average atomic mass
DESCRIPTION
Average Atomic Mass. Average Atomic Mass. atomic masses reported in periodic table represent: weighted average of masses of all naturally occurring isotopes of an element. Weighted Average:Test Grades. suppose have : 1 test of 0% and 9 tests of 90% - PowerPoint PPT PresentationTRANSCRIPT
Average Atomic Mass
Average Atomic Mass
atomic masses reported in periodic table represent:
weighted average of masses of all naturally occurring isotopes of an element
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?
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!
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%
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
Method of Weighted Averages
● convert % to decimal format (divide % by 100)
● multiply each isotope’s abundance factor by its atomic mass
● find the sum
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
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
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
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
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