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Understanding Recycling and Chemical Mathematics: The Carbon Cycle and Chemical Equations

This chapter delves into the intricate relationship between recycling in nature and chemical mathematics, focusing on the carbon cycle. It explores fundamental concepts such as chemical reactions and their equations, with an emphasis on respiration and the transformation of substances. By analyzing balanced equations, stoichiometric calculations, and atomic masses, readers will gain insights into chemical processes like the Hall-Heroult process for aluminum production. This information is essential for understanding both natural cycles and industrial applications in chemistry.

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Understanding Recycling and Chemical Mathematics: The Carbon Cycle and Chemical Equations

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  1. Chapter 4 Recycling and Chemical Mathematics

  2. Nature’s Recycling –The carbon cycle

  3. Chemical Equations Chemical reaction: the reorganization of the atoms in one or more substances to form a different substance(s). A chemical equation for respiration: C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l) What does this equation mean?

  4. What does this equation mean? C6H12O6(s) + 6O2(g) → 6CO2(g) + 6H2O(l) “One molecule of glucose solid reacts with six molecules of oxygen gas to give (or produce) six molecules of carbon dioxide gas and six molecules of water.”

  5. Accounting for atoms in the process of respiration

  6. Example:Recognizing Balanced Equations Is the following equation balanced? CaCl2 + 2Na3PO4→ Ca3(PO4)2 + 3NaCl

  7. Solution:Recognizing Balanced Equations This is the balanced chemical equation. 3CaCl2 + 2Na3PO4→ Ca3(PO4)2 + 6NaCl

  8. Producing Aluminum via the Hall-Heroult Process 2Al2O3(l) + 3C(s) → 4Al(l) + 3CO2(g)

  9. Example: Atomic Masses The mass of an atom is the weighted average of its naturally-occurring isotopes. Gallium has 2 isotopes, 60.10% 69Ga (= 68.93 amu) and 39.90% 71Ga (= 70.92 amu). What is the average atomic mass of Ga?

  10. Solution: Atomic Masses 60.10% 69Ga (= 68.93 amu) and 39.90% 71Ga (= 70.92 amu). What is the average atomic mass of Ga? (0.6010 x 68.93) + (0.3990 x 70.92) = contribution of 69Ga isotope contribution of 71Ga isotope 69.72 amu

  11. Formula Masses The sum of the atomic masses of all the atoms in the formula. H2O = 2 x 1.008 + 1 x 16.00 = 18.02 amu hydrogen oxygen Fe(OH)3 = 1 x 55.847+3 x (16.00 + 1.008) = 106.87 amu iron oxygenhydrogen

  12. Avogadro’s Number • 1 mol of anything = 6.02 x 1023 things • 1 mol of C atoms = 6.02 x 1023 C atoms • 1 mol of Al atoms = 6.02 x 1023 Al atoms • 1 mol of Al2O3 = 6.02 x 1023Al2O3 formula units • 1 mol of frosted flakes = 6.02 x 1023frosted flakes (Yum!)

  13. Conversions: Moles to Grams How many grams of Al2O3 are in 31.27 moles of Al2O3? = 3188 g Al2O3

  14. Conversions: Grams to Moles How many moles of (NH4)2Cr2O7 are in 586.2 grams of (NH4)2Cr2O7? = 2.326 moles of NH4Cr2O7

  15. Using Equations for Stoichiometric Calculations How many moles of iron can be formed from 2.8 moles of iron(III) oxide, Fe2O3? Fe2O3 + 2Al → 2Fe + Al2O3

  16. Solution: Using Equations for Stoichiometric Calculations How many moles of iron can be formed from 2.8 moles of iron(III) oxide, Fe2O3? Fe2O3 + 2Al → 2Fe + Al2O3 = 5.6 moles Fe

  17. Using Equations for Stoichiometric Calculations How many grams of Al2O3 can be formed from 1162 grams of Fe2O3? Fe2O3 + 2Al → 2Fe + Al2O3

  18. Using Equations for Stoichiometric Calculations How many grams of Al2O3 can be formed from 1162 grams of Fe2O3? Fe2O3 + 2Al → 2Fe + Al2O3 Strategy g Fe2O3 →mol Fe2O3 →mol Al2O3→g Al2O3

  19. Solution: Using Equations for Stoichiometric Calculations How many grams of Al2O3 can be formed from 1162 grams of Fe2O3? g Fe2O3 → mol Fe2O3 → mol Al2O3 →g Al2O3 = 741.8 g Al2O3

  20. Using Equations for Stoichiometric Calculations How many grams of CO2 can be formed from 80.7 grams of C6H12O6 in respiration? Assume excess oxygen. C6H12O6 + 6O2 → 6CO2 + 6H2O

  21. Using Equations for Stoichiometric Calculations How many grams of CO2 can be formed from 80.7 grams of C6H12O6 in respiration? Assume excess oxygen. C6H12O6 + 6O2 → 6CO2 + 6H2O Strategy g C6H12O6 → mol C6H12O6 → mol CO2 → g CO2

  22. Solution:Using Equations for Stoichiometric Calculations How many grams of Al2O3 can be formed from 1162 grams of Fe2O3? g C6H12O6 → mol C6H12O6 →mol CO2 →g CO2 = 118 g CO2

  23. Common Polymers and Their Monomers

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