4.3.2.5 - Mass concentration of solutions

Solute, solution and mass concentration

A concentration states how much dissolved substance is present in each unit volume of the complete solution.

The solute is the dissolved substance; the solvent is the liquid in which it dissolves. Together they form the solution. For salt dissolved in water, salt is the solute and water the solvent. A solute's particles remain present after dissolving even though the solid is no longer visible.

Mass concentration is mass of solute divided by volume of solution. It can be given in grams per cubic decimetre, written $\mathrm{g\,dm}^{-3}$ or $\mathrm{g/dm}^{3}$. A concentration of $12\,\mathrm{g\,dm}^{-3}$ means each $1\,\mathrm{dm}^{3}$ of a well-mixed solution contains 12 g of solute. It does not mean the whole container contains exactly 12 g: that depends on how much solution is in it.

Use the final solution volume, not merely the volume of solvent poured in. Dissolving a solid in water and making the mixture up to $250\,\mathrm{cm}^{3}$ produces $250\,\mathrm{cm}^{3}$ of solution. Adding the solid to $250\,\mathrm{cm}^{3}$ of water need not give exactly the same final volume.

Illustrative comparison: one bottle contains $0.150\,\mathrm{dm}^{3}$ solution at $18.0\,\mathrm{g\,dm}^{-3}$, while another contains $1.50\,\mathrm{dm}^{3}$ at $4.0\,\mathrm{g\,dm}^{-3}$. The first is more concentrated but contains 2.70 g solute, compared with 6.0 g in the larger bottle. Concentration and total solute mass answer different questions.

Converting solution volume units

The volume unit must match the unit in the concentration before the quantities are multiplied or divided.

One decimetre is ten centimetres, so a cubic decimetre contains $10\times10\times10=1000$ cubic centimetres:

Divide a value in $\mathrm{cm}^{3}$ by 1000 to convert it to $\mathrm{dm}^{3}$:

The result is a quarter of a litre, agreeing with the original 250 cubic centimetres. In the reverse direction, multiply by 1000:

One millilitre equals one cubic centimetre, so a 50 mL sample is $0.050\,\mathrm{dm}^{3}$.

In $m=cV$, a concentration in $\mathrm{g\,dm}^{-3}$ multiplied by volume in $\mathrm{dm}^{3}$ gives mass in grams. Multiplying the same concentration by a number in cubic centimetres without converting gives a value 1000 times too large. The problem is a unit mismatch, not a change in chemistry.

Check the scale before calculating. A 25 $\mathrm{cm}^{3}$ sample is a small fraction of a litre, so its volume in cubic decimetres should be much smaller than 1. Writing $25\,\mathrm{dm}^{3}$ would describe 25 litres.

Calculating solute mass and concentration

Mass concentration lets us scale the mass in one cubic decimetre to the volume actually sampled.

To find the solute mass in $150\,\mathrm{cm}^{3}$ solution at $16.0\,\mathrm{g\,dm}^{-3}$: