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Chemistry I Mr. Trotts 1 The Mole Summer 2008 23 6.02 X 10 2 What we’re going to Learn 1. The concept of the mole 2. Given moles calculate number of particles 3. Be able to calculate molecular mass and gram formula mass and weight 4. Be able to convert moles to mass, particles, and volume and convert mass to moles, volume, and particles 3 5. Calculate the percent composition of a compound by mass of each element. and 6. Calculate both the empirical (simplest) formula and molecular formula of a compound. NOTE: As we encounter Learning Checks write the answers down for a daily grade STOICHIOMETRY - the study of the quantitative aspects of chemical reactions. - Combines mole problems with balanced equations 4 5 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 Amedeo Avagadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present 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. 6 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 xray technology 7 8 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 9 Solution Suppose we invented a new collection unit called a mep. One mep contains 8 objects. A. How many paper clips in 1 mep? 3) 8 B. How many oranges in 2.0 meps? 3) 16 C. How many meps contain 40 gummy bears? 1) 5 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?) 10 11 A Mole of Particles Contains 6.02 x 1023 particles 1 mole C = 6.02 x 1023 C atoms 1 mole H2O = 6.02 x 1023 H2O molecules 1 mole NaCl = 6.02 x 1023 NaCl “molecules” (technically, ionics are compounds not molecules so they are called formula units) 6.02 x 1023 Na+ ions and 6.02 x 1023 Cl– ions Avogadro’s Number as Conversion Factor 12 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! 13 Example: How many moles of Calcium are in 2.408 x 1024 calcium atoms? 2.408 x 1024 Ca atoms x 1 mole Ca/6.02 x 1023 atoms Ca = 4.0 x 101 moles Ca Example: How many atoms of Calcium are in 40 moles of Calcium 40 moles Ca x 6.02 x 1023 atoms Ca/1 mole Ca = 2.408 x 1024 atoms Ca 14 Learning Check 4. 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 Al atoms 5.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 15 Solution 1. Number of atoms in 0.500 mol of Al 3) 3.01 x 1023 Al atoms 0.500 mol Al x 6.02 x 1023 Al atoms 1 mol Al 2. Number of moles of S if a sample of S contains 4.50 x 1024 S atoms 2) 3.0 mole S atoms 4.50 x 1024 S atoms x 1 mol S 6.02 x 1023 S atoms 16 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 17 Other Names Related to Molar Mass • Molecular Mass/Molecular Weight: If you have a single molecule, mass is measured in amu’s instead of grams. But, the molecular mass/weight is the same numerical value as 1 mole of molecules. Only the units are different. (This is the beauty of Avogadro’s Number!) • Formula Mass/Formula Weight: Same goes for compounds. But again, the numerical value is the same. Only the units are different. • THE POINT: You may hear all of these terms which mean the SAME NUMBER… just different units 18 Learning Check! Find the molar mass (usually we round to the tenths place) 6. 1 mole of Br atoms = 7. 1 mole of Sn atoms = 79.9 g/mole 118.7 g/mole 19 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 = 111.1 g/mol 1 mole Ca x 40.1 g/mol + 2 moles Cl x 35.5 g/mol 1 mole of N2O4 = 111.1 g/mol CaCl2 = 92.0 g/mol Learning Check! 8. Molar Mass of K2O = ? Grams/mole 9. Molar Mass of antacid Al(OH)3 = ? Grams/mole 20 21 Solution A. 1 mole of K2O = 94.2 g 2 K x 39.1 g/mole + 1 O x 16.0 g/mole B. 1 mole of antacid Al(OH)3 = 78.0 g 1 Al x 27.0 g/mole + 3 O x 16.0 g/mole + 3 x 1.0 22 Learning Check 10. Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. Find its molar mass. Complete the handout GRAM FORMULA MASS 23 Solution Prozac, C17H18F3NO, is a widely used antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of 309 g/mole 17C (12.0) + 18H (1.0) + 3F (19.0) + 1N (14.0) + 1 O (16.0) 24 Calculations with Molar Mass molar mass Grams Moles 25 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 26 1. Molar mass of Al 1 mole Al = 27.0 g Al 2. Conversion factors for Al 27.0g Al 1 mol Al or 1 mol Al 27.0 g Al 3. Setup 3.00 moles Al Answer x 27.0 g Al 1 mole Al = 81.0 g Al 27 Learning Check! 11. 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? 28 Atoms/Molecules and Grams • Since 6.02 X 1023 particles = 1 mole AND 1 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 to dozen first! 29 Calculations molar mass Grams Avogadro’s number Moles particles Everything must go through Moles!!! 30 Atoms/Molecules and Grams How many atoms of Cu are present in 35.4 g of Cu? 35.4 g Cu 1 mol Cu 63.5 g Cu 6.02 X 1023 atoms Cu 1 mol Cu = 3.4 X 1023 atoms Cu 31 Molar Mass Factors Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors. Molar mass of CH4 = 16.0 g CH4 1 mole CH4 and 16.0 g 1 mole CH4 16.0 g CH4 32 Molar Mass Factors Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors. Molar mass of CH4 = 16.0 g CH4 1 mole CH4 and 16.0 g 1 mole CH4 16.0 g CH4 33 Learning Check 12. Acetic acid CH3COOH is the acid in vinegar . It has a molar mass of 60.0 g/mole. 1 mole of acetic acid = 1 mole acetic acid g acetic acid or ____________ g acetic acid 1 mole acetic acid 34 Solution Acetic acid CH3COOH is the acid in vinegar . It has a molar mass of 60.0 g/mole. 1 mole of acetic acid = 1 mole acetic acid 60.0 g acetic acid or 60.0 g acetic acid 60.0 g acetic acid 1 mole acetic acid 35 Learning Check! 13. How many atoms of K are present in 78.4 g of K? 36 Learning Check! 14. What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)? 37 More mole equivalents 1 mole of a gas at standard temperature (0 Celsius) and pressure (1 atmosphere) occupies 22.4 liters by volume Example: 2 moles of oxygen at STP would occupy 2 moles x 22.4L/1 mole or 44.8L 38 Learning Check! 15. How many atoms of O are present in 78.1 g of oxygen? 78.1 g O2 1 mol O2 6.02 X 1023 molecules O2 2 atoms O 32.0 g O2 1 mol O2 1 molecule O2 Complete the handout Mixed Mole Problems Given 1 mole = 6.02 x 1023 particles = gfm = 22.4L @ STP Complete Atoms Worksheet #2 (The Mole) 39 Percent Composition 16. 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 Complete Percentage Composition Worksheet 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. 40 Types of Formulas 41 • Empirical Formula The formula of a compound that expresses the smallest whole number ratio of the atoms present. The Ionic formula is always the empirical formula • Molecular Formula The formula that states the actual number of each kind of atom found in one molecule of the compound. 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. 4. 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 42 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 N 0.167 O 0.334 NO 2 Formula: N O 0.167 0.334 0.167 0.167 43 Empirical Formula from % Composition A substance has the following composition by mass: 60.80 % Na ; 28.60 % B ; 10.60 % H What is the empirical formula of the substance? Consider a sample size of 100 grams This will contain 28.60 grams of B and 10.60 grams H Determine the number of moles of each Determine the simplest whole number ratio 44 45 Empirical Formulas from Percent Composition • Given a compound that is 32.4% Na, 22.5% S, and 45.1% O • 32.4gNa x 1 mole/23.0g = 1.41 mole Na • 22.5gS x 1 mole/32g = .70 mole S • 45.1gO x 1 mole/16g = 2.82 mole O • Na = 1.41/.70 = 2 • S = .70/.70 = 1 • O = 2.82/.70 = 4 therefore = Na2SO4 • Complete the Determining Empirical Formula worksheet Calculation of the Molecular Formula 17. 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? N = 14.0g/mole O2 = 2 x 16 g/mole = 32g NO2 = 46g 92.0g/46g = 2 2 x (NO2) = N2O4 Complete Determining Molecular Formulas Worksheet 46