Express how much solute a solution carries in g/dm3 and in mol/dm3, convert between the two, and work out what dilution does to the figure.
Every amount so far has been a solid on a balance. Half the work at the bench is not like that. The corroded boards go into a bath of dilute acid, and what matters there is not how much acid there is in total but how crowded it is: how much solute, the dissolved substance, sits in each unit of liquid. That is what concentration measures, and it is why two bottles of the same acid can behave completely differently.
The unit of volume for this is the cubic decimetre. A decimetre is 10 cm, so a cubic decimetre is a cube 10 cm along each edge, which holds 1000 cm³. It is the same volume as a litre. To turn a volume in cm³ into dm³, divide by 1000: 250 cm³ is 0.25 dm³, and 50 cm³ is 0.05 dm³. Concentration in mol/dm³ is then the moles of solute divided by the volume of solution in dm³.
Dissolve 0.5 moles of a solute and make the solution up to 2 dm³, meaning add water until the whole solution reads 2 dm³. The concentration is 0.5 / 2 = 0.25 mol/dm³. The relation has three forms, like the mole relation before it. Concentration equals moles divided by volume. Moles equals concentration multiplied by volume. Volume equals moles divided by concentration. The volume in all three is in dm³, never cm³, so convert before you start rather than halfway through.
There is a second way to state a concentration: grams per cubic decimetre, which skips the moles and reports the mass of solute in each dm³. Turning one into the other uses the Mr. To go from mol/dm³ to g/dm³, multiply by the Mr. To go back, divide by it. A solution of sodium hydroxide at 0.5 mol/dm³ has an Mr of 40, so it is 0.5 x 40 = 20 g/dm³. The same solution, two numbers, depending on which unit you were asked for.
To make up a solution, run the relation backwards. For 250 cm³ of 0.1 mol/dm³ sodium hydroxide: 250 cm³ is 0.25 dm³, so moles equals 0.1 x 0.25 = 0.025. Sodium hydroxide has an Mr of 40, so weigh out 0.025 x 40 = 1 g and make it up to 250 cm³. Now dilute it. Add water until the volume is 500 cm³, which is 0.5 dm³. The moles have not changed, because no solute was added or taken away, so the concentration is 0.025 / 0.5 = 0.05 mol/dm³, exactly half.
A cubic decimetre is 1000 cm³, the same volume as a litre, so divide a volume in cm³ by 1000 before anything else. Concentration in mol/dm³ is moles divided by that volume, and the relation rearranges to give moles or volume instead. Multiply by the Mr to reach g/dm³ and divide by it to come back. Adding water leaves the moles alone and only grows the volume, so the concentration falls in step.
Adapted from OpenStax Chemistry 2e (CC-BY 4.0), openstax.org · license
Last week every amount was a solid on a balance. This week the club needs a degreasing bath for the stripped parts: 250 cm³ of sodium hydroxide solution at 0.1 mol/dm³, and somebody has to weigh out the solid.
The concentration is per cubic decimetre, but the bath is 250 cm³. What has to happen first?
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