“THE MOLE”
E-16
NGSS: HS: PS1-7 Use mathematical representations to support the claim that atoms, and therefore
mass, are conserved during a chemical reaction. CC Energy and Matter. SEP Using Mathematical
and Computational Thinking.
Many items we purchase today are conveniently pre-packaged either by count (numbers) or by mass.
Usually the product itself determines which method is used. Bakery rolls, doughnuts, and various fruits can
be purchased in dozens (12). Large food warehouses sell items by count in cases (24) and by the gross
(144). Other items like potatoes, sugar, and flour are usually purchased by mass in 1 lb., 2 lb., 5 lb., and
larger quantities. We don’t want to count out thousands of grains of sugar to make a recipe, so we measure a
larger quantity like a cup. Beverages are usually measured in Liters or gallons.
Chemists are also interested in measured quantities of substances, either by number or by mass. In E-15
Molar Mass, you learned how to calculate the mass of an element or compound by using the atomic mass
units from the Periodic Table. In E-16 you will learn how chemists measure by number using the mole.
A mole can be a number quantity, a unit of mass, or a fixed volume of gas at STP. A mole (mol) is defined
as the number of atoms in exactly 12 g of carbon-12 or Avogadro's number (6.022 X 1023). The molar mass
of a substance is numerically equal to its formula mass in grams. For example, 1 mole of helium gas has a
mass of 4.00 grams. At STP, 1 mole of any gas occupies a volume of 22.4 L. So, if you had four grams of
helium, the balloon would have a volume of 22.4 Liters of the gas and would contain 6.022 x 10 23 atoms.
Thus, each of these measured quantities becomes a useful conversion factor that chemists use when
measuring elements and their atoms and ions; and compounds and their formula units and molecules.
Remember that an ion is simply an atom that has gained or lost electrons, so there is a charge on it.
However, the mass is unaffected because the electrons are so light.
The following chart shows how the mole relates to three different types of measurements:
1. The mass of a substance (element, compound, or ion)
2. The volume of a gas (at STP)
3. The number of atoms, ions, or molecules
Number of
atoms, ions, or
molecules
6.022 x 1023
Mass of
substance
(in grams)
Molar
mass
THE
MOLE
22.4 L
Volume of gas
(in L at STP)
These are the three conversion factors that you must know!
1 mole =
1 mole =
1 mole =
6.022 x 1023 ions, atoms, or molecules
molar mass of an element or compound (from periodic table) in grams
22.4 Liters of any gas at STP
1
If the problem gives you or asks for moles, you will use only one of these conversion factors!
If the problem does not give or ask for moles, you will use two of these conversion factors!
“1 mole” must either be in the numerator or the denominator of every conversion factor!
Steps to solve a problem:
1. Remember that you will always start by writing the information you are given on the far left of the page.
2. Look at the label for the given quantity and find where you are starting on the chart above.
3. Next, decide which direction you need to go to find your answer. For example, if you are starting in
grams you will need to go to moles first.
4. Determine which conversion factor to use (again look at the chart). For example, if you want to go from
grams to moles you must use molar mass. You will need to use the Periodic Table to calculate the molar
mass.
5. Set up the conversion factor so that the unit in the denominator (bottom) is the same as your original
label. Place the desired unit in the numerator (top). So if you want to go from grams to moles, the
molar mass (grams) goes in the denominator and “1 mole” goes in the numerator. * Another hint: if
you are going towards the mole, “1 mole” will be in the numerator; if you are leaving the mole, “1
mole” will be in the denominator (ALWAYS!)
6. If the label in the numerator is the same as what the question wants, then complete the math and write
down the answer with the correct label and circle it. If not, then repeat steps 2-6 to finish the problem.
One-Step Problems:
If the problem gives you or asks for moles, you will use only one conversion factor!
Example 1: Determine the volume of 0.25 moles of He gas at STP.
1.
The given information is written down.
0.25 moles He gas
2.
3.
4.
5.
We are starting in the center of the chart at moles.
We need to find volume, so we need to go to the right.
The conversion factor between moles and volume is “1mole = 22.4 L”.
When we set up the conversion factor, we want moles in the denominator since we are leaving
moles and entering volume. The 22.4 L goes in the numerator since we want volume (which is
measured in liters).
0.25 moles He gas 
6.
22.4 L
1 mol
The label in the numerator is liters, so we are done. To solve we multiply all numbers in the
numerator and divide by all numbers in the denominator. So 0.25 x 22.4 1 = 5.6 L
0.25 moles He gas 
22.4 L
=
1 mol
5.6 L of He gas
Example 2:
How many atoms are contained in 1.24 moles of carbon?
Solution:
1.24 mol of carbon 
6.022  10 23 atoms
1 mol carbon
=
7.47 x 1023 atoms of carbon
2
Example 3:
How many moles in 4.46 x 1023 molecules of water?
Solution:
4.46 x 1023 water molecules 
Example 4:
Find the mass of 2.5 moles of H2SO4.
Solution:
2.50 mol H2SO4 
Example 5:
Determine the number of moles in 212 g of K2CrO4.
Solution:
212 g of K2CrO4 
Example 6:
What volume will 0.572 mol of N2(g) occupy at STP?
Solution:
0.572 mol of N2 (g) 
1 mol water
= 0.741 mol water
6.022 x 10 23 molecules
98.08 g of H 2SO 4
1 mol of H 2SO 4
=
245 g of H2SO4
1 mol of K 2 CrO 4
= 1.09 mol K2CrO4
194.20 g of K 2 CrO 4
22.4 L N 2 (g)
= 12.8 L of N2 (g)
1 mol N 2 (g)
Two-Step Problems:
If the problem does not give or ask for moles, you will use two conversion factors!
Example 1: Determine the mass of 2.0 x 1022 molecules of CO2.
1. The given information is written down.
2.0 x 1022 molecules of CO2
2.
3.
4.
5.
We are starting at the top of the chart at molecules.
We have to go to moles first (since that’s the only way we can move)
The conversion factor between moles and molecules is “1mole = 6.022 x 1023 molecules”.
When we set up the conversion factor, we want “6.022 x 1023 molecules” in the denominator since we
are leaving molecules and entering moles. The “1 mole” goes in the numerator since we want moles
2.0 x 1022 molecules of CO2

1 mol CO2
6.022 x 10 23 molecules
6. The label in the numerator is liters, so we are NOT done. We need to get the mass of the CO 2 and mass
is measured in grams, not moles! So we go back and repeat steps 2-6.
* We are at moles and we need to get to mass (in grams), so we need to go to the left. The molar mass is
the conversion factor we need to use. The molar mass of CO2 is 44.01 g (12.01 + 2 x 16.00). We want
to eliminate the moles label, so “1 mole” is the denominator, and the “44.01 g” is the numerator.
2.0 x 1022 molecules of CO2
*

1 mol CO2
44.01 g
=

23
6.022 x 10 molecules 1 mol CO2
1.5 g of CO2
The last label in the numerator is grams, so we are done. To solve we multiply all numbers in the
numerator and divide by all numbers in the denominator.
3
Example 2:
How many molecules are in 1.3 L of H2 gas at STP?
Solution:
1 mol H 2 6.022 x 10 23 molecules
1.3 L H2 (g) 
= 3.5 x 1022 molecules of H2 (g)

22.4 L H 2
1 mol H 2
Example 3:
How many liters would 3.75 g of He (g) occupy at STP?
Solution:
3.75 g He (g) 
Example 4:
What is the mass of 2.45 x 1024 molecules of H2O?
Solution:
2.45 x 1024 H2O molecules 
1 mol of He 22.4 L He (g)

1 mol He (g)
4.00 g He
=
21.0 L He (g)
1 mol H 2 O
18.02 g of H 2O
= 73.3 g H2O
´
23
1 mol of H 2O
6.022 x 10 molecules
PRACTICE PROBLEMS
**If the measurement is in mg or mL, you have to change to grams or Liters first. Recall that the prefix
“milli” stands for 1000, so 1 g = 1000 mg and 1 L = 1000 mL.
One Step Problems:
1.
Determine the mass for each of the following quantities:
a.
3.0 mol Na
c.
0.25 mol MgCl2
b.
2.50 mol Ca+2
d.
8.50 mol CaCO3
2.
Determine the volume of each of the following quantities at STP:
a.
4.00 mol Br2 (g)
c.
6.53 x 10-4 mol Ne (g)
b.
0.23 mol CO2 (g)
d.
2.54 x 10-3 mol Xe (g)
3.
Determine the number of atoms, molecules, or ions for each of the following quantities:
a.
0.500 mol Mg+2
c.
1.25 mol Br2 (g)
b.
5.65 mol Na+
d.
0.541 mol CO2 (g)
4.
Determine the number of moles for each of the following quantities:
a.
200. g of F2
g.
1.505 X 1023 ions of Na+
b.
500. g of NaOH
h.
3.011 X 1023 molecules of NaOH
+1
c.
25 g of Li
i.
6.50 L of SO2(g)
d.
32 g of SO2
j.
50.0 L of H2(g)
e.
6.022 X 1023 atoms of Na
k.
2500. mL of O2(g)
f.
1.204 X 1023 molecules of CO2
l.
1000. mL of N2(g)
Two-Step Problems:
5.
Determine the mass in each of the following:
a.
50.0 L of H2(g) at STP
b.
6.50 L of SO2(g) at STP
c.
1000. mL of N2(g) at STP
d.
2500. mL of O2(g) at STP
e.
f.
g.
h.
6.022
3.011
1.204
1.505
X
X
X
X
1023 atoms of Na
1023 molecules of NaOH
1023 molecules of CO2
1023 ions of Na+
4
6.
Determine the volume of each of the following quantities at STP:
a.
200. g of H2S (g)
e.
3.0 X 1023 atoms of He (g)
b.
3.00 g of SO2 (g)
f.
1.50 X 102 atoms of Ne (g)
c.
300. mg of Cl2 (g)
g.
1.2 X 1020 molecules of CO2
d.
155 mg of Ne (g)
h.
1.50 X 1022 molecules of NO
7.
Determine the number of atoms, molecules, or ions for each of the following quantities:
a.
200. g of H2S (g)
e.
350.0 L of H2(g) at STP
b.
3.00 g of SO2 (g)
f.
6.50 L of SO2(g) at STP
c.
300. mg of Cl2 (g)
g.
1000. mL of N2(g) at STP
d.
155 mg of Ne (g)
h.
2500. mL of O2(g) at STP
5
A Gallimaufry of E-16 Problems
1.
Find the mass of 2.50 mol Na.
2.
Find the mass of 1.0 X 1024 molecules of NaOH.
3.
Determine the number of molecules in 5.50 g H2O.
4.
Determine the mass at STP of 2.25 L of NO2 (g)
5.
Find the mass of 0.052 mol CaCO3
6.
Determine the number of moles of 5.68 g of NaOH
7.
Determine the volume at STP of 0.75 mol of Br2 (g)
8.
Determine the number of moles of 20.50 g of F2
9.
Find the mass of 8.95 mol Ca+2.
10.
Determine the number of moles at STP in 200. L of O2 (g)
11.
Determine the volume at STP of 800. g of Cl2(g)
12.
Determine the number of ions in 0.700 mol Mg+2.
13.
Find the mass of 2.0 x 1023 atoms of Na.
14.
Determine the number of moles at STP in 6.0 L of SO2 (g)
15.
Determine the number of atoms in 25 g of Na.
16.
Find the mass of 1.00 x 1024 ions of Na+
17.
Determine the number of moles at STP in 0.500 L of H2 (g)
18.
Determine the mass at STP of 10. L of SO3 (g)
19.
Determine the number of moles at STP in 1500. L of N2 (g)
20.
Determine the number of molecules in 34. g H2S.
21.
Determine the mass at STP of 16.0 L of CH4(g)
22.
Determine the number of moles of 13.5 g of Li+1
23.
Determine the mass at STP of 2000. L of Cl2 (g)
24.
Determine the number of moles of 64 g of SO2.
25.
Determine the volume at STP of 100. g of H2S(g)
26.
Find the mass of 1.2 x 1023 molecules of CO2
27.
Determine the volume at STP of 32.00 g of SO2(g)
28.
Find the mass of 0.25 mol of CaCl2.
6
A Gallimaufry of E-16 Problems
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Find the mass of 2.50 mol Na.
Find the mass of 1.0 X 1024 molecules of NaOH.
Determine the number of molecules in 5.50 g H2O.
Determine the mass at STP of 2.25 L of NO2 (g)
Find the mass of 0.052 mol CaCO3
Determine the number of moles of 5.68 g of NaOH
Determine the volume at STP of 0.75 mol of Br2 (g)
Determine the number of moles of 20.50 g of F2
Find the mass of 8.95 mol Ca+2.
Determine the number of moles at STP in 200. L of O2 (g)
Determine the volume at STP of 800. g of Cl2(g)
Determine the number of ions in 0.700 mol Mg+2.
Find the mass of 2.0 x 1023 atoms of Na.
Determine the number of moles at STP in 6.0 L of SO2 (g)
Determine the number of atoms in 25 g of Na.
Find the mass of 1.00 x 1024 ions of Na+
Determine the number of moles at STP in 0.500 L of H2 (g)
Determine the mass at STP of 10. L of SO3 (g)
Determine the number of moles at STP in 1500. L of N2 (g)
Determine the number of molecules in 34. g H2S.
Determine the mass at STP of 16.0 L of CH4 (g)
Determine the number of moles of 13.5 g of Li+1
Determine the mass at STP of 2000. L of Cl2 (g)
Determine the number of moles of 64 g of SO2.
Determine the volume at STP of 100. g of H2S (g)
Find the mass of 1.2 x 1023 molecules of CO2
Determine the volume at STP of 32.00 g of SO2 (g)
Find the mass of 0.25 mol of CaCl2
57.5 g
66 g
1.84 x1023 molecules
4.62 g
5.2 g
0.142 mol
17 L
0.5395 mol
359 g
8.93 mol
254 L
4.22 x 1023 ions
7.6 g
0.27 mol
6.5 x 1023 atoms
38.2 g
0.0223 mol
36 g
66.96 mol
6.0 x 1023 molecules
11.5 g
1.95 mol
6,330. g
1.0 mol
65.7 L
8.8 g
11.19 L
28 g
7