Concentration calculator: g/dm³ and mol/dm³

• g/dm³: 10 g of salt dissolved to make 250 cm³ of solution. $V = 0.25$ dm³, so $c = 10 \div 0.25 = 40$ g/dm³.
• mol/dm³: 0.5 mol of sodium hydroxide in 2 dm³. $c = 0.5 \div 2 = 0.25$ mol/dm³.
• Moles from concentration: 25 cm³ of 0.1 mol/dm³ acid. $n = 0.1 \times 0.025 = 0.0025$ mol.

Use the relative formula mass ($M_r$):

• mol/dm³ → g/dm³: multiply by $M_r$.
• g/dm³ → mol/dm³: divide by $M_r$.

Example: 0.25 mol/dm³ NaOH ($M_r = 40$) is $0.25 \times 40 = 10$ g/dm³. Our relative formula mass calculator finds $M_r$ from the formula.

In a titration you know the volume and concentration of one solution and the volume of the other. Find the moles of the first ($n = c \times V$), use the ratio from the balanced equation to get the moles of the second, then divide by its volume. Remember to convert each volume from cm³ to dm³ along the way. See our titration questions for full examples.

Concentrated means a lot of solute per dm³. Strong (for acids) means the acid fully ionises in water. A dilute solution of a strong acid like hydrochloric acid is still strong; a concentrated solution of ethanoic acid is still weak. Mixing up these words is a common way to lose a mark.

• Dividing by cm³ instead of dm³ (answers 1,000 times too small).
• Using the volume of water added instead of the final volume of solution.
• Mixing up g/dm³ and mol/dm³.

Practise with our concentration questions, and see the moles calculator.

• Write the volume in dm³ as its own line of working.
• Keep at least three significant figures until the final answer.
• For titrations, use the mean of concordant titres (within 0.10 cm³ of each other).
• Check the units the question asks for: g/dm³ and mol/dm³ are not interchangeable.

When you add water to a solution, the number of moles of solute stays the same, so:

Example: 50 cm³ of 2 mol/dm³ acid is diluted to 200 cm³. $c_2 = 2 \times 50 \div 200 = 0.5$ mol/dm³. The volumes can stay in cm³ here because they appear on both sides. Diluting four times lowers the concentration to a quarter.