The unit your reagent bottles are labeled in

Molarity is the concentration unit you encounter every time you reach for a stock solution. It tells you how many moles of solute are dissolved per liter of finished solution:

M = moles of solute / liters of solution

A 1.00 M NaCl solution contains 1.00 mol of NaCl in 1.00 L of total solution — solute plus solvent, dissolved together to the line on a volumetric flask. The volume is the finished volume, not the volume of water you started with. That distinction is the single biggest source of bench-prep errors, and it shows up in every titration, every kinetics run, every cell-culture media recipe you will ever follow.

The four-step method

Inventory what you have. You need two of: moles of solute, volume of solution, molarity. If the solute is given in grams, you will convert with its molar mass first.
Get units in line. Grams ÷ molar mass = moles. Milliliters ÷ 1000 = liters.
Apply M = n/V. Solve for whichever variable is unknown.
Report with units. Always write “mol/L” or “M” — without it, a number is just a number.

Worked example 1: molarity from moles and volume

Dissolve 0.500 mol KCl into enough water to make 2.00 L of solution.

M = 0.500 mol ÷ 2.00 L = 0.250 M

Worked example 2: molarity from grams

Dissolve 11.7 g NaCl in enough water to make 500.0 mL of solution.

M(NaCl) = 22.990 + 35.453 = 58.443 g/mol
moles = 11.7 ÷ 58.443 = 0.2002 mol
volume = 500.0 mL ÷ 1000 = 0.5000 L
M = 0.2002 ÷ 0.5000 = 0.400 M

This is also the math behind physiological saline: 0.9% NaCl by mass, which works out to roughly 0.154 M.

Worked example 3: moles from molarity

How many moles of HCl in 250.0 mL of 0.100 M HCl?

n = M × V = 0.100 mol/L × 0.2500 L = 0.0250 mol

That’s the basis of every HCl titration — multiply your dispensed volume by the molarity to get moles, then use stoichiometry from there.

Worked example 4: volume from molarity

What volume of 6.00 M H₂SO₄ contains 0.300 mol of H₂SO₄?

V = n ÷ M = 0.300 ÷ 6.00 = 0.0500 L = 50.0 mL

Worked example 5: preparing 250 mL of 0.500 M NaOH

This is the everyday bench problem.

moles needed = 0.500 × 0.250 = 0.125 mol
M(NaOH) = 22.990 + 15.999 + 1.008 = 39.997 g/mol
mass = 0.125 × 39.997 = 5.00 g

Weigh 5.00 g NaOH on a balance. Dissolve in maybe 200 mL of water in a beaker (with stirring — NaOH dissolution is exothermic, the beaker gets warm). Transfer quantitatively to a 250 mL volumetric flask. Add water to the line. Cap, invert several times to mix. Now you have 0.500 M NaOH.

The reason for the volumetric flask: 5.00 g of NaOH dissolved in 250 mL of water gives a total volume slightly greater than 250 mL. The line on the volumetric flask gives you exactly 250.0 mL of finished solution.

Where bench prep goes wrong

Volume of solvent vs. volume of solution. Adding 5.00 g NaOH to a graduated cylinder that already contains 250 mL of water gives you a solution somewhat more concentrated than 0.500 M, because the final volume exceeds 250 mL. Use a volumetric flask for any prep where concentration accuracy matters.
Forgetting the mL → L conversion. A 250 mL volume entered as “250” instead of “0.250” gives a molarity 1000× too low.
Grams where moles belong. The numerator of M is moles. If you skip the grams-to-moles step, your answer is in g/L, not mol/L — close cousins, but not the same number.
Confusing M with m. Molarity (M, mol/L solution) and molality (m, mol/kg solvent) are different quantities. Lab work generally uses M; colligative-property problems use m.
Assuming density = 1. Concentrated reagents like 18 M H₂SO₄ are denser than water by a substantial margin. One liter of 18 M H₂SO₄ does not weigh 1000 g — closer to 1840 g.

Where molarity shows up after the prep

Titrations. Knowing the molarity of your titrant lets you back-calculate the moles of analyte from the dispensed volume at the equivalence point.
Solution-phase kinetics. Rate laws are typically expressed in mol/L of each reactant.
Cell biology and biochemistry. Buffer recipes, enzyme kinetics, and DNA quantitation all hinge on accurate molarities.

Use the Molarity Calculator to solve for concentration, moles, or volume — it shows the step-by-step work alongside the answer.

How to Calculate Molarity