Making a solution of a set strength comes down to one question: how much solute goes into how much liquid? Enter the target molarity and final volume, and this calculator tells you how many grams to weigh. It can also run the other way, giving the concentration of a solution you have already made or the volume a weighed sample should be made up to.
How to use the molarity calculator
- Under Solve for, choose Molarity, Mass of solute or Solution volume.
- Under Molar mass of the solute from, pick Chemical formula and type it (e.g.
NaOHorCuSO4·5H2O), or pick Known value and enter the molar mass in g/mol, kg/mol or kDa. - Fill in the two remaining quantities: Molarity (c) in M, mM, µM or nM; Mass of solute (m) in g, mg, kg or µg; and Volume of solution (V) in mL, L, µL or m³.
- Pick a unit in Show the result in. The result also lists the moles of solute, the mass concentration in g/L, the percent (w/v), the molar mass used and a short preparation note.
All three inputs must be greater than zero.
Molarity formula
c is the molarity in mol/L (M), n the moles of solute, V the solution volume in liters, m the mass of solute in grams and M its molar mass in g/mol.
Worked example: 250 mL of 0.5 M sodium chloride
Moles needed: n = 0.5 mol/L × 0.250 L = 0.125 mol
Mass to weigh: m = 0.125 mol × 58.440 g/mol = 7.305 g of NaCl
The same solution holds 29.22 g/L, which is 2.922% (w/v).
Other directions work the same way. Dissolving 4.00 g of NaOH (39.997 g/mol) to a final 500 mL gives 0.1000 mol ÷ 0.500 L = 0.200 M. And if you have 10 g of NaCl and want a 0.1 M solution, it must be made up to 1,711 mL.
Hydrate or anhydrous?
Many salts are sold as hydrates, and the water locked in the crystal counts toward what you weigh. Type the formula exactly as printed on the label, including the water. For 100 mL of 0.1 M copper(II) sulfate:
| What you weigh | Molar mass (g/mol) | Mass for 0.010 mol |
|---|---|---|
| CuSO₄·5H₂O (blue crystals) | 249.677 | 2.497 g |
| CuSO₄ (anhydrous, gray-white) | 159.602 | 1.596 g |
Both give 0.010 mol of copper sulfate. Using the anhydrous mass with the pentahydrate would leave you at about 0.064 M instead of 0.1 M. Anhydrous salts that pick up moisture from the air cause the opposite problem, so keep them tightly closed or dry them first.
Preparing the solution accurately
- Weigh the solute and dissolve it in roughly two-thirds to three-quarters of the final volume of solvent.
- Transfer it to a volumetric flask of the right size, rinsing the beaker into the flask a few times so no solute is left behind.
- Let the solution reach room temperature (flasks are usually calibrated at 20 °C), then add solvent until the bottom of the meniscus sits on the mark at eye level.
- Stopper and invert the flask several times to mix.
A graduated cylinder works for rough solutions, but a Class A volumetric flask is far more accurate.
Molarity, molality and percent concentration
| Measure | Definition | Notes |
|---|---|---|
| Molarity (M) | mol solute per L of solution | Changes slightly with temperature |
| Molality (m) | mol solute per kg of solvent | Temperature-independent; not calculated here |
| Percent (w/v) | g solute per 100 mL of solution | Common for clinical and household solutions |
| Mass concentration | g solute per L of solution | Equals mg/mL |
For dilute water solutions, molarity and molality are almost the same number, because a liter of solution contains close to a kilogram of water. At high concentrations they diverge.
Once you have a concentrated stock, the dilution calculator tells you how to make weaker solutions from it. For acids and bases, the pH calculator turns a molarity into a pH.
Frequently asked questions
How many grams of NaCl do I need for 250 mL of a 0.5 M solution?
You need 0.5 mol/L × 0.250 L = 0.125 mol of NaCl. At 58.440 g/mol that is 0.125 × 58.440 = 7.305 g, dissolved and then made up to a final volume of 250 mL.
What is the difference between molarity and molality?
Molarity (M) is moles of solute per liter of finished solution. Molality (m) is moles of solute per kilogram of solvent. Molality does not change with temperature because it uses masses, while molarity shifts slightly as the liquid expands or contracts.
Should I enter the hydrate formula or the anhydrous one?
Enter whatever is actually in the bottle you weigh from. For 100 mL of 0.1 M copper sulfate you need 2.497 g of CuSO4·5H2O but only 1.596 g of anhydrous CuSO4, because the crystals carry five waters per formula unit.
How do I convert molarity to a percent concentration?
Multiply the molarity by the molar mass to get grams per liter, then divide by 10 to get grams per 100 mL (% w/v). A 0.154 M NaCl solution holds 9 g/L, which is 0.9% w/v, the strength of normal saline.
Why do I fill up to the volume instead of adding that much water?
Molarity counts liters of solution, not of solvent. Dissolving a solid changes the volume, so 7.305 g of salt plus 250 mL of water ends up slightly over 250 mL and slightly weaker than 0.5 M.