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Chemistry - Molecular Quantities

Sample sizes of chemical substances are often measured in moles. One mole of a substance is defined as a sample having 6.022 × 1023 (Avogadro’s number) molecules1. An elemental sample’s mass is equal to its molecular quantity in moles multiplied by the element’s atomic mass in amu (atomic mass units, otherwise known as Daltons). For example, 2.00 moles of naturally-occurring potassium will have a mass of 78.2 grams. The value of Avogadro’s number is not arbitrary – it was chosen to be a direct proportion between an element’s atomic mass value and the mass of a pure monatomic sample of that element, in order to simplify calculations of sample masses based on known composition. Molar quantities make it convenient to relate macroscopic samples of elements and compounds with each other. We know, for instance, that one mole of naturally occurring iron (Fe) atoms will have a mass of 55.8 grams, and that one mole of naturally occurring oxygen (O) atoms will have a mass of 16.0 grams, because the average atomic mass of naturally occurring iron is 55.8 amu, and the average atomic mass of naturally occurring oxygen is 16.0 amu. One mole of naturally occurring oxygen molecules (O2) will have a mass of 32.0 grams, since each molecule is a pair of oxygen atoms at 16 amu each, and “moles” counts the number of discrete entities which in the case of molecular oxygen is the number of O2 molecules rather than the number of O atoms. Applying the same reasoning, one mole of ozone (O3) molecules will have a mass of 48.0 grams.

The same mathematical proportions apply to compounds as they do to elements, since compounds are nothing more than different elements bound together in whole-number ratios, and the Conservation of Mass tells us a molecule cannot have a mass greater or less than the sum total of the constituent elements’ masses. To illustrate this principle, we may calculate the mass of one mole of iron oxide (Fe2O3), the principal component of rust: 55.8×2 + 16.0×3 = 159.6 grams. Likewise, we may calculate the mass of five moles of pure glucose (C6H12O6): 5×(12.01×6 + 1.01×12 + 16.0×6) = 900.0 grams. A convenient sum of the atomic weights of a molecule’s constituent atoms is called the molecular weight. In the case of iron oxide, the molecular weight is 159.6 (typically rounded up to 160). In the case of molecular oxygen (O2), the molecular weight is 32, since each O2 molecule contains two atoms at 16 amu each.

When referring to liquid solutions, the concentration of a solute is often expressed as a molarity, defined as the number of moles of solute per liter of solution. Molarity is usually symbolized by an italicized capital letter M. It is important to bear in mind that the volume used to calculate molarity is that of the total solution (solute plus solvent) and not the solvent alone.

Suppose we had a solution of salt-water, comprised of 33.1 grams of table salt thoroughly mixed with pure water to make a total volume of 1.39 liters. In order to calculate the molarity of this solution, we first need to determine the equivalence between moles of salt and grams of salt. Since table salt is sodium chloride (NaCl), and we know the atomic masses of both sodium (23.0 amu) and chlorine (35.5 amu), we may easily calculate the mass of one mole of salt:

1 mole of NaCl = 23.0 g + 35.5 g = 58.5 g

Another way to state this is to say that sodium chloride (NaCl) has a formula weight of 58.5 amu (58.5 grams of mass per mole).

We may use this equivalence as a unity fraction to help us convert the number of grams of salt per unit volume of solution into a molarity (moles of salt molecules per liter):


 

1Truth be told, a “mole” is 6.022 × 1023 of literally any discrete entities. There is nothing wrong with measuring the amount of eggs in the world using the unit of the mole. Think of “mole” as a really big dozen!


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