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Average Atomic Mass

Average Atomic Mass. What is an a.m.u.?. atomic mass unit amu  1/12 the mass of the C-12 atom. C-12 is used as the reference for atomic masses. Isotopes. Atoms of the same element that have different # of Neutrons are said to be ISOTOPES of that element

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Average Atomic Mass

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  1. Average Atomic Mass

  2. What is an a.m.u.? • atomic mass unit • amu  1/12 the mass of the C-12 atom. • C-12 is used as the reference for atomic masses.

  3. Isotopes • Atoms of the same element that have different # of Neutrons are said to be ISOTOPES of that element • All isotopes of an element are chemically the same, i.e., they react exactly the same

  4. Isotopes • All elements found in nature are MIXTURES of isotopes • Isotopes of an element are designated by mass number in either of two ways • 1: 23592U • 2: U-235 or Uranium-235 • Using the above how would we designate the isotope of carbon that has 8 neutrons? 146C or C-14 (Carbon-14)

  5. 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.

  6. Weighted Avg. of Test Grades • Suppose you have 1 test of 60% and 14 tests of 90%. What if I said your avg. was 75? • 60 + 90 = 150. Divide by 2 = 75. • Would you be happy?

  7. NO! • The long way to do this problem: • (90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 90 + 60)  15 • Avg. = 88. You like this a lot better!

  8. The smart way to do this problem!  14 out of 15 is 93.3%  1 out of 15 is 6.7% • So … 93.3% of the test grades are 90, and … 6.7% of the test grades are 60. Weighted Average = [.933 x 90] + [.067 x 60] = 83.97 + 4.02 = 88%

  9. This is an even smarter way to calculate the average if you have lots of items to average.

  10. Method of Weighted Averages • Convert % to decimal format. (Divide by 100%.) • Multiply each isotope’s abundance factor by its atomic mass. • Sum.

  11. Avg. Atomic Mass of Chlorine Chlorine has two isotopes

  12. Avg. Atomic Mass of Chlorine = Convert percents to decimals. (.75770)(34.969 amu) + (.24230)(36.966 amu) • = 26.496 amu + 8.957 amu • = 35.453 amu Multiply by appropriate mass. Sum

  13. Avg. Atomic Mass of Chlorine • To estimate the answer: • 75% Cl is 34.969 and 25% Cl is 36.966. • The final answer has to be between 34.969 and 36.966, but closer to 34.969. • 35.453 amu

  14. Avg. Atomic Mass of Si 92.21% of Si has a mass of 27.97693 4.70% of Si has a mass of 28.97649 3.09% of Si has a mass of 29.97376

  15. Avg. Atomic Mass of Si .9221 X27.97693  25.7975 .0470 X 28.97649  1.3619 + .0309 X 29.97376  0.9262 28.0856

  16. Check your work! • Answer has to be between high & low. • Answer has to be closest to 27.97693. • Answer is 28.0856.

  17. Avg. Atomic Mass of Pb 1.5% Pb-204.  23.6% Pb-206.  22.6% Pb-207.  52.3% Pb-208. 

  18. Avg. Atomic Mass of Pb 1.5% Pb-204.  .015 X 204 : 3.06 23.6% Pb-206.  .236 X 206 : 48.62 22.6% Pb-207.  .226 X 207 : 46.78 52.3% Pb-208.  .523 X 208 : 108.78 207.24

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