Molarity Calculator

What molarity counts

Molarity counts particles, not grams. One mole of a substance holds 6.02214076 times 10 to the 23rd formula units, the Avogadro constant fixed by the 2019 revision of the SI, so a mole of sodium chloride and a mole of glucose contain the same number of formula units but weigh different amounts. Molarity puts that count over a volume: moles of solute per liter of solution.

The volume is the volume of the finished solution, not the water you started with. Dissolve 5.844 g of salt in a little water and then top the flask to 500 mL, and the solution is 0.200 M. Add the same salt to 500 mL of water and the volume grows slightly past 500 mL, so the molarity lands a hair below 0.200 M. For dilute solutions the gap is small; for concentrated ones it is not.

The wording has an official quirk. NIST's guide to the SI notes that the term molarity and the symbol M are obsolete and recommends amount-of-substance concentration in mol/L. Labs still say molarity, and reagent bottles still print M, so this page uses both while keeping the unit mol/L in every calculation.

The three steps behind the answer

Every molarity problem runs on the same three relations. Moles equal mass divided by molar mass. Molarity equals moles divided by liters of solution, the definition given in OpenStax Chemistry. Rearranged, the mass needed for a target equals molarity times volume in liters times molar mass. The molar mass comes from the formula, with atomic weights added up; PubChem lists sodium chloride at 58.44 g/mol and calcium chloride at 110.98 g/mol.

Take 5.844 g of sodium chloride in a 500 mL flask. The molar mass is 58.44 g/mol, so 5.844 / 58.44 = 0.1000 mol. The volume is 0.500 L, so 0.1000 / 0.500 = 0.200 mol/L. That is 0.200 M, and it is also 100.0 mmol in the flask and 11.69 g of salt per liter.

The same three steps run in any order. If a procedure asks for 250 mL of 0.200 M sodium chloride, the mass is 0.200 x 0.250 x 58.44 = 2.922 g. If it asks how much of a 2.0 M stock makes 250 mL of 0.5 M solution, the volume relation takes over, covered below. The arithmetic is never the hard part; keeping track of which volume and which molar mass belongs to which substance is.

Saline, glucose and other everyday solutions

Medical and kitchen strengths are usually written as a percentage, which hides the molarity. Normal saline is 0.9 percent weight by volume, meaning 9 g of sodium chloride per liter. Divide by 58.44 and the molarity is 9 / 58.44 = 0.154 M, which is why IV saline is described as about 154 mM sodium. Five percent dextrose is 50 g of glucose per liter, and with a molar mass of 180.16 g/mol that comes to 0.278 M.

Those numbers are worth reading twice because they show how a small mass change moves the concentration. Half strength saline is 4.5 g/L against 9 g/L, so the molarity halves from 0.154 M to 0.077 M. A nurse or a lab tech who mixes 9 g into 2 L instead of 1 L gets exactly that, which is correct for half strength and wrong for normal saline.

Household solutions follow the same math with messier numbers. A cleaning mix labeled 1 percent sodium hypochlorite holds 10 g of active ingredient per liter, but the molar mass of sodium hypochlorite is 74.44 g/mol, so the molarity is about 0.134 M. The label talks in percent because that is what shoppers understand; the chemistry talks in moles because that is what reacts.

Working backwards from a target concentration

Most lab work starts with the target, not the starting mass. To make 250 mL of 0.200 M sodium chloride, multiply 0.200 mol/L by 0.250 L to get 0.0500 mol, then multiply by 58.44 g/mol to get 0.200 x 0.250 x 58.44 = 2.922 g. Weigh that, dissolve it, and top up to 250 mL in a volumetric flask.

Weighing is where the precision of the answer is decided. A kitchen scale that resolves 1 g turns the 2.922 g target into 3 g, a 2.7 percent error that becomes a 0.205 M solution instead of 0.200 M. A balance that resolves 0.001 g keeps the error under 0.1 percent. Analytical balances go to 0.0001 g, which matters when the target mass is a few milligrams.

The molar mass has to match the bottle in front of you. Calcium chloride comes anhydrous at 110.98 g/mol and as a dihydrate at 147.01 g/mol, and the two need different masses for the same molarity. The label states which one you have; the formula on the front is not enough. With hydrates, the water of crystallization is part of the mass you weigh, so ignoring it makes the solution weaker than intended.

Diluting a stock solution

Dilution keeps the number of moles constant while the volume grows, which gives the relation C1 times V1 equals C2 times V2. To make 250 mL of 0.5 M solution from a 2.0 M stock, solve for V1: 0.5 times 250 divided by 2.0 equals 62.5 mL. Measure 62.5 mL of stock into a 250 mL volumetric flask, then add water to the mark.

Note what the procedure does not say: add 187.5 mL of water. Volumes do not always add, because mixing a salt solution with water can contract or expand slightly, and the final volume is what defines the molarity. Bring the flask to the 250 mL line and the concentration is right regardless of how much water that took. The dilution factor here is 2.0 divided by 0.5, which is 4, so the final solution is one quarter as concentrated as the stock.

Serial dilutions multiply the factors. A tenfold dilution followed by another tenfold dilution gives a hundredfold total, and each step should be made in its own volumetric flask rather than by pipetting tiny volumes into a big one. A 1 to 100 dilution made in a single step needs 2.5 mL of stock in 250 mL, which is easy to measure badly; two 1 to 10 steps need 25 mL then 25 mL, which is easy to measure well. The error in a dilution is dominated by the smallest volume in the chain.

Molarity, molality and mass percent

Three concentration units show up on the same reagent bottle, and they answer different questions. Molarity is moles per liter of solution and changes when the solution warms up, because the volume expands while the moles stay put. Molality is moles per kilogram of solvent and does not change with temperature, which is why colligative properties like boiling point elevation use it. Mass percent is grams of solute per 100 g of solution and ignores moles entirely.

A 0.200 M sodium chloride solution carries 0.200 x 58.44 = 11.69 g of salt per liter, which is 1.17 percent weight by volume. In dilute solutions the molality sits close to the molarity because a liter of water weighs about 1 kg, so 0.200 M is roughly 0.20 mol/kg. The gap opens as the solution gets denser: seawater at 3.5 percent salt has a molarity near 0.60 M but a molality near 0.62 mol/kg, and a saturated brine diverges further.

Temperature drift is small but real. Water expands by roughly 0.02 percent per degree Celsius near room temperature, so a solution made at 20 C and used at 30 C is about 0.2 percent less concentrated by volume. That is below the precision of most teaching labs and above the tolerance of a calibration standard, which is why certified reference materials state the temperature at which their molarity holds.

Where the numbers go wrong

The first mistake is a factor of 1,000. A 500 mL flask holds 0.500 L, not 500 L, and forgetting the conversion turns 0.2 M into 0.0002 M. The same slip appears in reverse when a procedure says 250 mL and the calculation uses 250 L. Write the unit next to every number until the habit sticks.

The second is the wrong molar mass. Anhydrous copper sulfate is 159.61 g/mol and the pentahydrate is 249.69 g/mol, a ratio of 1.56. Weighing the pentahydrate while calculating with the anhydrous value gives a solution 56 percent too strong, and the error is silent until an assay comes back wrong. Check the formula on the bottle, including any water of crystallization, and use the matching number.

The third is purity. A bottle labeled 97 percent calcium chloride contains 3 g of something else per 100 g, so the effective mass is 0.97 times what the balance reads. For teaching work the difference rarely matters; for a standard solution it does, and the certificate of analysis states the assay you should use. The fourth is confusing M with m: capital M is molarity, lower case m is molality, and the two agree only in dilute aqueous solutions.

Finally, volume additivity. Mixing 50 mL of ethanol with 50 mL of water gives about 96 mL, not 100 mL, because the molecules pack differently. Any calculation that treats the solvent volume plus the solute volume as the final volume will be off, and the error grows with concentration. Use a volumetric flask, fill to the mark, and let the glass define the volume.