Slide 1 / 158 Slide 2 / 158 Mole Calculations Slide 3 / 158 Table of Contents Click on the topic to go to that section · Avogadro's Number · Molar Mass · Molar Volume · Percent Composition · Emperical Formula
Slide 4 / 158 Avogadro's Number Return to Table of Contents Slide 5 / 158 Atomic Mass Recall an atom's atomic mass is equal to the number of protons plus the number of neutrons in the atom. Atomic Number 6 or number of protons (Z) C Average 12.01 Atomic Mass in amu The unit for atomic mass is amu. Carbon-12 has 6 protons and 6 neutrons. One amu is equal to 1/12 the mass of carbon-12 or approximately the mass of one proton or neutron mass of 1 proton = 1 amu mass of 1 neutron = 1 amu Slide 6 / 158 Atomic Mass What if you wanted to measure the mass of one atom in the laboratory? Would it be possible? A single atom has a very small mass. One carbon atom has a mass of about 2.0 x 10 -23 grams .
Slide 7 / 158 The Mole It takes a lot of atoms to give us enough material to directly measure in a lab. Hydrogen has a mass of 1 amu. How many atoms of hydrogen would be needed to make a 1 gram sample of hydrogen? 602,200,000,000,000,000,000,000 The amount 6.02x10 23 is called Avogadro's number or a mole . How big is a mole? Slide 8 / 158 Calculating Avogadro's Number The atomic mass of one carbon atom is 12.01 amu or 2x10 -23 g. How many carbon atoms would it take to get 12.01 grams of carbon? Givens: mass of 1 carbon atom = 2x10 -23 g total mass of carbon atoms = 12.01 g 2x10 -23 g x ? of atoms = 12.01 g 12.01 g ? of atoms = 2x10 -23 g ? of atoms = 6.02 x 10 23 atoms Slide 9 / 158 Holy Mole-y! 1 mole of pennies could One mole of marbles would cover the entire Earth (oceans included) for a be distributed to all the depth of two miles! currently-living people of the world so that they could spend a million dollars per hour every hour (day and night) for the rest of their lives! If you were able to count at the rate of 1 million numbers a second, it would take about 20 billion years to count out one mole!
Slide 10 / 158 The Mole A mole is just a grouping of numbers...like dozen, ream, etc. A dozen means 12 of something. A mole means 6.02 x 10 23 of something. Common Grouping Quantities 1 dozen = 12 1 gross =144 1 ream = 500 1 mole = 6.02 x 10 23 Slide 11 / 158 1 How many eggs are in two dozen eggs? A 12 B 24 C 0.0833 D 2 E 6.02 x 10 23 Slide 12 / 158 2 How many eggs are in half a dozen eggs? A 12 B 24 C 6 D 0.5 6.02 x 10 23 E
Slide 13 / 158 3 How many particles of sand are in 0.5 moles of sand? 1.5 x 10 23 A B 3.01 x 10 23 C 6.02 x 10 23 D 1.2 x 10 24 E 6.02 x 10 24 1 mole = 6.02 x 10 23 Slide 14 / 158 4 How many pieces of gold dust are in 2 moles of gold dust? A 1.5 x 10 23 B 3.01 x 10 23 C 6.02 x 10 23 D 1.2 x 10 24 E 6.02 x 10 24 1 mole = 6.02 x 10 23 Slide 15 / 158 5 How many dozen eggs are in a container of 6 eggs? A 4 B 0.5 C 1 D 2 6.02 x 10 23 E
Slide 16 / 158 6 How many dozen eggs are in a container of 18 eggs? 1.5 A B 3 C 0.67 D 2 6.02 x 10 23 E Slide 17 / 158 Dimensional Analysis How many eggs are in 47 dozen eggs? The number 47 makes this question a bit more difficult to calculate mentally. In chemistry, it is common practice to use equalities and dimensional analysis to solve problems. Equalities are two quantities that are identical in value but use different units. Examples of equalities include: 1 dozen = 12 1 mole = 6.02x10 23 1 meter = 1000 millimeters 1 hour = 60 minutes Slide 18 / 158 Dimensional Analysis How many eggs are in 47 dozen eggs? To solve the above problem: 1. Choose the equality with the correct dimensions or units: 1 dozen eggs = 12 eggs 2. Turn the equality into a fraction. Since 1 dozen and 12 are equal quantities 1 dozen = 12 can also be written as a fraction: 1 dozen eggs 12 eggs = 1 = = 12 eggs 1 dozen eggs
Slide 19 / 158 Dimensional Analysis How many eggs are in 47 dozen eggs? 3. Start with your given: 47 dozen Use dimensional analysis ! Choose the fraction that has the appropriate dimensions or units to convert from your given dimensions to your unknown dimensions. unknown dimension 12 eggs 1 dozen is in the numerator or 12 eggs 1 dozen 4. Multiply your given by your chosen fraction and cancel out the units: 47 dozen x 12 eggs = 564 eggs 1 dozen Slide 20 / 158 7 The Milky Way Galaxy may have up to 400 billion (4 x 10 14 stars). How many moles of stars does it have? A 1.5 x 10 9 B 6.7 x 10 -10 C 10 D 0.5 6.02 x 10 23 E 1 mole of stars = 6.02 x 10 23 stars 6.02 x 10 23 stars 1 mole of stars or 6.02 x 10 23 stars 1 mole of stars Slide 21 / 158 8 Mathematicians estimate Earth's beaches contain nearly 5.6 x 10 21 grains of sand. How many moles of sand are on Earth's beaches? A 1.5 B 9.3 x 10 -3 C 10.0 D 107.5 6.02 x 10 23 E 1 mole = 6.02 x 10 23
Slide 22 / 158 Measuring Matter with Moles The mole is the SI unit for measuring the amount of particles in a chemical substance. One mole (mol) of a substance is 6.02 x 10 23 representative particles of that substance. 1 mole of Carbon Slide 23 / 158 Measuring Matter with Moles How many moles of Gold are there in a sample containing 3.01 x 10 23 atoms of Gold? 1 mol = 6.02 x10 23 atoms Given quantity: 3.01 x 10 23 Au atoms 1 mol Au 6.02 x10 23 Au atoms or Equalities: 6.02 x10 23 Au atoms 1 mol Au Solve and cancel units: 1 mol Au 3.01 x 10 23 Au atoms x = 0.5 mol Au 6.02 x10 23 Au atoms Slide 24 / 158 9 How many atoms of titanium are in a sample containing 0.5 mole of titanium? A 1.5 x 10 23 B 3.01 x 10 23 C 6.02 x 10 23 D 1.2 x 10 24 E 6.02 x 10 24 1 mol = 6.02 x 10 23
Slide 25 / 158 10How many atoms of sodium are in a sample containing 2.0 moles of sodium? A 1.5 x 10 23 B 3.01 x 10 23 6.02 x 10 23 C D 1.2 x 10 24 6.02 x 10 22 E 1 mol = 6.02 x 10 23 Slide 26 / 158 11 How many moles of potassium are in a sample containing 3.01 x 10 23 atoms of potassium? A 1.0 B 2.0 C 0.5 D 0.75 6.02 x 10 24 E 1 mol = 6.02 x 10 23 Slide 27 / 158 12 How many moles of potassium are in a sample containing 1.2 x 10 24 atoms of potassium? 0.25 mol A B 0.50 mol 1.0 mol C D 2.0 mol 3.0 mol E 1 mol = 6.02 x 10 23
Slide 28 / 158 13 How many moles of tungsten atoms are there in a sample containing 1.8 x 10 24 atoms of tungsten? A 0.33 mol B 0.50 mol C 1.0 mol D 1.5 mol E 3.0 mol 1 mol = 6.02 x 10 23 Slide 29 / 158 14 How many moles of silver are there in a pure sample containing 1.5 x 10 23 atoms of silver? A 0.10 mol 0.25 mol B C 0.50 mol D 1.0 mol E 1.5 mol 1 mol = 6.02 x 10 23 Slide 30 / 158 15 How many atoms are there in 5.00 mol of hafnium? A 6.02 x10 23 atoms B 1.20 x 10 23 atoms 1.20 x 10 22 atoms C D 3.43 x 10 23 atoms E 3.01 x 10 24 atoms 1 mol = 6.02 x 10 23
Slide 31 / 158 Measuring Matter with Moles A mole of ANY substance contains Avogadro’s number of representative particles, or 6.02 x 10 23 representative particles. 1 mole of C atoms = 6.02 X 10 23 atoms of C 1 mole of bicycles = 6.02 x 10 23 bicycles The term representative particle refers to the species or types of particles in the substance For Example: atoms, molecules, formula units, ions Slide 32 / 158 Measuring Matter with Moles laboratory sample size molecule of H 2 O H Avagadro's O number of H molecules 18.0 amu (6.02 x10 23 ) 1 mol H 2 O (18.0 g) In 1 mole of carbon there are 6.02 x 10 23 carbon atoms. In 1 mole of water there are 6.02 x 10 23 water molecules. In 1 mole of NaCl there are 6.02 x 10 23 formula units. Slide 33 / 158 16 Formula units refer to particles of __________ compounds and molecules refer to particles of __________ compounds. A molecular/covalent, ionic B ionic, molecular/covalent C atoms, molecular D atoms, ionic E ionic, atomic
Slide 34 / 158 17 How many molecules are there in 2.10 mol CO 2 ? A 3.79 x 10 24 B 3.49 x 10 -24 C 1.05 x 10 -23 D 2.53 x 10 24 E 1.26 x 10 24 1 mol CO 2 = 6.02 x 10 23 CO 2 molecules Slide 35 / 158 18 How many moles of helium atoms are there in a pure sample containing 6.02 x 10 24 atoms of helium? A 2.0 mol B 4.0 mol C 6.0 mol D 10.0 mol 2.4 x 10 24 mol E 1 mol He = 6.02 x 10 23 He atoms Slide 36 / 158 19 How many moles of NaCl are there in a pure sample containing 6.02 x 10 23 formula units of sodium chloride, NaCl? A 1.0 mol B 2.0 mol C 4.0 mol D 6.0 mol E 6.02 x 10 23 mol 1 mol NaCl = 6.02 x 10 23 NaCl formula units
Slide 37 / 158 20 How many formula units of Pb(NO 3 ) 2 are there in 0.5 mole of Pb(NO 3 ) 2 ? A 0.5 formula units B 2.0 formula units C 3.01 x 10 23 formula units D 1.2 x 10 24 formula units 6.02 x 10 23 formula units E 1 mol Pb(NO 3 ) 2 = 6.02 x 10 23 Pb(NO 3 ) 2 formula units Slide 38 / 158 Real World Application Calcium deficiency can cause osteoporosis (weakening of the bones). The minimum amount of calcium in 1 mL of blood should be around 1.3 x 10 18 atoms. A patient has her blood tested and the lab finds there are 3 x 10 -5 moles of calcium in the blood. Is this patient at risk for osteoporosis? (6.02 x 10 23 atoms/mole) x (3 x 10 -5 moles) = 1.8 x 10 23 atoms Ca slide for answer This exceeds the normal range so they are OK! Slide 39 / 158 Review: Ionic and Molecular Compounds The total number of atoms or ions in a compound depends on electronegativity and bonding. Ionic Compounds Molecular Compounds NaCl H 2 O 1 Na + ion 1 Cl - ion 2 hydrogen 1 oxygen atoms atom K 2 CrO 4 2 K + ions 1 CrO 42- ion C 6 H 6 6 carbon 6 hydrogen Sn(OH) 2 atoms atoms 1 Sn 2 + ion 2 OH - ions
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