D. Quantities in Chemical Reactions · Quantities in Chemical Reactions

Stoichiometry: Calculating Masses and Particles in Reactions

D2.5 D3.4 D2.3 D1.1About 75 minutes

Learning goals

I can follow the stoichiometry road map: mass → moles → mole ratio → moles → mass.
I can calculate the mass of a product formed or a reactant needed from the mass of another substance.
I can include particle counts in stoichiometry problems.
I can use stoichiometry to answer real questions about fuels, antacids and baking.

Words to know

stoichiometry
Calculating the quantities of reactants and products in a chemical reaction from a balanced equation.

gravimetric stoichiometry
Stoichiometry calculations that use masses (from Latin gravis, heavy).

given substance
The substance whose quantity you know.

required (wanted) substance
The substance whose quantity you need to find.

How much exhaust does a full tank make?

Canadians often talk about how much carbon dioxide a car produces. Here is a surprising fact you will prove in this lesson: burning 1 kg of gasoline produces about 3 kg of carbon dioxide. The exhaust is heavier than the fuel! Where does the extra mass come from? Stoichiometry answers questions like this with nothing more than a balanced equation and a calculator.

The road map

In the lab we measure mass, but equations work in moles. So every stoichiometry problem follows the same road:

Balance the equation.
Given mass → moles: n(A) = m(A) ÷ M(A).
Mole ratio: n(B) = n(A) × (coefficient of B ÷ coefficient of A).
Moles → wanted quantity: m(B) = n(B) × M(B), or N(B) = n(B) × N_A.

You may be given particles instead of mass at the start, or asked for particles at the end; just enter or leave the road at the moles box.

The stoichiometry road map. You can never jump from grams of one substance straight to grams of another; you must cross the mole-ratio bridge.

Worked example

Example 1: Mass of product

Propane burns in a barbecue: C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g). What mass of carbon dioxide is produced when 100. g of propane burns completely?

Equation is balanced. Given: m(C₃H₈) = 100. g; M(C₃H₈) = 44.11 g/mol.
n(C₃H₈) = 100. ÷ 44.11 = 2.2671 mol
n(CO₂) = 2.2671 × (3 ÷ 1) = 6.8012 mol
m(CO₂) = 6.8012 × 44.01 = 299.3 g

About 299 g of CO₂ (three significant figures; the decimal point in "100." shows that all three digits are significant).

Worked example

Example 2: Why is the exhaust heavier than the fuel?

Gasoline is mostly octane: 2C₈H₁₈(l) + 25O₂(g) → 16CO₂(g) + 18H₂O(g). Find the mass of oxygen used and of carbon dioxide produced when 1.00 kg of octane burns.

n(C₈H₁₈) = 1000 g ÷ 114.26 g/mol = 8.7520 mol
n(O₂) = 8.7520 × (25 ÷ 2) = 109.40 mol → m(O₂) = 109.40 × 32.00 = 3500.8 g
n(CO₂) = 8.7520 × (16 ÷ 2) = 70.016 mol → m(CO₂) = 70.016 × 44.01 = 3081.4 g
The carbon in the fuel combines with oxygen from the air. Each CO₂ molecule is mostly oxygen by mass, so the product weighs more than the fuel alone.

3.50 kg of O₂ is used and 3.08 kg of CO₂ is produced for every 1.00 kg of octane.

Burning 1.00 kg of octane, drawn to scale. Mass is conserved overall (4.50 kg on each side), but most of the mass of the exhaust came from oxygen in the air.

Worked example

Example 3: Mass of reactant needed (an antacid)

Milk of magnesia contains magnesium hydroxide, which neutralizes stomach acid: Mg(OH)₂(s) + 2HCl(aq) → MgCl₂(aq) + 2H₂O(l). What mass of HCl can 0.500 g of Mg(OH)₂ neutralize?

M(Mg(OH)₂) = 24.31 + 2(16.00 + 1.01) = 58.33 g/mol
n(Mg(OH)₂) = 0.500 ÷ 58.33 = 0.0085719 mol
n(HCl) = 0.0085719 × (2 ÷ 1) = 0.017144 mol
m(HCl) = 0.017144 × 36.46 = 0.6251 g

0.500 g of Mg(OH)₂ neutralizes 0.625 g of HCl.

Worked example

Example 4: Mass to particles

How many water molecules form when 10.0 g of hydrogen gas burns? 2H₂(g) + O₂(g) → 2H₂O(g)

n(H₂) = 10.0 ÷ 2.02 = 4.9505 mol
n(H₂O) = 4.9505 × (2 ÷ 2) = 4.9505 mol
N(H₂O) = 4.9505 × 6.02 × 10²³ = 2.980 × 10²⁴

2.98 × 10²⁴ water molecules.

A table keeps you organized

Many students like to set up a stoichiometry table under the equation, one column per substance:

row 1: the balanced equation
row 2: m (given or wanted)
row 3: M
row 4: n

Fill in what you know, find n for the given substance, use the mole ratio to get n for the wanted one, then finish its column. It is the road map in table form.

Just for fun

I told my friends a joke about stoichiometry, but nobody reacted.

I think I had the wrong ratio of chemists in the room.

Hands-on activity

How much vinegar does a spoonful of baking soda need?

Baking soda (sodium hydrogen carbonate) reacts with the acetic acid in vinegar:

NaHCO₃(s) + CH₃COOH(aq) → NaCH₃COO(aq) + H₂O(l) + CO₂(g)

You need: a kitchen scale, baking soda, white vinegar labelled 5% acetic acid, a measuring cup (mL), a tall glass, and a spoon. Work in the sink; the mixture foams. Do not drink the result. Vinegar can sting eyes, so keep your face back from the glass.

Predict. For 5.0 g of NaHCO₃, find the mass of acetic acid needed. Then find the mass of vinegar: mass of acetic acid ÷ 0.05. (Vinegar is about 1 g/mL, so grams ≈ millilitres.)
Weigh 5.0 g of baking soda into the tall glass.
Add vinegar 10 mL at a time, stirring and waiting for the fizzing to stop each time. Near your predicted volume, add 2 mL at a time. Stop when a new addition no longer fizzes.
Compare the total volume with your prediction.

What to look for: n(NaHCO₃) = 5.0 ÷ 84.01 = 0.0595 mol, so 0.0595 mol × 60.06 g/mol = 3.57 g of acetic acid, or about 71 g (about 70 mL) of vinegar. Your result should be in that range. Differences come from the exact strength of the vinegar, foam spilling over, and judging when fizzing has really stopped.

Your turn

2H₂(g) + O₂(g) → 2H₂O(l). What mass of water forms from 8.00 g of hydrogen?

2Mg(s) + O₂(g) → 2MgO(s). What mass of magnesium oxide forms from 6.08 g of magnesium?

Limestone is heated to make lime for cement: CaCO₃(s) → CaO(s) + CO₂(g). What mass of CaO forms from 50.0 g of CaCO₃?

N₂(g) + 3H₂(g) → 2NH₃(g). What mass of hydrogen is needed to make 1.00 kg of ammonia?

Zn(s) + 2HCl(aq) → ZnCl₂(aq) + H₂(g). How many hydrogen molecules are produced from 3.27 g of zinc?

When baking soda is heated in an oven, 2NaHCO₃(s) → Na₂CO₃(s) + H₂O(g) + CO₂(g). This gas helps baked goods rise. What mass of CO₂ comes from 8.40 g of baking soda?

More practice: warm-up

List the four steps of a mass-to-mass stoichiometry problem.

What is the mass of 2.00 mol of CO₂?

What amount is 36.04 g of water?

In 2H₂ + O₂ → 2H₂O, what amount of water forms from 2.00 mol of O₂?

Which conversion factor connects two different substances?

More practice: on your own

Fe₂O₃(s) + 3CO(g) → 2Fe(l) + 3CO₂(g). What mass of iron can be made from 1.00 kg of iron(III) oxide?

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. What mass of oxygen does a plant release while making 90.0 g of glucose?

A chalk-based antacid reacts: CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g). What mass of HCl does 1.00 g of CaCO₃ neutralize?

AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq). What mass of silver chloride precipitate forms from 2.00 g of NaCl (with enough AgNO₃)?

Jo says: "In 2H₂ + O₂ → 2H₂O, 2 g of hydrogen reacts with 1 g of oxygen." Explain the mistake and correct it.

Challenge

Octane has a density of 0.703 g/mL. Using 2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O, find the mass of CO₂ produced by burning 1.00 L of octane.

The thermite reaction is used to weld railway tracks: Fe₂O₃(s) + 2Al(s) → Al₂O₃(s) + 2Fe(l). What mass of aluminium is needed to react with 100. g of Fe₂O₃?

Ammonium nitrate fertilizer is made by NH₃(g) + HNO₃(aq) → NH₄NO₃(s). What mass of ammonia is needed to make 1.00 tonne (1.00 × 10⁶ g) of NH₄NO₃?

Check your understanding

Quiz

What is the correct order for a mass-to-mass stoichiometry problem?

2H₂ + O₂ → 2H₂O. What mass of O₂ reacts with 4.04 g of H₂?

CaCO₃ → CaO + CO₂. What mass of CO₂ forms from 100.09 g of CaCO₃?

Why does burning 1 kg of gasoline produce more than 1 kg of CO₂?

N₂ + 3H₂ → 2NH₃. How many NH₃ molecules form from 1.00 mol of N₂?

Which step is the only way to get from one substance to another in stoichiometry?

For parents and teachers

Big idea: Stoichiometry predicts how much product a reaction makes or how much reactant it needs. The route is always mass → moles → mole ratio → moles → mass (or particles). This lesson is the core of D2.5, with D3.4 and real-world links for D1.1 (fuels, antacids, baking).

How to help: The vinegar-and-baking-soda activity is a great way to see a prediction come true. Ask your teen to explain the 1 kg of gasoline → 3 kg of CO₂ result in their own words; if they can, they understand both stoichiometry and conservation of mass.

Common difficulties:

Skipping the mole step and using a "gram ratio".
Using the molar mass of the given substance for the wanted substance.
Flipping the mole ratio.
Forgetting to convert kg to g, or L to g with density.
Rounding between steps; keep all digits and round at the end.