# Weighted average (PowerPoint)

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```					FINDING THE ATOMIC
MASS OF AN ELEMENT

by finding the weighted
average of the masses of
each of the element’s
isotopes.
Mass number
   The mass number of an individual atom is
the sum of protons and neutrons in the
nucleus.

Mass number = p + n
   Mass number apply to individual atoms or
to an element with just one isotope in it.
   Mass number is always a whole number.
Elements, as found on earth
consist of a mixture of isotopes
of that element.

Example: Nearly all of the carbon in a
sample of pure carbon is carbon-12.
However, the sample also has traces of
carbon-13 and carbon-14 isotopes.
Atomic mass

The atomic mass
of an element is the
WEIGHTED AVERAGE
of the mass numbers
of all of the isotopes in the sample.
What is the atomic number
of chlorine?

What is the atomic mass
of chlorine?
Mass number ≠ atomic mass

Mass number = protons + neutrons

Atomic mass = weighted average of
the mass numbers of all of the isotopes
of an element present in a sample.
What is a
weighted average?
Weighted average
A total of 50 students at Carmel HS took the AP
exam in U. S. History. Here are the results of the
test. What is the weighted average score?

Test score        Number of students
5                      12
4                      18
3                      14
2                       6
1                       0
A total of 50 students at Carmel HS took the AP exam in
U. S. History. What is the weighted average score?

Test score    Number of      Multiply        Product
students

5           12           5 x 12 =          60

4           18           4 x 18 =          72
3           14           3 x 14 =          42
2           6            2x6=              12
1           0            1x0=              0

Sum =                        186
Weighted average score = 186/50 =             3.72
The Eminemium exercise

M & M s
The element   Eminemium
has several isotopes
• Each color represents an
isotope of the element. For
example red is E-20.
• Count your M&Ms and figure %
abundance of each isotope.
• The weighted value for each
isotope is:
mass number x % abundance.
The weighted average of the mass numbers of
each of the isotopes of eminemium is the sum
of the weighted values for each of the
isotopes (colors) of eminemium.

This weighted average is the atomic mass of
that sample of eminemium atoms.
Let’s try the exercise.
In case you’re curious…
The M&M website shows the relative
distribution (% abundance) of it products.

Let’s do a calculation for
using the real isotopes of
the element magnesium.

Modern chemical instrumentation
enables us to determine the actual
masses of each of the isotopes to a
tremendous degree of accuracy!
Therefore, magnesium-24 has been
found to have an actual mass of
23.985 atomic mass units.
Calculation of the weighted
average of isotopes of magnesium
Isotope   Actual mass      Relative
(AMU)       abundance (%)
Mg-24       23.985          78.99

Mg-25       24.986          10.00

Mg-26       25.982          11.01

100.00%
Isotope      Relative    Weighted value
Atomic mass   abundance

23.985        78.99%             18.946

24.986         10.00              2.499

25.982         11.01              2.861

100.00%     Sum:   24.306
The weighted average of mass
number of magnesium isotopes
as found in nature is its
ATOMIC MASS.

Atomic mass of Mg = 24.306

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 views: 17 posted: 10/28/2011 language: English pages: 19
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