D. Quantities in Chemical Reactions · Quantities in Chemical Reactions

Mass, Moles and Particles: Using the Mole Map

D2.3 D3.2 D2.1 A1.13About 70 minutes

Learning goals

I can use a mole map to plan multi-step conversions.
I can convert between mass and number of particles through moles.
I can find the number of atoms or ions of one element in a given mass of a compound.
I can find the mass of a single atom or molecule.
I can show my work with units and round to the correct significant figures.

Words to know

mole map
A diagram showing how mass, amount (mol) and number of particles are connected, with molar mass and Avogadro's constant as the conversion factors.

conversion factor
A ratio equal to 1 in meaning (such as 18.02 g = 1 mol H₂O) used to change units.

dimensional analysis
Setting up a calculation so units cancel, leaving the unit you want.

density
Mass per unit volume (g/mL); it lets you change a liquid volume into a mass.

One map, every route

You now have two conversion factors: molar mass, which links grams and moles, and Avogadro's constant, which links moles and particles. Put them together and you can answer questions like "How many molecules are in this glass of water?" or "How much does one atom of gold weigh?"

The secret is to always travel through moles. Mass and particles are never connected directly.

The mole map. Mass and particles are both connected to amount in moles, never directly to each other. To count atoms of one element in a compound, multiply by its subscript.

A three-step plan

Write what you know and what you want, with units. Sketch the route on the mole map.
Convert to moles first (n = m ÷ M, or n = N ÷ N_A).
Convert from moles to what you want (N = n × N_A, or m = n × M). If the question asks about atoms of one element, multiply the moles of compound by that element's subscript.

Keep the unrounded value in your calculator between steps. Round only the final answer, usually to three significant figures.

Worked example

Example 1: Mass to molecules

How many molecules are in 10.0 g of carbon dioxide, CO₂?

Route: mass → moles → molecules.
M(CO₂) = 44.01 g/mol, so n = 10.0 g ÷ 44.01 g/mol = 0.22722 mol.
N = 0.22722 mol × 6.02 × 10²³ mol⁻¹ = 1.3679 × 10²³ molecules.
Round to 3 significant figures.

10.0 g of CO₂ contains 1.37 × 10²³ molecules.

Worked example

Example 2: Molecules to mass

An aspirin tablet is mostly acetylsalicylic acid, C₉H₈O₄ (M = 180.17 g/mol). What is the mass of 5.00 × 10²¹ molecules of it?

Route: molecules → moles → mass.
n = 5.00 × 10²¹ ÷ 6.02 × 10²³ = 8.3056 × 10⁻³ mol.
m = 8.3056 × 10⁻³ mol × 180.17 g/mol = 1.4964 g.

The molecules have a mass of 1.50 g.

Example 3 as a strip: grams of glucose to moles of glucose, then moles of H atoms (12 per molecule), then the number of H atoms.

Worked example

Example 3: Atoms of one element in a compound

How many hydrogen atoms are in 5.00 g of glucose, C₆H₁₂O₆?

M(C₆H₁₂O₆) = 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol.
n(glucose) = 5.00 ÷ 180.18 = 0.027750 mol.
Each molecule has 12 H atoms, so n(H) = 12 × 0.027750 = 0.33300 mol.
N(H) = 0.33300 × 6.02 × 10²³ = 2.0047 × 10²³.

There are 2.00 × 10²³ H atoms.

Worked example

Example 4: The mass of one molecule

What is the mass of one water molecule?

One mole of water (6.02 × 10²³ molecules) has a mass of 18.02 g.
Mass of one molecule = 18.02 g ÷ 6.02 × 10²³ = 2.9934 × 10⁻²³ g.

One water molecule has a mass of about 2.99 × 10⁻²³ g, far too small for any balance.

Liquids: start with density

For liquids you often know a volume, not a mass. Density changes volume into mass: m = density × V. Water has a density of about 1.00 g/mL, so 250 mL of water has a mass of about 250 g. Then follow the mole map as usual.

How many molecules are in a 250 mL glass of water? Volume → mass (density) → moles (molar mass) → molecules (Avogadro's constant).

Is my answer sensible?

A number of particles should be huge (usually 10¹⁸ or more for any sample you can see).
The mass of one atom or molecule should be tiny (around 10⁻²³ to 10⁻²¹ g).
If you get 10⁴⁶ or 10⁻⁴⁶, you probably multiplied by N_A when you should have divided, or the reverse.
If units do not cancel to the unit you want, the setup is wrong.

Just for fun

A 250 mL glass of water holds about 8 × 10²⁴ molecules. If every molecule were a grain of sand, you would have roughly a million times more sand than scientists estimate lies on all the world's beaches (on the order of 10¹⁹ grains).

Hands-on activity

How many molecules did you just drink?

You need: a drinking glass, a measuring cup (mL), water, a kitchen scale and a calculator.

Pour a full glass of water, then pour it into the measuring cup to find its volume in mL.
Weigh the glass empty and full to find the mass of the water in grams. Compare it to the volume: is the density close to 1.00 g/mL?
Use the mole map to find the number of water molecules in your glass.
Now drink it. Then find how many hydrogen atoms you drank.
Repeat for one teaspoon of sugar (a level teaspoon of white sugar is about 4 g; weigh it if your scale can read small masses) and find the number of sucrose molecules (M = 342.34 g/mol).

What to look for: a 300 mL glass of water is about 300 g, 16.6 mol and about 1.0 × 10²⁵ molecules (2.0 × 10²⁵ H atoms). Four grams of sugar is about 0.0117 mol, or 7.0 × 10²¹ molecules. Even though the sugar molecules are much bigger, there are far fewer of them in a spoonful.

Your turn

How many formula units are in 50.0 g of sodium chloride?

What is the mass of 2.00 × 10²⁴ molecules of ammonia, NH₃?

How many atoms are in 1.00 g of aluminium foil?

How many oxygen atoms are in 20.0 g of calcium carbonate, CaCO₃?

What is the mass of one gold atom (M = 196.97 g/mol)?

How many sucrose molecules are in a 1.00 kg bag of sugar (M = 342.34 g/mol)?

More practice: warm-up

On the mole map, which quantity is always in the middle?

Which conversion factor links mass and moles?

Which conversion factor links moles and particles?

A sample has 1.204 × 10²⁴ helium atoms. What amount is it?

What is the mass of 2.00 mol of helium (M = 4.00 g/mol)?

More practice: on your own

Which contains more molecules: 10.0 g of hydrogen gas, H₂, or 10.0 g of oxygen gas, O₂? By about how many times?

How many chloride ions are in 25.0 g of calcium chloride, CaCl₂ (M = 110.98 g/mol)?

A sample of carbon dioxide contains 3.01 × 10²³ oxygen atoms. What is the mass of the sample?

Rubbing alcohol for a lab is ethanol, C₂H₅OH (M = 46.08 g/mol), with a density of 0.789 g/mL. How many ethanol molecules are in 15.0 mL?

Lee's answer for the number of atoms in 4.00 g of carbon is 2.89 × 10²⁵. Without recalculating fully, explain how you know it is wrong and find the correct answer.

Challenge

A tiny ice crystal has a mass of 1.0 mg. How many water molecules does it contain?

One molecule of an unknown gas has a mass of 7.31 × 10⁻²³ g. Find its molar mass and suggest a formula from this unit.

What mass of sulfur contains the same number of atoms as 10.0 g of iron?

Check your understanding

Quiz

On the mole map, what must you do to change a mass in grams into a number of molecules?

How many molecules are in 9.01 g of water (M = 18.02 g/mol)?

How many hydrogen atoms are in 1.00 mol of methane, CH₄?

What is the mass of one molecule of oxygen gas, O₂?

A student calculates that 2.0 g of salt contains 7.0 × 10²⁵ formula units. What is the most likely error?

Which sample contains the most atoms?

For parents and teachers

Big idea: All conversions go through moles. Mass ↔ moles uses molar mass; moles ↔ particles uses Avogadro's constant. This lesson is the core of expectation D2.3 (calculations with moles, number of particles and mass) and reinforces D3.2.

How to help: Ask your teen to draw the mole map from memory, then to talk you through one problem: "What do I know? What do I want? Which arrows do I follow?" The glass-of-water activity is a good dinner-table conversation.

Common difficulties:

Trying to go straight from grams to particles. There is no single arrow; go through moles.
Forgetting to multiply by the subscript when the question asks for atoms of one element.
Rounding after each step, which causes last-digit errors. Keep the full number in the calculator.
Mixing up "mass of one molecule" (tiny) with "molar mass" (mass of a mole).
Not checking whether the answer is sensible: particle counts are huge, single-particle masses are tiny.