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Mole Theory & Dimensional Analysis: Conversions, Mass, and Volume Measurements

Learn how to convert between different units using dimensional analysis, calculate the mass of a mole, and determine the volume of a gas at STP. Understand the concept of representative particles and percent composition in compounds.

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Mole Theory & Dimensional Analysis: Conversions, Mass, and Volume Measurements

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  1. Unit 06 The Mole Theory Ch. 4 and 7

  2. Dimensional Analysis● just converting one thing to another Problem 1: How many seconds are in a day? sec day What do we know? Let’s solve. Conversion factors: the numerator and denominator are equal × × = 86,400 sec 1 day

  3. Dimensional Analysis Problem 2: You're throwing a pizza party for 15 and figure each person might eat 4 slices. How much is the pizza going to cost you? You call up the pizza place and learn that each pizza will cost you $14.78 and will be cut into 12 slices. You tell them you'll call back. How much money is the pizza going to cost you, which in math terms is: cost (in dollars) per party, or just $/party 14.78 x 4 x 15 = $73.90 12 party

  4. How do you measure matter? • Counting (dozen, 3/$1, 6 pack) • Mass ( 1 lb, 4 oz, 57g) • Volume (liter, gallon, pint, quart) In chemistry- this is all measured by a measuring unit called the mole.

  5. Mass of a Mole • Molar Mass- the mass of a mole of any element or compound (in grams) • Also called: • Gram Formula mass – sum of the atomic masses of all the atoms in a formula of a compound

  6. How to determine molar mass- 12g 35g 16g 19g • The atomic mass expressed in grams- rounded to whole number (ones place) • Examples: • C = • Cl = • O = • F =

  7. How to determine molar mass-  1 S atom 3 O atoms 32g + 16g + 16g + 16g = 80g • For compounds- Add together all the atoms that make up the compound • Examples: • SO3 =

  8. How to determine molar mass- • What is the gram formula mass of ammonium carbonate (NH4) 2CO3? • Take inventory: multiply the number of atoms by the rounded mass number for each element then add up all of the elements. • N- 2 × 14 = 28 • H- 8 × 1 = 8 • C- 1 × 12 = 12 • O- 3 × 16 = 48 96g

  9. Mole – Mass Relationship • Use the following conversion factors: 1mole or molar mass molar mass 1 mole (we have to calculate the molar mass of the substance)

  10. Moles  Grams Ex.) How many grams are in 9.45 moles of N2O3? Known: 9.45 moles of N2O3 Unknown: mass (grams) of N2O3 Step 1: calculate the molar mass of N2O3 N = 2 x 14 = 28 O = 3 x 16 = 48 76g Step 2: solve 9.45 moles x 76g = 718.2 g N2O3 1 1 mole

  11. Mass  Moles • Ex.) Find the number of moles in 92.2g of Fe2O3? • Known: mass of Fe2O3 is 92.2g • Unknown: moles of Fe2O3 • Step 1: Find the molar mass of Fe2O3 Fe = 2 x 56 = 112 O = 3 x 16 = 48 160g • Step 2: Solve 92.2g x 1 mole = 0.576 mole Fe2O3 1 160g

  12. Number of particles in a Mole 1 mole = 6.02 × 10 23representative particles (also called Avogadro’s Number) Atom- rep. particle for most elements Molecule- rep. particle for covalent compounds and diatomic molecules “BrINCl HOF” Formula unit- rep. particle for ionic compounds What is a representative particle? How the substance normally exists:

  13. Converting from moles –› particles Conversion Factors: 1 dozenor 12 eggs 12 eggs 1 dozen For moles and particles: 1 mole = 6.02 × 1023 rep particles– therefore Conversion Factors 1 mole OR 6.02 × 1023 particles 6.02 × 1023 particles 1 mole Analogy: 1 dozen = 12 eggs

  14. How to solve mole problems: How many moles are in the number of molecules? Sample problem: 1.25 × 1023 atoms Mg 1. Determine known and unknown. Known: 1.25 × 1023 atoms Mg Unknown: moles 2. Determine the conversion factor(s) needed. 3. Multiply the known by the appropriate conversion factor(s) so units cancel. 4. Calculate answer 2.08 × 10-1 moles or .208 moles 1 mole 6.02 × 1023 particles 6.02 × 1023 particles 1 mole or 1.25 × 1023 atoms Mg 1 mole 6.02 × 1023 atoms

  15. The Mole and Avogadro’s Number 1.) How many molecules are in 2.0 moles? 6.02  1023 molecules 1 mole 2.0 mole = 1.20  1024 molecules

  16. 1.) How many moles are in 6.02 × 1023 particles? The Mole and Avogadro’s Number 1 mole 6.02 × 1023 particles 6.02 × 1023 particles = 1 mole

  17. Molar Conversion Examples Find the mass of 2.1  1024 molecules of NaHCO3. 2.1  1024 molecules 1 mole 6.02  1023 molecules 84 g 1 mole = 293.02 g NaHCO3

  18. Volume of a Mole of Gas • The Volume of a gas varies with a change in temperature or pressure. • Measured at standard temperature and pressure (STP) • 0°C at 1 atmosphere (atm) • 1 mole of any gas occupies a volume of 22.4L Conversion Factors: 1mole OR 22.4 L 22.4 L 1 mole

  19. Volume  Moles • Ex.) Determine the volume, in liters, if 0.60 mole of SO2 gas at STP. known: 0.60 mole unknown: volume • Start with the known and then use the correct conversion factor to solve for the unknown. 0.60 mole x 22.4 L = 13.44 L SO2 1 1 mole

  20. All the conversion factors you need to know! 6.02 × 1023 particles 1 mole 1 mole 6.02 × 1023 particles OR • Mass 1 Mole OR Molar Mass Molar mass 1 Mole • Volume • 1 mole OR 22.4 L • 22.4 L 1 mole Representative Particles

  21. Your clothing labels have Percent Composition.

  22. Percent Composition molar mass (g) of compound • The percent by mass of each element in a compound • Information needed: • Formula of the compound • Mass of the elements and the compound % mass = mass grams of element × 100

  23. Calculating Percent Composition • Calculate the percent carbon in C3H8 - Find the molar mass C = 3 x 12 = 36g H = 8 x 1 = 8g 44g • % C = mass(g) of carbon X 100 mass of C3H8 % C = 36g X 100 44g % C = .818181 X 100 % C = 81.8 or 82%

  24. Now, calculate the percent hydrogen in C3H8 %H = 8g X 100 44g %H = .181818 X 100 %H = 18.2 or 18%

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