30. Concentration Calculations (grams per dm³)

The relationship between mass, concentration, and volume is given by:

Concentration (g/dm³) = Mass (g) / Volume (dm³)

Decimeter Cubed (dm³): This is a unit of volume equal to 1,000 cm³ (the same as 1 liter).
Formula Triangle: You can use a triangle with Mass at the top and Concentration and Volume at the bottom.
- To find Mass: Concentration × Volume
- To find Volume: Mass / Concentration
- To find Concentration: Mass / Volume

One of the most common ways to lose marks is by using the wrong units. Always check:

Mass: Should be in grams (g). If given in kilograms (kg), multiply by 1,000.
Volume: Should be in decimeters cubed (dm³). If given in centimeters cubed (cm³), divide by 1,000.

Finding Concentration: * If you have 40g of sodium hydroxide dissolved in 2.5 dm³ of water:
- 40 / 2.5 = 16 g/dm³.
Converting Units First:
- If you have 24g of copper sulfate in 480 cm³ of water:
- First, convert volume: 480 / 1,000 = 0.48 dm³.
- Then calculate: 24 / 0.48 = 50 g/dm³.
Finding Mass:
- How much hydrogen chloride is in 400 cm³ of a 20 g/dm³ solution?
- Convert volume: 400 / 1,000 = 0.4 dm³.
- Rearrange formula: Mass = 20 × 0.4 = 8g.

Instead of writing "per dm³" or "/dm³", you can use dm⁻³. For example, a concentration can be written as 16 g dm⁻³.