Chemistry · General chemistry I · Concept

Molarity and dilution calculations

Molarity, M, is the number of moles of solute per liter of solution: M = n/V. Diluting a solution adds solvent but no solute, so the moles of solute stay the same and M₁V₁ = M₂V₂.

What molarity measures

Molarity is the amount of solute, in moles, in each liter of the whole solution. A 0.400 M NaCl solution holds 0.400 mol of NaCl in every liter. The volume is that of the finished solution, not of the water you started with.

M = \frac{n_{solute}}{V_{solution}}

Making a solution

Weigh the solute, dissolve it in less water than you need, then add water up to the mark of a volumetric flask. Dissolving the solute in exactly 500 mL of water would not give exactly 500 mL of solution, so the concentration would be off.

Molarity as a conversion factor

A molarity links volume and amount: 0.150 M means 0.150 mol in every 1 L. Multiply a volume in liters by the molarity to get moles, or divide an amount in moles by the molarity to get the volume that holds it.

n = M V

Dilution keeps the solute

Adding solvent spreads the same moles of solute through a larger volume, so the product of molarity and volume stays the same. Use the same volume unit on both sides; milliliters are fine, because the unit cancels.

M_{1} V_{1} = M_{2} V_{2}

Ions in solution

A soluble ionic compound separates into its ions, so each ion’s concentration depends on the formula. 0.10 M CaCl₂ contains 0.10 M Ca²⁺ and 0.20 M Cl⁻, because each formula unit releases two chloride ions.

Common mistakes

Dividing by the volume of solvent instead of the volume of the solution.
Leaving the volume in milliliters when molarity needs liters.
Using M₁V₁ = M₂V₂ for a reaction: it describes dilution only, where no solute is used up.
Forgetting that one formula unit can release more than one ion, as CaCl₂ releases two Cl⁻.

Key terms

Molarity: Moles of solute per liter of solution (mol/L, or M). The volume is that of the whole finished solution, not just the solvent you started with.
Solution: A homogeneous mixture of two or more substances, in which a solute is dispersed as molecules or ions throughout a solvent.
Solute: The substance that is dissolved, usually the smaller part of a solution, such as the salt in salt water. A concentration tells you how much solute is in a given amount of solution or solvent.
Solvent: The substance that does the dissolving, usually the larger part of a solution, such as water. Molality uses the solvent’s mass, not the whole solution’s.
Dilution: Lowering a solution’s concentration by adding solvent. The amount of solute stays the same, so M₁V₁ = M₂V₂.
Stock solution: A concentrated solution kept on hand to make more dilute ones. The volume of stock you measure out sets how much solute goes into the new solution.

Work through an example

11.7 g of NaCl is dissolved in water to make 500.0 mL of solution. What is the molarity of the solution?

Find the molarity of a solution →

Dilute a stock solution →

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