Molarity

Molarity is the most common way to express the concentration of a solution in chemistry. It is defined as moles of solute per liter of solution, with units of mol/L (often abbreviated M). A 1 M solution contains 1 mole of solute dissolved in enough solvent to make exactly 1 liter of solution. Molarity is the workhorse unit for stoichiometry, titration calculations, and most quantitative chemistry. Master molarity and you can convert between mass, moles, and volume in any solution problem.

The Formula

$$ \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} $$

$$ M = \frac{n}{V} $$

Notice the denominator is the volume of the FINAL solution, not the volume of solvent added. This distinction matters — adding 100 g of NaCl to 1 L of water yields more than 1 L of solution because the dissolved ions take up space. To prepare a 1 M solution precisely, you dissolve the solute in some water, then dilute up to the 1 L mark in a volumetric flask.

Worked Examples

Example 1. Calculate the molarity of a solution made by dissolving 58.5 g of NaCl in enough water to make 0.500 L of solution.

NaCl molar mass = 58.5 g/mol, so 58.5 g = 1.00 mol. Molarity = 1.00 mol / 0.500 L = 2.00 M.

Example 2. How much solute is needed to make 250 mL of 0.10 M glucose solution? Glucose molar mass = 180.16 g/mol.

Moles needed = 0.10 mol/L × 0.250 L = 0.025 mol. Mass = 0.025 mol × 180.16 g/mol = 4.50 g.

Example 3. What volume of 6.0 M HCl gives 0.30 mol of HCl?

Volume = moles / molarity = 0.30 mol / 6.0 mol/L = 0.050 L = 50 mL.

Dilution

When a stock solution is diluted with more solvent, the number of moles of solute stays constant while the volume increases. The dilution equation:

$$ M_1 V_1 = M_2 V_2 $$

where subscripts 1 and 2 refer to before and after dilution. To prepare a less concentrated solution from a stock, measure out the volume \( V_1 \) of stock needed and dilute up to the desired final volume \( V_2 \).

Example. To make 500 mL of 0.20 M NaOH from 2.0 M stock: \( V_1 = (0.20)(500)/2.0 = 50 \) mL. Measure 50 mL of stock solution, then dilute up to 500 mL total.

Molarity vs Other Concentration Units

Unit	Definition	When used
Molarity (M)	moles solute / liters solution	Default for most chemistry; varies with temperature (volume changes)
Molality (m)	moles solute / kg solvent	Used when temperature changes are important (mass is temperature-invariant)
Mass %	(mass solute / mass solution) × 100	Industrial and food applications
Mole fraction	moles solute / total moles	Vapor-pressure calculations, gas mixtures
Parts per million (ppm)	(mass solute / mass solution) × 10⁶	Very dilute solutions, environmental chemistry
Normality (N)	equivalents solute / liters solution	Acid-base and redox titrations; now mostly replaced by molarity

Using Molarity in Stoichiometry

Molarity is the link between volume and moles in solution stoichiometry. For a reaction in solution:

• Convert solution volume × molarity → moles of solute.
• Use the balanced equation’s mole ratio → moles of other species.
• Convert moles → mass, or → volume of another solution (if also given a molarity).

Example. What volume of 0.150 M AgNO₃ is needed to precipitate all the chloride from 25.0 mL of 0.100 M NaCl? Reaction: \( \text{AgNO}_3 + \text{NaCl} \to \text{AgCl} + \text{NaNO}_3 \) (1:1 mole ratio). Moles NaCl = 0.0250 × 0.100 = 0.00250 mol. Moles AgNO₃ needed = 0.00250 mol (1:1). Volume = 0.00250 / 0.150 = 0.0167 L = 16.7 mL.

Related study notes: Mole Concept, Avogadro’s Number, Stoichiometry, Titration.

Frequently Asked Questions