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