Transcript the MOLE… Counting Atoms • Everything we’ve done so far in chemistry has dealt with individual atoms or molecules – However, it isn’t practical.

the MOLE…
Counting Atoms
• Everything we’ve done so far in
chemistry has dealt with individual
atoms or molecules
– However, it isn’t practical to work
with 1 atom or 1 molecule or even
1,000,000 atoms or molecles
– They are just too small!
• Therefore, chemists don’t work with
1 atom or even 1,000,000 atoms,
they work with a huge collection
of atoms
Counting Atoms
• It is impractical to get caught up into
working with 1 atom or 1 atom’s mass.
– It makes more sense to work with
a collection of atoms rather than
individually
• Scientists were challenged to figure
out a way to define a universal
collection of particles
– And which could still be described in
terms of a relative mass
Counting Atoms
• We’ve already got the periodic table
with masses for each element
– So how many atoms are in that
collection (assuming gram masses)
– That number of atoms would
immediately connect all other atoms
and give us measurable amounts


1 atom
23


15.999g
 6.0235*10 atoms
 23 
 2.6561*10 g 
Counting Atoms


1 atom
23


1.00797g
 6.0231*10 atoms
 24 
 1.6735*10 g 


1 atom
23
  6.0235*10 atoms
12.0115g
 23
 1.9941*10 g 
Counting Atoms
• The number of atoms that are in
the gram mass on the PT is called
Avogadro’s Number
• And is defined as 1 mole
• The mole becomes a counting unit
much like the dozen.
– 1 dozen eggs = 12 eggs
– 1 mole of eggs =
Counting Atoms
• The word “mole” was introduced by
Wilhelm Oswald, who derived the
term from the word moles meaning
a “heap” or “pile.”
– We are just defining the pile as containing 6.02x1023 items
– Any time we are counting how many
we have and we want to describe it
in terms of moles than…
Counting Atoms
• The mole, whose abbreviation is “mol”,
is the SI base unit for measuring
amount of a pure substance.
– It’s used exclusively for counting
atoms, molecules, ions, or other things
that are extremely small
– It’s the chemist’s six-pack or dozen.
Many objects in our everyday lives
come in similar counting units.
• 1 ream = 500 sheets of paper
• 1 pair of socks = 2 socks
• 1 cube = 24 cans
Counting Atoms
• We will learn in the near future that
when a chemist reasons through a
chemical reaction (recipe) they think
in terms of X number of mols of this
compound reacts with Y number
of mols of this compound.
– So we need to know how to calculate
the number of molecules or atoms
are involved in that X number of mols
Counting Atoms
Using the mole in calculations #1
How many moles is equivalent
to 1.355x1024 atoms of Au?
unit equality:
1 mol Au = 6.02 x 1023 atoms Au
Counting Atoms
The desired conversion is:
atoms moles
1.355x1024 atoms Au
1 mole Au
6.02x1023atoms Au
= 2.251 mol Au
Counting Atoms
Using the mole in calculations #2
How many molecules of
carbon dioxide is 0.0357 mols?
unit equality:
1 mol CO2 = 6.02x1023 molecules of CO2
Counting Atoms
The desired conversion is:
moles atoms
0.0357 mols CO2
6.02x1023molecules CO2
1 mole CO2
= 2.15x1022 molecules CO2
Your Turn:
Make the following mole conversions using
dimensional analysis
1) 0.0753 mols of Na to atoms
2) 2.55x1025 molecules of CO2 to mols
3) 1.89x1019 molecules of H2O to mols
4) 1.25 mols of O2 to molecules
Counting Atoms
• Now suppose you want to determine
how many atoms are in a mol of a
compound or molecule
– To do this you must know how many
atoms are involved in the molecule.
• To determine the number of atoms
represented in a molecule requires
knowing the chemical formula
– Eg, each molecule of Carbon Dioxide
(CO2) is composed of 3 atoms
Counting Atoms
Using the mole in calculations #3
How many atoms of Carbon are in
2.12 mols of Propane (C3H8)?
unit equalities:
1 mol C3H8 = 6.02x1023 molecules C3H8
1 molecule C3H8 = 3 atoms C
Counting Atoms
The desired conversions are:
moles  molecules  atoms
2.12
mols
C3H8
6.02x1023
molecules C3H8
3 atoms C
1 mole C3H8
1 molecule
C3H8
=3.83x1024 atoms C
Your Turn:
Make the following mole conversions using
dimensional analysis
1) How many atoms of Oxygen are
there in 0.118 mols of CO2
2) How many atoms of Oxygen are
there in 1.223 Ca(NO3)2.
Counting Atoms
• We can’t literally count the number
of atoms in a sample, but we can
count them by mass
– So, there needs to be a connection
between the mass of a sample and
the number of moles in that sample
– If we weigh out a particular mass
of a substance, that can represent
a particular number of mols
• If we weighed out 12.011 g of Carbon
– It will represent 1 mole of Carbon
and/or 6.02x1023 Carbon atoms
Counting Atoms
• This allows us to use the mass off of
the periodic table to represent the mass
of 1 mole (or 6.02x1023 atoms) of that
element
– 1 mol of C atoms weighs 12.01 g
– 1 mol of H atoms weighs 1.008 g
– 1 mol of W atoms weigh 183.8 g
Counting Atoms
• This new understanding of mass from
the periodic table is known as the gram
molar mass, or molar mass.
– Molar Mass = mass of 1 mole of atoms
in grams
– We have a list of every possible molar
mass for any given element on the
periodic table
• This mass can be used as a conversion
factor…1 mole = 1.0079 g H, etc.
Counting Atoms
• So what if we have a compound instead
of an element?
• How do we figure out the mass of a
mole of a compound?
– This would be called a molecular mass,
formula mass, or still can be called a
molar mass
– All we need is the formula for a
representative particle of the
compound and the periodic table.
Counting Atoms
• For instance how do we calculate
the mass of 1 mole of Ca(OH)2?
• You can calculate the mass of a molecule of Ca(OH)2 by breaking it up
into individual pieces
• We can start with Calcium, then 2 O’s,
then 2 H’s…until we run out of pieces
40.09
Ca: (1)(40.09 g/mol) =
O: (2)(15.99 g/mol) = + 31.98
H: (2)(1.008 g/mol) = + 2.016
74.09 g/mol
Counting Atoms
What is the MM of glucose (C6H12O6)?
(6C’S)(12.011g/mol) = 72.066g/mol
(12H’S)(1.008 g/mol) = 12.096g/mol
(6O’S)(15.99 g/mol) = 95.94g/mol
180.1g/mol
1 mole of C6H12O6 or
6.02x1023 molecules of the compound –
weighs 180.1 grams
Practice Time:
Calculate the molar mass of each of the formulas
1) C9H20
2) (NH4)2CO3
3) Zn(C2H3O2)2
4) CCl4
Counting Atoms
Using the molar mass in calculations:
How many grams are in 9.45 mol
of Dinitrogen Trioxide (N2O3)
The only connection to N2O3 and its mass
is how much 1 mol of the compound
weighs. But, using it as a comparison
we can calculate the mass of 9.45 mol.
Counting Atoms
Step 1: Determine the mass of 1 mol
of N2O3
(2N’s)(14.01g) = 28.02g
(3O’s)(15.99g) = 47.97g
75.99g
If 1 mole of N2O3 weighs 75.99g than how
much will 9.45 mols of N2O3 weigh?
Counting Atoms
Step 2: Convert the given moles to
grams using the Molar mass
equality.
9.45 mol N2O3
75.99 g N2O3
1 mol N2O3
=718 g N2O3
Counting Atoms
Find the number of moles of
92.2g of Iron (III) Oxide (Fe2O3)
The only connection to the mass of Fe2O3
and how that corresponds to mols is how
that 1 mol of the compound weighs a certain
# of grams. Using that we can figure out
how many moles weigh 92.2 g
Counting Atoms
Step 1: Determine the mass of 1 mol of
Fe2O3
(2Fe’s)(55.85g) = 111.7g
(3O’s)(15.99g) = 47.97g
159.67g
If 1 mole of Fe2O3 weighs 157.67g than how
many mols will weigh 92.2 g of Fe2O3?
Counting Atoms
Step 2: Convert the given mass to mols
using the Molar mass equality
92.2 g Fe2O3
1 mol Fe2O3
159.67 g Fe2O3
=.577mol Fe2O3
Practice Time:
• Determine the number of mols of
CO2 in 454 grams.
• What is the mass of 1.488 mols of
propane gas, C3H8?
• How many mols of methane
molecules, CH4, are in 80.45 grams
of methane?
• How many grams does
3.40x10-5 mols of Na2CO3 weigh?
Counting Atoms
• Another generality about the mole is
that with matter in the gas phase we
can develop another equality.
– Under the same conditions,
equal volumes of gases contain
equal numbers of particles.
– 1 mol of a gas will occupy the same
volume as 1 mol of any other gas
under the same conditions.
Molar Volume of a Gas
1 mole of any gas
under the specific
conditions of 0°C
and 1 atm (STP)
will occupy a
volume of 22.4 L.
6.02x1023
6.02x1023
molecules of O2 molecules of CO2
Counting Atoms
What volume, in Liters, does 0.60 mol
of SO2 gas occupy at STP?
The only connection to the volume of any
gas and how that corresponds to mols is
that 1 mol of a gas occupies 22.4 Liters of
space. Using that we can figure out the
volume of 0.60 mols of a gas at STP.
Counting Atoms
Step 1: Use the equality 1 mol = 22.4 L
to do the conversion
0.60 moles SO2
22.4 L SO2
1 mole SO2
= 13 L SO2
Practice Time:
• What volume is occupied by
12.5 mols of nitrogen gas at STP?
• How many moles of gas would be in
15,000 L of air?
Counting Atoms
Aspartame is an artificial sweetener
that is 160 times sweeter than sugar
when dissolved in water. It is marketed
as Nutra-Sweet (C14H18N2O5).
1. What number of molecules are
in 5.0 mg of aspartame?
2. What number of atoms of nitrogen
are in 1.2 g of aspartame?
3. What is the mass in g of 1 molecule
of aspartame?
Counting Atoms
 1 g  1 mole  6.02x1023 molecules
 


5.0mg
1 mole
 1000mg  294.37g 

19
1.0x10 molecules
 1 mole  6.02x1023 molecules 2 atomsN 


1.2 g 

1 mole
 294.37g 
 1 molecule
21
4.9x10 atomsN
1 mole

 294.37g 
- 22
1 molecule

  4.9x10 g
23
 6.02x10 molecules 1 mole 
Your Turn:
• What is the mass of 7.21x1021
molecules of silver acetate
(AgC2H3O2)?
• How many grams of neon gas will fill a
room with a volume of 4000L at STP?
• How many molecules are there in
122 g of Cu(NO3)2?
• Which has the greater mass?
a. 9.5x1024 atoms of C
b. 2.1 mol Br2
c. 1.86x1022 molecules of CCl4
d. 59.5g Hg