Average Atomic Mass
8/12/10
GPS Standards:
SC3. Students will use the modern atomic theory to explain the characteristics of atoms.
d. Explain the relationship of isotopes to the relative abundance of atoms of a particular element.
SC2. Students will relate how the Law of Conservation of Matter is used to determine chemical composition
in compounds and chemical reactions.
c. Apply concepts of the mole and Avogadro’s number to conceptualize and calculate mass, moles and
molecules relationships.
Part I: Average Atomic Mass
• atomic mass (or weight) = weighted average of all
the mass numbers of all the isotopes of an element.
Not written on symbol, but is found on PT.
• atomic mass is calculated by multiplying the mass
number of each isotope by its abundance in the
environment (a percentage).
Carbon 6
C
12.01
NOTE: numbers given as percentages must be converted
before they can be entered into the calculator. Move the
decimal 2 places to the left, then enter the number.
• Ex: hydrogen has three isotopes…
Ex: hydrogen has three isotopes…
1. protium (1 p+, 0 n0) @ 99.985%
Hydrogen 1
1.0073 amu x 0.99985 = 1.007148905 amu
2. deuterium (1 p+, 1 n0) @ 0.0149%
1.01
2.0160 amu x 0.000149 = 0.000300384 amu
3. tritium (1 p+, 2 n0) @ 0.0001%
3.0247 amu x 0.000001 = 0.0000030247 amu
1.007452314 amu
≈ 1.01 amu
• let’s try another one…..
H
Isotope
Average Mass
(in amu)
Abundance
(%)
Multiplied Mass
nickel-58
nickel-60
nickel-61
nickel-62
nickel-64
57.935347
59.930789
60.931059
61.928346
63.927968
68.27
26.1
1.13
3.59
0.91
39.5524614
15.64193593
0.688520967
2.223227621
0.581744509
• atomic mass tells you two very important things about an
element:
Atomic
Mass
58.69
Always round
this number to
2 places after
the decimal!
Nickel 28
Ni
58.69
• atomic mass tells you two very important things about an element:
1. the mass of one atom of an element, measured in amu.
• hydrogen = 1.01 amu per atom
• carbon = 12.01 amu per atom
• gold = 196.97 amu per atom
2. the mass of one mole of an element, measured in grams.
• hydrogen = 1.01 grams per mole
• carbon = 12.01 grams per mole
• gold = 196.97 grams per mole
• So what is a mole? Remember that molecules and atoms are
extremely small units of matter. A small drop of water contains
approx. 1.7 x 1022 molecules of H2O!
Part II: The Mole Concept
• So what is a mole? Remember that molecules and atoms are
extremely small units of matter. A small drop of water contains
approx. 1.7 x 1022 molecules of H2O!
• since extremely large numbers of molecules are a bit cumbersome
to work with (meaning calculate with), scientists simplify this process
by using a counting unit called a mole.
• counting units are often used in everyday life. Examples: 1
dozen = 12, a pair = 2, a gross = 144, 1 ream = 500.
• 1 mole = 6.022 x 1023 or …
602,200,000,000,000,000,000,000
This number is known as Avogadro’s number.
• 1 mole = 6.022 x 1023 or …
602,200,000,000,000,000,000,000
•
•
•
•
This number is known as Avogadro’s number.
Avogadro was a scientist who figured out a way to tie
the weight of individual atoms to the weight of their
compounds in grams.
mole = a counting unit representing the number of
particles (6.022 x 1023) it takes for a substance’s
atomic weight to equal it’s weight in grams.
why tie these two quantities together? Grams (a measure of weight)
are way easier to work with! Weighing out a few grams of a
compound is much easier to do than counting out individual atoms or
molecules!
just to drive home the point:
• just to drive home the point:
• 1 mole of dollar bills, stacked, would reach
3,800,000,000,000,000 miles (3.8 x 1016) into
outer space! This distance is like going to the
sun and back 160,000,000 times!
• 1 mole of regular M&Ms would cover the 48 contiguous
United States to a depth of 17,000 feet (3.2 miles) thick!
• 1 mole of sand grains would be more than all the
grains of sand found on Miami Beach (which is
several miles long and quite wide as well)!
• 1 mole of blood cells is more than all the blood cells found
in all the humans alive on the earth (over 6 billion people)!
• 1 mole of blood cells is more than all the blood cells found
in all the humans alive on the earth (over 6 billion people)!
• 1 mole of any object, counted at 1 object per second,
would take 1 x 1019 years to count out! That’s older
than the universe itself, which is approx. 15 billion
(1.5 x 109) years old!