Problem Solving 1

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Problem Solving 1

  1. 1. How to Solve Problems and Consider Significant Figures Special Issue
  2. 2. Every problem has its own “anatomy”. A problem consists of tale and data . Tale may be boring and funny. Data may be necessary and unnecessary.
  3. 3. The tale and the data : Silver (Ag: Z = 47 ) has 46 known isotopes, but only two occur naturally , 107 Ag and 109 Ag . Given the following mass spectrometric data, calculate the atomic mass of silver: 107 Ag: atomic mass 106.90509 , abundance 51.84 109 Ag: atomic mass 108.90476 , abundance 48.16
  4. 4. Let us handle a problem step by step: Sphalerite is a mineral, a chief ore of zinc. A sample of sphalerite contains 327.1 g of Zn and 160.4 g of S. Please calculate masses (g) of zinc and sulfur in 541 kg of this mineral.
  5. 5. 1.Read the problem carefully: <ul><li>Sphalerite is a mineral, a chief ore of zinc. A sample of sphalerite contains 327.1 g of Zn and 160.4 g of S. Please calculate masses (g) of zinc and sulfur in 541 kg of this mineral. </li></ul>
  6. 6. 2. Flesh out the given data: <ul><li>Sphalerite is a mineral, a chief ore of zinc. A sample of sphalerite contains 327.1 g of Zn and 160.4 g of S . Please calculate masses (g) of zinc and sulfur in 541 kg of this mineral . </li></ul><ul><li>m 1 (Zn)=327.1 g ; m 1 (S)=160.4 g ; m(ore)=541 kg </li></ul>
  7. 7. 3. Understand what is required: <ul><li>Sphalerite is a mineral, a chief ore of zinc. A sample of sphalerite contains 327.1 g of Zn and 160.4 g of S. Please calculate masses (g) of zinc and sulfur in 541 kg of this mineral . </li></ul><ul><li>m 2 (Zn)= ? ; m 2 (S)= ? </li></ul>
  8. 8. 4.Speculate starting from the question posed: <ul><li>To find mass of zinc and sulfur in a given mass of their compound, we must know their mass fractions (or mass percents) in this compound. </li></ul><ul><li>To find the mass fraction of zinc, we should divide mass of zinc in the sample by the mass of this sample. The same about sulfur. </li></ul><ul><li>To find the mass of the sample, we have to add masses of zinc and sulfur in this sample. </li></ul>
  9. 9. 5. Solve (slide 1) starting from the end of the speculation: <ul><li>Find the mass of the ore sample: 327.1g + 160.4g = 487.5g </li></ul><ul><li>Find the mass fraction of zinc: 327.1g/487.5g = 0.67097436 </li></ul><ul><li>Consider the number of significant figures: 3 . </li></ul><ul><li>Round the value of zinc mass fraction: 0.67097436 ≈ 0.671 </li></ul>
  10. 10. 5. Solve (slide 2) starting from the end of the speculation: <ul><li>Find the mass fraction of sulfur: 160.4g/487.5g = 0.32902564 </li></ul><ul><li>Consider the number of significant figures: 3 . </li></ul><ul><li>Round the value of sulfur mass fraction: 0.32902564 ≈ 0.329 </li></ul><ul><li>or just 1.000 - 0.671 = 0.329 - much faster! </li></ul>
  11. 11. 5. Solve (slide 3) starting from the end of the speculation: <ul><li>Find the mass of zinc in 541 kg of the mineral: 0.671 x 541 kg = 363.011 kg </li></ul><ul><li>Consider the number of significant figures: 3. </li></ul><ul><li>Round the mass of zinc: 363.011kg≈363 kg </li></ul><ul><li>Convert to grams: 363kg=363000g=3.63x10 5 g </li></ul><ul><li>Finalize for WebAssign: 3.63e5 </li></ul>
  12. 12. 5. Solve (slide 4) starting from the end of the speculation: <ul><li>Find the mass of sulfur in 541 kg of the mineral: 0.329x541kg=177.989kg </li></ul><ul><li>Consider the number of significant figures: 3. </li></ul><ul><li>Round the mass of sulfur: 177.989kg≈178kg </li></ul><ul><li>Or just 541 kg - 363 kg = 178 kg - much faster! </li></ul><ul><li>Convert to grams: 178kg=178000g=1.78x10 5 g </li></ul><ul><li>Finalize for WebAssign: 3.63e5 </li></ul>
  13. 13. Let us handle another problem step by step: Gallium has two naturally occurring isotopes, 69 Ga (isotopic mass 68.9256 amu, abundance 60.11%) and 71 Ga (isotopic mass 70.9247 amu, abundance 39.89%). Please calculate the atomic mass of gallium.
  14. 14. 1.Read the problem carefully: <ul><li>Gallium has two naturally occurring isotopes, 69 Ga (isotopic mass 68.9256 amu, abundance 60.11%) and 71 Ga (isotopic mass 70.9247 amu, abundance 39.89%). Please calculate the atomic mass of gallium. </li></ul>
  15. 15. 3. Understand what is required: <ul><li>Gallium has two naturally occurring isotopes, 69 Ga (isotopic mass 68.9256 amu, abundance 60.11%) and 71 Ga (isotopic mass 70.9247 amu, abundance 39.89%). Please calculate the atomic mass of gallium . </li></ul>
  16. 16. 4.Speculate starting from the question posed: <ul><li>To find the atomic mass of gallium, we must add the portions contributed by each isotope of gallium. </li></ul><ul><li>To find a portion contributed, we have to multiply an isotope’s mass number by its fractional abundance. </li></ul>
  17. 17. 5. Solve (slide 1) starting from the end of the speculation: <ul><li>Find the portion contributed by 69 Ga: 68.9256x60.11% / 100%=41.431178 or 68.9256x0.6011=41.431178 </li></ul><ul><li>Consider the number of significant figures: 4 . </li></ul><ul><li>Round the value of 69 Ga portion: 41.431178 ≈ 41.43 </li></ul>
  18. 18. 5. Solve (slide 2) starting from the end of the speculation: <ul><li>Find the portion contributed by 71 Ga: 70.9247x39.89% / 100%=28.291863 or 70.9247x0.3989=28.291863 </li></ul><ul><li>Consider the number of significant figures: 4 . </li></ul><ul><li>Round the value of 71 Ga portion: 28.291863 ≈ 28.29 </li></ul>
  19. 19. 5. Solve (slide 3) starting from the end of the speculation: <ul><li>Add the portions contributed by 69 Ga and 71 Ga: 41.43+28.29=69.72 . It is atomic mass of gallium. </li></ul>
  20. 20. THE END

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