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The Mole

The Mole. 6.02 X 10 23. The Mole. A counting unit Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000 6.02 X 10 23 (in scientific notation)

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The Mole

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  1. The Mole 6.02 X 1023

  2. The Mole • A counting unit • Similar to a dozen, except instead of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000 • 6.02 X 1023 (in scientific notation) • This number is named in honor of AmedeoAvogadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present

  3. Just How Big is a Mole? • Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles. • If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. • If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

  4. Everybody Has Avogadro’s Number!But Where Did it Come From? • It was NOT just picked! It was MEASURED. • One of the better methods of measuring this number was the Millikan Oil Drop Experiment • Since then we have found even better ways of measuring using x-ray technology

  5. Learning Check Suppose we invented a new collection unit called a rapp. One rapp contains 8 objects. 1. How many paper clips in 1 rapp? a) 1 b) 4 c) 8 2. How many oranges in 2.0 rapp? a) 4 b) 8 c) 16 3. How many rapps contain 40 gummy bears? a) 5 b) 10 c) 20

  6. The Mole • 1 dozen cookies = 12 cookies • 1 mole of cookies = 6.02 X 1023 cookies • 1 dozen cars = 12 cars • 1 mole of cars = 6.02 X 1023 cars • 1 dozen Al atoms = 12 Al atoms • 1 mole of Al atoms = 6.02 X 1023 atoms Note that the NUMBER is always the same, but the MASS is very different! Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

  7. A Mole of ParticlesContains 6.02 x 1023 particles 1 mole C 1 mole H2O 1 mole NaCl = 6.02 x 1023 C atoms = 6.02 x 1023H2O molecules = 6.02 x 1023NaCl “molecules” (technically, ionics are compounds not molecules so they are called formula units) 6.02 x 1023 Na+ ions and 6.02 x 1023Cl– ions

  8. Avogadro’s Number as Conversion Factor 6.02 x 1023 particles 1 mole or 1 mole 6.02 x 1023 particles Note that a particle could be an atom OR a molecule!

  9. Learning Check 1. Number of atoms in 0.500 mole of Al a) 500 Al atoms b) 6.02 x 1023 Al atoms c) 3.01 x 1023 Alatoms 2. Number of moles of S in 1.8 x 1024 S atoms a) 1.0 mole S atoms b) 3.0 mole S atoms c) 1.1 x 1048 mole S atoms

  10. Molar Mass • The Mass of 1 mole (in grams) • Equal to the numerical value of the average atomic mass (get from periodic table) 1 mole of C atoms = 12.0 g 1 mole of Mg atoms = 24.3 g 1 mole of Cu atoms = 63.5 g

  11. Learning Check! Find the molar mass (usually we round to the tenths place) = 79.9 g • 1 mole of Br atoms • 1 mole of Sn atoms = 118.7 g

  12. Molar Mass of Molecules and Compounds Mass in grams of 1 mole equal numerically to the sum of the atomic masses 1 mole of CaCl2 = ? g 1 mole Ca x 40.1 g = 40.1 g Ca + 2 moles Cl x 35.5 g = 71 g Cl 1 mole of CaCl2 = 111.1 g

  13. Learning Check! • Molar Mass of K2O = ? Grams 1 mole O x 16 g = 16 g O + 2 moles K x 39.1 g = 78.2 g Cl 1 mole of K2O = 94.2 g K2O B. MolarMass of antacid Al(OH)3 = ? Grams 1 mole Al x 26.98 g = 26.98 g Al 3 moles O x 16 g = 48 g Cl + 3 moles H x 1.01 g = 3.03 g H 1 mole of Al(OH)3 = 78.01 g Al(OH)3

  14. Learning Check Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. Find its molar mass. 1 mole C17H18F3NO = 309.2 No!!!!! 1 mole C17H18F3NO = 309.2 g C17H18F3NO

  15. Calculations with Molar Mass molar mass Grams Moles

  16. Converting Moles and Grams Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al? 3.00 moles Al ? g Al

  17. 1. Molar mass of Al 1 mole Al = 27.0 g Al 2. Conversion factors for Al 27.0g Al or 1 mol Al 1 mol Al 27.0 g Al 3. Setup3.00 moles Al x 27.0 g Al 1 mole Al Answer = 81.0 g Al

  18. Learning Check! The artificial sweetener aspartame (Nutra-Sweet) formula C14H18N2O5 is used to sweeten diet foods, coffee and soft drinks. How many moles of aspartame are present in 225 g of aspartame? 225 g C14H18N2O5 x 1 mol C14H18N2O5 294.2 gC14H18N2O5 225 g C14H18N2O5 = 0.8 mol C14H18N2O5

  19. Atoms/Molecules and Grams • Since 6.02 X 1023 particles = 1 mole AND1 mole = molar mass (grams) • You can convert atoms/molecules to moles and then moles to grams! (Two step process) • You can’t go directly from atoms to grams!!!! You MUST go thru MOLES. • That’s like asking: 2 dozen cookies weigh how many ounces if 1 cookie weighs 4 oz? You have to convert a dozen first!

  20. Calculations molar mass Avogadro’s numberGrams Moles particles Everything must go through Moles!!!

  21. Atoms/Molecules and Grams How many atoms of Cu are present in 35.4 g of Cu? 35.4 g Cu 1 mol Cu 6.02 X 1023 atoms Cu 63.5 g Cu 1 mol Cu = 3.4 X 1023 atoms Cu

  22. Learning Check! How many atoms of K are present in 78.4 g of K? 78.4 g K = 1.2 x 1024 atoms

  23. Learning Check! What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)? 1.20 X 1024 molecules glucose = 358.9 g glucose

  24. Learning Check! How many atoms of O are present in 78.1 g of oxygen? 78.1 g Oxygen = 2.9 x 1024 atoms Oxygen 78.1 g O2 1 mol O2 6.02 X 1023molecule O2 2 atoms 32.0 g O2 1 mol O2 1 molecule

  25. Calculations molar mass Avogadro’s numberGrams Moles particles 22.4 L Volume of Gas Everything must go through Moles!!!

  26. Calculating Volume at STP • The molar volume is used to convert a known number of moles of gas to the volume of gas at STP. • 22.4 L = 1 mol at STP • Volume of gas = moles of gas x 22.4 L 1 mol

  27. Learning Check!!! • SO2 is a gas produced by burning coal. It is an air pollutant and one of the causes of acid rain. Determine the volume, in liters, of .60 mol SO2 gas at STP. • Volume of gas = moles of gas x 22.4 L 1 mol • 60 molSO2 x 22.4 L mol SO2 • Volume = 13 L SO2

  28. Percent Composition • The relative amounts of the elements in a compound/molecule % mass of element = mass of element x 100% MASS OF COMPOUND

  29. Percent Composition • When a 13.6 g sample of a compound containing only magnesium and oxygen is decomposed, 5.4 g of oxygen is obtained. What is the % compensation of this compound? • Mass of the compound = 13.60 g • Mass of oxygen = 5.4 g • Mass of magnesium = 13.6 g - 5.4 g = 8.20 g Mg • % composition O = 5.4 gX 100% = 39.7% O 13.6g • % compostion Mg = 8.20 gX 100% = 60.3% Mg 13.6 g

  30. Percent Composition What is the percent carbon in C5H8NO4 (the glutamic acid used to make MSG monosodium glutamate), a compound used to flavor foods and tenderize meats? a) 8.22 %C b) 24.3 %C c) 41.1 %C

  31. Chemical Formulas of Compounds • Formulas give the relative numbers of atoms or moles of each element in a formula unit - always a whole number ratio (the law of definite proportions). NO2 2 atoms of O for every 1 atom of N 1 mole of NO2 : 2 moles of O atoms to every 1 mole of N atoms • If we know or can determine the relative number of moles of each element in a compound, we can determine a formula for the compound.

  32. Types of Formulas • Empirical Formula The formula of a compound that expresses the smallest whole number ratio of the atoms present. Ionic formula are always empirical formula • Molecular Formula The formula that states the actual number of each kind of atom found in one molecule of the compound.

  33. To obtain an Empirical Formula 1. Determine the mass in grams of each element present, if necessary. 2. Calculate the number of moles of each element. 3. Divide each by the smallest number of moles to obtain the simplest whole number ratio. • If whole numbers are not obtained* in step 3), multiply through by the smallest number that will give all whole numbers *Be careful! Do not round off numbers prematurely

  34. A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for this substance. require mole ratios so convert grams to moles moles of N = 2.34g of N = 0.167 moles of N 14.01 g/mole moles of O = 5.34 g = 0.334 moles of O 16.00 g/mole Formula:

  35. A compound is analyzed and found to contain 25.9% nitrogen and 74.1% oxygen. What is the empirical formula of the compound Convert percentages into grams and then multiply by the molar mass • 25.9 g N x 1 mol x 100 = 1.85 mol N 14 g N • 74.1 g O x 1 mol x 100 = 4.63 mol O 16.0 g O Divide by the smallest number of moles 1.85 mol N = 1 mol N 4.63 mol O = 2.5 mol O 1.85 1.85

  36. Must have whole numbers • To obtain the lowest whole number ratio, multiply each part of the ratio by the smallest whole number that will convert both subscripts to whole numbers 1 mol N x 2 = 2 mol N 2.5 mol O x 2 = 5 mol O The empirical formula = N2O5

  37. Calculation of the Molecular Formula • The molecular formula of a compound is either the same as its experimentally determined empirical formula, or it is a simple whole – number multiple of it • First determine the empirical formula • Second, divide the molar mass by the empirical formula mass (efm) to obtain a whole number • Third, multiply the formula subscripts by the value from step 2

  38. Calculation of the Molecular Formula A compound has an empirical formula of NO2. The colourless liquid, used in rocket engines has a molar mass of 92.0 g/mole. What is the molecular formula of this substance? Divide molar mass by efm 92 g/mol= 2 46 g/mol Multiply formula subscripts by above value N = 1 x 2 = 2 O = 2 x 2 = 4 Molecular Formula = N2O4

  39. Learning Check • Calculate the molecular formula of a compound whose molar mass is 60.0 g/mol and empirical formula is CH4N. • CH4N • C2H4N2 • C2H8N2

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