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The Mole Concept and Avogadro's Number

The Chemist's Dozen

Suppose we are interested in carrying out the following chemical reaction.

2 Na(s) + Cl2(g) ==> 2 NaCl(s)

We can see from the equation that we need two atoms of sodium for each molecule of chlorine. How can we determine the quantity of sodiun needed to react with a given amount of chlorine?  What we need is a means of counting atoms, molecules, ions etc. The difficulty is the small size of the units we wish to count and the enormous numbers involved.  Therefore we must have an indirect way of counting atoms, molecules etc.  We do this through a unit called the mole.  The mole (mol) is defined as an amount of substance that contains as many elementary units as there are atoms in exactly 12 g of the carbon-12 isotope.  The actual number of elementary units in a mole is called Avogadro's number, NA, named for Amedeo Avogadro, who was the the first grasp the significance of this number.  The mole is the SI base unit for the amount of a substance.  The numerical value of Avogadro's number must be determined experimentally.  Recent measurements put the value of Avogadro's number at 6.0221367 x 1023. 

The molar mass of a substance is the mass of one mole of the substance.  Carbon-12 has a molar mass of exactly 12 g/mol, by definition.   So through the concept of the mole and molar mass we can indirectly count elementary units by weighing.  The two defining equations for the mole (which should be commited to memory) are given below.

number of moles of substance = mass of substance / molar mass of substance

number of moles of substance = number of elementary units of substance / NA

Example

Suppose we want to know how many molecules are in 0.0500 g of water (about one drop).  The molar mass of water to 3 significant figures is 18.0 g/mol. The number of moles would be obtained using the first equation above.

mol H2O = 0.0500 g H2O / 18.0 g  H2O/mol  H2O = 0.00278 mol  H2O

Next we convert this to molecules of  H2O by using the second equation above.

molecules of  H2O = mol  H2O x 6.02 x 1023 molecules   H2O / mol  H2O   = 1.67 x 1021  molecules of  H2O







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