1. Atomic Masses & the MOLE…

3. Counting Atoms Masses of atoms expressed in grams are extremely small.
An atom of O-16 literally weighs g
For most calcs in chemistry it is easier to use a relative atomic mass.
for relative masses, an atom was arbitrarily chosen as the standard, by which all other masses are compared

4. Counting Atoms
The mass of all the other atoms are then expressed in relation to the standard
C-12 atom acts as the standard
A single C-12 atom was assigned a mass of 12 atomic mass units (amu)
1 amu is exactly 1/12 of the mass of a C-12 atom
Carbon has 12 nucleons therefore, the mass of a proton = 1 amu 6
CARBON C 12

5. Counting Atoms
The masses of all other atoms are based on the mass of 1 amu
Hydrogen has 1 proton therefore, it weighs 1 amu
Helium has 2 protons and 2 neutrons therefore, it weighs 4 amus
Most elements occur naturally as a mixture of isotopes.
For instance in the two isotopes of Chlorine (Cl-35 & Cl-37)

6. Counting Atoms Cl-35 atoms are naturally more abundant than Cl-37
75% of all of the Cl atoms found in nature are the isotope Cl-35
25% of the all of the Cl atoms found in nature are the isotope Cl-37
Cl-35 atoms are naturally more abundant than Cl-37
Therefore, the average mass of Cl (taking into account isotopic abun-dance) should be closer to 35 than to the median of 36.

7. Here’s how the masses were calculated on the Periodic Table:
Counting Atoms
Masses on the PT are weighted aver-ages of all of the naturally occurring isotopes of an element
The average atomic mass on the PT is reflective of both the mass numbers of each isotope & the abundance of each isotope
Here’s how the masses were calculated on the Periodic Table:

8. Counting Atoms Calculating average atomic masses:
Naturally occurring copper consists of 69.17% Cu-63, which has a mass of amu, and 30.83% Cu-65, with a mass of amu.
The average atomic mass of Cu is calculated by multiplying the atomic mass of each isotope by its abundance and adding the results.

9. Counting Atoms 63.55 amu 63.54564387858 amu Cu-63
The reported average atomic mass of naturally occurring Cu is amu.

10. Your Turn:
Gallium consists of two isotopes of masses amu and amu with abundances of 60.16% and 39.84%, respectively. What is the average atomic mass of gallium?
Naturally occurring element X exists in three isotopic forms: X-28 ( amu, 92.21% abundance), X-29 ( amu, 4.70% abundance), and X-30 ( amu, 3.09% abundance). Calculate the atomic weight of X.

11. 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 collection of particles
And which could still be described in terms of a relative mass

12. Counting Atoms
If we assume we can relate the relative masses from the PT in the terms of grams
With the literal masses of an atom (g) for each atom we use we seem to get the same number of atoms
Oxygen:

13. Counting Atoms
Hydrogen:
Carbon:

14. Counting Atoms
The number of atoms that are in the relative masses of elements identical in grams to the atomic masses on the PT is called Avogadro’s Number
And is defined as a mole
The mole becomes a counting unit much like the dozen.
1 dozen eggs = 12 eggs
1 mole of eggs =
602,000,000,000,000,000,000,000 eggs

15. 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 con-taining 6.02x1023 items
Any time we are counting how many we have and we want to describe it in terms of moles than…
1 mole is always = x 1023 items

16. 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

17. 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

18. How many moles of Magnesium
Counting Atoms
Using the mole in calculations #1
How many moles of Magnesium
is 1.25 x 1023 atoms of Magnesium?
unit equality:
1 mol Mg = 6.02 x 1023 atoms Mg

19. Counting Atoms = .208 mol Mg The desired conversion is: atoms moles
1 mole Mg
1.25x1023 atoms Mg
6.02x1023atoms Mg
= .208 mol Mg

20. How many atoms of Gold do we have if we have .0327 moles of Gold?
Counting Atoms
Using the mole in calculations #2
How many atoms of Gold do we have if we have moles of Gold?
unit equality:
1 mol Au = 6.02 x 1023 atoms Au

21. Counting Atoms = 2.23x1022 atoms Au
The desired conversion is: moles atoms
6.02x1023atoms Au
.0327 mole Au
1 mole Au
= 2.23x1022 atoms Au

22. Your Turn:
Fill in the missing information in the following table, be sure to show your work.
Moles
Atoms or molecules
mols Al(OH)3
2.017 x 1012 molecules H2O
6.017 x 1042 atoms W
.2116 mols Al+3

23. 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

24. How many atoms of Carbon are in 2.12 mols of Propane (C3H8)?
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

25. The desired conversions are:
Counting Atoms
The desired conversions are:
moles  molecules  atoms
6.02x1023 molecules C3H8
2.12
mols C3H8
3 atoms C
1 molecule C3H8
1 mole C3H8
=3.83x1024 atoms C

26. Your Turn:
Fill in the missing information in the following table, be sure to show your work.
Moles
Atoms or molecules
# of ____ atoms
mols Al(OH)3
7.2511x1024 molecules
# of O atoms
3.350x10-12 mols H2O
2.017 x 1012 molecules H2O
# of total atoms
9.995x1018 mols W
6.017 x 1042 atoms W
.2116 mols Al+3
1.274x1023 ions Al+3

27. 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 g of Carbon
It will represent 1 mole of Carbon and/or 6.02x1023 Carbon atoms

28. 18.99g F atoms=1 mol F atoms=6.02x10 F 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 g
1 mol of H atoms weighs g
1 mol of W atoms weigh g
18.99g F atoms=1 mol F atoms=6.02x10 F atoms 23

29. 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 = g H, etc.

30. 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.

31. Counting Atoms
For instance how do we calculate the mass of 1 mole of Ca(OH)2?
You can calculate the mass of a mol- ecule of Ca(OH)2 by breaking it up into individual pieces
We can start with Calcium, then oxygens, then 2 hydrogens… until we run out of pieces
74.09 g/mol
Ca: (1)(40.09 g/mol) =
40.09
O: (2)(15.99 g/mol) =
H: (2)(1.008 g/mol) =

32. 6.02x1023 molecules of the compound –weighs 180.1 grams
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 grams

33. Practice Time: Molar Mass Moles Atoms or molecules # of ____ atoms
mols Al(OH)3
7.2511x1024 molecules
# of O atoms
2.1753x1025 atoms O
3.350x10-12 mols H2O
2.017 x 1012 molecules H2O
# of total atoms
6.051x1012 atoms
9.995x1018 mols W
6.017 x 1042 atoms W
.2116 mols Al+3
1.274x1023 ions Al+3

34. How many grams are in 9.45 mol of Dinitrogen Trioxide (N2O3)
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.

35. 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?

36. Counting Atoms 75.99 g N2O3 9.45 mol N2O3 1 mol N2O3 =718 g N2O3
Step 2: Convert the given moles to grams using the Molar mass equality.
75.99 g N2O3
9.45 mol N2O3
1 mol N2O3
=718 g N2O3

37. Counting Atoms Find the number of moles of
92.2g of Iron (III) Oxide (Fe2O3)
The only connection to the mass of Fe2O 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

38. Counting Atoms (2Fe’s)(55.85g) = 111.7g (3O’s)(15.99g) = 47.97g
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 g than how many mols will weigh 92.2 g of Fe2O3?

39. Counting Atoms 1 mol Fe2O3 92.2 g Fe2O3 159.67 g Fe2O3 =.577mol Fe2O3
Step 2: Convert the given mass to mols using the Molar mass equality
1 mol Fe2O3
92.2 g Fe2O3
g Fe2O3
=.577mol Fe2O3

40. Practice Time:
Vitamin C (C6H8O6), cannot be stored by the body and therefore, must be present in the diet. If an orange contains 70 mg of Vit C how many oranges are necessary to consume 2.5 mols of Vit C?

41. 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.

42. Molar Volume of a Gas
22.4 L
22.4 L
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
molecules of O2
6.02x1023
molecules of CO2

43. What volume, in Liters, does 0.60 mol of SO2 gas occupy at STP?
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.

44. Counting Atoms 22.4 L SO2 0.60 moles SO2 1 mole SO2 = 13 L SO2
Step 1: Use the equality 1 mol = 22.4 L to do the conversion
22.4 L SO2
0.60 moles SO2
1 mole SO2
= 13 L SO2

45. Practice Time:
The Snoopy balloon featured at the Macy’s Thanksgiving Day Parade has a volume of ft3. How many moles of Helium are required to fill it STP?

47. 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).
What number of molecules are in 5.0 mg of aspartame?
What number of atoms of nitrogen are in 1.2 g of aspartame?
What is the mass in g of 1 molecule of aspartame?

49. Counting Atoms

50. Counting Atoms

52. 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 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