Download The Mole

The Mole
23
6.02 X 10
The Mole
• 1 pair = 2 representative particles
• 1 dozen = 12 representative particles
• 1 mole = 6.02 x 1023 representative particles
The Mole (mol): A unit to count numbers of
particles
– 1 dozen cookies = 12 cookies
– 1 mole of cookies = 6.02 X 1023 cookies
– 1 dozen Al atoms = 12 Al atoms
– 1 mole of Al atoms = 6.02 X 1023 atoms
Note that the NUMBER is always the same, but the
MASS is very different!
A Mole of Particles
Contains 6.02 x 1023 particles
• Representative Particle:
– Refers to the species present.
– Usually atoms, molecules, or formula units.
– Example:
• Atomic Nitrogen = N
• Nitrogen gas = N2
1 mole of all of these =
• Water = H2O
23 rep. particles
6.02
x
10
• Calcium ion = Ca2+
• Glucose = C6H12O6
Avogadro’s Number as
Conversion Factor
6.02 x 1023 particles
1 mole
or
1 mole
6.02 x 1023 particles
Note that a particle could be an atom OR a molecule!
Learning Check
1.
Number of atoms in 0.500 mole of Al
a) 0.500 mole of Al
b) 6.02 x 1023 Al atoms in 1 mole
c) So, in 0.5 mole, 3.01 x 1023 Al atoms
2.Number of moles of S in 1.8 x 1024 S atoms
a) 6.02 x 1023 S atoms in 1.0 mole of S atom
b) So, 3 x 6.02 x 1023 = 1.8 x 1024 S atoms
in 3 x 1 mole= 3.0 mole S atoms
c) 3.0 mole S atoms
Gram Atomic Mass
• Gram Atomic Mass –
– Atomic mass of an element expressed in grams.
– The gram atomic mass is the mass of 1 mol of atoms
of any element.
1 mole of C atoms
=
12.0 g
1 mole of Mg atoms
=
24.3 g
1 mole of Cu atoms
=
63.5 g
# of C atoms in12.0 g of C atoms = # of Mg atoms in24.3
g of Mg atoms = # of O atoms in 16.0 g
• How many is that?
6.02 x 1023!!
Other Names
• Gram Molecular Mass/Molecular Weight
• Gram Formula Mass/Formula Weight
• What is the gram atomic mass (GAM) of 1
mol of the following compounds?
– Gram Molecular Mass of SO3 and H2O = ?
• SO3 = 80.1g
H2O = 18 g
– Gram Formula Mass of NaCl and CaI2 = ?
• NaCl = 58.5 g
CaI2 = 293.9 g
Molar Mass( atoms, molecules and
compounds)
Molar Mass: mass of one mol of any substance(usually
we round to the tenths place).
A. 1 mole of Br atoms =
B. 1 mole of Sn atoms =
79.9 g/mole
118.7 g/mole
Mass in grams of 1 mole equal numerically to the
sum of the atomic masses
1 mole of CaCl2 = 111.1 g/mol
1 mole Ca x 40.1 g/mol
+ 2 moles Cl x 35.5 g/mol = 111.1 g/mol CaCl2
1 mole of N2O4
= 92.0 g/mol
Learning Check!
A. Molar Mass of K2O = ? Grams/mole
B. Molar Mass of antacid Al(OH)3 = ? Grams/mole
Example:
1. How many grams are in 9.45 mol dinitrogen
trioxide?
718.20 g N2O3
2. How many moles are in 92.2 g iron (III) oxide?
•
0.58 mol Fe2O3
What is the formula mass of Ca3(PO4)2 ?
1 formula unit of Ca3(PO4)2
3 Ca
3 x 40.08
2P
2 x 30.97
8O
+ 8 x 16.00
310.18 amu
10
Volume of a Mol
• Standard temperature and pressure:
– STP
– 0°C and 101.3 kPa or 1 atm
– At these conditions, 1 mol of any gas = 22.4 L
• 1. What is the volume, in L, at 0.60 mol SO2 gas at
STP?
13.44 L SO2 (g)
• 2. The density of a gaseous compound containing
carbon and oxygen is 1.964 g/L at STP. What is
the molar mass?
43.99 g/mol
Problems, cont.
• 3. A gaseous compound composed of
sulfur and oxygen is linked in the formation
of acid rain and has a density of 3.58 g/L
at STP. What is the molar mass?
80.19 g/mol
• 4. What is the density of Kr gas at STP?
3.74 g/L
Big Helper…
23
N
=6.02
x
10
A
Molar Mass
Representative
Grams
moles
particles
Gram atomic mass/
Gram molecular mass/
(Molecules,
formula mass
Atoms,
Molar
22.4 liters
Ions,
volume (STP)
Formula units)
Liters
Converting Moles and Grams
Aluminum is often used for the structure
of light-weight bicycle frames. How
many grams of Al are in 3.00 moles of
Al?
3.00 moles Al
? g Al
1. Molar mass of Al
1 mole Al = 27.0 g Al
2. Conversion factors for Al
27.0g Al
1 mol Al
or
1 mol Al
27.0 g Al
3. Setup 3.00 moles Al
Answer
x
27.0 g Al
1 mole Al
= 81.0 g Al
Atoms/Molecules and Grams
• Since 6.02 X 1023 particles = 1 mole
AND
1 mole = molar mass (grams)
• You can convert atoms/molecules to
moles and then moles to grams! (Two
step process)
• You can’t go directly from atoms to
grams!!!! You MUST go thru MOLES.
Calculations
molar mass
Grams
Avogadro’s number
Moles
particles
Everything must go through
Moles!!!
Atoms/Molecules and Grams
How many atoms of Cu are present
in 35.4 g of Cu?
35.4 g Cu
1 mol Cu
63.5 g Cu
6.02 X 1023 atoms Cu
1 mol Cu
= 3.4 X 1023 atoms Cu
Learning Check!
How many atoms of K are present in 78.4
g of K?
Learning Check!
How many atoms of O are present in 78.1 g
of oxygen?
78.1 g O2 1 mol O2 6.02 X 1023 molecules O2 2 atoms O
32.0 g O2 1 mol O2
1 molecule O2
Percent Composition
• Percent composition:
– The percent by mass of each element in
a compound.
X 100%
% mass of element = grams of element
grams of
compound
• 1. Calculate the percent composition of
each element in propane, C3H8.
• C = 81.82%
• H = 18.18%
Types of Formulas
• Empirical Formula
The formula of a compound that
expresses the smallest whole number
ratio of the atoms present.
Ionic formula are always empirical formula
• Molecular Formula
The formula that states the actual
number of each kind of atom found in one
molecule of the compound.
Empirical Formula
• Empirical Formulas:
• The lowest whole number ratio of atoms of the
elements in a compound.
– Example: CO (could be C2O2, C4O4, but not
CO2)
• *Empirical Formula may or may not be the
molecular formula.
• Examples:
–Hydrogen Peroxide = H2O2 but the
empirical formula is HO
–Carbon dioxide = CO and it is the
To obtain an Empirical Formula
1. Determine the mass in grams of each
element present, if necessary.
2. Calculate the number of moles of each
element.
3. Divide each by the smallest number of
moles to obtain the simplest whole
number ratio.
4. If whole numbers are not obtained* in
step 3), multiply through by the smallest
number that will give all whole numbers
* Be
careful! Do not round off numbers prematurely
Empirical Problems
• 1. What is the empirical formula of a
compound that is 25.9% nitrogen and
74.1% oxygen?
• Looks hard, but follow the three steps…
Problem, cont.
• Step 1:
– Convert % to moles.
• 1.85 mol N
• 4.63 mol O
• Step 2:
– Divide both answers by the lowest one.
• 1.85 mol N is lowest.
1 mol N
–2.5 mol O
Problem, cont.
• Step 3:
– If one answer is a decimal, multiply both by a
number so it is converted to a whole number.
• 2.5 mol O becomes 5 mol
• 1 mol N becomes 2 mol
• Answer: N2O5
Chemical Formulas of Compounds
• Formulas give the relative numbers of atoms or
moles of each element in a formula unit - always a
whole number ratio (the law of definite
proportions).
NO2
2 atoms of O for every 1 atom of N
1 mole of NO2 : 2 moles of O atoms to every 1
mole of N atoms
• If we know or can determine the relative number
of moles of each element in a compound, we can
determine a formula for the compound.
A sample of a brown gas, a major air pollutant,
is found to contain 2.34 g N and 5.34g O.
Determine a formula for this substance.
require mole ratios so convert grams to moles
moles of N = 2.34g of N = 0.167 moles of N
14.01 g/mole
moles of O = 5.34 g = 0.334 moles of O
16.00 g/mole
N 0.167 O 0.334  NO 2
Formula: N O
0.167
0.334
0.167
0.167
Determine Empirical Formula
1. 75% carbon, 25% hydrogen
2. 52.7% potassium, 47.3% chlorine
3. 22.1% aluminium, 25.4% phosphorous,
52.5% oxygen
4. 13% magnesium, 87% bromine
5. 32.4% sodium, 22.5% sulfur, 45.1% oxygen
Molecular Formulas
• Molecular Formulas:
– Either the same as the empirical formula or a
simple whole number multiple of it.
Known molar mass of molecule =
Molar mass of empirical form.
the number of
empirical formula
units needed (EFU).
Multiply empirical formula with EFU to get the molecular formula
Calculation of the Molecular Formula
A compound has an empirical formula
of NO2. The colourless liquid, used in
rocket engines has a molar mass of
92.0 g/mole. What is the molecular
formula of this substance?