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WHY?
To keep track of the huge numbers of atoms and molecules in samples that are large enough to
see, chemists have established a unit of counting called the mole (abbreviated mol) and a unit of
measure called the molar mass , which has units of g/mol. By using the idea of a mole and molar
mass , you will be able to count out specific numbers of atoms or molecules simply by weighing
them. This capability is necessary in understanding chemical reaction equations, conducting
research in chemistry and biology, and applying chemistry in technology and the health sciences.
LEARNING OBJECTIVES
- Understand the relationship between the mole and Avogadro’s number
- Understand the meaning of the molar mass of a substance
- Recognize that the molar mass is an average of all the isotopic masses of an element
S UCCESS CRITERIA
- Quickly convert between the number of atoms, moles, and the mass of a sample by using
Avogadro’s number and the molar mass appropriately
- Calculate the molar mass from isotopic abundances and isotopic masses
P REREQUISITES
- Activity 01-2: Unit Analysis
- Activity 01-3: Signifi cant Figures in Measurements and Calculations
- Activity 02-1: Atoms, Isotopes, and Ions
MODEL 1: A MOLE IS A COUNTING UNIT
1 pair of objects = 2 objects
1 dozen objects = 12 objects
1 gross of objects = 144 objects
1 mole of objects = 6.02214 × 10 23 objects
Mole and Molar Mass
ACTIVITY 03-
40 Chapter 3: Molecules and Compounds
Foundations of Chemistry
K EY QUESTIONS
1. How many pencils are there in a dozen pencils? 12
2. How many pencils are there in a gross of pencils? 144
3. How many pencils are there in a mole of pencils? 6.02214 × 10 23
4. How many atoms are there in a dozen atoms? 12
5. How many atoms are there in a gross of atoms? 144
6. How many atoms are there in a mole of atoms? 6.02214 × 10 23
7. In what way are the meanings of the terms pair , dozen , gross , and mole similar?
They all refer to a number of objects and are used to group objects to make counting them easier.
In what way are the meanings different?
The numbers they represent differ. A mole is a much larger number because it is typically used to count very small objects.
INFORMATION
The number of objects in a mole (6.02214 × 10^23 ) is so important in chemistry that is given a name.
It is called Avogadro’s number , which has units of objects /mol.
Avogadro’s number is determined by the number of carbon atoms in exactly 12 g of pure carbon-12.
The molar mass is the mass of a mole of objects. It has units of g/mol.
1 amu = 1.66054 × 10-24^ g
E XERCISES
1. A single carbon-12 atom has a mass of 12 amu by definition of the atomic mass unit. Convert 12
amu to grams, and then calculate the mass in grams of a mole of carbon-12 atoms.
-24 - -23 23
12 amu (1.66054 10 g / amu) = 1.99265 10 g / atom (1.99265 10 g / atom) (6.02214 10 / mol) = 12.0000 g / mol
2. A single oxygen-16 atom has a mass of 15.9949 amu. Convert this mass to grams, and then calculate
the mass in grams of a mole of oxygen-16 atoms.
-24 -
-23 23
15.9949 amu (1.66054 10 g / amu) = 2.65602 10 g / atom
(2.65602 10 g / atom) (6.02214 10 / mol) = 15.9949 g / mol
3. Based on your results for Exercises 1 and 2, identify the relationship between the numerical values
of the mass of an atom in amu and the molar mass in g/mol.
They are numerically the same because the conversion factor from amu to g is just the inverse of Avogadro’s number!
42 Chapter 3: Molecules and Compounds
Foundations of Chemistry
E XERCISES
4. Using your calculation of the molar mass of beads as a guide, show how to determine the molar
mass of boron from the data given in Table 2.2 below. Remember, molar mass has units of g/mol
and 1 amu = 1.66054 × 10–^24 g.
Isotope
Atomic Mass (amu)
Percent Abundance
boron-10 10.0129 19.78%
boron-11 11.0093 80.22%
Table 2
The average atomic mass requires calculating weighted average of the masses. Average atomic mass = 0.1978 (10.0129 amu) + 0.8022 (11.0093 amu) Average atomic mass = 10.812 amu The molar mass (in g/mol) will be the same number as the average atomic mass (in u), as noted in Exercise 3, so the molar mass of boron is 10.812 g/mol.
5. Compare the number you calculated for the molar mass of boron in Exercise 4 with the number
given below the symbol for boron in the Periodic Table. From this comparison, identify the
information that is provided by the numbers just below the atomic symbols in the Periodic Table.
The numbers are the same. All the numbers on the Periodic Table are average atomic masses in amu or the molar masses in g/mol. The other number given in the Periodic Table is the atomic number, which is the number of protons in the atom.
6. Calculate the number of atoms in exactly 2 moles of helium.
2 mol × (6.02214 × 10 23 /mol) = 12.04428 × 10 23
7. Calculate the number of moles corresponding to 2.007 × 10^23 atoms of helium.
23 23
= 0.3333 mol 6.02214 10
8. Calculate the mass in grams of 2.5 moles of argon. The molar mass of argon is 39.95 g/mol.
2.5 mol Ar × 39.95 g/mol Ar = 99.875 g Ar = 100 g Ar
Note 1: The units in the answer can be derived by carrying out the arithmetic operations on the units.
Note 2: The number of significant figures reported in the answer is derived from the number of significant figures in the numbers being multiplied. The two figure precision for moles of Ar limits the answer to two significant figures (1.0 × 10 2 )
9. Calculate the number of moles in 75 g of iron. The molar mass of iron is 55.85 g/mol.
1 mol Fe 75 g Fe ( ) 1.3 mol Fe 55.85 g Fe
Activity 03-3 Mole and Molar Mass 43
10. Calculate the number of atoms in 0.25 moles of uranium.
0.25 mol × (6.02214 × 10 23 /mol) = 1.5 × 10^23
11. Calculate the mass of 12.04 × 10^23 atoms of uranium. The molar mass of uranium is 238.0 g/mol.
23 23
= 238.0 g / mol = 475.8 g 6.02214 10
GOT IT!
1. Identify the statement below that is correct and explain why it is correct:
a) The molar mass of an element divided by Avogadro’s number gives the average mass of an
atom of that element in grams.
b) The molar mass of an element divided by Avogadro’s number gives the mass of one atom of
that element in grams.
a is correct because the molar mass is the mass of a sample consisting of all the natural isotopes of an element so dividing the molar mass by number of atoms in a mole gives the average mass of an atom.
b is not correct because atoms of different isotopes in a natural sample have different masses.
2. If you have 1 g samples of several different elements, will the sample with the largest or smallest
molar mass contain the fewest atoms? Explain.
If the atoms are heavy, i.e. have a large molar mass, then few of them will be needed to add up to 1 g. So the sample with the largest molar mass will contain the fewest atoms.
Mathematically 1g / molar mass = a small number of moles if the molar mass is large.
Note: If students have trouble thinking about this situation, ask them which will have fewer particles, a pound of sand or a pound of coarsely crushed rock.
3. Write the units that result from the following mathematical operations.
a) number of objects / Avogadro’s number = mol
b) moles × Avogadro’s number = gives the number of objects, no units
c) mass / molar mass = mol
d) moles × molar mass = g
