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# How Big Is A Mole

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### How Big Is A Mole

1. 1. The Mole
2. 2. <ul><li>1 amu = 1.66 x 10 -24 grams </li></ul><ul><li>1 C-12 atom = 12 amu </li></ul><ul><li>(12)(1.66 x 10 -24 g) = 1.992 x 10 -23 g </li></ul><ul><li>1.992 x 10 -23 grams is the mass of one carbon-12 atom </li></ul><ul><li>But … we do not work with single atoms or with gram values this small </li></ul><ul><li>We need reasonable numbers to work with in the laboratory </li></ul>
3. 3. The Mole Concept
4. 4. NO… not that kind of mole !!!!
5. 5. The Mole <ul><li>The mole is a number….. </li></ul><ul><li>A HUGE number…… </li></ul><ul><li>But still just a number….. </li></ul><ul><li>A mole is a collection of </li></ul><ul><li>6.02 x 10 23 particles </li></ul><ul><li>602,000,000,000,000,000,000,000 </li></ul><ul><li>These particles may be atoms, molecules, ions, or electrons </li></ul>
6. 6. <ul><li>1 dozen = 12 </li></ul><ul><li>1 gross = 144 </li></ul><ul><li>1 mole = 6.02 x 10 23 </li></ul><ul><li>Just how large is this number? </li></ul><ul><li>602,000,000,000,000,000,000,000 </li></ul><ul><li>It is really hard to relate to a number this large ……….but let’s try and see if we can make sense the enormity of the number. </li></ul>
7. 7. If all 5 billion people on Earth were to do nothing but count the atoms in 1 mole of an element, 24 hours a day, at the rate of 1 atom per second…….
8. 8. It would take 4 million years !!
9. 9. 1 mole of seconds represents a span of time…..
10. 10. 4 million times as long as the Earth has already existed !!
11. 11. 1 mole of marbles is enough marbles to cover the entire Earth…
12. 12. to a depth of 50 miles
13. 13. 1 mole of rice grains has a mass equal to….
14. 14. each of the 5 billion people on earth having 1 million cars each
15. 15. A mole of dollars ??
16. 16. How many years would it take you to spend 1 mole of dollars, if you spend at a rate of \$1 billion per second ? \$ 6.02 x 10 23 = ? Years
17. 17. Using dimensional analysis: \$6 . 02x10 23 \$1x10 9 1sec 60sec 1min 60min 1hr 24hr 1day 365day 1 yr = 19,089,294.77 years over 19 million years!!!
18. 18. And yet there is 1 mole of water molecules – 6.022 x 10 23 molecules of water in only 18 mL of water !!
19. 19. Questions ???
20. 20. A Mole Poem
21. 21. Say you had a mole of paper and stacked it toward the sky, Paper's really thin, but that pile would get so high, It'd reach up into outer space, in fact I think you'd find, It'd go up to the moon and back, eighty billion times.
22. 22. Say you had a mole of atoms, would the pile be immense? Should I say the answer now, or leave you in suspense? Well, atoms are so very, very small, you understand, You could hold a mole of atoms in the palm of your hand.
23. 23. There are more atoms in that sugar than stars up in the sky. So shake a little sugar in the middle of your palm Now you don't want to spill it, so try and stay calm. You hardly can imagine and barely realize,
24. 24. <ul><li>Why is this number so special? </li></ul><ul><li>The mole is defined as the number of atoms of 12 C in exactly 12.000 grams of pure 12 C </li></ul><ul><li>There are exactly 1 mole of atoms in the atomic mass of an element when that mass is expressed in grams </li></ul>
25. 25. Avogadro’s Number <ul><li>1 mole = 6.022 x 10 23 particles </li></ul><ul><li>1 mole = Avogadro’s number </li></ul><ul><li>1 mole = the atomic mass of an element expressed in grams </li></ul>
26. 26. What is the mass of 1 mole of carbon ? 12.011 grams How many atoms? 6.022 x 10 23 atoms What is the mass of ½ mole of carbon ? 6.0055 grams
27. 27. 12.011 grams of carbon contains the same # of atoms as 1 mole of carbon
28. 28. What is the mass of 1 mole of gold ? 196.967 grams How many atoms? 6.022 x 10 23 atoms What is the mass of ½ mole of gold ? 98.4835 grams
29. 29. 12.011 grams of carbon contains the same # of atoms as 196.967 grams of gold.
30. 30. What is the mass of 1 mole of Mg ? 24.305 grams What is the mass of 2 moles of Mg ? 48.610 grams How many atoms? 1.204 x 10 24 atoms
31. 31. 12.011 grams of carbon contains the same # of atoms as 196.967 grams of gold and the same # of atoms as 24.305 grams of magnesium.
32. 32. What is the mass of 1 mole of Cu ? 63.546 grams What is the mass of ¼ mole of Cu ? 15.8865 grams How many atoms? 1.5055 x 10 23 atoms
33. 33. 12.011 grams of carbon contains the same # of atoms as 196.967 grams of gold and the same # of atoms as 24.305 grams of magnesium and the same # of atoms as 63.546 grams of copper.
34. 34. Questions ???
35. 35. Molar Mass: The mass of 1 mole of a substance in grams The substance can be a compound or an element
36. 36. Molar Mass of a Compound H 2 O 2 H = 2 x 1.008 = 2.016 g 1 O = 1 x 16.00 = 16.00 g 16.00 g + 2.016 g = 18.016 g molar mass of water = 18.02 grams
37. 37. Calculate the molar masses: HCl 36.46 g CO 2 44.01 g Mg 3 (PO 4 ) 2 262.87 g C 12 H 22 O 11 342.30 g Mg(OH) 2 58.33 g
38. 38. Questions ???
39. 39. Mole Conversions
40. 40. Moles to Mass Moles of substance Mass of substance Molar mass of substance
41. 41. Calculate the number of moles in 26.00 g of NaOH: 26.00 g NaOH 40.00 g NaOH 1 mol NaOH = 0.65 mol Calculate the number of g in 0.02 moles of NaOH: 0.02 mol NaOH 1 mol NaOH 40.00 g NaOH = 0.8 g
42. 42. Questions ???
43. 43. Moles to Number of Entities Moles of substance Number of atoms or molecules Avogadro’s number
44. 44. Calculate the number of atoms of Na in 0.34 moles of Na: 0.34 mol Na 1 mol Na 6.022 x 10 23 atoms Na Calculate the number of moles of Na in 3.61 x 10 18 atoms of Na: 3.61 x 10 18 atoms Na 6.022 x 10 23 atoms Na 1mol Na = 2.05 x10 23 atoms Na = 6.0 x 10 -6 mol Na
45. 45. Questions ???
46. 46. Moles of substance Mass of substance Number of atoms or molecules Avogadro’s number Molar mass of substance
47. 47. Calculate the number of grams of Na present in 3.00 x 10 18 atoms of Na: 3.00 x 10 18 atoms 6.022 x 10 23 1 mol 1 mol 23 g = 0 .0001146 g or 1.146 x 10 -4 g of Na
48. 48. Calculate the number of atoms of Na in 160.00 grams of Na: 160.00 g Na 23.00 g Na 1 mol Na 1 mol Na 6.022 x 10 23 = 4.189 x 10 24 atoms of Na
49. 49. Americium is an element that does not occur naturally. It can be made in very small amounts in a particle accelerator. Calculate the mass in grams of a sample of americium containing only six atoms.
50. 50. 6 atoms 6.022 x 10 23 atoms 1 mol 1 mol 243 grams = 2.42 x 10 -21 grams of Am
51. 51. A silicon chip used in an integrated circuit of a microcomputer has a mass of 5.68 mg. How many silicon (Si) atoms are present in the chip?
52. 52. 5.68 mg 1000 mg 1 g 28.09 g Si 1 mol Si 1 mol Si 6.022 x 10 23 atoms = 1.22 x 10 20 atoms of Si
53. 53. Aluminum is often used for the structure of light-weight bicycle frames. How many atoms of Al are in 20.00 grams of Al?
54. 54. 20.00 g Al 26.98 g Al 1 mol Al 1 mol Al 6.022 x 10 23 atoms Al = 4.46 x 10 23 atoms Al
55. 55. The artificial sweetener aspartame (Nutri-Sweet) formula C 14 H 18 N 2 O 5 is used to sweeten diet foods, coffee and soft drinks. How many moles of aspartame are present in 225 mg of aspartame?
56. 56. C 14 H 18 N 2 O 5 = 294 g/mol 225 mg 294 g 1 mol 1000 mg 1 g = 7.65 x 10 -4 mol
57. 57. Prozac, C 17 H 18 F 3 NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. How many atoms of carbon are in 0.003 grams of Prozac?
58. 58. C 17 H 18 F 3 NO = 309 g/mol 0.003 g 309 g 1 mol C 17 H 18 F 3 NO 1 mol C 17 H 18 F 3 NO 17 mol C 1 mol C 6.022 x 10 23 atoms C = 9.94 x 10 19 atoms C
59. 59. Questions ???
60. 60. More Calculations with the Mole
61. 61. Penicillin, the first of a now large number of antibiotics, has the formula C 14 H 20 N 2 SO 4 . Calculate the mass of 2.0 x 10 10 molecules of penicillin.
62. 62. 2.0 x 10 10 molecules Molar mass C 14 H 20 N 2 SO 4 = 312.4 grams 6.022 x 10 23 molecules 1 mol 1 mol 312.4 grams = 1.04 x 10 -11 grams of penicillin
63. 63. A student drinks 3 cups of coffee in order to stay awake and study. Coffee contains the compound caffeine, a stimulant , with the formula C 8 H 10 N 4 O 2 If the caffeine content in an average cup of coffee is 0.5 mg. How many molecules of caffeine did the student ingest?
64. 64. (0.5 mg) (3) = 1.5 mg 1.5 mg molar mass caffeine = 194.2 grams 1000 mg 1 g 194.2 g 1 mol 1 mol 6.022 x 10 23 molecules = 4.65 x 10 18 molecules of caffeine
65. 65. Humulone, C 21 H 30 O 5 , is one of the flavor components that gives a bitter taste to beer. What is the molar mass of humulone? How many moles are in 275 mg of humulone? What is the mass of 9.00 x 10 18 molecules of humulone?
66. 66. Molar mass = 362.45 grams 275 mg 1000 mg 1 g 362.45 g 1 mol = 7.59 x10 -4 mol 7.59 x10 -4 mol 1 mol 6.022 x 10 23 molecules = 4.57 x 10 20 molecules
67. 67. Isopentyl acetate (C 7 H 14 O 2 ) is the compound responsible for the scent of bananas. Bees release about 1  g of this compound when they sting. The resulting scent attracts other bees to join the attack.
68. 68. How many molecules of isopentyl acetate (C 7 H 14 O 2 ) are released in a typical bee sting of about 1  g (1 x 10 -6 g) ?
69. 69. Molar mass = 130.18 grams 1.0 x 10 -6 g 130.18 g 1 mol 1 mol 6.022 x 10 23 molecules = 4.626 x 10 15 molecules
70. 70. How many atoms of carbon would be in the 4.626 x 10 15 molecules of isopentyl acetate (C 7 H 14 O 2 ) ?
71. 71. C 7 H 14 O 2 Has 7 atoms of carbon for every one molecule 4.626 x 10 15 molecules 1 molecule C 7 H 14 O 2 7 atoms C = 3.24 x 10 16 atoms of C
72. 72. A diamond contains 5.0 x10 21 atoms of carbon. How many moles of carbon and how many grams of carbon are in this diamond? Diamond is a natural form of pure carbon
73. 73. 5.01 x 10 21 atoms C 6.022 x 10 23 atoms C 1 mol C 8.32 x 10 -3 mol C 1 mol C 12.01 g C = 0.099 g C
74. 74. How many atoms of carbon are in a 2.00 carat diamond? ( 1.00 carat = 0.200 grams )
75. 75. 2 carat 1 carat 0.200 g 12.01 g 1 mol 1 mol 6.022 x 10 23 atoms = 2.006 x 10 22 atom of carbon
76. 76. The formula for acetylsalicylic acid (aspirin) is C 9 H 8 O 4 A typical aspirin tablet contains 1.67 x 10 21 molecules of aspirin. How many moles and how many grams of aspirin are in a typical tablet?
77. 77. C 9 H 8 O 4 = 180.154 grams 1.67 x 10 21 molecules 6.022 x 10 23 molecules 1 mol 0.00277 mol 1 mol 180.154 g = 0.499 g 500 mg
78. 78. Sucrose or table sugar has the formula C 12 H 22 O 11 How many moles of sugar are in 20 grams of sugar? What is the mass of 1.00 x 10 20 molecules of sugar?
79. 79. Molar mass = 342.296 g 20 g 342.296 g 1 mol = 0.058 mol sugar 1.00 x 10 20 molecules 6.022 x 10 23 molecules 1 mol 1 mol 342.296 g = 0.0568 g
80. 80. What is the mass of 2.00 moles of Iron (III) oxide, commonly known as rust?
81. 81. Rust = Fe 2 O 3 Molar mass = 159.70 g 2.00 mol 1 mol 159.70 g = 319.40 g Fe 2 O 3
82. 82. A chemistry student prepares 2.09 grams of the compound copper (II) sulfate in the laboratory. How many moles of the compound does he make? What is the % copper in the compound?
83. 83. CuSO 4 = 159.62 grams 2.09 g 159.62 grams 1 mol = 0.0131 mol % Cu = ( mass Cu / mass of CuSO 4 ) x 100 % Cu = 63.55 g 159.62 g = 39.81% Cu x 100
84. 84. Calcium carbonate is the principle compound found in pearls, marble, shells, and chalk.
85. 85. A certain sample of calcium carbonate contains 4.86 moles. What is the mass of this sample and how many formula units of calcium carbonate are present in the sample? CaCO 3 is an ionic compound and is not a molecule, but a crystal lattice with the simplest ratio of ions.
86. 86. Formula = CaCO 3 Molar mass = 100.09 grams 4.86 mol CaCO 3 1 mol CaCO 3 100.09 grams = 486.44 grams CaCO 3
87. 87. How many atoms of carbon are in the 486.44 grams of CaCO 3 ? 486.44 g CaCO 3 100.09 grams 1 mol CaCO 3 1 mol 6.022 x 10 23 molecules = 1.42 x 10 27 molecules CaCO 3 = 1.42 x 10 27 atoms of C
88. 88. Juglone is a natural herbicide produced from the husks of black walnuts. The formula for juglone is C 10 H 6 O 3. Calculate the molar mass of juglone and how many moles of juglone would be in a 1.56 x 10 -2 gram sample.
89. 89. Molar mass = 174.1 grams (10 x 12.01) + (6 x 1.008) + (3 x 16.00) 1.56 x 10 -2 g 174.1 g juglone 1 mol juglone = 8.96 x 10 –5 mol juglone
90. 90. Questions ???