Molar Concentration Calculator

Molar Concentration (Molarity)

Molarity is the most common way to express the concentration of a solution in chemistry. It tells you how many moles of solute are dissolved in one liter of solution.

The Formula

M = n / V

Where:

• M = Molarity in mol/L (written as M)
• n = Moles of solute
• V = Volume of solution in liters

Rearranging:

• n = M × V (moles = molarity × volume)
• V = n / M (volume = moles ÷ molarity)

Converting Between Moles and Grams

To find moles from mass, you need the molar mass (molecular weight) of the solute:

n = mass (g) / molar mass (g/mol)

mass = n × molar mass

Common Molar Masses

Standard Solution Concentrations

Preparing a Solution

1. Calculate mass needed: mass = M × V × molar mass
2. Weigh the solute accurately.
3. Dissolve in about 80% of the target volume of solvent.
4. Transfer to a volumetric flask and add solvent to exactly the target volume.
5. Do not dissolve the solute directly at the final volume mark, because the volume shifts as it dissolves.

Worked Example: 250 mL of 0.5 M Sodium Chloride

Say you need 250 mL of 0.5 M NaCl, which is a common benchtop stock.

• Volume in liters: 250 mL ÷ 1000 = 0.25 L
• Moles needed: 0.5 mol/L × 0.25 L = 0.125 mol
• Mass needed: 0.125 mol × 58.44 g/mol = 7.305 g
• As a percentage by weight per volume: 7.305 g ÷ 250 mL × 100 = 2.92% w/v
• Mass per liter, if you would rather think in those terms: 29.22 g/L

Weigh out 7.305 g, dissolve it in roughly 200 mL of water, then top up to the 250 mL mark. Not the other way round. Dissolving salt changes the volume of the water it goes into, so a solution made up to volume after dissolving is the only one that actually lands at 0.5 M.

A useful cross-check while you work: the mass and the molarity move together in a straight line. Half the mass gives half the molarity at the same volume, and double the volume halves the molarity for the same mass. If your answer does not scale that way, one of the three numbers went in wrong.

Safety Note

When diluting concentrated acids, always add acid to water. Never add water to acid.
The dissolution is exothermic, and water poured onto concentrated acid can flash-boil at the surface and spit acid back out of the container.