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# The Mole

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1. The Mole Q: how long would it take to spend a mole of \$1 coins if they were being spent at a rate of 1 billion per second?

2. Background: atomic masses • Look at the “atomic masses” on the periodic table. What do these represent? • E.g. the atomic mass of C is 12 (atomic # is 6) • We know there are 6 protons and 6 neutrons • Protons and neutrons have roughly the same mass. So, C weighs 12 u (atomic mass units). • What is the actual mass of a C atom? • Answer: approx. 2 x 10-23 grams (protons and neutrons each weigh about 1.7 x10-24 grams) Two problems • Atomic masses do not convert easily to grams • They can’t be weighed (they are too small)

3. The Mole Withtheseproblems,whyuseatomicmassatall? • Masses give information about # of p+, n0, e– • It is useful to know relative mass E.g. Q - What ratio is needed to make H2O? A - 2:1 by atoms, but 2:16 by mass • It is useful to associate atomic mass with a mass in grams. It has been found that 1gH,12gC,or 23gNahave6.02x1023atoms • 6.02 x 1023 is a “mole” or “Avogadro’s number” • “mol” is used in equations, “mole” is used in writing; one gram = 1 g, one mole = 1 mol. • Read 4.3 (167-9). Stop after text beside fig 2. • Do Q1-6. Challenge: 1st slide (use reasonable units)

4. The Mole: Answers • A mole is a number (like a dozen). Having this number of atoms allows us to easily convert atomic masses to molar masses. • 6.02x1023 • 602 000 000 000 000 000 000 000 • 3.00 x 6.02x1023 = 18.06x1023 or 1.81x1024 (note: there are 3 moles of atoms in one mole of CO2 molecules. In other words, there are 5.42x1024 atoms in 3.00 mol CO2) • 3.01x1023 • a) 1.43 kg  12 = 0.119 kg per orange b) 1.01 g  6.02x1023 = 1.68 x 10–24 g

5. Mollionaire Q: how long would it take to spend a mole of \$1 coins if they were being spent at a rate of 1 billion per second? A: \$ 6.02 x 1023 / \$1 000 000 000 = 6.02 x 1014 payments = 6.02 x 1014 seconds 6.02 x 1014 seconds / 60 = 1.003 x 1013 minutes 1.003 x 1013 minutes / 60 = 1.672 x 1011 hours 1.672 x 1011 hours / 24 = 6.968 x 109 days 6.968 x 109 days / 365.25 = 1.908 x 107 years A: It would take 19 million years

6. Comparing sugar (C12H22O11) & H2O Same 1 gram each 1 mol each volume? No, they have dif. densities. No, molecules have dif. sizes. mass? Yes, that’s what grams are. No, molecules have dif. masses # of moles? No, they have dif. molar masses Yes. # of molecules? No, they have dif. molar masses Yes (6.02x1023 in each) # of atoms? No, sugar has more (45:3 ratio) No

7. Molar mass • The mass of one mole is called “molar mass” • E.g. 1 mol Li = 6.94 g Li • This is expressed as 6.94 g/mol • What are the following molar masses? S SO2 Cu3(BO3)2 32.06 g/mol 64.06 g/mol 308.27 g/mol Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3 O2 Pb3(PO4)2 C6H12O6 Cu x 3 = 63.55 x 3 = 190.65 B x 2 = 10.81 x 2 = 21.62 O x 6 = 16.00 x 6 = 96.00 308.27

8. Molar mass • The mass of one mole is called “molar mass” • E.g. 1 mol Li = 6.94 g Li • This is expressed as 6.94 g/mol • What are the following molar masses? S SO2 Cu3(BO3)2 32.06 g/mol 64.06 g/mol 308.27 g/mol Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3 O2 Pb3(PO4)2 C6H12O6 110.98 g/mol (Cax1, Clx2) 96.11g/mol(Nx2, Hx8, Cx1, Ox3) 32.00 g/mol (Ox2) 811.54 g/mol (Pbx3, Px2, Ox8) 180.18 g/mol (Cx6, Hx12, Ox6)

9. g mol g/mol Formula g/mol g mol (n) Equation HCl 0.25 g= g/mol x mol H2SO4 53.15 NaCl 3.55 Cu 1.27 Converting between grams and moles • If we are given the # of grams of a compound we can determine the # of moles, & vise-versa • In order to convert from one to the other you must first calculate molar mass g = mol x g/mol mol = g  g/mol • Thiscanberepresentedinan“equationtriangle” 36.46 9.1 98.08 0.5419 mol= g  g/mol 58.44 207 g= g/mol x mol 63.55 0.0200 mol= g  g/mol

10. H H H H H H Na Na Na Na Cl Cl Cl Cl O O O O O O Simplest and molecular formulae Consider NaCl (ionic) vs. H2O2 (covalent) • Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular”. Ionic compounds are always expressed as simplest formulas. • Covalent compounds can either be molecular formulas (I.e. H2O2) or simplest (e.g. HO) Q - Write simplest formulas for propene (C3H6), C2H2, glucose (C6H12O6), octane (C8H14) Q - Identify these as simplest formula, molecular formula, or both H2O, C4H10, CH, NaCl

11. For more lessons, visit www.chalkbored.com Answers Q - Write simplest formulas for propene (C3H6), C2H2, glucose (C6H12O6), octane (C8H14) Q - Identify these as simplest formula, molecular formula, or both H2O, C4H10, CH, NaCl A - CH2 A - H2O is both simplest and molecular C4H10 is molecular (C2H5 would be simplest) CH is simplest (not molecular since CH can’t form a molecule - recall Lewis diagrams) NaCl is simplest (it’s ionic, thus it doesn’t form molecules; it has no molecular formula) CH CH2O C4H7