Molarity Calculator

About the Molarity Calculator

Molarity is the most common way chemists describe the concentration of a solution: the number of moles of solute dissolved in each litre of solution, written mol/L or M. A 1 M solution of sodium chloride contains one mole — 58.44 g — of salt in every litre. Recipes for buffers, reagents and standard solutions are nearly always written in molarity, so turning them into grams to weigh out is an everyday job in any laboratory.

This molarity calculator works in three directions. It finds the molarity of a solution from the mass of solute and the volume, the mass of solute you need for a target molarity and volume, or the volume of solution a given mass will make. The molar mass comes straight from a chemical formula, or you can enter it directly.

How to Use the Molarity Calculator

Choose Find molarity, Find mass needed or Find volume.

Enter the solute formula, such as NaCl, or enter its molar mass directly.

Enter the two known values: the mass in grams, the molarity in mol/L, or the volume.

Choose mL or L for the volume.

The Formula

  moles    = mass ÷ molar mass
  molarity = moles ÷ volume in litres

  mass needed = molarity × volume (L) × molar mass
  volume      = mass ÷ (molar mass × molarity)

Step-by-Step Examples

Molarity of 5.844 g of NaCl in 500 mL.

  molar mass  58.44 g/mol
  moles       5.844 ÷ 58.44 = 0.1 mol
  molarity    0.1 ÷ 0.5 L = 0.2 mol/L (200 mM)

Mass of NaCl for 1 L of 0.5 M.

  0.5 mol/L × 1 L × 58.44 g/mol = 29.22 g

Mass of NaOH for 250 mL of 2 M.

  2 mol/L × 0.25 L × 40.00 g/mol = 20 g

Volume from 18.02 g of glucose at 0.1 M. Glucose is 180.156 g/mol, so 18.02 g is 0.1 mol, which makes 1 L (1,000 mL) at 0.1 M.

Making a Solution Accurately

1. Calculate the mass of solute and weigh it on a balance.
2. Dissolve it in less solvent than the final volume — roughly two-thirds — in a

beaker.

1. Transfer the solution to a volumetric flask, rinsing the beaker into the flask.
2. Add solvent up to the calibration mark, with the bottom of the meniscus on the line.
3. Stopper and invert the flask several times to mix.

Adding the solute to the full volume of solvent instead gives a slightly larger total volume and a slightly lower concentration, because the dissolved solute takes up space.

Concentration Units

  1 M       = 1 mol/L
  1 mM      = 0.001 mol/L        (millimolar)
  1 µM      = 0.000001 mol/L     (micromolar)
  g/L       = molarity × molar mass

A 0.2 M sodium chloride solution contains 0.2 × 58.44 = 11.69 g of salt per litre. Biology and medicine often use millimolar and micromolar concentrations, because many substances act at very low levels.

Molarity, Molality and Percent Solutions

Molarity is moles per litre of solution. Molality is moles per kilogram of solvent; because it does not depend on volume, it does not change as temperature changes the liquid's volume, which makes it useful in precise physical chemistry. Percent solutions — such as 0.9 percent saline, 0.9 g per 100 mL — are common in medicine and everyday use. For dilute water solutions, molarity and molality are almost the same number.

Hydrates and Purity

Many solids are sold as hydrates, which carry water in their crystals. Copper sulfate is commonly supplied as the pentahydrate, CuSO4·5H2O, at 249.68 g/mol rather than 159.60 g/mol for the anhydrous form. Using the wrong molar mass gives a solution about 36 percent weaker or 56 percent stronger than intended. Check the label, and enter the full hydrate formula. For reagents that are less than 100 percent pure, divide the mass needed by the purity as a fraction.

Molarity in Reactions and Titrations

Molarity makes reaction calculations straightforward, because multiplying a molarity by a volume in litres gives moles directly. In a titration, a solution of known molarity is added from a burette until a reaction is complete. If 25.0 mL of sodium hydroxide solution needs 20.0 mL of 0.100 M hydrochloric acid to neutralise it, the acid supplied 0.100 × 0.0200 = 0.00200 mol of hydrogen ions. Because the two react one to one, the sodium hydroxide also contained 0.00200 mol, and its concentration was 0.00200 ÷ 0.0250 = 0.0800 M. The same approach, using the ratios in a balanced equation, works for any reaction between solutions, and it is the basis of much quantitative analysis in chemistry, food science and medicine.

Storing and Labelling Solutions

Solutions change over time. Water can evaporate, making them stronger; some solutes absorb carbon dioxide from the air or react slowly with the container. Label each solution with its name, molarity, date of preparation and your initials, keep it capped, and store it as its safety data sheet recommends. Standard solutions used for accurate work are often checked against a primary standard before use, rather than trusted from the day they were made.

Understanding Your Result

The headline is the molarity, mass or volume you asked for.

The solution line restates the mass, molar mass, moles, volume and molarity together.

The other units line gives the concentration in millimolar and grams per litre.

The making it up line explains how to prepare the solution accurately.

When Should You Use This Calculator?

Use it to prepare solutions and buffers in the lab.

Use it for chemistry homework on concentration.

Use it to convert between grams per litre and molarity.

Common Mistakes

Using millilitres as litres. 500 mL is 0.5 L.

Using the anhydrous molar mass for a hydrate. Enter the formula on the label.

Filling to the volume with solvent before dissolving. Make up to the mark at the end.

Confusing molarity with molality. One is per litre of solution, the other per kilogram of solvent.