Average Atomic Mass

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Average Atomic Mass
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Chapter 7.4Average Atomic Mass

• Objective
• (1) To calculate the average atomic mass for an
  atom.

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Average Atomic Mass

• Weighted average of the masses of the existing
  isotopes of an element.

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Recall Atomic Mass Unit

• The unit that describes the mass of an atom
• Symbol amu

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Example 1

• The mass of a Cu-63 atom is 62.94 amu, and that
  of a Cu-65 atom is 64.93 amu. The percent
  abundance of Cu-63 is 69.17 and the percent
  abundance of Cu-65 is 30.83. What is the
  average atomic mass of Cu?

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Example 1

• The mass of a Cu-63 atom is 62.94 amu, and that
  of a Cu-65 atom is 64.93 amu. The percent
  abundance of Cu-63 is 69.17 and the percent
  abundance of Cu-65 is 30.83. What is the
  average atomic mass?
• Step 1 Find the contribution of each isotope
• Cu-63 (62.94 amu) x (0.6917) 43.535598 amu
• Cu-65 (64.93 amu) x (0.3083) 20.017919 amu
• Step 2 Add the relative abundances from each
  isotope together.
• 43.535598 amu 20.017919 amu 63.553517 amu
• Round answer to two numbers after the decimal
  63.55 amu

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Example 2

• Calculate the average atomic mass of chromium.
  It is made up of isotopes with the following
  percent compositions and atomic masses 83.79
  with a mass of 51.94 amu 9.50 with a mass of
  52.94 amu 4.35 with a mass of 49.95 amu 2.36
  with a mass of 53.94 amu.

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Example 2

• Calculate the average atomic mass of chromium.
  It is made up of isotopes with the following
  percent compositions and atomic masses 83.79
  with a mass of 51.94 amu 9.50 with a mass of
  52.94 amu 4.35 with a mass of 49.95 amu 2.36
  with a mass of 53.94 amu.
• Step 1 Find the contribution of each isotope
• (51.94 amu) x (0.8379) 43.520526 amu
• (52.94 amu) x (0.0950) 5.0293 amu
• (49.95 amu) x (0.0435) 2.172825 amu
• (53.94 amu) x (0.0236) 1.272984 amu
• Step 2 Add the relative abundances from each
  isotope together.
• 43.520526 amu 5.0293 amu 2.172825 amu
  1.272984 amu 51.995635 amu
• Round answer to two numbers after the decimal
  52.00 amu

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Example 3

• Calculate the average atomic mass of iron if its
  abundance in nature is 15 iron-55 and 85
  iron-56.

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Example 3

• Calculate the average atomic mass of iron if its
  abundance in nature is 15 iron-55 and 85
  iron-56.
• Step 1 Calculate the contribution of each
  isotope
• Iron-55 (55 amu) x (0.15) 8.25 amu
• Iron-56 (56 amu) x (0.85) 47.6 amu
• Step 2 Add the contribution from each isotope
  together
• 8.25 amu 47.6 amu 55.85 amu
• The element with an atomic mass of 10.8 amu is
  Boron.

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Example 4

• Chlorine exists as chlorine-35, which has a mass
  of 34.969 amu and makes up 75.8 of chlorine
  atoms. The rest of naturally occurring chlorine
  is chlorine-37, with a mass of 36.996 amu. What
  is the average atomic mass of chlorine?

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Example 4

• Chlorine exists as chlorine-35, which has a mass
  of 34.969 amu and makes up 75.8 of chlorine
  atoms. The rest of naturally occurring chlorine
  is chlorine-37, with a mass of 36.996 amu. What
  is the average atomic mass of chlorine?
• Step 1 Find the contribution of each isotope
• Cl-35 (34.969 amu) x (0.758) 26.506502 amu
• Cl-37 (36.996 amu) x (0.242) 8.953032 amu
• Step 2 Add the relative abundances from each
  isotope together.
• 26.506502 amu 8.953032 amu 35.459534 amu
• Round answer to two numbers after the decimal
  35.46 amu

1 0.758
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Example 5

• Element X has two isotopes. One has a mass of
  10.0 amu and an abundance of 20.0. The other
  has a mass of 11.0 amu and an abundance of 80.0.
  Estimate the average atomic mass. What element
  is it?

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Example 5

• Element X has two isotopes. One has a mass of
  10.0 amu and an abundance of 20.0. The other
  has a mass of 11.0 amu and an abundance of 80.0.
  Estimate the average atomic mass. What element
  is it?
• Step 1 Calculate the contribution of each
  isotope
• Isotope 1 (10.0 amu) x (0.20) 2 amu
• Isotope 2 (11.0 amu) x (0.80) 8.8 amu
• Step 2 Add the contribution from each isotope
  together
• 2 amu 8.8 amu 10.8 amu
• The element with an atomic mass of 10.8 amu is
  Boron.