Concentration of Solutions

When a substance dissolves in water it forms a solution, and how strong that solution is depends on how much solute is packed into a given volume. A spoonful of salt stirred into a glass of water makes a more concentrated solution than the same spoonful stirred into a bucket. This idea — concentration — opens Topic C5 (Monitoring and controlling reactions) of OCR Gateway Science A, and it underpins everything that follows, from titrations to rates. This lesson explains what concentration means, how to calculate it in grams per cubic decimetre (g/dm³) and, for Higher tier, in moles per cubic decimetre (mol/dm³), and how to convert between the two.

By the end of this lesson you should be able to define concentration, calculate a mass concentration in g/dm³, convert volumes from cm³ to dm³, and (Higher tier) calculate a molar concentration in mol/dm³ and convert between g/dm³ and mol/dm³ using the relative formula mass.

Concentration is one of the most useful ideas in chemistry because it lets us compare solutions fairly and predict how they will behave. Two solutions of the same substance can be very different — one strong and one weak in everyday terms — simply because they contain different amounts of solute in the same volume, and concentration is how we put a precise number on that difference.

What Concentration Means

The concentration of a solution is the amount of solute dissolved in a given volume of solution. The more solute there is in the same volume, the more concentrated the solution; the less there is, the more dilute.

There are two ways to measure the "amount" of solute:

by its mass in grams, giving a concentration in grams per cubic decimetre, g/dm³;
(Higher tier) by its amount in moles, giving a concentration in moles per cubic decimetre, mol/dm³.

A cubic decimetre ( $\text{dm}^3$ ) is the standard unit of volume in chemistry. It is exactly the same volume as a litre, and equal to 1000 cm³. Keeping track of the volume unit is the single most important habit in this whole topic.

To picture a cubic decimetre, imagine a cube measuring $10 \text{ cm}$ along each edge. Its volume is $10 \times 10 \times 10 = 1000 \text{ cm}^3$ , which is $1 \text{ dm}^3$ — about the size of a large carton of juice. A laboratory measurement of $25 \text{ cm}^3$ , by contrast, is a small fraction of that, which is exactly why cm³ values come out as small decimals once converted to dm³ (for instance, $25 \text{ cm}^3 = 0.025 \text{ dm}^3$ ). Because concentration is quoted per dm³, but lab volumes are usually a small number of cm³, almost every concentration calculation begins with that conversion.

Exam Tip: Concentration is always "amount per volume". Whenever you read a concentration value, check its unit — g/dm³ tells you it is a mass concentration, mol/dm³ tells you it is a molar concentration. The two are not interchangeable without using the relative formula mass.

Converting cm³ to dm³

Volumes in the laboratory are usually measured in cubic centimetres (cm³), but concentration is quoted per cubic decimetre (dm³). So you almost always have to convert first, and the rule is simple:

$\text{volume in dm}^3 = \dfrac{\text{volume in cm}^3}{1000}$

To convert cm³ to dm³, divide by 1000. For example, $500 \text{ cm}^3 = \dfrac{500}{1000} = 0.5 \text{ dm}^3$ , and $25 \text{ cm}^3 = \dfrac{25}{1000} = 0.025 \text{ dm}^3$ .

Volume in cm³	Volume in dm³
1000	1
500	0.5
250	0.25
100	0.1
25	0.025

Exam Tip: Forgetting to convert cm³ to dm³ is the most common mistake in the whole of C5. If a volume is given in cm³, divide it by 1000 before you put it into any concentration calculation. A missed conversion makes the answer wrong by a factor of 1000.

Mass Concentration in g/dm³

The mass concentration of a solution is found from:

$\text{concentration (g/dm}^3) = \dfrac{\text{mass of solute (g)}}{\text{volume of solution (dm}^3)}$

A triangle helps you rearrange it: cover the quantity you want, and the triangle shows the calculation.

So the three forms are:

$\text{conc} = \dfrac{\text{mass}}{\text{volume}} \qquad \text{mass} = \text{conc} \times \text{volume} \qquad \text{volume} = \dfrac{\text{mass}}{\text{conc}}$

Worked Example 1 — Mass concentration

Calculate the concentration, in g/dm³, of a solution containing $20 \text{ g}$ of sodium hydroxide dissolved in $0.5 \text{ dm}^3$ of solution.

Step 1 — write the equation: $\text{concentration} = \dfrac{\text{mass}}{\text{volume}}$ .

Step 2 — substitute (the volume is already in dm³): $\text{concentration} = \dfrac{20}{0.5}$ .

Step 3 — calculate: $\text{concentration} = 40 \text{ g/dm}^3$ .

Answer: $40 \text{ g/dm}^3$ .

Worked Example 2 — Converting the volume first

Calculate the concentration, in g/dm³, of a solution containing $6 \text{ g}$ of solute in $250 \text{ cm}^3$ of solution.

Step 1 — convert the volume: $250 \text{ cm}^3 = \dfrac{250}{1000} = 0.25 \text{ dm}^3$ .

Step 2 — substitute: $\text{concentration} = \dfrac{6}{0.25}$ .

Step 3 — calculate: $\text{concentration} = 24 \text{ g/dm}^3$ .

Answer: $24 \text{ g/dm}^3$ .

Worked Example 3 — Finding the mass of solute

What mass of solute is dissolved in $2 \text{ dm}^3$ of a solution of concentration $15 \text{ g/dm}^3$ ?

Step 1 — rearrange: $\text{mass} = \text{concentration} \times \text{volume}$ .

Step 2 — substitute: $\text{mass} = 15 \times 2$ .

Step 3 — calculate: $\text{mass} = 30 \text{ g}$ .

Answer: $30 \text{ g}$ of solute.

Exam Tip: Always write the three lines — equation, substitution, answer with unit — and put the volume in dm³ before you substitute. A concentration in g/dm³ must end with the unit "g/dm³"; a bare number with no unit loses a mark.

Higher Tier: Molar Concentration in mol/dm³

Higher tier only: Chemists more often express concentration in moles per cubic decimetre (mol/dm³), because the mole counts the actual number of particles taking part in a reaction. (Recall from Topic C3 that one mole is $6.02 \times 10^{23}$ particles, and that $\text{moles} = \dfrac{\text{mass}}{M_r}$ .) The molar concentration is:

$\text{concentration (mol/dm}^3) = \dfrac{\text{moles of solute}}{\text{volume of solution (dm}^3)}$

It rearranges in exactly the same way as the mass version:

$\text{moles} = \text{concentration} \times \text{volume} \qquad \text{volume} = \dfrac{\text{moles}}{\text{concentration}}$

Worked Example 4 — Molar concentration

Calculate the concentration, in mol/dm³, of a solution containing $0.25 \text{ mol}$ of solute in $500 \text{ cm}^3$ of solution.

Step 1 — convert the volume: $500 \text{ cm}^3 = \dfrac{500}{1000} = 0.5 \text{ dm}^3$ .

Step 2 — substitute: $\text{concentration} = \dfrac{0.25}{0.5}$ .

Step 3 — calculate: $\text{concentration} = 0.5 \text{ mol/dm}^3$ .

Answer: $0.5 \text{ mol/dm}^3$ .

Worked Example 5 — From mass to molar concentration

A solution contains $4 \text{ g}$ of sodium hydroxide ( $M_r = 40$ ) in $1 \text{ dm}^3$ . Calculate its concentration in mol/dm³.

Step 1 — convert the mass to moles: $\text{moles} = \dfrac{\text{mass}}{M_r} = \dfrac{4}{40} = 0.1 \text{ mol}$ .

Step 2 — substitute into the concentration equation: $\text{concentration} = \dfrac{0.1}{1}$ .

Step 3 — calculate: $\text{concentration} = 0.1 \text{ mol/dm}^3$ .

Answer: $0.1 \text{ mol/dm}^3$ .

Higher Tier: Converting Between g/dm³ and mol/dm³

Higher tier only: The link between the two concentration units is the relative formula mass ( $M_r$ ), exactly as it links mass and moles. The conversions are:

$\text{concentration (g/dm}^3) = \text{concentration (mol/dm}^3) \times M_r$ $\text{concentration (mol/dm}^3) = \dfrac{\text{concentration (g/dm}^3)}{M_r}$

Worked Example 6 — g/dm³ to mol/dm³

A solution of sodium hydroxide has a concentration of $40 \text{ g/dm}^3$ . What is its concentration in mol/dm³? ( $M_r$ of NaOH $= 40$ .)

Step 1 — use the conversion: $\text{concentration (mol/dm}^3) = \dfrac{\text{concentration (g/dm}^3)}{M_r}$ .

Step 2 — substitute: $\text{concentration} = \dfrac{40}{40}$ .

Step 3 — calculate: $\text{concentration} = 1 \text{ mol/dm}^3$ .

Answer: $1 \text{ mol/dm}^3$ . This matches Worked Example 1 — $40 \text{ g/dm}^3$ of NaOH is a $1 \text{ mol/dm}^3$ solution.

Worked Example 7 — mol/dm³ to g/dm³

Convert a $0.1 \text{ mol/dm}^3$ solution of hydrochloric acid (HCl) to g/dm³. ( $A_r$ : H = 1, Cl = 35.5, so $M_r$ of HCl $= 36.5$ .)

Step 1 — use the conversion: $\text{concentration (g/dm}^3) = \text{concentration (mol/dm}^3) \times M_r$ .

Step 2 — substitute: $\text{concentration} = 0.1 \times 36.5$ .

Step 3 — calculate: $\text{concentration} = 3.65 \text{ g/dm}^3$ .

Answer: $3.65 \text{ g/dm}^3$ .

Exam Tip: To go from mol/dm³ to g/dm³, multiply by $M_r$ ; to go the other way, divide by $M_r$ . It mirrors $\text{mass} = \text{moles} \times M_r$ exactly — the only difference is that everything is "per dm³".

Concentration in the Laboratory

Concentration is not an abstract idea — it is something chemists set and measure all the time. When you make up a solution of a known concentration (a standard solution), you weigh out an accurate mass of the solute, dissolve it in a little water, and then make the total volume up to a known volume (often $250 \text{ cm}^3$ in a special flask called a volumetric flask). Knowing the mass and the volume lets you calculate the concentration exactly — which is precisely the kind of calculation in this lesson. Standard solutions of known concentration are essential for titrations (the next two lessons), where one solution of known concentration is used to find the unknown concentration of another.

Concentration also matters for the rate of a reaction (later in C5): a more concentrated solution has more reactant particles in a given volume, so the particles collide more often and the reaction goes faster. So the skill you are learning here — calculating and converting concentrations — runs right through the rest of the topic. Getting confident with the volume conversion and the two units now will pay off in every later lesson.

A useful sense-check on any concentration answer is to ask whether it is the right size. If you dissolve a small mass in a large volume, the concentration should come out small; if you dissolve a large mass in a small volume, it should be large. If a calculation gives a concentration that is a thousand times bigger or smaller than you expected, the most likely cause is a missed cm³-to-dm³ conversion — so check that first.

Exam Tip: Sense-check the size of a concentration answer. A small mass in a large volume gives a low concentration; if your answer is out by a factor of about 1000, you have probably forgotten to convert cm³ to dm³.

Common Misconceptions

Misconception	The correct idea
"You can use cm³ straight in the concentration equation"	The volume must be in dm³ — divide a cm³ value by 1000 first
"Concentration is just the mass of solute"	Concentration is mass (or moles) ÷ volume — the volume always matters
"g/dm³ and mol/dm³ are the same number"	They differ by a factor of the $M_r$ ; convert using $\text{g/dm}^3 = \text{mol/dm}^3 \times M_r$
"To convert cm³ to dm³ you multiply by 1000"	You divide by 1000 (a dm³ is bigger, so there are fewer of them)
"A concentrated solution is the same as a strong acid"	Concentration is how much solute is dissolved; it is not the same as acid strength

Model Answer — A Multi-Step Concentration Calculation

Question (6 marks): A student dissolves $11.7 \text{ g}$ of sodium chloride ( $M_r = 58.5$ ) in water to make $250 \text{ cm}^3$ of solution. Calculate the concentration of the solution in g/dm³ and in mol/dm³, showing your working.

Mid-band response: " $250 \text{ cm}^3 = 0.25 \text{ dm}^3$ . Concentration $= 11.7 \div 0.25 = 46.8 \text{ g/dm}^3$ . Moles $= 11.7 \div 58.5 = 0.2$ , so $0.2 \div 0.25 = 0.8 \text{ mol/dm}^3$ ."

Examiner-style commentary: The method and both answers are correct, but the steps are run together with no labels. To climb a band, set out the volume conversion, the two equations and each substitution on separate lines so every mark is easy to award, and quote the units.

Stronger response: "Convert the volume: $250 \text{ cm}^3 = \dfrac{250}{1000} = 0.25 \text{ dm}^3$ . Mass concentration $= \dfrac{\text{mass}}{\text{volume}} = \dfrac{11.7}{0.25} = 46.8 \text{ g/dm}^3$ . To find the molar concentration, first find the moles: $\text{moles} = \dfrac{11.7}{58.5} = 0.2 \text{ mol}$ . Then concentration $= \dfrac{0.2}{0.25} = 0.8 \text{ mol/dm}^3$ ."

Examiner-style commentary: A clear, correct answer with the volume converted and both concentrations calculated. To reach the top band, name each step and add a check that the two answers are consistent via the $M_r$ .

Top-band response: "Step 1 — convert the volume: $250 \text{ cm}^3 = \dfrac{250}{1000} = 0.25 \text{ dm}^3$ . Step 2 — mass concentration: $\text{concentration} = \dfrac{\text{mass}}{\text{volume}} = \dfrac{11.7}{0.25} = 46.8 \text{ g/dm}^3$ . Step 3 — moles of solute: $\text{moles} = \dfrac{\text{mass}}{M_r} = \dfrac{11.7}{58.5} = 0.2 \text{ mol}$ . Step 4 — molar concentration: $\text{concentration} = \dfrac{\text{moles}}{\text{volume}} = \dfrac{0.2}{0.25} = 0.8 \text{ mol/dm}^3$ . Check: $0.8 \text{ mol/dm}^3 \times 58.5 = 46.8 \text{ g/dm}^3$ , which matches Step 2 — the two concentrations are consistent."

Examiner-style commentary: Full marks. Every step is labelled, the volume is converted first, both concentrations are derived, and the answer is confirmed by converting between the two units with the $M_r$ — model technique for a concentration question.

Exam Tips

Concentration is amount of solute ÷ volume of solution; always quote the unit (g/dm³ or mol/dm³).
Convert cm³ to dm³ by dividing by 1000 before substituting — the commonest error in C5.
Mass concentration: $\text{conc (g/dm}^3) = \dfrac{\text{mass}}{\text{volume in dm}^3}$ .
Higher: molar concentration $= \dfrac{\text{moles}}{\text{volume in dm}^3}$ ; find moles with $\text{moles} = \dfrac{\text{mass}}{M_r}$ first.
Higher: convert with $\text{g/dm}^3 = \text{mol/dm}^3 \times M_r$ (and divide by $M_r$ to go back).

Summary

Concentration is the amount of solute dissolved in a given volume of solution; more solute per volume means more concentrated.
A cubic decimetre (dm³) equals a litre and $1000 \text{ cm}^3$ ; convert cm³ to dm³ by dividing by 1000.
Mass concentration: $\text{concentration (g/dm}^3) = \dfrac{\text{mass (g)}}{\text{volume (dm}^3)}$ .
Higher: molar concentration: $\text{concentration (mol/dm}^3) = \dfrac{\text{moles}}{\text{volume (dm}^3)}$ .
Higher: convert between units with $\text{g/dm}^3 = \text{mol/dm}^3 \times M_r$ .

This content is aligned with OCR Gateway Science A GCSE Chemistry (J248), Topic C5 Monitoring and controlling reactions (concentration of solutions in g/dm³ and, for Higher tier, mol/dm³). Refer to the official OCR specification document for the exact wording.

Concentration of Solutions

Concentration of Solutions

What Concentration Means

Converting cm³ to dm³

Mass Concentration in g/dm³

Worked Example 1 — Mass concentration

Worked Example 2 — Converting the volume first

Worked Example 3 — Finding the mass of solute

Higher Tier: Molar Concentration in mol/dm³

Worked Example 4 — Molar concentration

Worked Example 5 — From mass to molar concentration

Higher Tier: Converting Between g/dm³ and mol/dm³

Worked Example 6 — g/dm³ to mol/dm³

Worked Example 7 — mol/dm³ to g/dm³

Concentration in the Laboratory

Common Misconceptions

Model Answer — A Multi-Step Concentration Calculation

Exam Tips

Summary

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