dioxide is known to be approximately 44 g mol-1, however, in this experiment the molar mass of CO2 turned out to be only 41.9 g. There are several reasons for this error. The most likely being the concentration of CO2 in the flask. Some of the carbon dioxide would escape before the stopper has sealed the flask. The CO2 from the generator might have not been completely pure. Another reason might have been a systematic error caused by the scale leading to incorrect values, or simply an uncertainty error by rounding too much.
Conclusion: The relationship between the actual amount (44 g mol-1) and the calculated amount (41.9 g mol-1) was significant. The procedure of the experiment would not be functional in finding an unknown gas.