HS-PS1-7: Using Math to Show Atoms and Mass Are Conserved in Reactions
In plain English: HS-PS1-7 is the NGSS high school performance expectation that asks students to use mathematical representations, such as atom counts, balanced equations, molar masses and mass data, to support the claim that atoms, and therefore mass, are conserved in a chemical reaction. The mole links atom-scale masses to grams. It is usually taught in Chemistry or Physical Science.
Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction.
Clarification Statement: Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students' use of mathematical thinking and not on memorization and rote application of problem-solving techniques.
Assessment Boundary: Assessment does not include complex chemical reactions.
Next Generation Science Standards · Disciplinary Core Idea: Matter and Its Interactions · Official standard
Students use numbers to back up a claim they may already have heard: in a chemical reaction atoms are rearranged, not created or destroyed, so the total mass stays the same. They count atoms on both sides of balanced equations, add molar masses to show that one mole of reaction has the same mass before and after, and test the claim with mass data from open and closed systems. The mole is the bridge: a water molecule has a mass of 18.016 u, and 6.022 × 1023 of them have a mass of 18.016 g, so the same proportions hold at the atomic scale and in grams.
The NGSS Clarification Statement says: "Emphasis is on using mathematical ideas to communicate the proportional relationships between masses of atoms in the reactants and the products, and the translation of these relationships to the macroscopic scale using the mole as the conversion from the atomic to the macroscopic scale. Emphasis is on assessing students' use of mathematical thinking and not on memorization and rote application of problem-solving techniques." The Assessment Boundary says: "Assessment does not include complex chemical reactions." Every reaction on this page is a simple synthesis, decomposition, combustion, single replacement or precipitation reaction, and every data set is invented for teaching. Atomic masses used throughout: H = 1.008, C = 12.01, N = 14.01, O = 16.00, Na = 22.99, Mg = 24.31, Al = 26.98, S = 32.07, Cl = 35.45, K = 39.10, Ca = 40.08, Fe = 55.85, Cu = 63.55 and Zn = 65.38 g/mol. Students do the practice of using mathematical thinking: they build atom tallies, compute and compare masses, graph proportional mass data and critique claims with calculations.
Learning Objectives
By the end of this lesson, students will be able to:
Count the atoms of each element on both sides of a balanced equation, using coefficients and subscripts correctly
Use molar masses to show that the total mass of one mole of reaction is the same for reactants and products
Use the mole to translate a mass relationship between particles (in atomic mass units) into a relationship between measurable masses (in grams)
Analyze mass data from open and closed systems and explain any apparent gain or loss of mass by atoms entering or leaving the system
Use proportional mass relationships to predict the mass of a product and compare the prediction with data
Prior Knowledge Required
Students should already be comfortable with:
Modeling that atoms are rearranged, not created or destroyed, in a chemical reaction MS-PS1-5
Reading chemical formulas and recognizing reactants and products in an equation
Scientific notation for very large and very small numbers 8.EE.A.4
Using units to guide multi-step calculations and ratios HSN.Q.A.1
Show a photo of a campfire at night and the small pile of ash left the next morning. Ask students to respond in writing before any discussion:
Warm-Up Prompt
"A pile of logs has a mass of 20 kg. The next morning only about 0.5 kg of ash is left. Where did the rest of the mass go? What would you need to weigh to find out whether any matter was really destroyed?"
Collect answers. Many students say the wood "burned away" or "turned into energy". Record the ideas about what to weigh (the smoke, the gases, the air that was used) and return to them in the closure.
Direct Instruction15-20 minutes
Three mathematical representations of one claim. (1) An atom tally: multiply each coefficient by each subscript and add, element by element. (2) A mass balance: add the molar masses of everything on each side, using the coefficients as the number of moles. (3) Mass data: weigh everything that takes part, in a container that nothing can enter or leave. The three agree only if atoms are conserved. Diagram 1 shows the atom tally and the mass balance for burning methane. Stress that a coefficient changes the number of particles while a subscript changes the substance, so equations are balanced only with coefficients.
Atom tally and mass balance (synthesis)
Hydrogen burns in oxygen to form water: 2H2 + O2 → 2H2O.
Result: Atoms: H 2 × 2 = 4 on the left, 2 × 2 = 4 on the right; O 2 on each side. Mass of 1 mol of reaction: 2(2.016) + 32.00 = 36.032 g on the left and 2(18.016) = 36.032 g on the right.
Combustion of methane
Natural gas burns in a stove burner: CH4 + 2O2 → CO2 + 2H2O.
Result: Atoms: C 1 and 1, H 4 and 4, O 4 and 4. Mass: 16.042 + 2(32.00) = 80.042 g and 44.01 + 2(18.016) = 80.042 g. Three molecules become three molecules, but that is a coincidence: the atoms are what must match.
The mole as a bridge
Ammonia is made from nitrogen and hydrogen: N2 + 3H2 → 2NH3. One N2 molecule has a mass of 28.02 u, one H2 molecule 2.016 u and one NH3 molecule 17.034 u.
Result: Particle scale: 28.02 + 3(2.016) = 34.068 u and 2(17.034) = 34.068 u. Multiply every particle count by 6.022 × 1023: 28.02 g of N2 and 6.048 g of H2 make 34.068 g of NH3. The ratio is the same at both scales.
Decomposition with a gas product
A student heats 8.40 g of baking soda in a test tube (invented data): 2NaHCO3 → Na2CO3 + H2O + CO2. The solid left behind has a mass of 5.30 g.
Result: 8.40 g ÷ 84.008 g/mol = 0.100 mol NaHCO3, which gives 0.0500 mol Na2CO3 = 5.30 g. The missing 3.10 g matches 0.0500 mol of water vapor plus 0.0500 mol of CO2: 0.0500(18.016 + 44.01) = 3.10 g, which left the open tube.
An apparent gain of mass
0.243 g of magnesium ribbon burns in an open crucible (invented data from a teacher reference, not done by students): 2Mg + O2 → 2MgO. The white product has a mass of 0.403 g.
Result: 0.243 ÷ 24.31 = 0.0100 mol Mg, which forms 0.0100 mol MgO = 0.403 g. The extra 0.160 g is 0.00500 mol of O2 (0.00500 × 32.00 = 0.160 g) taken from the air, so no mass was created.
After each example ask: "Which representation is the evidence here, and what would it look like if atoms were not conserved?" Point out that in Examples 4 and 5 the mass of the solid changes because a gas leaves or joins the system, not because matter is created or destroyed.
Guided Practice15 minutes
Pairs build an atom tally and a mass balance for the reaction in a blast furnace that turns iron ore into iron: Fe2O3 + 3CO → 2Fe + 3CO2. They fill in the table, then build the reaction with model kits or paper cutouts to check their counts.
Guided practice: atom tally and mass of 1 mol of reaction
Quantity
Reactants
Products
Fe atoms
2
2
O atoms
3 + 3 × 1 = 6
3 × 2 = 6
C atoms
3
3
Mass (g)
159.70 + 3(28.01) = 243.73
2(55.85) + 3(44.01) = 243.73
Fill in each row, showing the coefficient times the subscript for every term.
Compute each molar mass from the atomic masses before you add the totals.
Explain why the number of particles changes (4 before, 5 after) while the number of atoms and the mass do not.
Write one sentence that states the claim and names the two representations that support it.
Independent Practice10-15 minutes
Each student analyzes the invented class data in Diagram 2, where five groups burned different masses of magnesium and weighed the magnesium oxide that formed.
Independent practice data (invented): magnesium burned in air
Trial
1
2
3
4
5
Mg (g)
0.10
0.20
0.30
0.40
0.50
MgO (g)
0.17
0.33
0.49
0.67
0.83
Students (1) compute the ratio of oxide mass to magnesium mass for each trial, (2) find the mass of oxygen that joined the magnesium in each trial, (3) compare the ratios with the prediction from atomic masses, 40.31 ÷ 24.31 ≈ 1.66, and (4) write a claim, evidence and reasoning paragraph about whether the data support conservation of atoms. The ratios range from about 1.63 to 1.70, and their mean is about 1.66.
Closure5 minutes
Exit ticket: "Calcium metal reacts with oxygen: 2Ca + O2 → 2CaO. Show with an atom tally and with molar masses that atoms and mass are conserved." (Ca 2 and 2, O 2 and 2; 2(40.08) + 32.00 = 112.16 g and 2(56.08) = 112.16 g.) Then return to the campfire: the missing mass left as carbon dioxide and water vapor, and oxygen from the air joined the reaction.
Differentiation Strategies
For Struggling Students
Provide an atom tally table with one column per term so students multiply coefficient by subscript before adding
Start with model kits or paper cutouts, then move to the tally, then to molar masses, so each representation builds on the last
Give molar masses for the first two reactions and have students compute them only after the tally is secure
For Advanced Students
Ask students to explain why a balloon on a reacting bottle can make the balance read a little less even though no gas escapes (the inflated balloon displaces more air, so buoyancy increases)
Have students decide how precise a balance must be to detect the mass of gas released by 0.10 g of baking soda, and justify the answer with a calculation
Ask students to design a data table and graph that would test the mass ratio in a new reaction, and predict the slope before collecting data
Assessment Guidance
What to Look For
Check that students multiply coefficients by subscripts and never change a subscript to balance an equation. Look for mass balances that use the coefficients as numbers of moles. When data show a change in mass, listen for explanations that name the substance entering or leaving the system instead of saying that mass was created or destroyed. Strong answers use the mole to connect the atom-scale ratio to grams.
02
Classroom Activities
3 Activities
1
Open or Closed? Baking Soda and Vinegar
25 minGroups of 3-4
Groups run the same reaction twice, once in an open cup and once in a capped plastic bottle, and weigh everything before and after. They compare the change in mass with the mass of carbon dioxide predicted from the equation NaHCO3 + HC2H3O2 → NaC2H3O2 + H2O + CO2.
Procedure
Safety: wear goggles for the whole activity. Use only a plastic bottle made for carbonated drinks, never a glass bottle, and never more than 0.50 g of baking soda. Keep the cap pointed away from faces and open it slowly.
Open system: put 50 mL of vinegar in a cup and 0.50 g of baking soda on a folded paper. Weigh the cup and the paper together, tip in the powder, and weigh again (with the paper) after the fizzing stops.
Closed system: pour 50 mL of vinegar into the bottle. Hold 0.50 g of baking soda in a folded paper boat, slide it into the neck without letting it fall, and cap the bottle. Weigh, tip the bottle to mix, wait for the fizzing to stop and weigh again. Then open the cap slowly and weigh a third time.
Vinegar is in excess, so all of the baking soda reacts.
Sample Data (invented)
Open cup: 63.42 g before, 63.18 g after. Capped bottle: 97.86 g before, 97.86 g after mixing, 97.61 g after the cap is opened. Predicted mass of carbon dioxide from 0.50 g of baking soda: 0.50 × 44.01 ÷ 84.008 ≈ 0.26 g.
Discussion Questions
In the open cup the mass fell by 0.24 g, a little less than the 0.26 g predicted. What could explain the small difference?
Why did the capped bottle show no change until the cap was opened? What does the loss of 0.25 g after opening tell you?
Write the claim this activity supports, and cite one number from each system as evidence.
Modification for Distance Learning
Students analyze the sample data above, compute the predicted mass of carbon dioxide themselves, and post a claim, evidence and reasoning paragraph to the class discussion board.
2
Precipitate in a Cup: Nothing Leaves
20 minPairs
Pairs mix two clear solutions that form a white solid, CaCl2 + Na2CO3 → CaCO3 + 2NaCl, and weigh the whole system before and after. No gas forms, so an open cup works as a closed system. They also predict the mass of solid that forms.
Procedure
Safety: wear goggles and gloves. Calcium chloride warms up as it dissolves and both solids irritate the eyes and skin. Do not taste anything, and wash hands at the end. Pour the mixture down the drain with plenty of water, or follow your school’s disposal rules.
Dissolve 1.11 g of calcium chloride in 25 mL of water in cup A and 1.06 g of sodium carbonate in 25 mL of water in cup B.
Weigh both cups together. Pour cup B into cup A, stir, and weigh both cups together again, including the empty cup B.
Build the reaction with paper atom cutouts and check that every atom on the left appears on the right.
Sample Data (invented)
Both cups before mixing: 97.85 g. Both cups after mixing: 97.85 g. Moles: 1.11 ÷ 110.98 ≈ 0.0100 mol of calcium chloride and 1.06 ÷ 105.99 ≈ 0.0100 mol of sodium carbonate.
Discussion Questions
Why must the empty cup B go back on the balance?
Use the equation to predict the mass of calcium carbonate that forms (about 1.00 g) and the mass of sodium chloride left dissolved (about 1.17 g). How do these two masses compare with the 2.17 g of solids you started with?
A new solid appeared, yet the mass did not change. What does that tell you about where the atoms of the solid came from?
Challenge Variation
Pairs filter and dry the white solid overnight, weigh it, and compare the result with the predicted 1.00 g. They explain why a measured value a little lower than predicted does not mean atoms were lost.
3
Critique the Claim: Data Stations
25 minGroups of 3-4
Four stations each show an invented data set and a student claim about it. Groups decide whether the data support or contradict conservation of mass, back their decision with a calculation, and rewrite any claim that is wrong. Groups rotate every 6 minutes. No reactions are run at the stations.
Station Data
Station 1, hydrogen peroxide and yeast in an open cup: 100.0 g of 3% hydrogen peroxide (3.00 g of H2O2) decomposes, 2H2O2 → 2H2O + O2. The cup loses 1.38 g. Claim: "1.38 g of matter was destroyed."
Station 2, chalk heated strongly in a crucible: 5.00 g of calcium carbonate leaves 2.80 g of calcium oxide, CaCO3 → CaO + CO2. Claim: "Heating destroys matter."
Station 3, copper powder heated in air: 2.54 g of copper becomes 3.18 g of black copper(II) oxide, 2Cu + O2 → 2CuO. Claim: "The reaction created 0.64 g of new matter."
Station 4, 10 mL of 3% hydrogen peroxide and yeast in a capped plastic bottle made for carbonated drinks: 38.62 g before and 38.62 g after. Claim: "No reaction happened, because the mass did not change."
Discussion Questions
At Station 1, the predicted mass of oxygen is 3.00 × 32.00 ÷ (2 × 34.016) ≈ 1.41 g. Is a loss of 1.38 g consistent with conservation? Why is it a little smaller?
At Stations 2 and 3, one solid loses mass and the other gains mass. Use the equations to show that both changes match a gas leaving or joining the system.
At Station 4, what evidence other than mass would show that a reaction happened?
Modification for Distance Learning
Post each station as a slide. Groups work in breakout rooms, and each group submits a corrected claim with its calculation for every station on a shared document.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Particle Model and Atom Tally for Burning Methane
A particle model of CH4 + 2O2 → CO2 + 2H2O. The same 1 carbon, 4 hydrogen and 4 oxygen atoms appear on both sides, only bonded differently, so one mole of reaction has a mass of 80.042 g before and after.
Diagram 2: Mass of Magnesium Oxide Against Mass of Magnesium
Invented class data for five trials, drawn to scale. The dashed line is the prediction from atomic masses: every 24.31 g of magnesium combines with 16.00 g of oxygen to make 40.31 g of oxide. The points lie close to this straight line through the origin, which supports the claim that atoms combine in fixed proportions and none are lost.
04
Homework Assignment
~30 min
HS-PS1-7 Homework: Showing That Atoms and Mass Are Conserved
Directions: All data sets are invented for practice. Use these atomic masses: H = 1.008, C = 12.01, N = 14.01, O = 16.00, Na = 22.99, Mg = 24.31, Al = 26.98, S = 32.07, Cl = 35.45, K = 39.10, Ca = 40.08, Fe = 55.85, Cu = 63.55 and Zn = 65.38 g/mol. Show every calculation with units, and end each problem with a one- or two-sentence claim that names your evidence.
Part 1: Atom Tallies and Mass Balances (Problems 1-2)
Propane burns in a gas grill: C3H8 + 5O2 → 3CO2 + 4H2O. (a) Make an atom tally for C, H and O on both sides. (b) Compute the molar mass of each substance. (c) Show that one mole of reaction has the same mass before and after.
A student writes the equation for aluminum reacting with oxygen as Al + O2 → Al2O3. (a) Explain, with an atom tally, why this equation does not show conservation of atoms. (b) Balance it using only coefficients. (c) 2.70 g of aluminum reacts completely. Find the mass of oxygen used and the mass of aluminum oxide formed, and show that the masses add up.
Part 2: Mass Data from Open and Closed Systems (Problems 3-4)
An antacid tablet is dropped into water. In a sealed bottle, the mass is 152.46 g before and 152.45 g after. In an open cup, the mass is 151.88 g before and 151.31 g after. The balance reads to 0.01 g. (a) Find the change in mass for each system. (b) Is the 0.01 g change in the sealed bottle evidence against conservation? Explain. (c) Explain the change in the open cup, and predict what the sealed bottle would read after it is opened.
A small tuft of damp steel wool (iron, 0.279 g) rusts completely inside a sealed 1 L jar of air over two weeks: 4Fe + 3O2 → 2Fe2O3. (a) How many moles of iron react? (b) What mass of oxygen is used, and what mass of iron(III) oxide forms? (c) The jar with its contents had a mass of 486.20 g at the start. Predict its mass at the end, and explain why the steel wool alone gets heavier.
Part 3: Arguing with Mathematical Evidence (Problems 5-6)
A student burns 1.00 g of ethanol in a spirit burner and sees that the fuel is gone. She claims: "Burning destroyed the ethanol, so mass is not conserved." The reaction is C2H5OH + 3O2 → 2CO2 + 3H2O. (a) Find the mass of oxygen used and the masses of carbon dioxide and water formed. (b) Show that the total mass of products equals the total mass of reactants. (c) Write a response to the student that uses your numbers.
Water can be split by electrolysis: 2H2O → 2H2 + O2. (a) Use molar masses to find the mass ratio of oxygen gas to hydrogen gas that forms. (b) Predict the masses of hydrogen and oxygen produced from 45.0 g of water. (c) Explain how the ratio in (a) follows from the atom-scale masses of hydrogen and oxygen atoms.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Atom Tally
Coefficients times subscripts for every element on both sides, and equations balanced only with coefficients
Tally mostly correct, with one counting error
Mass Calculations
Molar masses, moles and masses correct with units, and totals compared
Correct method with one arithmetic or unit error
Open and Closed Systems
Every change in mass is explained by a named substance entering or leaving the system
Change noted but the substance or its direction is not named
Claim, Evidence, Reasoning
Claim cites specific numbers and explains how they show atoms are conserved
Claim stated with general evidence or missing reasoning
05
Quiz: 20 Questions
Interactive, with answers
Instructions
All data sets are invented. Use these atomic masses: H = 1.008, C = 12.01, N = 14.01, O = 16.00, Na = 22.99, Mg = 24.31, Al = 26.98, S = 32.07, Cl = 35.45, K = 39.10, Ca = 40.08, Fe = 55.85, Cu = 63.55 and Zn = 65.38 g/mol. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
How many oxygen atoms are represented by 3Ca(NO3)2?
Answer: C
Inside the parentheses there are 3 oxygen atoms, the subscript 2 doubles them to 6 per formula unit, and the coefficient 3 triples that to 18. Choice B multiplies 3 × 3 and ignores the subscript 2. Choice A forgets the coefficient. Choice D counts every atom in 3Ca(NO3)2 (3 × 9 = 27), not only the oxygen atoms.
Question 2 of 20 · Multiple Choice
Which equation shows that atoms are conserved?
Answer: A
In choice A there are 2 Na and 6 N atoms on each side. Choice B has 2 H and 2 Cl on the left but only 1 of each on the right. Choice C has 1 Fe on the left and 2 on the right. Choice D has 2 O on the left and 4 on the right: the oxygen was never balanced.
Question 3 of 20 · Multiple Choice
Invented data (this reaction is not done in class): a capped 2 L plastic bottle made for carbonated drinks holds excess dilute hydrochloric acid and 1.31 g of zinc: Zn + 2HCl → ZnCl2 + H2. The bottle and contents have a mass of 185.62 g before the zinc reacts. What is the mass after the reaction, with the bottle still capped?
Answer: D
In a capped bottle no atoms can enter or leave, so the mass stays 185.62 g: the hydrogen gas is still inside. Choice A adds the mass of the zinc again, although it was already part of the 185.62 g. Choice B adds the mass of the hydrogen gas, which was already counted as part of the acid and zinc. Choice C subtracts the whole mass of zinc, as if the zinc vanished when it dissolved.
Question 4 of 20 · Multiple Choice
The same reaction as in the previous question is run in an open bottle that starts at 185.62 g. About how much will the bottle read after the reaction?
Answer: B
The zinc is 1.31 ÷ 65.38 ≈ 0.0200 mol, which makes 0.0200 mol of hydrogen gas, or 0.0200 × 2.016 ≈ 0.04 g. That gas escapes, so the bottle reads about 185.58 g. Choice A ignores the escaping gas. Choice C adds the gas instead of subtracting it. Choice D subtracts the whole mass of zinc, but the zinc stays in the bottle as dissolved zinc chloride.
Question 5 of 20 · Multiple Choice
Using H = 1.008, S = 32.07 and O = 16.00 g/mol, what is the molar mass of sulfuric acid, H2SO4?
Answer: C
Two hydrogen, one sulfur and four oxygen atoms: 2(1.008) + 32.07 + 4(16.00) = 98.09 g/mol. Choice A counts only one oxygen atom. Choice B counts only one hydrogen atom. Choice D counts three oxygen atoms instead of four.
Question 6 of 20 · Multiple Choice
Iron reacts with chlorine gas (invented data; this reaction is not done in class): 2Fe + 3Cl2 -> 2FeCl3. If 5.59 g of iron reacts completely with 10.64 g of chlorine, what mass of FeCl3 forms?
Answer: A
Mass is conserved, so the product has the mass of both reactants: 5.59 + 10.64 = 16.23 g. (Check: 5.59 ÷ 55.85 ≈ 0.100 mol of Fe makes 0.100 mol of FeCl3, and 0.100 × 162.20 ≈ 16.2 g.) Choice B subtracts the masses. Choice C is the molar mass of FeCl3, the mass of 1 mol, not of this sample. Choice D doubles the chlorine and ignores the iron.
Question 7 of 20 · Multiple Choice
A student balances H2 + O2 -> H2O by changing the product to H2O2. Why is this not allowed?
Answer: B
A subscript is part of the identity of a substance, so the "balanced" equation would describe a different reaction. The correct fix is 2H2 + O2 -> 2H2O. Choice C is false: the changed equation does balance hydrogen, and that is exactly why it is tempting. Choice D is not a rule: coefficients may be placed on any term.
Question 8 of 20 · Multiple Choice
Why is the mole useful when you use math to show that mass is conserved?
Answer: D
A particle with a mass of x u has a molar mass of x g/mol, so a mass ratio worked out for atoms and molecules is the same ratio for grams of substance in the lab. Choice C is false: the number of molecules can change in a reaction. Choice A confuses a mole with an atomic mass unit.
Question 9 of 20 · Multiple Choice
One molecule of glucose, C6H12O6, has a mass of 180.16 u. What is the mass of one mole of glucose molecules?
Answer: C
By the definition of the mole, the mass in grams of one mole equals the particle mass in atomic mass units: 180.16 g. Choice A is the mass of a single molecule. Choice B confuses the number of particles with their mass. Choice D multiplies the particle mass by Avogadro’s number without converting atomic mass units to grams.
Question 10 of 20 · Multiple Choice
A group runs a reaction in a sealed container four times. The change in mass is 0.00, -0.01, +0.01 and 0.00 g, and the balance reads to 0.01 g. Which conclusion do the data best support?
Answer: A
Changes of 0.01 g are the smallest step the balance can show, so they are measurement uncertainty, not evidence of a change. The mean change is 0.00 g. Choice B treats uncertainty as a real result. Choice C confuses "no change in mass" with "no reaction": in a sealed container the mass stays the same whether or not a reaction occurs.
Question 11 of 20 · Multiple Choice
What mass of carbon is contained in 22.0 g of carbon dioxide?
Answer: B
Carbon makes up 12.01 ÷ 44.01 of the mass of every CO2 molecule, so 22.0 × 12.01 ÷ 44.01 ≈ 6.00 g. Choice A assumes carbon is half the mass. Choice C is the mass of the oxygen. Choice D uses 12.0 g, the mass of 1 mol of carbon, although 22.0 g is only half a mole of CO2.
Question 12 of 20 · Multiple Choice
About how many methane molecules, CH4, are in 32.08 g of methane?
Answer: D
The molar mass of methane is 12.01 + 4(1.008) ≈ 16.04 g/mol, so 32.08 g is 2.000 mol, or 2 × 6.022 × 1023 = 1.204 × 1024 molecules. Choice B multiplies the mass by Avogadro’s number instead of first dividing by the molar mass. Choice C is the number in one mole, but the sample is two moles.
Question 13 of 20 · Multiple Choice
A student draws a particle model of N2 + O2 -> NO. The drawing shows one N2 molecule and one O2 molecule on the left and one NO molecule on the right. What is the best way to fix the model?
Answer: C
The left side has 2 N and 2 O atoms, so the right side needs two NO molecules: N2 + O2 -> 2NO. Choice B changes the substance. Choice A adds oxygen atoms that have nowhere to go. Choice D destroys atoms, which is exactly what the model must not show.
Question 14 of 20 · Multiple Choice
For the reaction 2C2H6 + 7O2 -> 4CO2 + 6H2O, which statement is true?
Answer: A
There are 4 C, 12 H and 14 O atoms on each side (30 atoms), but 9 molecules before and 10 after. Atoms are conserved and molecules are not. Choice D assumes more molecules means more mass, but the mass depends on the atoms, which do not change.
Question 15 of 20 · Short Answer
Show with an atom tally and with molar masses that 2SO2 + O2 -> 2SO3 conserves atoms and mass.
Atoms: S 2 and 2; O 2 × 2 + 2 = 6 on the left and 2 × 3 = 6 on the right. Molar masses: SO2 = 32.07 + 32.00 = 64.07 g/mol and SO3 = 32.07 + 48.00 = 80.07 g/mol. Mass of 1 mol of reaction: 2(64.07) + 32.00 = 160.14 g on the left and 2(80.07) = 160.14 g on the right.
Question 16 of 20 · Short Answer
Zinc and sulfur react to form zinc sulfide, Zn + S -> ZnS (invented data; this reaction is not done in class). 6.54 g of zinc reacts completely, and 9.75 g of zinc sulfide forms. What mass of sulfur reacted, and how do the masses show that the atoms combine one to one?
Mass of sulfur = 9.75 - 6.54 = 3.21 g. Moles: 6.54 ÷ 65.38 ≈ 0.100 mol of Zn and 3.21 ÷ 32.07 ≈ 0.100 mol of S. Equal numbers of moles mean equal numbers of atoms, so the mass ratio 6.54 : 3.21 is the same as the atomic mass ratio 65.38 : 32.07.
Question 17 of 20 · Short Answer
Plan an investigation to test whether mass is conserved when Epsom salt solution (magnesium sulfate) is mixed with washing soda solution (sodium carbonate), which forms a white solid. Name what you measure, how you keep the system closed, and what result would support the claim.
Wear goggles and gloves. Dissolve each solid in water in its own cup, then weigh both cups together. Pour one solution into the other, stir, and weigh both cups together again, including the empty one, so no material is left out. No gas forms, so the open cups act as a closed system. Repeat three times. Mass changes no larger than the balance precision (for example ±0.01 g) support the claim, even though a new solid appears.
Question 18 of 20 · Short Answer
A candle has a mass of 20.0 g. After burning for an hour its mass is 18.2 g. A student claims: "1.8 g of matter was destroyed by the flame." Explain what happened to the mass, and describe data that would test the claim.
The wax reacted with oxygen from the air to make carbon dioxide and water vapor, which escaped into the room. The candle is an open system, so its mass alone cannot test conservation. To test the claim, weigh the candle, the oxygen used and all the products: for example, in a teacher demonstration or a video, compare the mass of a sealed container of air with a candle inside before and after the flame goes out (a flame in a closed container is not a student activity). Chemistry predicts that the total stays the same, and that the products have more mass than the 1.8 g of wax, because oxygen joined the wax.
Question 19 of 20 · Short Answer
Invented data: a teacher reference reports that heating 2.45 g of potassium chlorate, 2KClO3 -> 2KCl + 3O2, leaves 1.49 g of potassium chloride. Use the equation to predict the mass of the residue and the mass of oxygen given off, and decide whether the data support conservation of mass.
2.45 ÷ 122.55 ≈ 0.0200 mol KClO3 gives 0.0200 mol KCl, or 0.0200 × 74.55 ≈ 1.49 g, and 0.0300 mol O2, or 0.0300 × 32.00 = 0.96 g. 1.49 + 0.96 = 2.45 g, the starting mass, and the residue matches the data. The data support conservation.
Question 20 of 20 · Short Answer
A graph of the mass of sodium chloride formed (vertical axis) against the mass of sodium that reacts (horizontal axis) is a straight line through the origin with a slope of about 2.54. Explain the slope using molar masses, explain why the line passes through the origin, and predict the mass of salt formed from 0.690 g of sodium.
Each Na atom ends up in one NaCl unit, so the slope is 58.44 ÷ 22.99 ≈ 2.54: every gram of sodium becomes 2.54 g of salt. With no sodium, no salt can form, so the line passes through the origin. Prediction: 0.690 × 58.44 ÷ 22.99 ≈ 1.75 g. The extra mass comes from the chlorine atoms that combine with the sodium.
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Frequently Asked Questions
10 Questions
What does HS-PS1-7 mean?
HS-PS1-7 asks students to use math, not just words, to support the claim that atoms, and therefore mass, are conserved in a chemical reaction. Students count atoms in balanced equations, add molar masses, use the mole to move from particles to grams, and analyze mass data. The code means High School, Physical Science, core idea 1 (Matter and Its Interactions), performance expectation 7.
Is HS-PS1-7 chemistry or physical science?
It is usually taught in a high school Chemistry course, in the unit on balanced equations and the mole, and it can also sit in Physical Science. The math needed is multiplication, ratios, proportions and scientific notation.
What is the assessment boundary for HS-PS1-7?
The official Assessment Boundary says that assessment does not include complex chemical reactions. Simple synthesis, decomposition, combustion, single replacement and precipitation reactions are in scope. Long multistep reactions, redox equations that need half-reactions, and reactions in which students must predict unfamiliar products are beyond this standard.
Does HS-PS1-7 require stoichiometry?
It requires the mathematical thinking behind stoichiometry: proportional relationships between the masses of atoms and molecules, and the mole as the bridge to grams. The Clarification Statement puts the emphasis on students’ mathematical thinking and not on memorized problem-solving steps, so a student who can explain why a mass ratio holds matters more than one who can follow a template.
Why did our reaction lose mass in the lab?
Usually because a gas escaped. When a reaction makes carbon dioxide, oxygen or hydrogen in an open container, the gas leaves and takes its mass with it. Repeat the reaction in a sealed, sturdy plastic bottle and the mass stays the same until the cap is opened. Small spills, water evaporating and a balance that reads only to 0.1 g can also cause small differences.
Why can a balloon over a reacting bottle make the mass seem lower?
The gas stays inside, but the balloon swells and pushes aside more air, so the air holds it up a little more. Air has a density of about 1.2 g per liter, so a balloon that grows by half a liter can make the balance read about 0.6 g less. A rigid, capped plastic bottle made for carbonated drinks avoids this effect.
How do you show conservation of mass with a balanced equation?
Make an atom tally, element by element, multiplying each coefficient by each subscript. Then find the molar mass of every substance and multiply by its coefficient. If the tally matches, the two mass totals match too, because each atom brings the same mass to both sides.
Is the number of molecules conserved in a chemical reaction?
No. Atoms are conserved, but molecules are not. Two hydrogen molecules and one oxygen molecule (three molecules) become two water molecules. Students who think "the numbers of molecules must match" often try to balance equations incorrectly, so it is worth showing a reaction in which the number of molecules changes.
What safe labs work for HS-PS1-7?
Baking soda and vinegar in an open cup and in a capped plastic bottle made for carbonated drinks, a precipitation reaction such as calcium chloride with sodium carbonate, and hydrogen peroxide (3%) with yeast all work with goggles and gloves. Use small amounts, never seal gas-producing reactions in glass, and leave reactions with burning metals or toxic gases to invented data sets.
What comes after HS-PS1-7?
HS-PS1-4 uses models of bond energy to explain why reactions release or absorb energy, and the life science standard HS-LS1-7 applies conservation of matter to cellular respiration. The mole and mass ratios from HS-PS1-7 are also the base for later stoichiometry, gas and solution calculations in Chemistry.
07
Related Standards
6 standards
These standards connect to HS-PS1-7: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-PS1-5Prerequisite
Model that the number of atoms does not change in a reaction, so mass is conserved
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