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Average Atomic Mass

Average Atomic Mass. How much does an atom weigh?. Protons & Neutrons:  1.67 X 10 -24 gram Electrons:  9.10 X 10 -28 gram To avoid working with these really small numbers, scientists have developed the atomic mass scale. What is an a.m.u.?. atomic mass unit

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Average Atomic Mass

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  1. Average Atomic Mass

  2. How much does an atom weigh? • Protons & Neutrons:  1.67 X 10-24 gram • Electrons:  9.10 X 10-28 gram • To avoid working with these really small numbers, scientists have developed the atomic mass scale.

  3. 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. This is the STANDARD.

  4. Atomic Weight or Mass • Atomic mass is relative. • C-12 is the standard. 1 atom of C-12 has a mass of exactly 12.000… atomic mass units. • So all the atoms are compared to C-12.

  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. • 6.7% of the test grades are 60. • .933 X 90 + .067 X 60 = 83.97 + 4.02 • Avg. = 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. (.75) (35 amu) + (.25) (37 amu) • = 26.25 amu + 9.25 amu • = 35.5 amu Multiply by appropriate mass. Sum

  13. Avg. Atomic Mass of Chlorine • To estimate the answer: • 75% Cl is 35 and 25% Cl is 37. • The final answer has to be between 35 and 37, but closer to 35. • 35.5 amu

  14. Avg. Atomic Mass of Si 92.21% of Si has a mass of 28 4.70% of Si has a mass of 29 3.09% of Si has a mass of 30

  15. Avg. Atomic Mass of Si .9221 X28  25.8188 .0470 X 29  1.363 + .0309 X 30  0.927 28.1088

  16. Check your work! • Answer has to be between high & low. • Answer has to be closest to 28. • Answer is 28.11.

  17. 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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