Lecture 8

Atoms, Molecules, Moles, Molar Mass

A. The Mole Defined

In everyday life, we use terms like "pair," "dozen," or "ream" to refer to a specific number of items (a ream is 500).

In Chemistry, we could always just specify the number of atoms or molecules that are needed for some purpose. This would be cumbersome, because atoms and molecules are so small that the numbers needed are unimaginably huge. So we need to define a unit that is convenient for specifying a sensible number of atoms or molecules. That unit is the mole.

The Mole: Definition. The mole is defined as the mass of a substance that contains the same number of particles as there are atoms in exactly 12 grams of carbon-12.

Measurements show that there are exactly 6.022 x 10²³ carbon atoms in 12 grams of carbon-12. Thus one mole of carbon-12 has a mass of exactly 12 g, as this is the mass that contains 6.022 x 10²³ carbon-12 atoms.

Just as the number "12" is called a dozen, the number 6.022 x 10²³ is called Avogadro's number.

 

B. Application of the Mole to Chemical Reactions

Consider the reaction between sodium and chlorine to produce sodium chloride,

2 Na + Cl₂ ---> 2 NaCl.

The equation tells us that two atoms of sodium react with one molecule of chlorine to give two formula units of sodium chloride (the term "formula unit" is used instead of "molecule" when we refer to ionic compounds). We can scale these quantities by any number we choose; for convenience we'll do a scale-up by 6.022 x 10²³. And, since 6.022 x 10²³ is the number of particles in one mole, we can convert these unwieldy numbers to moles.

C. Relating Moles to Mass

To continue with the sodium chloride example: what would be the mass of 2 moles of NaCl? If we wanted to make 2 moles of NaCl, what masses of Na and Cl₂ would be required?

Recall that the atomic weights (masses) of individual atoms are expressed in terms of their masses relative to an atom of carbon-12 having a mass of exactly 12 amu. Let's determine the mass of a mole of sodium-23 atoms.

One sodium-23 atom has a mass 1.9158 times the mass of a carbon-12 atom (as determined by mass spectroscopy). Thus, one mole of sodium-23 atoms will have a mass 1.9158 times the mass of a mole of carbon-12 atoms, or

12.000 g x 1.9158 = 22.990 g/mol Na-23 atoms

Similarly, one beryllium-9 atom has a mass only 0.75102 times as much as the mass of a carbon-12 atom. Thus one mole of beryllium-9 atoms will have a mass 0.7510 times as much as the mass of a mole of carbon-12 atoms, or

12.000 g x 0.75102 = 9.0122 g/mol Be-9 atoms

The mass in grams of 6.022 x 10²³ atoms of an element is called the molar mass of that element. For elements, the molar mass is an amount in grams that is numerically equal to the atomic weight of the element.

 

D. Formula Weights and Molar Masses of Molecules and Ionic Compounds

• Cl₂ is a molecule that is made up of two chlorine atoms. Chlorine has an atomic weight of 35.45. A mole of Cl₂ molecules would contain two moles of chlorine atoms, each mole weighing 35.45 g. Thus the mass needed to obtain Avogadro's number of Cl₂ molecules is equal to 70.90 g. The molar mass of Cl₂ is 70.90 g/mol.
  
• NaCl is an ionic compound. Sodium has an atomic weight of 22.990, and chlorine an atomic weight of 35.45. A mole of NaCl contains a mole of sodium ions and a mole of chloride ions. Since a mole of sodium has a mass of 22.990 g and a mole of chlorine has a mass of 35.45 g, the molar mass of NaCl is 58.44 g/mol.
  
• P₄S₃ is a molecular compound. Phosphorus has an atomic weight of 30.97, and sulfur has an atomic weight of 32.07. A mole of P₄S₃ contains four moles of phosphorus atoms and three moles of sulfur atoms. Thus its molar mass is
  4 mol P (30.97 g P/mol P) + 3 mol S (32.07 g S/mol S) = 220.09 g P₄S₃ /mol P₄S₃

E. Calculations Involving the Molar Mass

• How many moles of P₄S₃ are there in 0.125 g of P₄S₃?
  (0.125 g P₄S₃) x (1 mol P₄S₃ /220.09 g P₄S₃)
  = 5.68 x 10^-4 mol P₄S₃
• What mass of P is needed to prepare 2.00 moles of P₄S₃?
  (2.00 mol P₄S₃) x (4 mol P/ mol P₄S₃) x (30.97 g P /mol P)
  = 247.8 g P needed

F. Calculating Percent Composition From the Molar Mass

Let's calculate the percentage of P in P₄S₃. We know from Section D that there are 4 moles of P in one mole of P₄S₃. Now one mole of P has a mass of 30.97 g, and one mole of P₄S₃ has a mass of 220.09 g. So the % P in P₄S₃ is:

 

This page is http://chemiris.labs.brocku.ca/~chemweb/courses/chem180/CHEM1P80_Lecture_8.html
Last modified October 3, 2000 by M. F. Richardson
© Brock University, 2000