L0 1st Semester

The Mole
The mole (mol) is a unit of measure for an amount of a chemical substance

PAIR = 2 items GROSS = 144 items

REAM = 500 items DOZEN = 12 items

 Counting with moles
Each of the counting units showed before (pair, gross, dozen, ream) represents a specific number
of items.
This units make counting objects easier: appropriate for a certain kind of objects (size or
function).
Regardless of the object, the number that the unit represents remains constant.

How many coins are in the container?

How can we determine the amount of substance present if we can’t count the
atoms directly?
 The Mole
Recall that matter is composed of atoms, molecules, and ions:

• These particles are much, much smaller than grains of sand, and an extremely large
number of them are in a small sample of a substance.
• Obviously, counting particles one by one is not practical.
 The Mole and Avogadro's Number
Mole (mole): amount of a substance that contains as many elementary entities (atoms,
molecules, or other particles) as there are atoms in exactly 12 g of the 12C isotope

The mole (mol) is the SI unit of measure for an

amount of a chemical substance.
A mole is Avogadro’s number (NA) of fundamental
particles, that is 6,022 × 1023 particles.

1 mol = NA entities = 6,022 × 1023 entities

A. Avogadro (1776-1856)

We can use the mole relationship to convert between the number of particles and the mass
of a substance.
 How big is a mole?
Q: How much is a mole?
A: A mole is a quantity used by chemists to count atoms and molecules. A mole of something is equal to
6,022 x 1023 “somethings.”

1 mole = 602 200 000 000 000 000 000 000

six hundred sextillion

Q: Can you give me an example to put that number in perspective?

A: A computer that can count 10 000 000 (1·107) atoms per second would take 2 000 000 000 (2·109) years
to count 1 mole of a substance.
 How big is a mole?
If the atoms were the size of peas, one mole of these atoms
would cover the surface of the Earth with a layer about 15 m

If you receive one mole of euros at your birth, and you spend
one million of euros each second, after 100 years you will
still have 99,99998 % of the money.

If you could travel at the highest possible speed, the speed of

light (300 000 km·s-1), it would take you 62 billion years to
travel “one mole” of kilometers
 Counting with moles
The mole allows chemists to count the number of representative particles in a substance.
 Counting with moles

The mole allows chemists to count the number of representative particles in a substance

Representative Particles and Moles

Substance Representative particle Chemical formula Representative particles in 1,00 mol
Copper Atom Cu 6,02 × 1023
Atomic nitrogen Atom N 6,02 × 1023
Nitrogen gas Molecule N2 6,02 × 1023
Water Molecule H2O 6,02 × 1023
Calcium ion Ion Ca2+ 6,02 × 1023
Calcium fluoride Formula unit CaF2 6,02 × 1023
 Counting with moles

Chemists use the relationships between the mole and quantities such as mass, volume,
and number of particles.

The mole is at the center of your chemical calculations.

It allows you to convert among the amount of representative particles in a substance,

the mass of a substance, and the volume of a gas at STP
 Mole and Mass

Do you expect a dozen eggs to have the same mass as a dozen oranges?
 Molar Mass
The molar mass of an element is the mass per mole of its atoms.

The molar mass of a molecular compound is the mass per mole of its
molecules.

The molar mass of an ionic compound is the mass per mole of its formula
units.
The units of molar mass in each case are grams per mole (g·mol–1).

All molar masses will be expressed and rounded, if necessary, to two numbers after the
decimal (16,00 would not be rounded to 16).

Mass of sample = amount in moles x mass per mole

𝒎=𝒏·𝑴
Acceptable shorthand: n = moles, m = mass and M = molar mass
 All molar masses will be expressed and rounded, if necessary, to two numbers after the
decimal (16,00 would not be rounded to 16).
C

S
Hg

What is the mass of one mole of:

Cu Fe
 How many atoms are contained in the molar mass of an element?

1 mol of sulfur atoms = 32.06 g

1 mol of carbon atoms = 12.01 g 1 mol of iron atoms = 55.85 g

The molar mass of an element contains 1 mole or 6,022·1023 atoms of that element
 The mole is at the center of your chemical calculations.

Exercise 1. Calculate the mass, in grams, of 0.433 mol of calcium nitrate.

 How many atoms are contained in the molar mass of an element?

Exercise 2. How many copper atoms are in 3 g of Cu?

 Molar Volume
Molar Volume (Vm) is often used to describe a gas
𝑷𝑽 = 𝒏𝑹𝑻
Gases can change volume based on temperature and pressure

STP: standard temperature and pressure ?

• Standard Pressure is 101,3 kPa or 1atm
• Standard Temperature is 0ºC or 273 K

The volume of 1 mole at STP is 22,4 L

𝐕𝐨𝐥𝐮𝐦𝐞 𝑽
𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐦𝐨𝐥𝐞𝐬 = 𝒏=
𝐌𝐨𝐥𝐚𝐫 𝐕𝐨𝐥𝐮𝐦𝐞 𝑽𝒎
 Calculations

Exercise 3. How many sodium atoms are in 0,120 mol Na?

• Step 1: we want atoms of Na
• Step 2: we have 0,120 mol Na
• Step 3: 1 mole Na = 6,02 × 1023 atoms Na

6,02 × 1023 atoms Na

0,120 mol Na × = 7,22 × 1022 atoms Na
1 mol Na
 Calculations

Exercise 4. What is the mass of 2,55 × 1023 atoms of lead?

• We want grams, we have atoms of lead.
• Use Avogadro’s number and the molar mass of Pb

1 mol Pb 207,2 g Pb
2,55 × 1023 atoms Pb × × = 87,8 g Pb
23
6,02×10 atoms Pb 1 mol Pb
 Calculations
Exercise 5. Given 15,00 g of carbon tetrafluoride, how many moles of fluorine atoms are
there in the compound? And fluorine atoms?
How many moles of carbon atoms? And carbon atoms?

15,00 g CF4 × 1 mol CF4 × 4 mol F

= 0,6817 mol F atoms
88, 01 g CF4 1 mol CF4

0,6817 mol F × NA F atoms 23 F atoms

1 mol F = 4,105·10

15,00 g CF4 × 1 mol CF4 × 1 mol C

= 0,1704 mol C atoms
88, 01 g CF4 1 mol CF4

0,1704 mol C × NA C atoms

= 1,026·1023 C atoms
1 mol C
 Calculations

Exercise 6. Determine the number of moles in 33,6 L of He gas at STP.

33,6 L He(g) × 1 mol He(g)

= 1,50 mol He(g)
22,4 L
 Calculations
Exercise 7. The density of a gaseous compound containing carbon and oxygen is found
to be 1,964 g/L at STP. What is the molar mass of the compound?

Analyse List the knowns and the unknowns

Knowns Unknowns
• density = 1,964 g/L • Molar mass = ? g/mol
• Molar volume = 22,4 L/mol

𝐌𝐨𝐥𝐚𝐫 𝐦𝐚𝐬𝐬 = 𝐝 𝐱 𝐕𝐦

g L g
M = 1,964 · 22,4 = 44,0
L mol mol
 Calculations

Exercise 8. The density of water is 1.00 g/mL at 4°C. How many water molecules
are present in 2.56 mL of water at this temperature?
 Calculations

Exercise 8. The density of water is 1.00 g/mL at 4°C. How many water molecules
are present in 2.56 mL of water at this temperature?

1.00 𝑔 1 𝑚𝑜𝑙 6.02 × 1023

NH2O = 2.56 𝑚𝐿 × × × = 8.55 × 1022 molecules
1 𝑚𝐿 18.02 𝑔 1 𝑚𝑜𝑙
 Calculations

Exercise 9. Consider a sample of calcium carbonate in the form of a cube measuring

2.005 inch on each edge. If the sample has a density of 2.71 g/cm3 , how many oxygen
atoms does it contain? (1 in = 2.54 cm)
 Calculations

Exercise 9. Consider a sample of calcium carbonate in the form of a cube measuring

2.005 inch on each edge. If the sample has a density of 2.71 g/cm3 , how many oxygen
atoms does it contain? (1 in = 2.54 cm)

2.54 𝑐𝑚 3 2.71 𝑔 1 𝑚𝑜𝑙 3 𝑚𝑜𝑙 𝑂 6.02 × 1023

NO = (2.005 in)3 ×( ) × × × × = 6.46 × 1024
1 𝑖𝑛 1 𝑐𝑚3 100.09 𝑔 1 𝑚𝑜𝑙 𝐶𝑎𝐶𝑂3 1 𝑚𝑜𝑙
SUMMARY