Molar concentration: definition
The molar concentration C (in mol/L or mol·L⁻¹) of a solute in a solution is the amount of solute n (in moles) divided by the volume V of the solution (in litres):
C = n / V
equivalently: n = C × V
Unit: 1 mol/L = 1 M (molar). In biology you will also see mmol/L (millimolar, mM).
Important: V is the volume of the final solution, not the volume of solvent added.
Preparing a solution from a solid
Procedure (direct dissolution): 1. Calculate the mass m to weigh: m = n × M = C × V × M (M = molar mass in g/mol). 2. Weigh the mass on an analytical balance. 3. Dissolve in a beaker with a small volume of distilled water, then transfer quantitatively into a volumetric flask of volume V. 4. Fill with distilled water up to the graduation mark (read at the meniscus). 5. Stopper and invert the flask several times to homogenize.
Example: prepare 250 mL of NaCl solution at C = 0.100 mol/L. - M(NaCl) = 23.0 + 35.5 = 58.5 g/mol - n = 0.100 × 0.250 = 0.0250 mol - m = 0.0250 × 58.5 = 1.46 g → weigh 1.46 g of NaCl
Mass concentration and mass fraction
The mass concentration Cm (in g/L) is Cm = m / V. Its relation to C is:
C = Cm / M
The mass fraction w (dimensionless, often given as %) is the mass of solute over total solution mass: w = m(solute) / m(solution). Converting w to C:
C = (w × ρ) / M
where ρ is the solution density (in g/L). These formulas apply to commercial solutions (concentrated sulfuric acid, hydrogen peroxide, etc.) whose labels give w and ρ.
Concentration and amount: guided exercise
You have a volume V₁ = 50.0 mL of sulfuric acid solution at C₁ = 0.500 mol/L.
How many moles of H₂SO₄ are in this volume?
n = C × V = 0.500 × 0.0500 = 0.0250 mol
If you pipette out 10.0 mL, how many moles of H₂SO₄ does the aliquot contain?
n = 0.500 × 0.0100 = 5.00 × 10⁻³ mol = 5.00 mmol
The concentration does not change when you take an aliquot, but the amount of substance decreases proportionally to the volume taken.