Molarity, properly called amount concentration, is the amount of solute per volume of solution. Its unit is mol/L, written M. It is the most common way to express concentration in biochemistry, because it counts molecules rather than grams.
The definition
c = n / V
Here c is concentration in mol/L, n is amount of solute in moles and V is the volume of the final solution in litres. Note that V is the volume of solution, not the volume of solvent added. For dilute solutions the difference is small. For concentrated stocks it is not.
Bringing in mass
Since n = m / M, the definition becomes the working formula the calculator uses:
m = c × V × M
Any one term can be solved from the other two, given the molar mass:
- Mass to weigh:
m = c × V × M - Volume to make up to:
V = m / (c × M) - Concentration achieved:
c = m / (V × M)
Worked example 1: mass for 10 mL of 1 mM
GHK, M = 340.38 g/mol. c = 1 mM = 0.001 mol/L and V = 10 mL = 0.010 L.
m = 0.001 × 0.010 × 340.38 = 0.003404 g = 3.404 mg.
Worked example 2: concentration from what you weighed
You weighed 2.1 mg and made it up to 5 mL. c = 0.0021 g ÷ (0.005 L × 340.38 g/mol) = 0.001234 mol/L = 1.234 mM.
Molar prefixes
| Unit | mol/L | Same as |
|---|---|---|
M |
1 |
mol/L, mmol/mL |
mM |
10−3 |
mmol/L, µmol/mL |
µM |
10−6 |
µmol/L, nmol/mL |
nM |
10−9 |
nmol/L, pmol/mL |
Making the solution match the calculation
- Make up to volume. Dissolve the solid in less than the final volume, then add solvent to the mark in a volumetric flask. For small volumes in a vial, adding the calculated volume of solvent directly is usually acceptable for dilute solutions.
- Correct for purity. If the material is not 100% of the compound, the weighed mass contains less solute than you think. The stock solution calculator applies a purity or net-content correction.
- Weigh enough. A typical analytical balance reads to 0.1 mg, so weighing 0.5 mg already carries a large relative uncertainty. Weigh a larger amount into a larger volume, then dilute.
Molarity versus molality
Molality (mol/kg of solvent) is a different quantity that does not change with temperature. For dilute aqueous solutions at room temperature the numbers are close, but they are not interchangeable in precise work.