Buoyancy in Air—Mass vs. Weight

Introduction

In a chemical reaction, matter is neither created nor destroyed, but rather is conserved. That is true everywhere, except in this apparent contradictory demonstration! Use this discrepant event to teach your students what is really measured when they “weigh” something on a balance.

Concepts

• Conservation of mass
• Buoyancy
• Mass vs. weight

Background

The law of conservation of mass states that the mass of the reactants in a chemical reaction equals the mass of the products. Matter is neither created nor destroyed. In this demonstration, the reaction of sodium bicarbonate, NaHCO₃, and acetic acid, CH₃CO₂H, will be used to confirm this law.

When mixed, the bicarbonate and acetic acid react to form carbonic acid and sodium acetate.

The carbonic acid decomposes to form carbon dioxide gas and water.

In Part 1 of the demonstration, the reaction mixture will be contained in a closed bottle. This allows for the measurement of the mass of the reactants and the mass of the products without the loss of any material from the reaction and with no change in the volume.

In Part 2, the demonstration setup is modified by replacing the cap with a balloon. The carbon dioxide gas produced will inflate the balloon, changing the total volume of the setup. This is also massed before and after the reaction.

Both parts of the demonstration are carried out in air. Air is a fluid. Just as in water, an object will be buoyed in air. The degree to which objects are buoyant is related to their density and the density of the fluid. The smaller the density of the fluid, the smaller the buoyant force.

Balances do not directly measure mass of an object. They measure the force an object exerts—its weight. Calibrated masses are used to convert these weights to mass readings. As long as an object being massed has approximately the same density as the calibrated masses, the mass readings will be accurate. This holds true for most solids and liquids. For any object being massed on a balance, there are three forces acting on the object: (1) the weight of the object, mg; (2) the force of the balance on the object, N; and (3) the buoyant force of the air, F_B (see Figure 1).

Since the object on a balance is at rest, the sum of the forces must be equal to zero:

If the actual measured weight on the balance is W_m, then W_m = N. Substituting W_m into Equation 3, we get:

This means that the measured weight in air (W_m) differs from the weight in a vacuum (mg) by the buoyant force of the atmosphere on the object (F_B).

The buoyant force is equal to the volume of air displaced by the object, V_a, times the density of air, ρ_a, times the acceleration due to gravity, g.

Substituting this into Equation 2 produces:

where m_m is the measured mass on the balance.

Dividing both sides by g yields:

For the bottle and balloon in Part 2, the true mass is the same before and after the reaction. The difference between the measured masses is

The volume of air displaced in the reaction by the production of carbon dioxide is estimated by measuring the diameter of the balloon. If we assume the balloon is a sphere, then the volume is:

Materials

Safety Precautions

Acetic acid is a corrosive liquid. Avoid exposure of all chemicals to eyes and skin. The pressure bottle is safe if used properly. At very high pressures, the bottle might split, but it will not shatter. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Please review current Safety Data Sheets for additional safety, handling and disposal information.

Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. The product solutions may be disposed of according to Flinn Suggested Disposal Method #26b.

Prelab Preparation

An optional student worksheet, along with a discussion of buoyancy, is included for testing student understanding of the demonstration. If using these worksheets, pass out copies of the worksheet to the students.

Procedure

Part 1. Conservation of Mass

1. Place a weighing dish on the balance. Add approximately 5.0 g of sodium bicarbonate to the weighing dish. Have students record the mass of the weighing dish and the sodium bicarbonate in Data Table A of their worksheet.
2. Add 100 mL of 1 M acetic acid to the 1-L bottle.
3. Mass the bottle and its cap. Have students record the mass of the bottle, acetic acid, and cap in Data Table A.
4. Set the bottle down on the lab bench.
5. Fold the weighing dish with the sodium bicarbonate in half, creating a spout.
6. Hold the folded weighing dish with one hand and the bottle cap with the other.
7. Quickly pour the contents of the weighing dish into the bottle. Immediately cap the bottle tightly.
8. The bottle will bulge as gases are produced from the bicarbonate reacting with acetic acid. The cap is strong enough to keep the bottle sealed under pressure.
9. Once the reaction is complete, mass the bottle and the now empty weighing dish together on the balance. Have students record the total mass in Data Table A.

1. Remove the cap from the bottle and drain the solution from it. Rinse the bottle sev¬eral times and fill the bottle with 100-mL of 1 M acetic acid.
2. Obtain a balloon. Weight out approximately 5 g of sodium bicarbonate in a weighing dish. Fold the weighing dish and carefully pour the sodium bicarbonate into the balloon.
3. Secure the mouth of the balloon around the bottle opening (see Figure 2).
   {13353_Procedure_Figure_2}
4. Place the bottle on a balance capable of reading 0.01 g. Record the mass of bottle and balloon in Data Table B.
5. Raise the balloon until a few grains of sodium bicarbonate fall into the bottle. As the pieces dissolve, carbon dioxide gas is released, inflating the balloon. The rest of the sodium bicarbonate now falls into the solution, further inflating the balloon.
6. When all the sodium bicarbonate has dissolved and the balloon is no longer being inflated, have students record the mass of the apparatus in Data Table B.
7. Estimate the diameter of the inflated balloon in centimeters. Have students record this value in the Data Table.

Student Worksheet PDF

13353_Student.pdf

Teacher Tips

• This kit contains enough chemicals to perform the demonstration seven times: 1500 mL of 1.0 acetic acid solution, 100 g of sodium bicarbonate, 10 balloons and a reusable 1-L bottle and cap.
• It may be difficult to pour the sodium bicarbonate in the bottle and cap it before any carbon dioxide escapes. Practice with table salt to perfect the technique before running the procedure with sodium bicarbonate.
• The buoyancy of objects in air is the same principle as objects in water. Review this principle with students. A handout discussion section on mass and buoyancy in air is included, along with a discussion and question section. Make copies to pass out to the students before the demonstration.

Sample Data

Data Table A

1. Mass of weighing dish and sodium bicarbonate  ___7.54___ g
2. Mass of bottle, acetic acid solution and cap        ___132.61___ g
3. Total mass before reaction (1 and 2)                   ___140.15___ g
4. Total mass after reaction                                     ___139.88___ g
5. Mass loss or gain (±)                                            ___–0.27___ g

1. Mass of assembly before reaction (step 10)        ___138.36___ g
2. Mass of assembly after reaction (step 14)           ___136.63___ g
3. Mass loss or gain (±)                                           ___–1.73___ g
4. Diameter of inflated balloon                              ___13___ cm

Answers to Questions

1. Use the diameter of the inflated balloon and Equation 6 and 7 to calculate the theoretical change in weight for the Part 2 dem-onstration. How does this compare with the actual change in weight? The density of air, ρ_a, at 20 °C, is 1.21 x 10^–3 g/cm³.

   V = 4/3πr³

   V = 4/3πr³ = 4/3(3.1416)(13/2)³cm³ = 1150 cm³

   Δm = (1150 cm³) x (1.21 x 10^–3 g/cm³) = 1.39 g

   The actual weight loss was 1.73. The calculated value was 0.34 g too low.