--- title: "Concentration of Solutions in Moles per Cubic Decimetre" description: "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." canonical: https://lightmysky.com/learn/science/concentration-of-solutions-in-moles-per-cubic-decimetre-mt_vRK78ynnXb source: https://lightmysky.com/learn/science/concentration-of-solutions-in-moles-per-cubic-decimetre-mt_vRK78ynnXb.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Concentration of Solutions in Moles per Cubic Decimetre 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. Subject: Science · Area: Matter & Materials · Ages 15 to 16 Page: https://lightmysky.com/learn/science/concentration-of-solutions-in-moles-per-cubic-decimetre-mt_vRK78ynnXb ## Ready when they can - Converts a volume in cubic centimetres to cubic decimetres and calculates a concentration - Converts between grams per cubic decimetre and moles per cubic decimetre using the formula mass - Works out what mass to weigh out to make a stated volume of a stated concentration - Predicts the new concentration after adding a measured volume of water ## Lesson: Concentration of solutions in moles per cubic decimetre 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. *(drawing: Divide by 1000 to go from cm³ to dm³. Nearly every mistake in this stop is a volume left in the wrong unit.)* **Example.** 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. *(drawing: Multiply by the Mr going one way and divide by it coming back. The solution in the bottle has not changed.)* **Example.** 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. **Recap.** 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](https://creativecommons.org/licenses/by/4.0/) ## Practice 24 questions on this page, each with its working shown. ## Needs first - [Reacting Masses, Limiting Reactants and Yield](https://lightmysky.com/learn/science/reacting-masses-limiting-reactants-and-yield-mt_C2K6kp5Chv) - [Dissolving & Solutions](https://lightmysky.com/learn/science/dissolving-and-solutions-mt_Mf-T-fYRLX) ## Opens up - [Why Some Things Dissolve and Others Do Not](https://lightmysky.com/learn/science/why-some-things-dissolve-and-others-do-not-mt__njIrlqqqL) - [Titration: Finding an Unknown Concentration](https://lightmysky.com/learn/science/titration-finding-an-unknown-concentration-mt_7WLN35XxYx) - [Gas Volumes and the Ideal Gas Equation](https://lightmysky.com/learn/science/gas-volumes-and-the-ideal-gas-equation-mt_I1fz_6wjuD) - [Solubility Equilibria and When a Precipitate Appears](https://lightmysky.com/learn/science/solubility-equilibria-and-when-a-precipitate-appears-mt_IMdWLxIAFt) - [Rates of Reaction: Collision Theory and What Changes a Rate](https://lightmysky.com/learn/science/rates-of-reaction-collision-theory-and-what-changes-a-rate-mt_Ma2bOotr9g)