This document provides instructions for determining the molar volume of carbon dioxide gas through experiment. Students will measure the mass and volume of a CO2 gas sample under laboratory conditions. By calculating the mass of CO2 using the mass difference between an empty flask and one filled with CO2, and knowing the volume and temperature/pressure, students can use the ideal gas law to calculate the molar volume of CO2. The percentage error between the calculated and theoretical molar volume will also be determined to evaluate the accuracy of the experiment.

1. Determining the molar volume of
Carbon Dioxide
Author: Dr. Robert D. Craig, Ph.D.
Purpose of the experiment:
Determine the molar volume of an ideal gas,
By measuring the mass and volume of carbon dioxide gas sample

2. Determining the molar volume of
Carbon Dioxide
Background information
Ideal gases are gases that have no attractive or
repulsive forces between molecules.

3. Determing the molar volume of
Carbon Dioxide
Avogadro’s law states that equal volumes of
ideal gases, under identical temperature and
pressure Conditions, contain equal numbers
of molecules. Thus, at the same temperature
and pressure, one mole of any ideal gas has
the same volume as one mole of any other
ideal gas.

4. Determing the molar volume of
Carbon Dioxide
• This volume is called the molar volume (Vm)
of ideal gases. Understandard condition
(STP) ,which are one atmosphere (at,) of 760
mm Hg pressure and 273 kelvin (K), the molar
volume of any ideal gas is 22.4 L

5. • The ideal gas law (equation 1) expresses the
relationship between pressure ( P) volume
(V) , number of moles present (n), and
temperature (T in kelvins) for any ideal gas
sample

6. .

7. ,
• R is the gas law constant. So long as T, P and
V are expressed in kelvins , atmospheres , and
liters, respectively, R equals 8.21 x 10-2 L atm.
Mol. K

8. .
• If we measure the volume of a known mass of
an ideal gas under one set of condition (to
those labeled “2”) we can use equation 1 to
write

9. .
N = P1 V1/ RT1
and
N = P2 V2/R T2

10. .
• Because the mass of gas does not change , n
remains constant. Therefore, we can combine
the two equations to form equation 2 on the
next page. As part of this process, we can
cancel R on each side , because R is a constant

11. Pg 138
• As part of this process, we can cancel R on
each side , because R is a constant

12. .
• In order for equation 2 to be valid, we must
express the temperature in Kelvins. We can
convert any temperature from degrees Celsius
to kelvins by adding 273

13. .
• In equation 2, we can express the pressure in
any of several units: inches or centimeters of
mercury, torr, or atmospheres. Similarly, we
can express the volume in either milliliters or
liters

14. .
• We can use equation2 and an ideal gas sample
to determine the molar volume of that gas
under standard conditions.

15. • For example, suppose a 0.250 g sample of
carbon dioxide (CO 2) gas has a volume of
0.145 L at 754 torr and 27 oC .

16. .
• To determine the molar volume of this sample
at STP we begin by solving equation 2 for V
stp, where condition 2 is STP
• V stp = P1 V 1 T stp / T 1 P stp

17. .
Next we substitute experimental values into
equation 3
Vstp = (754 torr ) ().145 L ) (273 K)/
• (27 + 273) K ( 760 torr)

18. .
Vstp = (754 torr ) ().145 L ) (273 K)/
(27 + 273) K ( 760 torr)
• = 0.131L

19. .
• The resulting volume is not 22.4 L, as you
might have expected, because the sample
mass was only 0.250 g/mol. However, we can
use this result to calculate the molar volume
of CO2 at STP, using equation 4

20. .
Vm , L/mol = ( V stp, in L ) ( M.WT of sample)
(mass of sample, g)
= (0.131 L/0.250 g CO 2) ( 44.01 g CO 2/ 1 mol CO 2) =
23.1 L/ mol

21. .
We can find the percent error for this result relative
to the theoretical ideal gas molar volume of 22.4
L/mol using equation 5
Percent error, %
= [ (experimental value of Vm, L/mol) -22.4 L/mol)
x ( 100 %)
•

22. .
For the molar volume determined above
Percent error , % = ( 23. 1 L/mol – 22.4 L/ mol)/
22.4 L/ mol
=3%

23. • In this experiment, you will calculate the
molar volume of CO 2 gas ( in L/mol) by
determining the mass of a known volume of
CO 2 gas at laboratory temperature and
pressure.
•

24. • You will determine the CO 2 mass by first
weighing t a flask filled with air, and tghen
reweighing the same flask filed with CO2 gas.
You will fill the flask with CO2 gas by allowing
a piece of solid CO 2 (dry ice) to vaporize in
the flask.

25. • The vaporizing CO 2 will force all the air from
the flask, because CO2 gas is considerably
more dense than air. The flask becomes filled
with CO2 gas, which we can assume is at
laboratory temperature and pressure.

26. .
The gas volume is the same in both cases; it is the
volume of the flask.
The mass you will determine from the first
weighing of the flask (m1) is the mass of the
flaske (mf) plus the mass of air contained in the
flask (ma) , as shown in equation 6
m1 = mf + ma

27. .
m1 = m F + ma
The mass you will determine from the second
weighing of the flask (m2) is the mass of the
flask (mf) plus the mass of CO2 gas contained
in the flask(mCO2) (equation 7)
m2 = mf+ mCO2

28. .
We can calculate the difference between the
second and first masses using equation 8.
m2 - m1 = ( mF + mCO2) - (mF+ ma )
= mCO 2 - ma
We can calculate the mass of CO2 gas usingEquation
9, which is a rearrangement of Equation 8.

29. mCO2 = m2– m1+ ma
Equation 8.
mCO2 = m2– m1+ ma
As equation 9 shows, the mass of CO2 gas in the
flask is equal to the difference between the
two weighings plus the mass of air contained
In the flask

30. .
We can calculate the mass of air, ma, by
multiplying the density of air at laboratory
temperature and pressure by the volume of
air contained in the flask (equation 10)
ma = (density of air, g/mL )(volume of flask, mL)

31. .The CRC
You can obtain the literature value for the
density of air under your lab conditions in the
CRC
*based on you data, you will calculate the molar
volume of CO2 gas
** please also calculate the percent error in
your analysis

32. http://itl.chem.ufl.edu/2045_s99/lect
ures/lec_bc.html