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Atomic Masses & the MOLE…. Counting Atoms. Masses of atoms expressed in grams are extremely small. An atom of O-16 literally weighs 0.0000000000000000000000266 g For most calcs in chemistry it is easier to use a relative atomic mass.

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Counting Atoms

  • Masses of atoms expressed in grams are extremely small.
    • An atom of O-16 literally weighs 0.0000000000000000000000266 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





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

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)

Counting Atoms

  • 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.

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:


Counting Atoms

Calculating average atomic masses:

Naturally occurring copper consists of 69.17% Cu-63, which has a mass of 62.9296011 amu, and 30.83% Cu-65, with a mass of 64.9277937 amu.

  • The average atomic mass of Cu is calculated by multiplying the atomic mass of each isotope by its abundance and adding the results.

Counting Atoms

(0.6917)(62.9296011 amu)


+ (0.3083)(64.9277937 amu)


63.55 amu

63.54564387858 amu

  • The reported average atomic mass of naturally occurring Cu is 63.55 amu.

Your Turn:

  • Gallium consists of two isotopes of masses 68.95 amu and 70.95 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 (27.977 amu, 92.21% abundance), X-29 (28.976 amu, 4.70% abundance), and X-30 (29.974 amu, 3.09% abundance). Calculate the atomic weight of X.

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


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

Counting Atoms




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


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 = 6.02 x 1023 items


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

How many moles of Magnesium

is 1.25 x 1023 atoms of Magnesium?

Using the mole in calculations #1

unit equality:

1 mol Mg = 6.02 x 1023 atoms Mg


Counting Atoms

The desired conversion is: atoms moles

1 mole Mg

1.25x1023 atoms Mg

6.02x1023atoms Mg

= .208 mol Mg


Counting Atoms

How many atoms of Gold do we have if we have .0327 moles of Gold?

Using the mole in calculations #2

unit equality:

1 mol Au = 6.02 x 1023 atoms Au


Counting Atoms

The desired conversion is: moles atoms

6.02x1023atoms Au

.0327 mole Au

1 mole Au

= 2.23x1022 atoms Au


Your Turn:

  • Fill in the missing information in the following table, be sure to show your work.

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

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

Using the mole in calculations #3

unit equalities:

1 mol C3H8 = 6.02x1023 molecules C3H8

1 molecule C3H8 = 3 atoms C

the desired conversions are
The desired conversions are:

Counting Atoms

moles molecules  atoms

6.02x1023 molecules C3H8

3 atoms C


mols C3H8

1 molecule C3H8

1 mole C3H8

=3.83x1024 atoms C


Your Turn:

  • Fill in the missing information in the following table, be sure to show your work.

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


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 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 mol-ecule of Ca(OH)2 by breaking it up into individual pieces
    • We can start with Calcium, then 2 oxygens, then 2 hydrogens… until we run out of pieces

74.09 g/mol


Ca: (1)(40.09 g/mol) =

+ 31.98

O: (2)(15.99 g/mol) =

H: (2)(1.008 g/mol) =

+ 2.016


Counting Atoms

What is the MM of glucose (C6H12O6)?

(6C’S)(12.011g/mol) =


(12H’S)(1.008 g/mol) =



(6O’S)(15.99 g/mol) =


1 mole of C6H12O6 or

6.02x1023 molecules of the compound –weighs 180.1 grams


Counting Atoms

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

Using the molar mass in calculations:

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) =

(3O’s)(15.99g) =



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.

75.99 g N2O3

9.45 mol 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) =

(3O’s)(15.99g) =



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

1 mol Fe2O3

92.2 g Fe2O3

159.67 g Fe2O3

=.577mol Fe2O3


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?

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

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.


molecules of CO2


molecules of O2


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

22.4 L SO2

0.60 moles SO2

1 mole SO2

= 13 L SO2


Practice Time:

  • The Snoopy balloon featured at the Macy’s Thanksgiving Day Parade has a volume of 15650 ft3. How many moles of Helium are required to fill it up @ STP?

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?

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