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Conserved-Solute Concentration & Volume

Solve the concentration-volume balance for a fixed amount of solute before and after a volume change.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

An aliquot of 0.1 L at 2 M contains 0.2 mol. At a final volume of 1 L, its concentration is 0.2 M.

Initial concentration × initial volume = final concentration × final volume

Worked example

Enter these known values and leave the other values blank.

Initial amount concentration
2 M
Initial solution aliquot volume
0.1 L
Final solution volume
1 L
Final amount concentration
0.2 M

Assumptions and limitations

  • All values are positive. The amount and chemical identity of the tracked solute are conserved, with no loss or reaction.
  • For dilution by adding solvent, final concentration cannot exceed initial concentration. The same balance also describes concentration by solvent removal if solute is retained.
  • Final solution volume is not necessarily initial volume plus added solvent volume. Metric spoons here are explicitly 15 mL and 5 mL; US and imperial volume units are distinct.

Common questions

Why is there no solvent-volume result?

This balance uses measured initial and final solution volumes. Their difference equals added solvent volume only when volume additivity is a suitable approximation.

Can this solve for the stock aliquot?

Yes. Supply stock concentration, desired final concentration and final solution volume; leave initial volume blank.

References

Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition. The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume.

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