Download - Average Atomic Mass
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Average Atomic Mass
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Average Atomic Mass
atomic masses reported in periodic table represent:
weighted average of masses of all naturally occurring isotopes of an element
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Weighted Average:Test Grades
suppose have: 1 test of 0% and 9 tests of 90%
What if I said your average was 45%?
(0 + 90 = 90; divide by 2 = 45%)
would you be happy?
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NO!
the long way to do this problem:
(90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 0)
then 10
average = 81% I bet you like this a lot better!
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The smart way to do this problem!
grades of 90: 9 out of 10 is 90% grades of 0: 1 out of 10 is 10%
90% test grades are 90 & 10% test grades are 0
so calc average like this… (90%)(90) + (10%)(0) =
(0.90 X 90) + (0.10 X 0) = 81 + 0
average = 81%
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Weighted average:Weighted average:
Smarter way to calculate Smarter way to calculate average if have average if have
numerous items of numerous items of differing value to differing value to
averageaverage
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Method of Weighted Averages
● convert % to decimal format (divide % by 100)
● multiply each isotope’s abundance factor by its atomic mass
● find the sum
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Avg. Atomic Mass of Chlorine
36.966 amu24.230%Isotope 2Isotope 2
34.969 amu75.770%Isotope 1Isotope 1
MassMassPercent Percent AbundanceAbundance
Chlorine has two isotopes
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Avg. Atomic Mass of Chlorine
to estimate the answer:75% of Cl is 34.969 amu &25% of Cl is 36.966 amu
average has to be between 34.969 amu & 36.966 amu, but closer to 34.969 amu
let’s calculate the averagelet’s calculate the average
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Avg. Atomic Mass of Chlorine =
(.75770)(34.969 amu) + (.75770)(34.969 amu) +
(.24230) (36.966 amu) (.24230) (36.966 amu)
= 26.496 amu + 8.957 amu= 26.496 amu + 8.957 amu
= 35.453 amu= 35.453 amu
convert % to convert % to decimalsdecimals
multiply by multiply by appropriate appropriate massmass
sumsum
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Avg. Atomic Mass of Si92.21% of Si has mass of 27.97693 amu92.21% of Si has mass of 27.97693 amu
4.70% of Si has mass of 28.97649 amu4.70% of Si has mass of 28.97649 amu
3.09% of Si has mass of 29.97376 amu3.09% of Si has mass of 29.97376 amu
(0.9221)(27.97693) (0.9221)(27.97693) ++ (0.0470)(28.97649) (0.0470)(28.97649)
++ (0.0309)(29.97376) (0.0309)(29.97376) = 28.0856 amu= 28.0856 amu
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Avg. Atomic Mass of Pb 1.5% Pb-2041.5% Pb-204
23.6% Pb-20623.6% Pb-206
22.6% Pb-20722.6% Pb-207
52.3% Pb-20852.3% Pb-208
(0.015)(204amu) + (0.236)(206amu) + (0.015)(204amu) + (0.236)(206amu) +
(0.226)(207amu) + (0.523)(208amu) (0.226)(207amu) + (0.523)(208amu) ==
sum 207.24amu sum 207.24amu