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Concentration
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 Na+ in 1 liter of water = Na+ concentration ([Na+]) of 1 mmol/l.
Avogadro’s Law
Avogadro’s Law states that 1 mole of any non-dissociable substance (a substance than cannot be further reduced to component units) contains the same number of particles (approximately 6.02 x 1023 = Avogadro’s number).
Thus, 1 mmol of Na+ contains the same number of atoms as 1 mmol of Cl- even though the former weighs 23 mg and the latter weighs 35.5 mg. However, 1 mmol of NaCl (58.5 mg) largely dissociates into Na+ and Cl- ions and therefore contains almost twice as many particles.
The concentration of uncharged molecules, e.g., glucose and urea, also can be measured in millimoles per liter and this is commonly the case where the Systeme International (SI units) is used. However, elsewhere, they are more commonly measured in the clinical laboratory as milligrams per deciliter (mg/dl or mg%). The molecular weight (mol wt) of glucose is 180. Consequently, a glucose concentration of 180 mg/l (or 18 mg/dl) is equal to 1 mmol/l. To convert from milligrams per deciliter to millimoles per liter, the following formula can be used:
mmol/l = (mg/dl x 10) ÷ mol wt)
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