Concentration Formula

The Formula

M = \frac{n}{V} (moles ÷ liters)

When to use: How 'strong' a solution is—more solute in the same volume = more concentrated.

Quick Example

1 M \text{HCl} = 1 mole of \text{HCl} dissolved in 1 liter of solution.

Notation

M or c denotes molarity. Square brackets [X] denote the molar concentration of species X. Units are \text{mol/L} or equivalently \text{mol}\,\text{dm}^{-3}.

What This Formula Means

The quantity of solute dissolved per unit volume of solution, most commonly expressed as molarity (M) in units of moles per liter (mol/L). Concentration quantifies how much solute is present relative to the total solution volume.

How 'strong' a solution is—more solute in the same volume = more concentrated.

Formal View

Molarity (molar concentration) is defined as c = \frac{n}{V}, where n is the amount of solute in moles and V is the total volume of solution in liters. Units: \text{mol}\,\text{L}^{-1} (equivalently written as M).

Worked Examples

Example 1

easy
Calculate the molarity of a solution made by dissolving 5.85 g of NaCl in water to make 500\,\text{mL} of solution. (NaCl molar mass = 58.44\,\text{g/mol})

Solution

  1. 1
    Moles of NaCl = \frac{5.85}{58.44} = 0.100\,\text{mol}.
  2. 2
    Volume in liters = 500\,\text{mL} = 0.500\,\text{L}.
  3. 3
    Molarity = \frac{n}{V} = \frac{0.100}{0.500} = 0.200\,\text{M}.

Answer

0.200\,\text{M}
Molarity (M) is the most common concentration unit in chemistry. It measures moles of solute per liter of solution, not per liter of solvent.

Example 2

medium
How many grams of KOH are needed to prepare 250\,\text{mL} of a 0.40\,\text{M} solution? (KOH = 56.11\,\text{g/mol})

Example 3

medium
Calculate the molarity of a solution made by dissolving 5.85 g of NaCl (molar mass 58.5 g/mol) in enough water to make 500 mL.

Common Mistakes

  • Using volume of solvent instead of volume of total solution — molarity is moles per liter of solution, which includes the solute
  • Forgetting to convert milliliters to liters before calculating — 250 mL = 0.250 L, not 250 L
  • Confusing molarity (M, mol/L) with molality (m, mol/kg solvent) — they have different denominators and different applications

Why This Formula Matters

Concentration is needed for all solution-based calculations in chemistry. Pharmacists use it to prepare drug dosages, environmental scientists measure pollutant levels in water, and chemists use it in stoichiometry to predict how much product a reaction will yield.

Frequently Asked Questions

What is the Concentration formula?

The quantity of solute dissolved per unit volume of solution, most commonly expressed as molarity (M) in units of moles per liter (mol/L). Concentration quantifies how much solute is present relative to the total solution volume.

How do you use the Concentration formula?

How 'strong' a solution is—more solute in the same volume = more concentrated.

What do the symbols mean in the Concentration formula?

M or c denotes molarity. Square brackets [X] denote the molar concentration of species X. Units are \text{mol/L} or equivalently \text{mol}\,\text{dm}^{-3}.

Why is the Concentration formula important in Chemistry?

Concentration is needed for all solution-based calculations in chemistry. Pharmacists use it to prepare drug dosages, environmental scientists measure pollutant levels in water, and chemists use it in stoichiometry to predict how much product a reaction will yield.

What do students get wrong about Concentration?

Molarity is moles per liter of solution (including the solute), not per liter of pure solvent.

What should I learn before the Concentration formula?

Before studying the Concentration formula, you should understand: mole, solution.

Want the Full Guide?

This formula is covered in depth in our complete guide:

Moles, Molecular Formula, and Concentration Explained →
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