D2.3 Convert among moles, particles, and mass

Ontario Grade 11 Chemistry

Quantities in Chemical Reactions

SCH3U study topic D2.3

A small amount of a substance can contain an enormous number of particles. Those particles are too small to count one by one, but the sample’s mass can be measured. Chemistry uses the mole to connect particle counts to amounts that can be measured or calculated. In this lesson, you will convert among amount in moles, number of particles, and mass.

What you will learn

Explain how moles connect a measurable sample to its particles.
Convert between moles and particles using Avogadro’s constant.
Convert between moles and mass using molar mass.
Choose a suitable conversion path and report answers with units and appropriate significant digits.

1. From familiar counting to the mole

A pair means two items, and a dozen means twelve. A mole is also a counting unit, but it represents a very large number of particles. One mole contains Avogadro’s constant number of particles:

6.02 \times 10^{23}

. The symbol for amount in moles is

n

, and the unit is the mole, written

\mathrm{mol}

.

A particle is one individual unit of a substance. Depending on the substance, the particle may be an atom, molecule, or ion. For example, a sample of helium is counted in helium atoms. A sample of water is counted in water molecules. Name the particle type when it matters, because a particle count without that information can be unclear.

The number of particles is written as

N

. Avogadro’s constant is written as

N_A

. The relationship says how many particles are in a given amount. To find a particle count from moles, multiply by Avogadro’s constant. To find moles from a particle count, divide by it.

N=nN_A

One mole represents $6.02 \times 10^{23}$ particles.
Use the particle type that matches the substance: atoms, molecules, or ions.
Keep units with each value so that the conversion path is clear.

2. Connecting moles and mass

Mass is measured with a balance, often in grams. A mole connects this measurable mass to a fixed number of particles. Different substances have different masses for one mole because their particles have different masses.

Molar mass is the mass of one mole of a substance. Its symbol is

M

, and its common unit is

\mathrm{g/mol}

. Find a substance’s molar mass using its chemical formula and the periodic table. For a formula with more than one atom, include the mass contribution of every atom shown in the formula. The formula’s subscripts tell you how many of each atom to include.

Once you know the molar mass, multiply the amount in moles by molar mass to find mass in grams. To find moles from a mass, divide the mass by molar mass. Check the units: multiplying

\mathrm{mol}

by

\mathrm{g/mol}

leaves

\mathrm{g}

.

m=nM

Molar mass tells you the mass of one mole of a substance.
Use $m=nM$ to find mass and $n=m/M$ to find amount.
Calculate molar mass from the substance’s formula and periodic-table values.

3. Choosing a conversion path

A conversion path is the sequence of relationships used to move from a known quantity to the quantity requested. Moles are the link between mass and particles. If you start with mass and need particles, first convert mass to moles, then convert moles to particles. If you start with particles and need mass, first convert particles to moles, then convert moles to mass.

Write down what is given and what is requested before calculating. Include units beside the values. Choose each relationship so that the unit you do not need cancels. This unit check helps catch a reversed operation: multiplying by molar mass gives mass, while dividing by molar mass gives moles.

For a final answer, use the number of significant figures supported by the given measured value. Significant figures are the digits that show a measurement’s reported precision. Exact counting relationships, such as the stated value of Avogadro’s constant in a course calculation, do not usually limit the significant figures. Keep extra digits during intermediate steps and round the final answer.

\text{mass} \leftrightarrow \text{moles} \leftrightarrow \text{particles}

Use moles as the middle step when converting directly between mass and particles.
Units should cancel in a way that leaves the requested unit.
Round the final result to match the precision of the measured data.

4. Units and reasonableness

A conversion is not complete until the unit and particle type are stated. For example, a result may be a number of water molecules, not merely a number of particles. A mass answer should include its mass unit, usually grams in these conversions.

Use a brief reasonableness check. A sample with a larger mass of the same substance contains more moles and therefore more particles. A mass smaller than the molar mass corresponds to less than one mole. A particle count smaller than Avogadro’s constant corresponds to less than one mole.

Calculator displays may show many digits. Those digits are not automatically justified. Keep guard digits in the calculation, then round once at the end. If a problem provides a mass to three significant figures, the final calculated mass or amount should generally reflect that precision.

State the unit and the kind of particle in the final answer.
Check whether the size of the answer makes sense compared with one mole.
Do not round each intermediate value.

Worked example

From mass to molecules

A sample contains

18.0\,\mathrm{g}

of water,

\mathrm{H_2O}

. Find the amount of water in moles and the number of water molecules. Use

M(\mathrm{H_2O})=18.02\,\mathrm{g/mol}

and

N_A=6.02\times10^{23}\,\mathrm{particles/mol}

.

Find the molar mass
Water’s formula has two hydrogen atoms and one oxygen atom. Adding the periodic-table masses for those atoms gives the supplied molar mass, $18.02\,\mathrm{g/mol}$ . This is the mass of one mole of water.
$M(\mathrm{H_2O})=18.02\,\mathrm{g/mol}$
Convert mass to moles
Divide the measured mass by the molar mass. The gram units cancel, leaving moles. The given mass has three significant figures, so report the amount to three significant figures.
$n=\frac{18.0\,\mathrm{g}}{18.02\,\mathrm{g/mol}}=0.999\,\mathrm{mol}$
Convert moles to molecules
Multiply the amount in moles by Avogadro’s constant. The mole units cancel, leaving a count of water molecules. Report the particle count to three significant figures.
$N=(0.999\,\mathrm{mol})(6.02\times10^{23}\,\mathrm{molecules/mol})=6.01\times10^{23}\,\mathrm{molecules}$

Answer: The sample contains

0.999\,\mathrm{mol}

of water, or

6.01\times10^{23}

water molecules.

Check: The mass is nearly equal to the mass of one mole of water, so an amount close to

1\,\mathrm{mol}

is reasonable. A mole contains about

6.02\times10^{23}

particles, matching the calculated molecule count.

Common mistakes and how to avoid them

Multiplying mass by molar mass when converting grams to moles.

Correction: Divide mass by molar mass. The gram units then cancel and leave moles.

Using Avogadro’s constant with grams directly.

Correction: Convert grams to moles first. Avogadro’s constant converts between moles and particles.

Reporting particles without naming what they are.

Correction: State whether the count is atoms, molecules, or ions, as appropriate.

Rounding intermediate values too soon.

Correction: Keep extra digits during the calculation and round only the final answer.

Lesson summary

A mole is a counting unit containing $6.02\times10^{23}$ particles.
Use molar mass to convert between mass and moles.
Use Avogadro’s constant to convert between moles and particles.
For mass-to-particles or particles-to-mass conversions, use moles as the middle step.
Check units, particle type, reasonableness, and significant figures.

Check your understanding

Question 1

How many molecules are in

2.00\,\mathrm{mol}

of a molecular substance?

$3.01\times10^{23}$ molecules
$1.20\times10^{24}$ molecules
$2.00$ molecules
$6.02\times10^{23}$ molecules

Show answer and explanation

1.20\times10^{24}

molecules

Multiply

2.00\,\mathrm{mol}

by

6.02\times10^{23}\,\mathrm{molecules/mol}

. The result is

1.20\times10^{24}

molecules to three significant figures.

Question 2

A substance has a molar mass of

40.0\,\mathrm{g/mol}

. How many moles are in

20.0\,\mathrm{g}

?

$800\,\mathrm{mol}$
$2.00\,\mathrm{mol}$
$0.500\,\mathrm{mol}$
$0.0500\,\mathrm{mol}$

Show answer and explanation

0.500\,\mathrm{mol}

Divide mass by molar mass:

20.0\,\mathrm{g}\div40.0\,\mathrm{g/mol}=0.500\,\mathrm{mol}

. The gram units cancel.

Question 3

Which sequence converts a particle count to mass?

Particles to mass using Avogadro’s constant
Particles to moles, then moles to mass
Mass to moles, then moles to particles
Particles to moles by multiplying by molar mass

Show answer and explanation

Particles to moles, then moles to mass

First divide the particle count by Avogadro’s constant to find moles. Then multiply moles by molar mass to find mass.

Key terms

Mole: A counting unit equal to $6.02\times10^{23}$ particles.
Particle: One individual unit counted in a sample, such as an atom, molecule, or ion.
Avogadro’s constant: The number of particles in one mole.
Molar mass: The mass of one mole of a substance, commonly measured in grams per mole.
Significant figures: The digits that show the precision of a measured value.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Chemistry (SCH3U), expectation D2.3. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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D2.3 · Convert among moles, particles, and mass

Ontario Grade 11 Chemistry

SCH3U study topic D2.3

What you will learn

1. From familiar counting to the mole

2. Connecting moles and mass

3. Choosing a conversion path

4. Units and reasonableness

From mass to molecules

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SCH3U

About this lesson and its review