The Mole and Conversion
My Goals for this Lesson:

Describe the mole and its use as a unit of measure in chemistry.

Use Avogadro’s number and atomic mass values to complete mathematical conversions.
I’m preparing to describe and use moles for calculations with atomic mass and conversions.
Fill in the blanks using the lesson page.
When you buy small items, like eggs, at the store, you may buy them by the
. The word dozen
the number 12, no matter what type of item is being counted. You can use the word dozen
to refer to anything, and you are not just limited to one dozen.
You can have:
half a dozen kids at the park
two dozen paper clips per package
3.5 dozen cookies in a batch
No matter what is being counted, the word dozen is a counting unit that always
the
number 12. When scientists deal with atoms, they deal with such large numbers that it would take more
than a lifetime for a person to count them and that would be if they could even see the individual atoms.
The Mole
Because samples of matter contain so many atoms, scientists use a counting unit called the mole (mol).
The word mole
a number, just like the word dozen
difference is that a mole
The number of
the number 12. The only
a much larger number than a dozen.
in a mole has been experimentally determined in a variety of ways. A device
called a mass spectrometer, which can count atoms precisely, was used to determine the number as
6.02214 × 1023 (we will round this to 6.022 × 1023). This number was named
honor the Italian scientist Amedeo
number to
(1776–1856) whose ideas were crucial in the early
understanding of chemistry.
Why use the mole (6.022 × 1023)?
Many properties and relationships in chemistry depend on the number of
in a sample, not
just on the mass of a sample.
Atoms and molecules are too small to count
without specialized equipment.
Knowing a relationship between the mass and
number of
of each type of atom allows us to determine the
in a sample by converting from mass to mole.
Molar Mass
Molar mass is the
, in grams, of
of ANY substance. Because of the way a mole is
determined, the mass value given for each element on the periodic table
both the
average atomic mass (in u/atom) and the molar mass (in g/mol) of the element.
Do you remember, in the introduction to this lesson, how Mike determined the number of crackers and
cookies per package by measuring their mass? Just as these equivalencies allowed him to convert
between the mass and the amount of crackers and cookies, molar mass does the same for atoms. Molar
mass is an important
in chemistry because it is much easier to measure the mass
of a sample of atoms than it is to count the atoms individually.
The molar mass of sulfur is given on the periodic table as 32.065. This means that a one
mole sample of pure sulfur has a mass of 32.065 grams.
This gives you a conversion factor that can be used two different ways in calculations.
32.065 g S/ 1 mol S OR 1 mol S/ 32.065 g S
Using the information here from the periodic table and the lesson interactive, write the
two possible conversion factors you could use in a conversion below:
OR
Be sure to always include the unit AND substance labeling in your conversion factors.
Conversions
For a pure substance, molar mass values from the periodic table can be used to convert from grams to
moles.
Given mass (in grams) × 1 mole of substance/ molar mass (in grams) of substance = number of moles of
substance
Or it can be used to convert from moles to grams:
Given number of moles × molar mass (in grams) of the substance/1 mole of substance = mass (in grams)
of substance
Example One
Problem: If the molar mass of carbon is 12.01 grams per mole, what is the mass of 2.35 moles of carbon?
Step One: What are you looking for?
In this question, the given information is 2.35 moles of carbon and 12.01 g/mol C. The final answer needs
to be mass, in the unit grams.
Step Two: What do you already know?
You know that when you are given the number of moles of an element and asked to convert to grams, you
can multiply by the molar mass. This means that you will use molar mass as a conversion with molar mass
in the numerator and one mole in the denominator. Mass = molar mass (g)/ 1 mole
1 mole of carbon has a mass of 12.01 g
1 mole C/ 12.01 g C OR 12.01 g C/ 1 mole C
Step Three: Where does the information go?
Set up the problem, starting with the given information.
2.35 mol C ×
Add the conversion factor that cancels moles leaving mass (in grams).
2.35 mol C × 12.01 g C/ 1 mol C
This setup allows the unit moles to cancel out, because they are diagonal from each other in the
dimensional analysis setup, leaving mass (in grams).
Step Four: Solve it!
Multiply the top numbers and divide by the bottom numbers.
2.35 mol C × 12.01 g C ÷ 1 mol C = 28.2 g C
Don't forget to include the unit and substance labeling in your answer.
Example Two
Problem: How many moles of potassium (K) are in a sample of twenty seven point eight grams K?
Step One: What are you looking for?
In this question, the given information is 27.8 grams of potassium and you will need to look on the
periodic table for the molar mass of potassium (K). The unit for the final answer will be moles.
Step Two: What do you already know?
When you are given the mass and asked to convert to moles, flip the molar mass fraction so that one
mole of potassium is in the numerator, and the molar mass from the periodic table will be in the
denominator.
The molar mass of potassium on the periodic table is 39.098 grams per mole.
39.098 g K/ 1 mol K OR 1 mol K/39.098 g K
Step Three: Where does the information go?
Set up the problem, starting with the given information from the word problem.
27.8 g K ×
Add the conversion factor that cancels mass (in grams) leaving moles.
27.8 g K × 1 mol K/39.098 g K
This setup allows the unit grams of the given information to cancel with the unit grams in the molar mass
conversion fraction leaving mol K.
Step Four: Solve it!
Multiply the top numbers and divide by the bottom numbers.
27.8 g K × 1 mol K ÷ 39.098 g K = 0.711 mol K
Notice that the final answer gets the unit (moles) as well as a symbol (K) to represent the substance
potassium.
More Practice
Combine what you have learned about Avogadro’s number and molar mass to solve the following two-step
conversions. Refer to the periodic table for the molar masses of each element.
Problem One: If a sample of magnesium (Mg) atoms has a mass of 36.8 g, how many atoms are in
the sample?
1) What are you looking for?
_____________________________
2) What do you already know?
_____________________________
Give the two molar mass conversion factors for the mass of magnesium using the value from the
periodic table in your course.
OR
Give the two conversion factors for the mole and Avogadro’s number.
OR
Be sure to always include the unit AND substance labeling in your conversion factors.
3) Where does the information go?
Set up the problem, starting with the given information from the word problem.
X
Add the conversion factor that cancels mass (in grams) leaving moles.
X
Add the conversion factor that cancels moles leaving # of particles (atoms Mg).
X
X
This setup allows the unit grams from the given information to cancel with the unit grams in the
molar mass conversion fraction leaving moles then using the Avogadro’s number conversion factor
to cancel the moles and leave the number of Mg atoms.
4) Solve it!
Multiply the top numbers and divide by the bottom numbers.
atoms Mg
Problem Two: What would be the mass of 3.24 × 1025 atoms of oxygen (O)?
1) What are you looking for?
_____________________________
2) What do you already know?
_____________________________
Give the two conversion factors for the mole and Avogadro’s number.
OR
Give the two molar mass conversion factors for the mass of oxygen using the value from the
periodic table in your course.
OR
Be sure to always include the unit AND substance labeling in your conversion factors.
3) Where does the information go?
Set up the problem, starting with the given information from the word problem.
X
Add the conversion factor that cancels # of particles (atoms O) leaving the moles O.
X
Add the conversion factor that cancels moles O leaving the mass of O in grams.
X
X
This setup allows the # of atoms from the given information to cancel with the # atoms in the
Avogadro’s number conversion fraction leaving moles then canceling the moles from the molar
mass conversion factor and leave the mass of oxygen in grams.
4) Solve it!
Multiply the top numbers and divide by the bottom numbers.
gO
Problem Three: How many atoms would be in a sample of 53.1 grams of pure copper (Cu)?
1) What are you looking for?
_____________________________
2) What do you already know?
_____________________________
Give the two molar mass conversion factors for the mass of copper using the value from the
periodic table in your course.
OR
Give the two conversion factors for the mole and Avogadro’s number.
OR
Be sure to always include the unit AND substance labeling in your conversion factors.
3) Where does the information go?
Set up the problem, starting with the given information from the word problem.
X
Add the conversion factor that cancels mass of copper (in grams) leaving the moles copper.
X
Add the conversion factor that cancels moles Cu leaving the number of Cu atoms.
X
X
This setup allows the unit grams from the given information to cancel with the unit grams in the
molar mass conversion fraction leaving moles then using the Avogadro’s number conversion factor
to cancel the moles and leave the number of Cu atoms.
4) Solve it!
Multiply the top numbers and divide by the bottom numbers.
atoms Cu
Problem Four: If a sample of neon (Ne) contains 1.01 × 1022 atoms, what is its mass?
1) What are you looking for?
_____________________________
2) What do you already know?
_____________________________
Give the two conversion factors for the mole and Avogadro’s number.
OR
Give the two molar mass conversion factors for the mass of neon using the value from the
periodic table in your course.
OR
Be sure to always include the unit AND substance labeling in your conversion factors.
3) Where does the information go?
Set up the problem, starting with the given information from the word problem.
X
Add the conversion factor that cancels # of particles (atoms Ne) leaving the moles Ne.
X
Add the conversion factor that cancels moles Ne leaving the mass of Ne in grams.
X
X
This setup allows the # of atoms from the given information to cancel with the # atoms in the
Avogadro’s number conversion fraction leaving moles then canceling the moles from the molar
mass conversion factor and leave the mass of neon in grams.
4) Solve it!
Multiply the top numbers and divide by the bottom numbers.
g Ne
Be sure to do the “Let’s Practice” interactive AND the practice sheet of problems found on the Activity
page of the lesson.