Molarity and Dilution Calculator
Calculate molarity, mass needed, dilution volumes and serial dilution series, with the distinction between molarity and molality and the volume-change caveat made explicit.
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Molarity is per litre of solution, not of solvent
A one molar solution contains one mole of solute in a total volume of one litre, which is not the same as one mole dissolved in one litre of water. Dissolving something changes the volume, sometimes substantially, so adding a mole to a litre of water gives more than a litre of solution and therefore less than one molar. This is why solutions are made up to a mark in a volumetric flask rather than by adding a measured volume of solvent.
Molarity changes with temperature and molality does not
Volume expands when warmed, so the same solution is less concentrated in molarity terms at 40 degrees than at 20. Molality, moles per kilogram of solvent, uses mass instead and is therefore temperature independent. For most laboratory work at room temperature the difference is small enough to ignore, and it matters for precise work and for the colligative property calculations that depend on it.
Serial dilution multiplies the errors
Each step in a serial dilution carries the error of the previous one, so a one percent pipetting error compounds across five steps into roughly five percent at the end. A single large dilution has one error rather than five and is more accurate when it is practical. Serial dilution is used because a single step to a very low concentration would need an impractically small volume or an impractically large flask, not because it is more precise.
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Frequently Asked Questions
What is the difference between molarity and molality?
Molarity is moles per litre of solution and molality is moles per kilogram of solvent. Molarity changes with temperature because volume expands; molality does not, which is why precise work and colligative property calculations use it.
Why make up to a mark rather than adding a litre of water?
Because dissolving changes the volume. A mole added to a litre of water gives more than a litre of solution and therefore less than one molar. The mark on a volumetric flask defines the total volume, which is what molarity is based on.
What is the dilution equation?
The number of moles does not change on dilution, so the initial concentration times the initial volume equals the final concentration times the final volume. Any three of the four values determine the fourth.
When should I use serial dilution?
When a single step would need an impractically small volume or an impractically large flask. It is less accurate than one step, since each stage carries forward the error of the last, so use it because it is practical rather than because it is better.
Does the calculation account for volume changes on mixing?
No. Adding solute or mixing solutions can change the total volume slightly, and the dilution equation assumes volumes add. The error is small for dilute aqueous solutions and can be significant for concentrated ones, particularly acids.
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How to Use
Choose what to solve for and enter the values you know.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.