# Average Atomic Mass Average Atomic Mass atomic masses

• Slides: 13

Average Atomic Mass

Average Atomic Mass atomic masses reported in periodic table represent: weighted average of masses of 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 + 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% grades of 0: 1 out of 10 is 10% So… 90% test grades are 90 & 10% test grades are 0 (90%)(90) + (10%)(0) = (0. 90 X 90) + (0. 10 X 0) = 81 + 0 Average = 81%

Weighted average: Smarter way to calculate average if have numerous items of differing value to average

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 has two isotopes Percent Abundance Mass Isotope 1 75. 770% 34. 969 amu Isotope 2 24. 230% 36. 966 amu

Avg. Atomic Mass of Chlorine = (. 75770)(34. 969 amu) + Convert % to decimals (. 24230) (36. 966 amu) = 26. 496 amu + 8. 957 amu = 35. 453 amu Multiply by appropriate mass Sum

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 amu

Avg. Atomic Mass of Si 92. 21% of Si has mass of 27. 97693 amu 4. 70% of Si has mass of 28. 97649 amu 3. 09% of Si has mass of 29. 97376 amu

Avg. Atomic Mass of Si (0. 9221)(27. 97693) + (0. 0470)(28. 97649) + (0. 0309)(29. 97376) = 28. 0856 amu

Avg. Atomic Mass of Pb 1. 5% Pb-204 23. 6% Pb-206 22. 6% Pb-207 52. 3% Pb-208 (0. 015)(204 amu) + (0. 236)(206 amu) + (0. 226)(207 amu) + (0. 523)(208 amu) = Sum 207. 24 amu