7.1 Calculating molar concentrations

To calculate concentration, you need to know the amount of a substance and the volume it is dissolved in.

Example 1

What is the molarity of a solution containing 0.30 mol of NaCl in 3.6 l?

Remember: \text{molarity (M)} = \frac{\text{moles of solute (mol)}}{\text{volume of solution (l)}}

\text{Molarity (M)} = \frac{\text{0.30 mol}}{\text{3.6 L}} = 0.08 M

Example 2

What is the molarity of a solution containing 210 g of NaCl in 3.6 l? The molecular weight of NaCl is 58.44 g mol–1.

In this case, you first need to work out the number of moles from the mass:

Remember: \text{number of moles (mol)} = \frac {\text{mass of substance (g)}}{\text{molecular weight}}

Step 1: \text{number of moles (mol)} = \frac {\text{210}}{\text{58.44}} = \text{3.6 mol}

Step 2: \text {molarity (M)} = \frac {\text{3.6 mol}}{\text{3.6 l}} = \text{1.0 M}

Example 3

It can be useful to be able to do these calculations in reverse to work out the mass needed to make up a particular solution.

How would you prepare 200 ml of 0.25 M KNO3 solution? The molecular weight of KNO3 is 101.1 g mol–1.

In this case you first need to work out the number of moles you need.

Remember: \text{Molarity (M)} = \frac {\text{moles of solute (mol)}}{\text{volume of solution (L)}}

You will need to rearrange the equation above to solve for moles of solute. It helps when rearranging equations to write out the units in full as it makes it much more obvious if you have made a mistake. Also remember to convert any volumes to litres.

\text{Molarity (mol l}^{-1}\text{)} = \frac{\text{moles of solute (mol)}}{\text{volume of solution (l)}}

Moles of solute mol = molarity (mol l–1) × volume of solution (l)

Moles of KNO3 = 0.25 mol l–1 × 0.2 L = 0.05 mol

Next you can work out the mass you need to weigh out.

Mass of substance (g) = number of moles (mol) × molecular weight (g mol–1)

Mass of KNO3 (g) = 0.05 mol × 101.1 g mol–1 = 5.06 g

So, the full answer to question is: weigh out 5.06 g of KNO3 and dissolve in water to a volume less than 200 ml. Adjust the final volume to 200 ml.

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