## Concentration, Atomic Weight and Molarity and Avogadro’s Law

The units of measurement of an amount of substance are conveniently reported as concentration which is mass per unit of volume. The unit of volume chosen is usually one appropriate to the expected concentration of the substance or to a volume that makes physiological sense – gram / liter (g/l), millimole / liter (mmol/l), milligram / milliliter (mg/ml).

If we know the concentration of a substance (mass/volume) and we know the total volume of solvent in which the substance (solute) is dissolved (volume), it follows that the total mass of solute is given by
concentration (mass/volume) x total volume = total mass

Similarly, knowing total mass and concentration gives total volume of solvent as
total mass/concentration (mass/volume) = total volume

And, given total mass and total volume provides a result for concentration as
total mass/total volume = concentration

### Atomic weight and molarity

The atomic weight of a substance is an assigned number which allows comparison of the relative masses (weights) of the different elements. By definition, one atom of oxygen is assigned a “weight” of 16, and the atomic weights of the other elements are determined in relation to that of oxygen. In a molecule, i.e., a substance containing two or more different atoms, the molecular weight is equal to the sum of the atomic weights of the individual atoms. For example, the molecular weight of water (H2O) is 18 ([2  x 1]  +  16).

One mole (mol) of any substance is defined as the molecular (or atomic) weight of that substance in grams. Similarly, one millimole (mmol) is equal to one-thousandth of a mole or the molecular (or atomic) weight in milligrams.

The atomic weight of sodium (Na+ ) is 23. Therefore, for Na+,

23 g = 1 mole
23 mg = 1 mmol

23 mg of Nain 1 liter of water = Na+ concentration ([Na+]) of 1 mmol/l.