C. Chemistry: Chemical Reactions · Chemical Reactions

The Law of Conservation of Mass

C2.4 C3.2 A1.5 A1.6 A1.8 A1.13About 75 minutes

Learning goals

I can state the law of conservation of mass and explain it using atomic theory.
I can explain why mass seems to change in open systems but not in closed systems.
I can use the law to calculate a missing mass.
I can carry out an inquiry on conservation of mass, compare masses before and after, and account for discrepancies.

Words to know

law of conservation of mass
In a chemical reaction, the total mass of the reactants equals the total mass of the products.

closed system
A system that no matter can enter or leave.

open system
A system that matter can enter or leave, such as an open container.

atomic theory
The theory that matter is made of atoms, which are rearranged but not created or destroyed in chemical reactions.

percentage difference
The difference between two measurements divided by the first, times 100%.

source of error
Something in an experiment that makes measurements differ from their true values.

Where does the mass go?

A big log goes into a campfire, and the next morning only a small pile of ash is left. Did most of the log simply disappear? On the other hand, an iron nail left outside gets heavier as it rusts. Did new matter appear out of nowhere?

Neither. In this lesson you will see why the mass of matter does not change in a chemical reaction, carry out an inquiry to test it (expectation C2.4), and explain why this is the reason we balance chemical equations (C3.2).

Remember from Grade 9

In Grade 9 you met the law of conservation of mass as part of the story of atomic models, and you counted atoms on both sides of equations such as photosynthesis. Now you will measure it yourself, deal with real data that does not come out perfectly, and use it to explain balancing.

The law of conservation of mass

In the late 1700s, the French chemist Antoine Lavoisier carried out reactions in sealed containers and weighed them very carefully before and after. He found that the total mass never changed. This is the law of conservation of mass:

In a chemical reaction, the total mass of the reactants equals the total mass of the products.

mass of reactants = mass of products

Earlier scientists had been fooled because they worked in open containers, where gases could escape into the air or be taken in from it.

Why it is true: atoms

Atomic theory explains the law. In a chemical reaction:

Atoms are not created and not destroyed.
Atoms are rearranged: bonds break and new bonds form.
Every atom of an element has (on average) the same mass before and after.

So the same atoms, with the same masses, are present before and after. The total mass must be the same.

This is exactly why chemical equations must be balanced. A balanced equation has the same number of each kind of atom on both sides, so it automatically shows that mass is conserved. An unbalanced equation would mean atoms appeared or vanished, which never happens.

Atoms have mass (here in atomic mass units, u, rounded). Two magnesium atoms and two oxygen atoms have a total of 80 u before the reaction and after it. A balanced equation is a mass-conservation statement.

Open and closed systems

A closed system is one in which no matter can get in or out, like a sealed bottle. An open system lets matter in or out, like an open cup or a campfire.

In an open system, if a gas is produced, it escapes, so the measured mass goes down. (The log loses carbon dioxide and water vapour to the air.)
In an open system, if a gas from the air is used up, the measured mass goes up. (Rusting iron takes in oxygen from the air.)
In a closed system, nothing escapes or enters, so the measured mass stays the same.

Mass is conserved in every reaction. Open systems just make it look as if it is not, because we are not weighing everything.

Mass is always conserved, but in an open system you only weigh part of it. Gases leaving make the mass seem to drop; gases joining make it seem to rise.

Baking soda and vinegar react in an open cup and in a sealed bottle. The open cup loses mass because carbon dioxide escapes; the sealed bottle's mass does not change. (Sample readings.)

Worked example

Example 1: Find a missing mass

When 10.0 g of calcium carbonate (limestone) is heated strongly, it decomposes into 5.6 g of calcium oxide (lime) and some carbon dioxide gas. What mass of carbon dioxide is produced?

Write the law: mass of reactants = mass of products.
10.0 g = 5.6 g + mass of CO₂
mass of CO₂ = 10.0 g − 5.6 g = 4.4 g

4.4 g of carbon dioxide. (If you heated the limestone in an open dish, the dish would lose 4.4 g as the gas escaped.)

Worked example

Example 2: Mass that comes from the air

A strip of magnesium with a mass of 2.4 g burns in air. The white magnesium oxide powder collected has a mass of 4.0 g. Explain the increase and find the mass of oxygen that reacted.

Reaction: 2Mg + O₂ → 2MgO. Oxygen from the air is a reactant, but it was not on the balance at the start.
Mass of reactants = mass of products: 2.4 g + mass of O₂ = 4.0 g.
mass of O₂ = 4.0 g − 2.4 g = 1.6 g.

The mass increased because 1.6 g of oxygen from the air combined with the magnesium. Mass was conserved; we just did not weigh the oxygen at the start.

Worked example

Example 3: Analyse lab data and account for a discrepancy

In a sealed flask, a student measures 152.46 g before a reaction and 152.31 g after. Calculate the difference and the percentage difference, and suggest reasons.

Difference: 152.46 g − 152.31 g = 0.15 g.
Percentage difference = (difference ÷ starting mass) × 100% = (0.15 ÷ 152.46) × 100% ≈ 0.098%, about 0.1%.
This is very small, so the results support the law of conservation of mass.
Possible sources of error: a little gas leaked past the stopper; liquid splashed or was spilled when the flask was sealed or moved; the balance has limited precision or was not zeroed the same way both times; moisture on the outside of the flask was wiped off between readings.

The mass changed by only 0.15 g (about 0.1%), which is within experimental error. A good conclusion says the data supports the law, and names specific sources of error and how to reduce them (tighter seal, same balance, dry the flask, repeat trials).

Reporting measurements (precision)

Write measurements with the precision your instrument gives you. A kitchen scale that reads to the nearest gram gives "310 g", not "310.0 g". A school electronic balance might read "152.46 g". When you subtract, your answer can't be more precise than your least precise measurement: 312 g − 310 g = 2 g, not 2.00 g.

Hands-on activity

Inquiry: is mass really conserved?

Question: Does the total mass change when baking soda reacts with vinegar in an open container compared with a closed container?

You need: a grown-up, eye protection, a digital kitchen scale, white vinegar, baking soda, a measuring cup and spoons, a drinking glass or jar, a small piece of paper, and a clean, empty plastic pop bottle (1 L or 2 L) with its cap.

Safety: wear eye protection. Use only the small amounts listed; too much gas could make the bottle pop its cap. Point the cap away from people when you open it, and open it slowly. Never do this in a glass bottle.

Part A: open system

Pour 100 mL of vinegar into the glass. Put 1 teaspoon of baking soda on the piece of paper.
Put the glass and the paper with baking soda on the scale together. Record the total mass.
Tip the baking soda into the vinegar and put the empty paper back on the scale. Wait until the fizzing stops, swirling gently.
Record the total mass again.

Part B: closed system

Pour 100 mL of vinegar into the bottle. Make a small "boat" by folding the paper, and put 1/2 teaspoon of baking soda in it. Carefully slide the boat into the bottle so it floats or rests without spilling (or use a funnel made from paper to drop the baking soda in quickly in step 3).
Cap the bottle tightly and record the mass.
Tip the bottle so the baking soda reaches the vinegar. Swirl until the fizzing stops.
Record the mass again with the cap still on. Then open the cap slowly (listen to the hiss) and weigh again.

Analyse: calculate the change in mass for each part. Did the data support your prediction? List at least two sources of error.

What to look for: Part A loses about 2 g (1 teaspoon of baking soda can make at most about 2.5 g of carbon dioxide, and a little stays dissolved) because carbon dioxide escapes. Part B shows no change within the scale's precision (±1 g) while the cap is on, and then loses about a gram after you open it, because the gas escapes. That last step is strong evidence that the "missing" mass in Part A was the gas. A kitchen scale reads only to the nearest gram, so small changes may not show at all; that is a limit of the instrument, not of the law.

Just for fun

"Nothing is lost, nothing is created, everything is transformed." A version of this saying is often credited to Lavoisier. It also makes a great excuse when you can't find your homework: it has not disappeared, it has simply been transformed.

Your turn

State the law of conservation of mass.

Use atomic theory to explain why mass is conserved.

What is the difference between an open and a closed system?

12.0 g of carbon burns completely in 32.0 g of oxygen. What mass of carbon dioxide forms?

Hydrogen peroxide decomposes in an open beaker. Will the beaker's mass go up, go down or stay the same? Why?

How does a balanced equation show the law of conservation of mass?

A student's closed-system data: 85.3 g before, 85.3 g after. What conclusion should she write?

More practice: warm-up

Which scientist is known for showing that mass is conserved?

Are atoms destroyed when wood burns?

Give an example of a closed system.

If 5 g of reactants react completely, what mass of products forms?

Why does a rusting nail gain mass?

More practice: on your own

When 20.0 g of mercury(II) oxide is heated, it decomposes into mercury and 1.5 g of oxygen. What mass of mercury forms?

A burning candle on a balance gets lighter. Explain why this does not break the law.

Iron (11.2 g) reacts completely with sulfur to form 17.6 g of iron(II) sulfide. What mass of sulfur reacted?

A student's open-cup data shows a loss of 2 g. Another student says the experiment "proves the law is wrong". Respond.

Calculate the percentage difference: 250.0 g before, 249.6 g after.

Challenge

A student does the closed-system inquiry with a balloon stretched over the bottle instead of a cap. The balloon inflates, and the scale reading drops by about 1 g, even though no gas escaped. Suggest an explanation.

8.0 g of methane burns completely in oxygen to produce 22.0 g of carbon dioxide and 18.0 g of water. What mass of oxygen was used? Show your reasoning.

In a closed-system lab, three trials gave mass changes of −0.02 g, −0.05 g and −0.31 g. Which trial is an outlier, what might explain it, and what should the student do?

Check your understanding

Quiz

The law of conservation of mass says that in a chemical reaction...

5.0 g of hydrogen reacts with 40.0 g of oxygen to form water. What mass of water forms (assuming everything reacts)?

Why does burning steel wool in air gain mass?

Which statement best explains why chemical equations must be balanced?

Baking soda and vinegar react in an open cup. The mass decreases by 2 g. The best explanation is...

A balance reads to 0.01 g. Which is the correct way to record a mass on it?

For parents and teachers

Big idea: C2.4 asks students to use an inquiry process to investigate the law of conservation of mass, "compare the values before and after the reaction, and account for any discrepancies". C3.2 asks them to explain, using atomic theory, why we balance equations. This lesson also practises precise measurement and error analysis (A1.5, A1.6, A1.8, A1.13).

Common difficulties:

Thinking mass is "lost" when gases form. The gas still has mass; it just left the container.
Thinking conservation only applies in closed containers. It always applies; closed containers just let us measure it.
Over-precise answers. Results should match the precision of the instrument.
Treating any discrepancy as failure. Real data has error; good scientists estimate it and explain it.

Safety at home: please supervise the bottle part of the inquiry. Use only the small amounts listed, a plastic pop bottle (never glass), eye protection, and open the cap slowly pointed away from faces. A kitchen scale that reads to 1 g is fine.