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Einstein's Big Idea

Classroom Activities

Learning Objective | Materials | Background | Procedure | Activity Answer | Links & Books | Standards  Print this Teacher's Guide (PDF, 37 pages)

Activity Summary
Students conduct an inquiry into the meaning of m in E = mc² by exploring how objects of mass interact during a chemical reaction in a plastic bag, and by measuring mass before and after chemicals are mixed together.

Learning Objectives
Students will be able to:

• explain what the m in E = mc² represents.

• relate that mass in a chemical reaction is always conserved.

• convey that atoms rearrange themselves in chemical reactions to form different molecules and compounds.

Materials for teacher demonstration

Station1
(electric field)

• 250 ml beaker with 100 g citric acid
• 250 ml beaker with 100 g baking soda

• copy of the "Messing With Mass" student handout (PDF or HTML)
• 1/4 tsp citric acid
• 1/4 tsp baking soda
• quart freezer bag
• plastic bowl (large enough to contain an expanded freezer bag)
• film container, filled with 20 ml water
• lab balance accurate to a tenth of a gram
• goggles

Background
Without the insights of scientists before him, Albert Einstein would not have had the foundation from which to make his brilliant leap of understanding about the equivalence of mass and energy. Two of the people responsible for providing a critical understanding about mass were Antoine-Laurent Lavoisier and his wife, Marie Anne. By day, Lavoisier was a tax collector. But his true passion was chemistry. A meticulous experimenter, Lavoisier was the first to demonstrate that matter is conserved in a chemical reaction. In the late 1700s, Lavoisier showed that when water was turned to steam, nothing was lost—the water was just transformed. His wife provided detailed drawings of his experiments and translations of other scientists' work.

In this activity, students examine the components of a chemical reaction and make measurements to confirm the conservation of mass in a closed system (quart freezer bag). Students will gain an understanding of the meaning of mass in a reaction. They will learn how objects of mass can interact and change and that mass is always conserved in a chemical reaction.

The reaction in this activity is between two fairly harmless chemicals-citric acid (H₃C₆H₅O₇) and baking soda (NaHCO₃), both white powders. The reaction can only occur in the presence of water. The reaction produces a gas (CO₂) and the compound sodium citrate (Na₃C₆H₅O₇). The balanced reaction looks like this:

H₃C₆H₅O₇ + 3NaHCO₃ ⇒ Na₃C₆H₅O₇ + 3H₂O + 3CO₂

The reaction is endothermic so students will feel the plastic bag get colder when the three ingredients are mixed. To further verify for students that a chemical reaction is taking place, you may want to add an acid-base indicator, such as phenol red, to reveal that a change (in pH) has occurred after the reaction has taken place.

Key Terms

chemical reaction: A process in which one or more substances are changed into other substances.

conservation of mass: A law stating that the products of a chemical reaction always have the same total mass as that of the reactants.

endothermic: Chemical reactions that take in heat from their surroundings.

exothermic: Chemical reactions that give off heat to their surroundings.

mass: The amount of matter an object contains.

products: Substances resulting from a chemical reaction.

reactants: Substances that take part in a chemical reaction.

weight: The force of gravity acting on matter.

1. Obtain the necessary chemicals from your chemistry lab, a science supply house, or stores in your area. Baking soda is sold in grocery stores and citric acid, which is used in canning and winemaking, is sold in some drug stores.

2. Begin by pointing out the m in E = mc² and asking what this letter stands for. Students may say, "How much something weighs." Pick up an object such as a stapler and ask how much the stapler would weigh independent of a gravitational field. The answer is "nothing" because weight is just a name for the force of gravitational attraction that exists between two objects, in this case Earth and the stapler. The fact that weight is simply a force of attraction, not a unit of mass, can be a difficult concept for some students. Try to help students understand that mass is the amount of "stuff," or atoms, an object contains. Mass is defined by units like grams and kilograms.

3. To help students start thinking about mass, conduct a demonstration about how mass interacts. Have one 250 milliliter beaker filled with 100 grams of citric acid and another filled with 100 grams of baking soda. Hold the two cups out in front of you and tell students the cups contain two different chemicals of equal mass. Ask students to predict what will happen if the two of them are mixed together. After students answer, mix the substances. (Nothing will happen.) Ask students why nothing occurred. What evidence did they have that led them to their conclusion? (No noise, no smoke, no visual changes seen, etc.)

4. Now that students understand that not all mass reacts, have them conduct their activity in which a chemical reaction does occur. Organize students into teams and give each team a copy of the student handout and other materials.

5. Review safety rules with students:

   • Wear goggles.

   • Do not allow the chemicals to touch bare skin. (If students accidentally touch a substance, tell them to wash their hands immediately. These chemicals are about as dangerous as lemon juice, but precautions should be followed.)

   • When chemicals are mixed in the plastic bag, make sure the opening of the bag is well sealed and pointed away from students.

   • Students may feel the bag while the reaction is proceeding, but they should not squeeze it.

6. Circulate around the room as student teams do the experiment. Help anyone having trouble using the balance.

7. When students are finished making their observations, collect the bags in a bucket or container. Give students time to answer the questions on their student handout. Then have a discussion about the nature of a chemical reaction. Why was there a reaction in the student activity but not one in the teacher demonstration? (The water in the student activity served as a solvent that allowed the two solids to react.) How was mass conserved in this reaction? (Although a chemical change occurred—two dry, white granular solids when mixed with water became a gas and a dissolved solid in a water medium—mass was conserved as evidenced by the almost identical masses before and after the reaction.) Brainstorm with students some possible reasons for any mass differences they saw. (Small weight differences, on order of 0.1 to 0.3 percent, may be seen; see Activity Answer for more information.)

8. As an extension, turn the investigation into a quantitative one and have students measure the temperature of the reaction as the reaction proceeds (a thermometer should be placed on a desk, the bag set down on the bulb end of the thermometer, and the temperature read every minute or so). Then, have students change the quantities of one of the checmicals and take more temperature data. Plot both sets of data on a single set of axes. Ask students interpret their results.

It is important to stress that mass is always conserved in a chemical reaction in a closed system. (An extremely small amount of mass—on order of a few parts per trillion—is lost or gained when light and/or heat is absorbed or released in a reaction. But for all practical purposes this is too small to measure.)

The reaction in a quart bag is a good example of a closed system. However, any measurement contains a degree of uncertainty. There may be a slight difference in mass due to loss of gas or errors in measurement. (Sample test results showed a 0.1 percent to 0.3 percent weight difference.) In an experiment in an open system, such as weighing a piece of wood, burning it, and weighing the ashes afterwards, it would appear that mass is not conserved. But in fact it is. It is just that the escape of invisible gases, both carbon dioxide and water, prevent the measurement of the mass of all of the products.

The word mass is used deliberately in the student activity instead of the more commonly used weight. If necessary, reinforce the difference between the two terms when students use their balances to weigh their bags.

Student Handout Questions

1. When a reaction gives off heat, it is called exothermic. When a reaction absorbs heat, it is called endothermic. Is the reaction you observed endothermic or exothermic? The reaction is endothermic. Students should feel the bag getting colder as the reaction proceeds. Exothermic reactions are much more familiar to students (striking a match, burning a candle) than endothermic ones. Students may need help in understanding that the chemicals in the bag cool because heat is being used in the reaction to turn the reactants into products.

2. How did the mass of the reactants compare to the mass of the products? Use this formula to calculate any percent difference in the mass between the two:

   absolute value of the difference between the two masses divided by mass before reaction x 100 = percent difference

   Students should arrive at the conclusion that the mass of the products is extremely close to the mass of the reactants.

3. What might have caused any difference in mass that you found? There may be a small difference in mass due to loss of gas from the plastic bag or errors in measurement. Accept reasonable answers.

4. What evidence would you give to show that a chemical reaction did indeed occur? There are two signs that a chemical reaction occurred: a change in temperature and the formation of a gas.

Web Sites

NOVA—Einstein's Big Idea
www.pbs.org/nova/einstein
Hear top physicists explain E = mc², discover the legacy of the equation, see how much energy matter contains, learn how today's physicists are working with the equation, read quotes from Einstein, and more on this companion Web site.

Periodic Table of the Elements
periodic.lanl.gov
Provides a periodic table and information about each element.

Welcome to Chembalancer!
www.dun.org/sulan/chembalancer
Includes a game focused on correctly balancing chemical equations.

Books

40 Low-Waste, Low-Risk Chemistry Experiments
by David Dougan. Walch Publishing, 1997.
Includes introductory labs on measurement, density, temperature, relative mass, and more.

Physics: The Human Adventure: From Copernicus to Einstein and Beyond
by Gerald James Holton and Stephen G. Brush. Rutgers University Press, 2001.
Introduces concepts and theories in physical science and features a chapter on the conservation of mass.

The Visual Dictionary of Chemistry
by Jack Challoner. DK Publishing, 1996.
Provides photographs of chemical experiments, illustrations of molecules and chemical reactions, and information about the periodic table of elements.

The "Messing With Mass" activity aligns with the following National Science Education Standards (see books.nap.edu/html/nses).

Grades 5-8
Science Standard
Physical Science

• Properties and changes of properties in matter
• Transfer of energy

Grades 9-12
Science Standard
Physical Science

• Chemical reactions

Classroom Activity Author

Jeff Lockwood taught high school astronomy, physics, and Earth science for 28 years. He has authored numerous curriculum projects and has provided instruction on curriculum development and science teaching methods for more than a decade.