How to use the dilution and molarity calculator
- Choose what to calculate: any one of V1, C1, V2 or C2 in a dilution, the molarity from a mass, or the mass needed for a target molarity.
- Pick the concentration unit (M, mM, uM or percent) and the volume unit (mL or L). Enter the known values in those units.
- For the mass modes, type the molar mass in g/mol yourself, using the value from your label or reference book. The tool does not look compounds up.
- Turn on the serial dilution table if you want a row of tubes, each diluted by the same factor from the one before.
Formula
C1 x V1 = C2 x V2
Moles = mass (g) / molar mass (g/mol)
Molarity (mol/L) = moles / volume (L)
Mass (g) = molarity x volume (L) x molar mass
A dilution keeps the amount of solute fixed, so concentration times volume is the same before and after. Concentrations just need to share one unit, and volumes another.
Worked example
To make 100 mL of 0.1 M solution from a 1 M stock, V1 = 0.1 x 100 / 1 = 10 mL of stock, with 90 mL of solvent added. The dilution factor is 10.
For molarity, 5.844 g of a solute with a molar mass of 58.44 g/mol is 0.1 mol. Dissolved and brought to 1000 mL, that is 0.1 M. Going the other way, a 0.9% (g per 100 mL) solution in 1 L needs 9 g.
Units and conversions
Conversions are explicit and listed in the steps: 1 L = 1000 mL, 1 M = 1000 mM = 1,000,000 uM and 1 g = 1000 mg. For percent in the mass modes, 1% means 1 g per 100 mL, which is 10 g/L. In a plain dilution, percent can describe any concentration, as long as C1 and C2 use the same basis.
Making a solution to volume
For a target molarity in a given volume, weigh the solute, dissolve it in less liquid than the final volume, then add liquid up to the final mark. That is why the result is a mass for a stated final volume rather than a mass added to a stated amount of solvent. The V2 minus V1 figure in a dilution is the solvent to add, which assumes the volumes simply add.
Serial dilutions
A serial dilution repeats the same dilution factor in a row of tubes. With a factor of 10 and 1 mL tubes, each tube takes 0.1 mL from the previous one plus 0.9 mL of diluent, so the concentration falls tenfold each step. The table shows the concentration, the transfer volume and the diluent volume for every tube.
Not for lab safety decisions
This tool only does arithmetic. It does not know about hazards, purity, hydrates or how a chemical reacts with water, and it cannot replace your lab procedure, a safety data sheet or a qualified person.
Assumptions and limits
- Volumes are assumed to be additive, which is a good approximation for dilute solutions and a poorer one for strong mixtures.
- You enter the molar mass. If your material is a hydrate or is not pure, use the molar mass and purity that apply to it.
- Temperature effects on volume and density are not modeled.
- A solution made to a stated final volume is assumed for the mass modes.
- Results are shown to six significant digits, with larger and smaller numbers in exponent form.
Frequently asked questions
What does C1V1 = C2V2 mean?
C and V are concentration and volume, with 1 for the stock and 2 for the diluted solution. The amount of solute does not change in a dilution, so the two products are equal.
Why is the solvent to add not the same as V2?
V2 is the final volume, which already includes the stock you measure out. Solvent to add is V2 minus V1.
Can C1 be lower than C2?
Not in a real dilution. If it is, the tool still does the arithmetic but warns you that the calculation describes concentrating the solution.
How do I convert molarity to percent?
Multiply molarity by molar mass to get grams per liter, then divide by 10 for grams per 100 mL. The molarity mode shows both.
Why does the tool ask for the molar mass?
Because a reliable value depends on the exact material you have, including any water of hydration. Enter it from your label or reference.