Chemistry for Idiots, Humans and Rebels/Mole Concept/Molarity

Molarity

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In chemistry, molar concentration (also called molarity, amount concentration, or substance concentration) is a measure of the concentration of a solute in a solution, or of any molecular, ionic, or atomic species in a given volume.

Definition - Molar concentration or molarity is most commonly in units of moles of solute per liter of solution. For use in broader applications, it is defined as amount of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase c. The number of moles of a substance is its weight in grams divided by its molecular weight.

The usefulness of defining concentration by moles per liter or molarity is that it defines the number of molecules or ions per liter. So even though substances have different molecular weights the molarity remains the same for all dissolved substances. This would not be the case when concentration is defined in weight per volume such as grams per liter.

The usefulness of this concept of molarity is that one liter of say one molar acid will neutralize one liter of one molar of base when the acid has one proton per molecule and the base one hydroxide per molecule. If the acid is diprotic, say like sulfuric acid then only half as much solution of acid would be needed to neutralize a volume of sodium hydroxide solution. This simplifies the calculation of amounts reacting in chemical reactions.

Units

The SI Units of measurement for molar concentration are mol/m³. However, most chemical literature traditionally uses mol/dm³, or mol dm^-3, which is the same as mol/L. These traditional units are often denoted by a capital letter M (pronounced "molar"), sometimes preceded by an SI prefix, as in:

mol/m³ = 10^-3 mol/dm³ = 10^-3 mol/L = 10^-3 M = 1 mM .

The words "millimolar" and "micromolar" refer to mM and μM (10^-3 mol/L and 10^-6 mol/L), respectively.

Name	Abbreviation	Concentration
Millimolar	mM	10-3 molar
Micromolar	μM	10-6 molar
Nanomolar	nM	10-9 molar
Picomolar	pM	10-12 molar
Femtomolar	fM	10-15 molar
Attomolar	aM	10-18 molar
Zeptomolar	zM	10-21 molar
Yoctomolar	yM	10-24 molar (1 molecule per 1.6 liters)

Examples

Most proteins are present in the bacteria such as E. coli at 60 copies or fewer. The volume of a bacterium is 10⁻¹⁵ L, which gives us c = N/(N_A V) = 10⁻⁷ M = 100 nM. (Here, nM is "nanomolar", i.e. 10^-9 moles per liter).

Consider the preparation of 100 ml of a 2 M solution of NaCl in water. Since the molar mass of NaCl is 58 g/mol, the total mass needed is 2*(58 g)*(100 ml)/(1000 ml) = 11.6 g. Dissolve this in ~80 ml of water, and add water until the total volume reaches 100 ml.

By contrast, consider 11.6 g of NaCl dissolved in 100 ml of water. The density of water is about 1 g/ml, meaning that the final concentration of NaCl by mass will be (11.6 g)/(11.6 g + 100 g) = 10.4 %. The density of such a solution is 1.07 g/ml, and its volume will be (11.6 g + 100 g)/(1.07 g/ml) = 104.3 ml. The molar concentration of NaCl in the solution will therefore be (11.6 g)/(58 g/mol)/(104.3 ml)*1000 = 1.92 M.

Water approximates 1 kilogram (1000 grams) per liter under usual circumstances with a molecular mass of 18.0153. So the concentration of water in pure water is 55.5 molar. Likewise the concentration of hydrogen in solid hydrogen is 88 grams per liter / molecular weight 2.016 = 43.7 molar, and the concentration of osmium tetroxide in osmium tetroxide is 5.1 kilograms per liter / molecular weight 254.23 = 20.1 molar.

Reference ranges for blood tests, sorted by molar concentration.