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The Mole

The Mole. 6.022 x 10 23. The Mole is a Unit of Measure. Dozen Pair Gross Ream How many pieces of paper in 10 reams? 10 reams x 500 pieces/ream = 5,000 pieces. The Mole is a Unit of Measure. How many cell phones in five moles of cell phones? 5 mol x 6.022x10 23 /mol =

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The Mole

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  1. The Mole 6.022 x 1023

  2. The Mole is a Unit of Measure • Dozen • Pair • Gross • Ream • How many pieces of paper in 10 reams? • 10 reams x 500 pieces/ream = 5,000 pieces

  3. The Mole is a Unit of Measure • How many cell phones in five moles of cell phones? • 5 mol x 6.022x1023/mol = • 3.011 x 1024 cell phones • But why would we ever use such a large unit as the Mole? • Because ATOMS ARE tiny

  4. Background: atomic masses • Look at the “atomic masses” on the periodic table. What do these represent? E.g. the atomic mass of Carbon is 12.01 (atomic # is 6) • We know there are 6 protons and 6 neutrons in C-12 • Protons and neutrons have roughly the same mass of about 1.66 x10-24 grams • Set this mass equal to 1amu(atomic mass units). • Carbon-12 thus has a mass of 12 amu. • The atomic mass shown on the Periodic Table is a weighted average of masses of all isotopes of an element • But more useful to associate atomic mass with a mass in grams.

  5. The Mole • Scientist set out to develop a basic unit of measurement to convert from atomic mass to grams. • Used Carbon-12 to set the standard. Scientists set one mole = the number of atoms of C-12 in 12 grams of C-12. • Experiments show that there are 6.022 x 1023 carbon atoms in 12 grams of Carbon-12. • 6.022 x 1023things is a “mole” of any thing! • Also known as “Avogadro’snumber”

  6. Who wants to be a Mollionaire? Q: how long would it take to spend a mole of $1 bills if they were being spent at a rate of one billion per second? A: $ 6.02 x 1023 bills x sec/$1,000,000,000 bills = 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

  7. Molar mass • The mass of one mole of something is called its “molar mass”. • Since one atom of C-12 = 12 amu and one mole of C-12 = 12 grams, we can use atomic masses to directly convert from amu/atom to grams/mol. • For an element, molar mass = Atomic Mass from Periodic Table, but use g/mole rather than amu • Example: Lithium’s atomic mass = 6.94 amu • Thus, 1 mole of Li = 6.94 g Li • This is expressed a molar mass of “6.94 g/mol” • Sometimes referred to as “gram formula mass”

  8. Molar mass =32.06 g/mol = 107.9 g/mol • What are the following element molar masses? S Ag • For a compound, molar mass = sum of molar masses of each element times the number of atoms of that element in the compound. CO2 = 44.00 g/mol C x 1 = 12.01 x 1 = 12.01 O x 2 = 16.00 x 2 = 32.00 44.00

  9. Molar Mass Calculations • Determine the mass in grams of: • 2.0 mol of Au • 4.37 mol of Zn • Determine the number of moles of: • 254 g of Cu • 12 g of Na 2.0 mol Au x 196.9 g/mol = 3.9 x 102g 4.37 mol Zn x 65.4 g/mol = 2.85 x 102g 254g Cu x mol/63.5g = 4.0 mol Cu 12g Na x mol/23.0g = 0.52 mol Na

  10. Molar mass =308.27 g/mol 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 • Cu3(BO3)2 Calculate molar masses (to 2 decimal places) CaCl2 (NH4)2CO3 O2 C6H12O6 110.98 g/mol (Cax1, Clx2) 96.11g/mol(Nx2, Hx8, Cx1, Ox3) 32.00 g/mol (Ox2) 180.18 g/mol (Cx6, Hx12, Ox6)

  11. Comparing sugar (C12H22O11) & H2O Same 1 gram each 1 mol each volume? No, they have different 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

  12. g mol g/mol 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 the molar mass (g/mol) • Then use dimensional analysis to convert: moles to grams: mol x g/mol = g grams to moles: g x mol/g = mol • This can be represented in an “equation triangle” ÷ x

  13. 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 1.27 Converting between grams and moles First: Determine the compound’s molar mass (g/mol) using the Periodic Table. ÷ x 36.46 9.1 98.08 0.5419 mol= g x mol/g 58.44 207 g= g/mol x mol Cu 63.55 0.0200 mol= g x mol/g

  14. H H H H H H Na Na Na Na Cl Cl Cl Cl O O O O O O Empirical and molecular formula Consider NaCl (ionic) vs. H2O2 (covalent) • Chemical formulas are either “simplest” (a.k.a. “empirical”) or “molecular” (all bonded atoms). • Ionic compounds are always expressed as the simplest ratio of the ions (formula units like NaCl or Li2O). Thus ionic formulas are always empirical. • Covalent compounds can be shown as either molecular formulas (e.g. H2O2) or empirical (e.g. HO)

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