THE MOLAR VOLUME OF CARBON DIOXIDE

DETERMINATION OF
THE MOLAR VOLUME OF CARBON DIOXIDE

PURPOSE

By making measurements on a sample of carbon dioxide, students are able to determine the molar volume of CO₂. They are also introduced to the concept of buoyancy and its importance when massing objects whose masses are small compared to their volumes.

DESCRIPTION

This activity could be carried out as an experiment or as a demonstration and is appropriate for a first-year college-prep or AP course. Using balloons and dry ice, students are able to determine the molar volume of carbon dioxide at STP by making three mass measurements and recording the temperature and atmospheric pressure. Students will use the concept of buoyancy to determine the volume of the sample of gas and correct the molar volume to STP.

TIME REQUIRED

One lab period.

MATERIALS

Chemicals:

dry ice

Equipment:

15-inch round balloons

#5 solid rubber stoppers small beaker (100-mL or 150-mL)

platform or top-loading centigram balance

thermometer

barometer or source of barometric pressure*

hammer

towel

*See Modifications / Substitutions

HAZARDS

Dry ice should not be touched with the bare hands; tissue damage can result. The recommended 15-inch balloons can hold up to about 1 mole of carbon dioxide gas; if a different size balloon is used, its capacity should be checked.

MODIFICATIONS/SUBSTITUTIONS

Dry ice is available from ice companies or from an ice cream distributor or store.
Round balloons are available from a drugstore or party store.
The barometric pressure can be obtained by calling the number listed for weather in most telephone directories.

PROCEDURE

Mass a balloon and rubber stopper to the nearest hundredth of a gram and record.
While one student holds the mouth of the balloon open, another student should add approximately 5-8 g of small pieces of dry ice to the balloon from a beaker and insert the stopper.
Quickly mass the balloon, stopper and dry ice as soon after assembling the system as possible.
Agitate the balloon and contents gently to vaporize the carbon dioxide. Dry the exterior of the balloon. Mass the balloon, stopper and gaseous carbon dioxide after the contents have reached room temperature.
Record the temperature of the room and the atmospheric pressure.
Calculate the mass of dry ice used.
Calculate the moles of carbon dioxide used.
Determine the mass of air displaced by the inflated balloon. ((Mass of balloon, stopper, and CO_{2 (s)}) minus (Mass of balloon, stopper, and CO_{2 (g)})) ÷ (Mass of displaced air).
Determine the volume of air displaced, using the density of air at the temperature and pressure in the room. Volume of air displaced = (Mass of air displaced) ÷ (Density of air at room conditions).
Determine the volume of the carbon dioxide (volume of stopper is small enough compared to the volume of the gas, that it can be ignored). Volume of CO₂ = Volume of air displaced.
Calculate the volume of carbon dioxide gas per mole of dry ice used. Molar vol. of CO_2(g) = ((Vol. of CO₂) ÷ (Mass of CO₂) × ((44 g CO_>2) ÷ (mole CO₂)).
If it is assumed that the pressure of CO_{2 (g)} in the balloon equals the atmospheric pressure, the molar volume of CO₂ can then be corrected to STP.

DISPOSAL

Carbon dioxide gas presents no disposal problems; it can be expelled from the balloons into the room.

DISCUSSION

When the apparent mass of the balloon, stopper and carbon dioxide gas is determined, it is much less than the mass of the system determined when the carbon dioxide was a solid. Because the volume of the balloon and gaseous contents is large compared to its mass, the mass of the displaced air, pushing against the balloon and buoying it up, is a significant fraction of the mass of the balloon and contents. The difference between the true mass of the balloon and contents and the apparent mass (when the carbon dioxide is a gas) is equal to the mass of the displaced air (the buoyancy correction). Using the mass of the displaced air and the density of air at room conditions (obtained from a handbook), students can calculate the volume of displaced air. The volume of displaced air is, to a good approximation, the volume of the carbon dioxide gas.

TIPS

As part of the pre-activity discussion, show students the approximate volume of one mole of gas by placing 44 g of dry ice in a 15-inch balloon and setting the balloon aside at the beginning of the period. By the end of the class, the dry ice will have vaporized.
Students will need an understanding of buoyancy to understand this activity. It is suggested that teachers demonstrate buoyancy in water and discuss buoyancy in air as part of the pre-activity discussion. These ideas might be reinforced again while students are waiting for the dry ice to vaporize.
It is important that the massing of the balloon, stopper and dry ice be done as quickly as possible to minimize the buoyancy factor at this point. While waiting for the dry ice to vaporize, students should be careful not to rub the balloon excessively; if the balloon picks up a static charge, it may interfere with the determination of the mass.
If 5-8 g of dry ice are vaporized in a 15-inch balloon attached to a manometer, the pressure exerted by the balloon fabric is 12-14 mm Hg. Since this pressure represents only about 1.5% of the total pressure, it is possible to approximate the pressure of the carbon dioxide with the atmospheric pressure without introducing substantial error.
If 5-8 g of carbon dioxide is placed in a 15-inch balloon, the measured molar volume is within 5% of the accepted value. Determining the volume of the balloon by measuring the circumference is not practical. Even if two or three circumference measurements are averaged, there is a 15-20% error in the molar volume, because any error in the circumference is compounded when the radius is cubed to calculate the volume of the balloon.

REFERENCES

Handbook of Chemistry and Physics, The Chemical Rubber Publishing Co., Cleveland, OH.
Use this reference to find the density of air at the temperature and pressure in the laboratory. Look up Density of Air in the index.

Submitted by Eva Lou Apel, Michael Bannon, Joseph Baron, John Brodemus, and Elna Clevenger