Grade by Grade
D. Quantities in Chemical Reactions · Quantities in Chemical Reactions

Chemical Quantities at Home, at Work and in Industry

D1.1 D1.2 D2.5 A2.1About 70 minutes
Learning goals
  • I can describe how chemical quantities and calculations are used at home, in workplaces and in the environmental sector.
  • I can calculate a dose from a label that gives mg per kg of body mass.
  • I can explain why some household chemicals must never be mixed.
  • I can assess why quantitative accuracy matters in industry, and the consequences when it fails.
  • I can name careers that use quantitative chemistry.

Words to know

dosage
The amount of a medicine to take, often calculated from body mass (mg per kg) or body surface area.
dilution ratio
How much of a concentrated product to mix with water, for example 30 mL per 1 L.
parts per million (ppm)
A unit for very small concentrations: 1 ppm is 1 part in 1 000 000 (for water solutions, about 1 mg per litre). You will use it fully in Solutions and Solubility.
pollen count
The number of pollen grains in one cubic metre of air, reported in allergy forecasts.
scrubber
Equipment that removes pollutant gases such as SO₂ from smokestack gases, often with limestone.
air–fuel ratio
The mass of air mixed with each unit mass of fuel in an engine.

Chemistry with a calculator, everywhere

Every day, someone in your community is doing a mole calculation or a ratio calculation that keeps people safe: a pharmacist checking a child's dose, a water-treatment operator adjusting chlorine, a farmer working out fertilizer for a field, an engineer tuning a smokestack scrubber. When those numbers are right, nobody notices. When they are wrong, the consequences can be serious. This lesson looks at quantitative chemistry in the real world (expectations D1.1 and D1.2).

At home: medicines

Many medicine labels give doses by age or by body mass, because the right amount depends on the size of the body. Doctors and pharmacists often calculate doses in mg per kg of body mass, and some medicines have a maximum dose no matter how heavy the person is.

Liquid medicines also need a concentration: for example, a label may say a liquid contains 160 mg in every 5 mL. That is a ratio you can use exactly like a molar mass.

Important: the examples below use an imaginary "Medicine X" for practice only. Real doses must always come from the package, a pharmacist or a doctor, and should be measured with the dosing cup or syringe that comes with the medicine, not a kitchen spoon.

Worked example

Example 1: A dose by body mass

Imaginary Medicine X: dose 10 mg per kg of body mass, maximum 400 mg. The liquid contains 160 mg per 5 mL. What volume should a 32 kg child take?

  1. Dose = 10 mg/kg × 32 kg = 320 mg. This is below the 400 mg maximum, so 320 mg is the dose.
  2. Volume = 320 mg × (5 mL ÷ 160 mg) = 10 mL.
  3. Check: 160 mg is in 5 mL, so 320 mg (twice as much) is in 10 mL. ✔

320 mg, which is 10 mL of the liquid.

01020304050600100200300400500maximum dose 400 mg32 kg → 320 mg10 mg per kgbody mass (kg)dose (mg)
Dose of imaginary Medicine X at 10 mg per kg. The dose rises with body mass until it reaches the 400 mg maximum, then stays there.

At home: cleaning products

Cleaning products are concentrated chemicals. Their labels give dilution ratios (such as "30 mL per litre of water") because the right concentration cleans well without wasting product, damaging surfaces or leaving harmful residues. More is not better.

Some cleaners must never be mixed, because they react to form toxic gases. Bleach (which contains sodium hypochlorite) reacts with ammonia to form chloramine gases, and with acids (such as some toilet-bowl cleaners or vinegar) to release chlorine gas. Both gases damage the lungs. This is why labels say "Do not mix with other chemicals".

bleach+ammonia cleaner!toxic chloramine gasesbleach+acid cleaner or vinegar!toxic chlorine gasNEVER mix cleaning products. Use one product at a time, as the label directs, with fresh air.
Two combinations that produce toxic gases. Never mix cleaning products; read and follow every label.

Pollen counts and the air we breathe

Allergy forecasts report a pollen count: the number of pollen grains in one cubic metre of air, measured by collecting pollen on a sticky surface from a known volume of air and counting it under a microscope. It is a quantity per volume, just like the concentrations you will meet in Solutions and Solubility. People with allergies use the count to plan medicine and outdoor time; tree pollen is often a problem in spring, and ragweed in late summer.

In the environmental sector: scrubbers

Burning coal and refining some metals release sulfur dioxide, SO₂, which forms acid rain. Many plants remove it with a scrubber: the gas passes through a spray of limestone (CaCO₃) mixed with water. Engineers use stoichiometry to decide how much limestone to feed in: too little lets SO₂ escape; too much wastes limestone and money.

furnace orpower plantgas with SO₂scrubberlimestone slurry(CaCO₃ + water)sprayed incleaner gasto the stackcalcium sulfate(gypsum) by-productCaCO₃ + SO₂ → CaSO₃ + CO₂, then 2CaSO₃ + O₂ → 2CaSO₄
A limestone scrubber. The SO₂ ends up in solid calcium sulfate (gypsum), which can be used to make drywall. (Simplified; not to scale.)
Worked example

Example 2: How much limestone?

A scrubber must remove 1.00 t (1.00 × 10⁶ g) of SO₂: CaCO₃(s) + SO₂(g) → CaSO₃(s) + CO₂(g). What mass of CaCO₃ is needed?

  1. n(SO₂) = 1.00 × 10⁶ g ÷ 64.07 g/mol = 1.561 × 10⁴ mol.
  2. Mole ratio 1 : 1, so n(CaCO₃) = 1.561 × 10⁴ mol.
  3. m(CaCO₃) = 1.561 × 10⁴ × 100.09 = 1.562 × 10⁶ g = 1.56 t.

About 1.56 t of limestone per tonne of SO₂ removed.

Worked example

Example 3: Why engines need the right air–fuel ratio

Gasoline engines run best with an air–fuel ratio of about 14.7 : 1 by mass, and their catalytic converters work best near this ratio. Use stoichiometry to show where a number like this comes from. Use octane, 2C₈H₁₈ + 25O₂ → 16CO₂ + 18H₂O, and the fact that air is about 23.1% oxygen by mass.

  1. From lesson 9: 1.00 kg of octane needs 3.50 kg of O₂.
  2. Mass of air = 3.50 kg ÷ 0.231 = 15.2 kg.
  3. So the ratio is about 15.2 : 1. Real gasoline is a mixture of many hydrocarbons, so its ratio (about 14.7 : 1) is a little different, but stoichiometry explains it.

About 15 kg of air per kg of fuel. With less air, oxygen becomes limiting and the engine makes more CO; with much more, the converter cannot clean the exhaust as well.

When accuracy fails: real consequences (D1.2)

  • Agriculture: fertilizer rates are calculated from nitrogen and phosphorus percentages. Over-applying fertilizer wastes money and lets nutrients wash into rivers and lakes, where they feed algal blooms. Lake Erie has had large algal blooms linked largely to phosphorus running off farmland.
  • Industry: a reactor fed the wrong ratio makes less product and leaves unreacted chemicals that must be recovered or treated as waste.
  • Units: in July 1983, Air Canada Flight 143, flying from Montréal to Edmonton with a stop in Ottawa, was loaded with less than half the fuel it needed. The fuel load had been worked out with a conversion factor in pounds per litre (1.77) where kilograms per litre (about 0.80) was needed, during Canada's switch to metric units. Both engines stopped in flight, and the crew glided the plane to a landing at a former air force base in Gimli, Manitoba. Everyone on board survived. The plane became known as the "Gimli Glider".
  • Medicine: a misplaced decimal point (0.5 mg vs 5 mg) is a tenfold error. Hospitals use double-checks, standard units and careful labelling to prevent this.

Common causes of quantitative errors: wrong or mixed units, rounding too early, using the wrong ratio, not checking purity, and not double-checking.

Careers that use these calculations (A2.1)

  • Pharmacist (university degree in pharmacy) and pharmacy technician (college program): check doses and prepare medicines.
  • Chemical engineer (university engineering degree): design reactors, scrubbers and processes, balancing yield, cost and safety.
  • Water and wastewater treatment operator (college program plus provincial certification): measure and adjust chemical doses for safe drinking water.
  • Analytical chemist / laboratory technologist (university or college): measure compositions and purity in labs for food, mining, medicine and the environment.
  • Environmental technologist (college program): monitor air, water and soil quality.

Grade 12 Chemistry (SCH4U) is a common requirement for these programs.

Just for fun

Why did the chemist always double-check her units?

Because a kilogram of prevention is worth about 2.2 pounds of cure.

Hands-on activity

Label detectives

Read labels only. Do not open, pour or mix any cleaning products or medicines.

  1. With a grown-up, find four products at home that give quantities: for example, a medicine (dose by age or mass), a cleaner (dilution ratio), a fertilizer or plant food (N-P-K numbers) and a food (sodium in mg per serving).
  2. For each, record the quantity, its units and what it is per (per kg, per litre, per serving, per 100 g).
  3. Do one calculation for each. Examples: the volume of cleaner for a 5 L bucket; the mass of nitrogen in the whole bag of fertilizer; the sodium in two servings of a snack.
  4. Find each product's safety warnings. Which ones say "Do not mix with other chemicals"? Which give a maximum amount?
  5. Choose one product and write two or three sentences on what could happen if someone measured it wrongly.

What to look for: every label number is a ratio, used just like a molar mass or a mole ratio. Good answers name the units, show the calculation, and connect a measuring error to a specific consequence (an overdose or underdose, wasted product, harm to plants or waterways, toxic gas from mixing).

Your turn

1

Imaginary Medicine Y has a dose of 15 mg/kg. What dose is right for a 48 kg teen? If tablets contain 240 mg, how many tablets is that?

2

Explain why bleach must never be mixed with an ammonia-based cleaner.

3

A floor cleaner label says to use 30 mL per 1.0 L of water. How much cleaner goes in a 5.0 L bucket?

4

A lawn needs 1.0 kg of nitrogen per 100 m². How much 21-0-0 fertilizer (21% N) is needed? What could happen if twice as much is spread?

5

A scrubber removes 500 kg of SO₂: CaCO₃ + SO₂ → CaSO₃ + CO₂. What mass of CaCO₃ is needed?

6

Name two careers that use quantitative chemistry, and give one calculation each might do.

More practice: warm-up

1

What does a pollen count measure?

2

What does "10 mg/kg" mean on a medicine label?

3

What does ppm stand for?

4

Why should medicine be measured with the dosing cup or syringe instead of a kitchen spoon?

5

What gas does a limestone scrubber remove?

More practice: on your own

1

A liquid medicine contains 160 mg per 5 mL. What volume gives a 240 mg dose?

2

Explain why the stoichiometric air–fuel ratio for octane is about 15 : 1 by mass, even though the equation has 25 O₂ for 2 C₈H₁₈.

3

In the Gimli Glider incident, the fuel was calculated with 1.77 (lb/L) instead of about 0.80 (kg/L). By about what factor was the mass of fuel per litre overstated, and what was the result?

4

A pool holds 50 000 L of water. A test shows 2 ppm of free chlorine (about 2 mg per litre). What mass of chlorine is that in the whole pool?

5

Describe one environmental consequence of inaccurate fertilizer calculations, and one way farmers can reduce it.

Challenge

1

An ammonia plant should feed N₂ and H₂ in a 1 : 3 mole ratio (N₂ + 3H₂ → 2NH₃). A faulty meter feeds 100 mol of N₂ with only 270 mol of H₂. Compare the maximum NH₃ with the intended amount, and say what is wasted.

2

A scrubber must remove 90.0% of 1.00 t of SO₂. The limestone used is 95.0% CaCO₃. What mass of limestone is needed?

3

A worker says, "Doubling the cleaner in the bucket makes it clean twice as well." Use chemistry ideas to evaluate this claim.

Check your understanding

Quiz

1.

Imaginary Medicine Z: 5 mg per kg of body mass. What dose is right for a 60 kg adult?

2.

Why must bleach never be mixed with acidic cleaners?

3.

What does a pollen count of 50 mean?

4.

What caused the Gimli Glider to run out of fuel?

5.

Which is an environmental consequence of applying too much fertilizer?

6.

A limestone scrubber is fed too little limestone. What happens?

7.

Which career mainly involves checking and preparing medicine doses?

For parents and teachers

Big idea: Quantitative chemistry is everywhere: medicine doses, cleaner dilutions, fertilizer rates, pollution control and engine tuning (D1.1). Accuracy matters because errors can harm people, waste resources and damage the environment (D1.2). The lesson also introduces related careers (A2.1).

Safety at home: this is a good moment to look at labels together and to agree on household rules: never mix cleaning products, store medicines safely, and always use the dosing device that comes with a medicine. The medicine examples use made-up products for practice; real doses must come from the label, a pharmacist or a doctor.

How to help: do the label activity together, reading only. Ask, "What is this number per?" for every label.

Common difficulties:

  • Forgetting the "per" part of a unit (mg per kg, mL per L).
  • Treating "more" as "better" for cleaners and fertilizers.
  • Mixing up mole ratios and mass ratios (as in the air–fuel ratio).
  • Unit conversions (kg ↔ g, t ↔ g, lb ↔ kg).