Unit 5.2 Moles – Molar Mass
Is there an easier way? When the weather is nice,
many people begin to work on their yards and homes.
For many projects, sand is needed as a foundation
for a walk or to add to other materials. You could
order up twenty million grains of sand and have
people really stare at you. You could order by the
pound, but that takes a lot of time weighing out. The
best bet is to order by the yard, meaning a cubic
yard. The loader can scoop up what you need and put
it directly in your truck. Very quick, very easy, and
everybody knows what you mean.
Avogadro’s Number
It certainly is easy to count bananas or to count elephants (as long as you stay out of their way).
However, you would be counting grains of sugar from your sugar canister for a long, long time. Atoms and
molecules are extremely small – far, far smaller than grains of sugar. Counting atoms or molecules is not
only unwise, it is absolutely impossible. One drop of water contains about 1 x 1022 molecules of water. If
you counted 10 molecules every second for 50 years without stopping you would have counted only
1.6 × 1010 molecules. Put another way, at that counting rate, it would take you over 30 trillion years to
count the water molecules in one tiny drop.
Chemists needed a name that can stand for a very large number of items. Amedeo Avogadro (1776 1856), an Italian scientist, provided just such a number. He is responsible for the counting unit of
measure called the mole. A mole (mol) is the amount of a substance that contains
23
6.02 × 10
representative particles of that substance. The mole is the SI unit for amount of a
substance. Just like the dozen and the gross (12 dozen), it is a name that stands for a number. There
23
are therefore 6.02 × 10
23
be 6.02 × 10
water molecules in a mole of water molecules. There also would
bananas in a mole of bananas, if such a huge number of bananas ever existed.
23
The number 6.02 × 10
is called Avogadro’s number, the number of
representative particles in a mole. It is an experimentally determined
number. A representative particle is the smallest unit in which a substance
naturally exists. For the majority of elements, the representative particle
is the atom. Iron, carbon, and helium consist of iron atoms, carbon atoms,
and helium atoms, respectively. Seven elements exist in nature as diatomic
molecules and they are H2, N2, O2, F2, Cl2, Br2, and I2. The representative
particle for these elements is the molecule, consisting or 2 atoms of the
element.
Likewise, all molecular compounds such as H2O and CO2 exist as molecules and so the molecule is their
representative particle. For ionic compounds such as NaCl and Ca(NO 3)2, the representative particle is
23
the formula unit. A mole of any substance contains Avogadro’s number (6.02 × 10 ) of representative
particles. Particles of the mole could be atoms, molecules, protons, electrons, ions, etc.
The animal mole is very different
from the counting unit of the
mole. Chemists nonetheless have
adopted the mole as their
unofficial mascot. National Mole
Day is a celebration of chemistry
that occurs on October 23
(10/23) of every year.
Molar mass of an element is the atomic mass in grams for the element, which is exactly 6.02 x
1023 atoms. For example, the molar mass of iron (Fe) is 55.85 g/mol which is the mass in grams
directly off the periodic table. When exactly 55.85 g of Fe is massed, it is 6.02 x 10 23 atoms of Fe.
The molar mass of a compound is the sum of the atomic masses of all of the atoms in one molecule
of the compound. For example, the molar mass of Cu(NO3)2 is calculated:
(1) Cu = 63.55 g
(14.01 g ) (2) N = 28.02 g
(16.00 g )(6) O = 96.00 g
Total molar mass = 187.57 g/mol
Converting Between Moles and Grams
Conversions between grams and moles can be accomplished if the formula for the molecule is known as
well as either grams of compound or moles of compound. The formula that is used is:
Moles
1
=
grams__
molar mass
Example: How many moles are present in 14.68 g of nickel?
Step 1: Identify the knows
unknowns
Mass of Ni = 14.68 g
g
Molar mass of Ni = 58.69 /mol
moles of Ni = ?
Step 2: Complete calculations
14.68 g Ni = 0 .2501 mol Ni
58.69 g/mol
Example: How many grams of magnesium are there in 0.33 mol of magnesium?
Step 1: Identify the knows
unknowns
g
Molar mass of Mg = 24.31 /mol
grams of Mg = ?
Moles of Mg = 0.33 mol
Step 2: Complete calculations
0.33 mol Mg =
x g Mg
24.31 g/mol
1
Cross multiply and divide
(0.33 mol Mg) (24.31 g/mol) = 8.02 g Mg
1
Example: How many moles of calcium carbonate (CaCO3) are there in 150 g of CaCO3?
Step 1: Identify the knowns
unknowns
Mass of CaCO3 = 150 g
Molar mass of CaCO3 = ?
Moles of CaCO3 = ?
Step 2: Calculate the molar mass of CaCO3
(1) Ca = 40.08 g
(1) C = 12.01 g
(16.00 g) (3) O = 48.00 g
Molar mass = 100.09 g/mol
Step 3 Calculate the moles of CaCO3
150 g CaCO3
=
1.05 mol CaCO3
g
100.09 /mol
Example: How many grams are there in 3.50 mol of Cu(NO3)2?
Step 1: Identify the knowns
mol of Cu(NO3)2 = 3.50 mol
unknowns
Molar mass of Cu(NO3)2 = ?
grams of Cu(NO3)2 = ?
Step 2: Calculate the molar mass of Cu(NO3)2
(1) Cu = 63.55 g
(14.01 g) (2) N = 28.02 g
(16.00 g) (6) O = 96.00 g
Molar mass = 187.57 g/mol
Step 3: Calculate the grams of Cu(NO3)2
3.50 mol Cu(NO3)2
=
x g Cu(NO3)2
187.57 g/mol
1
Cross multiply and divide
(3.50 mol) (187.57 g/mo;) = 656.50 g Cu(NO3)2
1
Summary
A mole of any substance contains Avogadro’s number (6.02 × 1023) of representative particles.



The molar mass of an element is the atomic mass taken in grams.
The molar mass of a compound is the sum of the atomic mass of all atoms in one molecule of the
compound.
Conversions can be completed between moles and grams of a substance using:

Moles =
1
grams__
molar mass
Review
1.
What does Avogadro’s number represent?
2.
What is the molar mass of calcium?
3.
What would be the mass of one mole of Manganese?
4.
Calculate the molar mass of the compound Ba(C2H3O2)2?
5.
Calculate the number of moles of sodium chloride (NaCl) in 46.75 g of NaCl.
Answers
1.
One mole, 6.02 x 1023 particles. It can be atoms, molecules, ions, electrons, etc.
2.
Molar mass of calcium is 40.08 g/mole.
3.
One mole of manganese would have a mass of 54.938 g.
4.
The molar mass of Ba(C2H3O2)2
(1) Ba = 137.33 g
(12.01 g) ( 4) C = 48.04 g
(1.01 g) (6) H = 6.06 g
(16.00 g) (4) O = 62.00 g
Total Molar mass = 253.97 g/moil
5. 1st calculate the molar mass of NaCl
(1) Na = 22.99 g
(1) Cl = 35.45 g
Molar mass = 58.44 g/mol
2nd Calculate the moles
46.75 g NaCl
58.44 g/mol
=
0.80 mol NaCl