Concentration in mol/dm³ tells you how many moles of solute are dissolved in each 1 dm³ of solution. Before you can use it, any volume given in cm³ must be converted to dm³ by dividing by 1000.
This skill opens almost every solution calculation in concentration, gas and yield calculations, and it is the step most easily skipped under time pressure.
How does concentration link moles and volume?
The relationship is moles = concentration × volume, with concentration in mol/dm³ and volume in dm³. Rearranged, concentration = moles ÷ volume, and volume = moles ÷ concentration.
A volume of 1 dm³ is the same as 1000 cm³. So 25.0 cm³ is 25.0 ÷ 1000 = 0.0250 dm³. Think of it as shifting the decimal point three places to the left.
What are the steps?
- Write down what you are given, with units, including any mass or volume.
- Convert every solution volume to dm³ by dividing the cm³ value by 1000.
- Apply the formula moles = concentration × volume, or rearrange it.
- Use the equation ratio if the question moves to a different substance.
- Check the size of the answer. Volumes of tens of cm³ at everyday concentrations give mole values of about 0.001 to 0.05, not whole numbers.
Worked example
The numbers are invented for practice. 2.00 g of sodium hydroxide, NaOH, is dissolved in water to make 250 cm³ of solution. Find its concentration in mol/dm³ and in g/dm³.
Step 1, relative formula mass: Mᵣ of NaOH = 23 + 16 + 1 = 40.
Step 2, moles: moles = 2.00 ÷ 40 = 0.0500 mol.
Step 3, convert the volume: 250 cm³ ÷ 1000 = 0.250 dm³.
Step 4, concentration in mol/dm³: 0.0500 ÷ 0.250 = 0.200 mol/dm³.
Step 5, concentration in g/dm³: 0.200 × 40 = 8.0 g/dm³.
Check: 2.00 g in 0.250 dm³ is 2.00 ÷ 0.250 = 8.0 g/dm³. Both routes agree.
What is the mistake to watch for?
A common slip is to put the cm³ figure straight into the formula.
Mistaken working: moles of NaOH in 25.0 cm³ of 0.200 mol/dm³ = 0.200 × 25.0 = 5.00 mol
The student forgot that 25.0 cm³ is 0.0250 dm³, so the answer is 1000 times too large.
The correct working is 0.200 × 0.0250 = 0.00500 mol. A quick sense check catches it. A small sample of solution cannot hold 5.00 mol of sodium hydroxide, which would have a mass of 200 g.
Check yourself
Try these without a calculator first, then open each answer.
1. How many moles of hydrochloric acid are in 50.0 cm³ of a 0.100 mol/dm³ solution?
Show answer
Volume = 50.0 ÷ 1000 = 0.0500 dm³. Moles = 0.100 × 0.0500 = 0.00500 mol.
2. What volume, in cm³, of 0.500 mol/dm³ solution contains 0.0125 mol of solute?
Show answer
Volume = 0.0125 ÷ 0.500 = 0.0250 dm³. Multiply by 1000 to get 25.0 cm³.
3. A solution has concentration 0.250 mol/dm³ and the solute has Mᵣ = 98. Give the concentration in g/dm³.
Show answer
0.250 × 98 = 24.5 g/dm³.
Where does this lead next?
With solutions under control, move to relating gas amount to volume, where the same moles-first idea applies to gases. The mole and equation-ratio tutor shows each amount step with units, which helps you see where a conversion belongs.
If you understand the formula but still drop the conversion in longer questions, that is a habit problem a teacher can spot quickly in online one-to-one Chemistry tuition.