The Mole
Mrs. Coyle
Chemistry
Part I
• The Mole
• Molar Mass
• Moles <->Particles
-How do we measure the mass of
chemical quantities?
-amu’s
-grams
-moles
Atomic Mass Unit (amu):
= 1/12 of the mass of a 12C atom
Relationship of amu to gram
1 amu = 1.66054 x 10 -24 g
Atomic Mass:
-The weighted average of the masses
of the naturally occurring isotopes of
an element.
-The atomic mass of an element is
listed on the periodic table.
Why the Mole?
Are the quantities scientists use
on a lab scale at the level of
the atom
or
at the level of grams?
The Mole = 6.02 x 1023
One mole of atoms
(6.02x1023 atoms) of an element
is contained
in an amount
equal to its atomic mass
measured in grams.
This mass is called molar mass.
Molar Mass of an Element:
an amount equal to
the atomic mass of the element
expressed in grams.
• Example: for Neon,
Atomic Mass = 20.18 amu
Molar Mass = 20.18 g
Molar Mass of a Compound:
an amount equal to the molecular mass
expressed in grams.
•
•
•
•
•
Also known as, Gram-Formula Mass,
Molecular Weight.
Examples:
What is the molar mass of:
H 2O
H2SO4
Mg(NO3)2
CuSO4 ∙ 5 H2O
The Definition of
The Mole
The mass of an element or
compound that contains as
many elementary
(representative) particles
(atoms, molecules, ions, etc.)
as there are atoms in exactly
12 grams of 12C.
How many atoms are there in
12 g of C-12 ?
6.022145 x
23
10
atoms
1 mole of atoms (mol)
Avogadro’s Number
Avogadro’s Number
• Can be used the same way the word
“dozen” is used to mean 12 for any object.
• One mole of books is 6.022x1023 books,
just like a dozen books is 12 books.
“Mole of Atoms of Hydrogen”
1 atom
Atomic Mass:1.008 amu
1 mole of atoms:
Molar Mass: 1.008 g
6.022 x 1023
atoms
“Mole of Molecules of Hydrogen”
1 molecule=
2 atoms
Molecular Mass: 2.016 amu
1 mole of
molecules=
Molar Mass: 1.008 g
6.022 x 1023
molecules=
2x6.022 x1023atoms
Problem Solving Methods
• Using Mathematical Formulas
• Factor-Label Method
Mathematical Formulas
#mol= Mass of Sample (g)
Molar Mass (g/mol)
#particles=#mol x 6.022 x10
23 particles/mol
particles can be atoms, molecules,
formula units, etc.
Equalities Used in
Factor- Label Method
1 mol = Molar Mass g
1mol= 6.022 x10 23 particles (atoms,
molecules, formula units, etc)
Problem # 1- Moles to Atoms
• How many atoms are there in 6 moles
of Fe?
Solution using Factor-Label
Method
• 6 mol of Fe x 6.02 x 1023 atoms Fe =
1 mol Fe
=3.6 x 10 24 atoms
Solution using Math Formula
• #atoms=#mol x 6.022 x10 23 atoms/mol=
=6 mol of Fe x 6.02 x 1023 atoms Fe/mol=
=3.6 x 10 24 atoms
Problem #2 –Moles to Atoms
• How many iron atoms are there in 6
moles of iron (III) oxide?
A: 7.2 x 10 24 atoms
Problem #3- Atoms to Moles
• How many moles of H2O are there in
18.06 x 10 23 molecules of H2O?
• A: 3 moles of H2O
Part II
• MolesMass Problem
Problem # 4 –Mass to Moles,
Mass to Atoms
For a sample of 20.0g of iron, Fe, calculate:
a) the number of moles of atoms
b) the number of atoms
• Solution using Math Formula Method:
a) #mol Fe= mass Fe(g)
= 20g Fe
molar mass Fe(g/mol) 55.85g/mol
#mol Fe
= 0.358 mol Fe atoms
Problem # 4 Cont’d
b)
#atoms Fe= #mol x (6.022 x 1023 atoms/mol)=
= (0.358 mol Fe)(6.022 x 10 23 atoms/mol)
#atoms Fe= 2.156x1023 atoms Fe
Problem # 5
For a sample of 150.0 g of H2SO4, calculate:
a) The number of moles of H2SO4 present.
b) The number of oxygen atoms present.
Solution:
MM H2SO4 = H: (2 atoms)(1.008g/mol)
S: (1 atom)(32.07g/mol)
O: (4 atoms)(16.00g/mol)
98.09g/mol
Problem # 5
• # mol H2SO4 = Mass (g) =150.0g H2SO4
MM (g/mol) 98.09g/mol
# mol H2SO4= 1.529 mol H2SO4
Problem # 5 Cont’d
b)
#atoms of O = (#mol O)(6.022x1023 atoms)=
= (4 x 1.529 mol O) (6.022x1023 atoms) =
= 3.683 x1024 atoms O
Part III
• Molar Volume of an Ideal Gas at STP
Molar Volume of an Ideal Gas
• At STP conditions,
Standard Temp of 0 deg C and
Standard Pressure of 1 atm,
the molar volume of an ideal gas
is
22.4 L
• For an ideal gas at STP:
#mol= Volume (L)
22.4 (L/mol)
or
1mol = 22.4 L
Problem # 6-Volume to Atoms
• How many atoms of oxygen are there in 44.8L of
oxygen gas at STP?
• Solution:
#mol O2= Volume (L) = 44.8 L = 2.00 mol O2
22.4 (L/mol) 22.4 L/mol
#atoms O =#mol x 6.022 x10 23 atoms/mol
= 2 x (2.00mol O)(6.022 x10 23 atoms/mol)
#atoms O= 2.41 x 1024 atoms O
Problem #7- Molecules to
Volume
• How many L at STP are contained in a
sample of 8.6 x10 24 molecules of CO2
gas?
A: 320L
Part IV
• Density of a Gas at STP from Molar Mass.
Density
• D= Mass
=
Volume
Molar Mass
Molar Volume
At STP,
Molar Volume of an Ideal Gas = 22.4 L
Problem #8- Density of a Gas
from MM
• What is the density of NO2 gas at STP?
• A: 2.05g/L