How to Determine the Density of Carbon Dioxide in a Lab

Each molecule of carbon dioxide is made of one carbon atom and two oxygen atoms.

There are two major factors in determining the density of gas: temperature and pressure. Gas expands or contracts in relation to these two factors. At higher temperatures and lower pressures, the volume of a gas expands. At lower temperatures and higher pressures, the volume of a gas shrinks.

Under ideal circumstances, the temperature is 0 degrees Celsius (273.15 Kelvin) and the atmospheric pressure is 1 atmosphere, you may use the standard molar volume gas constant (22.4 L/mol). In this case, only one equation is needed to determine the density of a gas. However, it is likely that the conditions in a lab will not be ideal. Several equations will be required to determine the density of carbon dioxide under nonideal conditions.

Things You'll Need

• Notebook
• Pen or pencil
• Barometer
• Thermometer
• Calculator

Instructions

Using the Standard Molar Volume (ideal conditions)

1. 

   Whenever you perform scientific calculations, use the International System of Units (SI) to keep all units consistent and to avoid calculation mistakes.

   Start with this equation: density=molecular weight g/mol ÷ 22.4 L/mol. The molecular weight of carbon dioxide is 44.01 g/mol as calculated from the molecular weights of its individual elements.

2. Plug the molecular weight of carbon dioxide into the equation: density (g/L) = 44.01 g/mol ÷ 22.4 L/mol.

3. 

   If you are adhering to the rules of significant figures, the answer will be rounded up to 2.0.

   Solve the equation. The solution should be density = 1.9647 g/L.

Calculating the Density of Carbon Dioxide (nonstandard conditions)

1. 

   To convert degrees Celsius to degrees Kelvin, add 273.15 degrees.

   Use an accurate thermometer to measure the temperature of the room. Record this temperature in a notebook.

2. 

   Remember to convert the pressure to atmospheres (atm) if necessary.

   Use a barometer to measure the pressure of the room. Record this pressure in a notebook.

3. 

   Use the right mathematical operators when rearranging and substituting equations.

   Three equations are used to determine the density: the ideal gas law equation (PV=nRT), the equation for density (d = m÷V), and the equation used to determine the number of moles of a substance (n= m÷MW).

   P is pressure in atmospheres (atm), m is mass, d is density, n is number of moles (a unit used to describe the amount of a substance), MW is molecular weight, V is volume in liters (L), T is the temperature (degrees Kelvin), and R is the gas constant (0.0821 L x atm /K).

   Arrange and substitute the ideal gas law equation so that it becomes an equation for density. Start by substituting n for m÷MW so that the ideal gas equation becomes PV= mRT÷MW.

4. Since density = m÷V, rearrange the equation to solve for density like so:

   PMW÷RT = m÷V. Therefore, density = PMW÷RT.

5. 

   Make sure that you have arranged the equation properly by checking to see if the extraneous units cancel out. You should be left with only mass and volume.

   Solve the equation using your measured atmospheric pressure and temperature, the gas constant and the molecular weight of carbon dioxide (44.01 g/mol).

   For example: measured pressure= 0.999 atm; measured temperature= 21.0 degrees Celsius + 273.15 = 294.15 Kelvin; density = PMW÷RT; density = (0.999 atm)(44.01 g/mol) ÷ (0.0821 L x atm/K)(294.15 K); density= 0.15 g/L.

References

• Dr. Miriam Douglass: Calculating Gas Density from Standard Molar Volume
• Molecularsoft.com: Ideal Gas Law with Density
• Lenntech.com: Carbon Dioxide