E2.2 Calculate solution concentration in multiple units

Ontario Grade 11 Chemistry

Solutions and Solubility

SCH3U E2.2 study topic: mol/L, g/L, and mass-based ppm

Two drinks with the same volume may have different colour intensity. The darker drink may contain more dissolved colouring in that volume. At the particle level, it has more colouring particles compared with the amount of solution. Concentration describes this comparison. Different concentration units are useful because a question may give the solute amount in moles or grams, and the solution amount as a volume or mass.

What you will learn

Explain concentration as an amount of solute compared with an amount of solution.
Calculate molar concentration in mol/L and mass concentration in g/L.
Calculate mass-based concentration in parts per million when solute and solution masses are known.
Track units and round answers to match the precision of the given measurements.

1. Connect the quantities to the mixture

A solution is a uniform mixture. The solute is the substance dissolved in the mixture. The solvent is the substance that dissolves the solute. In salt water, salt is the solute and water is the solvent.

Concentration compares an amount of solute with a stated amount of the whole solution. The denominator is not just the solvent. For example, if two samples have the same solution volume, the sample with more dissolved solute has the greater concentration.

Before calculating, identify three things: the solute, the amount of solute, and the amount of solution. The solute amount may be in moles or grams. The solution amount may be a volume in litres or a mass in grams or kilograms, depending on the requested unit.

At the particle level, concentration describes how much solute is present relative to a chosen amount of solution. The particles are not counted one by one in these calculations. Instead, measurable amounts such as mass and volume are used to describe the mixture.

In words, concentration is the amount of solute divided by the amount of solution. The particular quantities and units depend on the concentration form. A concentration value is incomplete without its unit.

Concentration compares solute with the whole solution.
Identify the requested unit before selecting the quantities.
Keep the amount of solution distinct from the amount of solvent.

2. Molar concentration and mass concentration

Molar concentration compares the amount of solute, in moles, with the volume of solution, in litres. A mole is a counting unit for particles. The symbol

n

represents amount in moles,

V

represents solution volume, and

c

represents molar concentration. The usual unit is

\mathrm{mol/L}

.

Mass concentration compares the solute mass, in grams, with the solution volume, in litres. Its unit is

\mathrm{g/L}

. This form uses mass rather than amount in moles, so it reports a different comparison.

For both forms, use the final solution volume. If a volume is given in millilitres, convert it to litres before calculating. There are

1000\ \mathrm{mL}

in

1\ \mathrm{L}

, so divide the millilitre value by

1000

.

If a question gives solute mass but asks for molar concentration, first convert the mass to moles. Molar mass is the mass of one mole of a substance, expressed in

\mathrm{g/mol}

. Divide the mass by the molar mass. The gram units cancel, leaving moles.

Choose the relationship that matches the requested unit. Moles per litre gives molar concentration. Grams per litre gives mass concentration. Do not substitute grams for moles in a molar concentration calculation.

c=\frac{n}{V}

Molar concentration is moles of solute per litre of solution.
Mass concentration is grams of solute per litre of solution.
Convert millilitres to litres for calculations in mol/L and g/L.
Use molar mass to convert solute mass to moles when needed.

3. Mass-based concentration in parts per million

Parts per million, written ppm, is a scale for a small amount of solute compared with a much larger amount of solution. In the mass-based form taught here, compare the solute mass with the solution mass. Both masses must use the same unit before division.

Multiply the mass ratio by one million to express the result as parts per million. For example,

3\ \mathrm{mg}

of solute per

1\ \mathrm{kg}

of solution is

3\ \mathrm{ppm}

, because

1\ \mathrm{kg}=1\,000\,000\ \mathrm{mg}

.

Do not use solution volume in place of solution mass for this mass-based ppm calculation. If only a solution volume is known, the mass ratio cannot be calculated unless the solution mass is also given.

A ppm result is not the same numerical value as a result in mol/L or g/L. Each unit compares different quantities. A conversion between forms is possible only when the information needed for both forms is available.

\mathrm{ppm}=\frac{m_{\mathrm{solute}}}{m_{\mathrm{solution}}}\times10^6

Mass-based ppm compares solute mass with solution mass.
Use the same mass unit above and below the fraction.
Multiply the mass ratio by one million.

4. Set up calculations, track units, and round

A clear calculation begins by identifying the known quantities and the requested unit. Convert units first when needed. Then substitute values with their units into the matching relationship.

Units help check the setup. Dividing moles by litres leaves

\mathrm{mol/L}

. Dividing grams by litres leaves

\mathrm{g/L}

. In mass-based ppm, matching mass units cancel in the ratio, and the factor of one million sets the ppm scale.

Significant digits show the precision of measured values. For multiplication and division, report the final result with the same number of significant digits as the least precise measured value. Exact unit conversions do not limit the digits.

Keep extra digits during intermediate calculations. Round only the final result, and include the unit. Also check that the denominator is the stated amount of the whole solution and that the result answers the requested form of concentration.

Match the quantities and units to the requested concentration form.
Use units to check both the setup and the final answer.
Round the final result to the precision supported by the measurements.

Worked example

Calculate concentration in three units

A solution has a final volume of

250.0\ \mathrm{mL}

and a mass of

250.0\ \mathrm{g}

. It contains

5.85\ \mathrm{g}

of sodium chloride,

\mathrm{NaCl}

. Calculate its mass concentration in

\mathrm{g/L}

, molar concentration in

\mathrm{mol/L}

, and mass-based concentration in ppm. Use a molar mass of

58.44\ \mathrm{g/mol}

for

\mathrm{NaCl}

.

Convert solution volume
Convert millilitres to litres because the two volume-based concentration units use litres. The millilitre units cancel in the conversion.
$250.0\ \mathrm{mL}\times\frac{1\ \mathrm{L}}{1000\ \mathrm{mL}}=0.2500\ \mathrm{L}$
Find mass concentration
Divide the solute mass by the final solution volume in litres. The remaining unit is grams per litre.
$\frac{5.85\ \mathrm{g}}{0.2500\ \mathrm{L}}=23.4\ \mathrm{g/L}$
Convert solute mass to moles
Divide the solute mass by its molar mass. The gram units cancel, leaving the amount of sodium chloride in moles.
$n=\frac{5.85\ \mathrm{g}}{58.44\ \mathrm{g/mol}}=0.100\ \mathrm{mol}$
Find molar concentration
Divide the amount in moles by the final solution volume in litres. The result has three significant digits, based on the solute mass.
$c=\frac{0.100\ \mathrm{mol}}{0.2500\ \mathrm{L}}=0.400\ \mathrm{mol/L}$
Find mass-based ppm
Use the solution mass, not its volume, for mass-based ppm. The mass units cancel in the ratio. The solution mass includes the solute.
$\frac{5.85\ \mathrm{g}}{250.0\ \mathrm{g}}\times10^6=2.34\times10^4\ \mathrm{ppm}$

Answer: The solution has a mass concentration of

23.4\ \mathrm{g/L}

, a molar concentration of

0.400\ \mathrm{mol/L}

, and a mass-based concentration of

2.34\times10^4\ \mathrm{ppm}

.

Check: The volume-based results both use

0.2500\ \mathrm{L}

of solution. For ppm, the solute mass is

0.0234

of the solution mass. Multiplying that ratio by one million gives

2.34\times10^4\ \mathrm{ppm}

.

Common mistakes and how to avoid them

Using the solvent volume instead of the final solution volume.

Correction: Use the volume of the whole solution for molar concentration and mass concentration.

Using grams directly in a molar concentration calculation.

Correction: Convert the solute mass to moles using molar mass before dividing by solution volume.

Leaving millilitres in a calculation that requires litres.

Correction: Convert the solution volume to litres before calculating mol/L or g/L.

Using solution volume in a mass-based ppm calculation.

Correction: Compare solute mass with solution mass, using the same mass units.

Reporting concentration without a unit or rounding too early.

Correction: Include the requested unit and round only the final answer.

Lesson summary

Concentration compares an amount of solute with a stated amount of solution.
Molar concentration uses mol/L; mass concentration uses g/L.
Mass-based ppm compares solute mass with solution mass and scales the ratio by one million.
Use the whole solution amount, track units, and round the final value appropriately.

Check your understanding

Question 1

A solution contains

4.0\ \mathrm{g}

of solute in a final volume of

0.200\ \mathrm{L}

. What is its mass concentration?

$20.\ \mathrm{g/L}$
$0.80\ \mathrm{g/L}$
$0.020\ \mathrm{g/L}$
$20.\ \mathrm{mol/L}$

Show answer and explanation

20.\ \mathrm{g/L}

Divide solute mass by solution volume:

4.0\ \mathrm{g}/0.200\ \mathrm{L}=20.\ \mathrm{g/L}

. The given values support two significant digits.

Question 2

A solution contains

2.0\ \mathrm{mg}

of solute in

1.0\ \mathrm{kg}

of solution. What is its mass-based concentration?

$2.0\ \mathrm{ppm}$
$0.0020\ \mathrm{ppm}$
$2.0\times10^3\ \mathrm{ppm}$
$2.0\ \mathrm{mol/L}$

Show answer and explanation

2.0\ \mathrm{ppm}

Convert

1.0\ \mathrm{kg}

to

1.0\times10^6\ \mathrm{mg}

. The mass ratio is

2.0\ \mathrm{mg}/(1.0\times10^6\ \mathrm{mg})

. Multiplying by one million gives

2.0\ \mathrm{ppm}

.

Key terms

Solution: A uniform mixture of a solute and a solvent.
Solute: The substance dissolved in a solution.
Solvent: The substance that dissolves the solute.
Concentration: A comparison between an amount of solute and a stated amount of solution.
Molar concentration: The amount of solute in moles divided by the volume of solution in litres.
Mass concentration: The mass of solute in grams divided by the volume of solution in litres.
Molar mass: The mass of one mole of a substance, usually expressed in grams per mole.
Parts per million: A concentration scale that expresses solute amount relative to one million matching parts of solution.

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E2.2 · Calculate solution concentration in multiple units