#### Transcript ATOMIC MASS & ISOTOPES

```ATOMIC MASS & ISOTOPES
• Atomic mass is a relative scale
• Similar to comparing the distances
between Cincinnati to Columbus and
Cincinnati to Toledo
• It is twice as far to Toledo
• If we set the distance to Columbus as
our standard making it 12; Then the
distance to Toledo would be 24
• Chemists originally used Oxygen as the
standard making it 16 but…
• Today we use Carbon-12
• Remember that carbon-12 indicates a
specific isotope of carbon
• Since the mass of hydrogen atoms is
1/12 that carbon-12 we set the Atomic
Mass of Hydrogen to 1
• Likewise, Magnesium atoms are twice
as massive as C-12, hence Mg = 24
a.m.u.
• Interestingly- if you add up the
actual masses of an atom’s protons
and neutrons, they will not equal their
a.m.u. value
• WHY?
• Remember- the a.m.u. value is
relative to carbon-12
• In fact, earliest methods involved
reacting the standard element with
the element to be determined
• From the resulting ratio the atomic
mass would be determined
Isotopes
• Defined as atoms of the same element
having different atomic masses due to
a difference in the number of
neutrons each atom possesses
• Designated by giving the atomic mass
along with the element’s name or
symbol
• carbon-12, C-12, carbon-14, C-14
Atomic Mass & Periodic Table
• The value printed on the Periodic Table
is a weighted average of all the
element’s isotopes
Average Atomic Mass =sum of the
(Mass Isotope A x Percent Abundance) +
(Mass Isotope B x Percent Abundance) +
(Mass Isotope n x Percent Abundance)
Divide by 100
Examples
• Calculate the average atomic mass for
Gallium made up of 60.4% Ga-68
(68.926 amu) and 39.6% Ga-71
(70.925)
• Solution
(68.926 x 60.4) + (70.925 x 39.6) =
100
69.7171604 calculator value
69.7 amu corrected to 3 sig figs
• How many times heavier is the Gallium
atom than the Carbon-12?
• 69.7÷12 = 5.8083333 or 5.81
• Another solution approach is to change
the percent abundance of each isotope
to a decimal thereby eliminating the
need to divide by 100
(68.926 x .604) + (70.925 x .396)=69.7
• Rubidium-85 has 84.912 amu and 72.15%
abundance; Rb-87 is 27.85% of the
element and has a 86.909 amu
• What is the average atomic mass?
• 85.4681645 calculator value
• 85.47 amu correct sig figs
• What is the atomic mass of silicon if
92.21% of its atoms have a mass of
27.977 amu, 4.70% have mass 28.976 and
3.09% have mass of 29.974?
• What is the atomic mass if, out of
every 100 atoms, 5 have a mass of
176 amu, 19 have mass of 177, 27
have mass of 178, 14 have mass of
179, and 35 have mass of 180?
• Answer = 179 amu (178.55 calculator)
Lithium is composed of two isotopes, 6Li
and 7Li. The mass of 6Li is 6.015 and
7Li is 7.016. What is the percent
abundance of each if average mass of
Lithium is 6.941
• Remember % 7Li +% 6Li = 100%
• Therefore we can set the percentage
of one isotope to X and the other will
100-X
• 6.941 = (6.015 x X) + (7.016 x 100-X)
•
100
• 6.941x100 = 6.015X + 701.6 – 7.016X
• 694.1 = 6.015X + 701.6 – 7.016X
• Collect like terms
• 694.1 -701.6 = 6.015X – 7.016X
Solution…continued
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•
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•
•
•
-7.5 = -1.001X
X = -7.5÷-1.001
X = 7.49% for Li-6
Li-7 = 100% - 7.49%
Li-7 = 92.51%
Remember that the sum of the
percentages must equal 100%
• If using decimal percent than = 1.00