Number of Protons = Number of Electrons Number of Protons = Atomic Number Atomic Mass = Protons + Neutrons.

Number of Protons = Number of ElectronsNumber of Protons = Atomic NumberAtomic Mass = Protons + Neutrons

Average Atomic Mass

Average Atomic Mass

The atomic masses reported in the periodic table represent the weighted average of the masses of the naturally occurring isotopes of that element

Weighted Avg. of Test Grades

Suppose you 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) 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% grade 0f 0: 1 out of 10 is 10%

So 90% of the test grades are 90 10% of the test grades are 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 the average if you have the average if you have

numerous items to numerous items 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 =

(.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 Chlorine

To estimate the answer:75% of Cl is 34.969 amu &25% of Cl is 36.966 amu

The final answer has to be between 34.969 amu & 36.966 amu, but closer to 34.969 amu

35.453 amu35.453 amu

Avg. Atomic Mass of Si

92.21% of Si has a mass of 27.97693 92.21% of Si has a mass of 27.97693 amuamu

4.70% of Si has a mass of 28.97649 4.70% of Si has a mass of 28.97649 amuamu

3.09% of Si has a mass of 29.97376 3.09% of Si has a mass of 29.97376 amuamu

Avg. Atomic Mass of Si

0.9221 X0.9221 X 27.97693 27.97693 25.7975 amu 25.7975 amu

0.0470 X 28.97649 0.0470 X 28.97649 1.3619 amu 1.3619 amu

+ 0.0309 X 29.97376 + 0.0309 X 29.97376 0.9262 amu0.9262 amu

28.0856 amu28.0856 amu

Avg. Atomic Mass of Pb

1.5% Pb-204 1.5% Pb-204 0.015 X 204amu: 0.015 X 204amu: 3.06amu3.06amu

23.6% Pb-206 23.6% Pb-206 0.236 X 206amu: 0.236 X 206amu: 48.62amu48.62amu

22.6% Pb-207 22.6% Pb-207 0.226 X 207amu: 0.226 X 207amu: 46.78amu46.78amu

52.3% Pb-208 52.3% Pb-208 0.523 X 0.523 X 208amu:208amu:108.78amu108.78amu

Sum 207.24amu Sum 207.24amu