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Atomic Masses & the MOLE…

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Neon is a gas that can be found in the atmosphere.Neon is a gas that can be found in the atmosphere. –Dry air contains about 0.002% Ne –That’s 500,000,000,000,000,000 atoms of neon every breath Scientists can deal with atoms quant- itatively because they know some fundamental properties of the atoms of each elementScientists can deal with atoms quant- itatively because they know some fundamental properties of the atoms of each element

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Masses of atoms expressed in grams are extremely small.Masses of atoms expressed in grams are extremely small. –An atom of Oxygen -16 literally weighs g

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-For most calcs in chemistry it is easier to use a relative atomic mass. - For relative masses, an atom was arbitrarily chosen as the standard, by which all other masses are compared

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I.Atomic Mass A. Relative Mass is when you measure the mass of all atoms based on the measurement of one particular atom.

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1.C-12 atom acts as the standard to compare all other atoms 2. A single C-12 atom was assigned a mass of 12 atomic mass units (amu) –1 amu is exactly 1/12 of the mass of a C-12 atom –Carbon has 12 nucleons therefore, the mass of a proton = 1 amu

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3. The masses of all other atoms are based on the mass of 1 amu –H has 1 proton= 1 amu –He has 2 protons and nuetrons= 4 amus

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A proton weighs amu A neutron weighs amu

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A. Most elements exist in nature as isotopes 75% of all of the Cl atoms found in nature are the isotope Cl-3575% of all of the Cl atoms found in nature are the isotope Cl-35 25% of the all of the Cl atoms found in nature are the isotope Cl-3725% of the all of the Cl atoms found in nature are the isotope Cl-37 II. Average Atomic Mass

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1.Average atomic mass is the mass on the PT and is the average of all of the naturally occurring isotopes of an element

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Example: We have 25 marbles that each weigh 2 g and 75 marbles that weigh one gram. What is the average atomic mass for these marbles?

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2. Calculating average atomic masses: a. Cu 69.17% Cu-63 has a mass of 63 amu, 30.83% Cu-65 has a mass of 65 amu. It’s calculated by multiplying the atomic mass of each isotope by its abundance and adding the results.It’s calculated by multiplying the atomic mass of each isotope by its abundance and adding the results.

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The reported average atomic mass of naturally occurring Cu is amu.The reported average atomic mass of naturally occurring Cu is amu. (0.6917)(63 amu) 63.6 amu Cu-63 Cu-65 + (0.3083)(65 amu)

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Your Turn: b. Practice #1. Gallium consists of two isotopes of masses amu and amu with abundances of 60.16% and 39.84%, respectively. What is the average atomic mass of gallium?68.95 amu and amu with abundances of 60.16% and 39.84%, respectively. What is the average atomic mass of gallium?

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c. Practice #2. Naturally occurring element X exists in three isotopic forms: Naturally occurring element X exists in three isotopic forms: X-28 ( amu, 92.21% abundance), X-28 ( amu, 92.21% abundance), X-29 ( amu, 4.70% abundance), X-29 ( amu, 4.70% abundance), X-30 ( amu, 3.09% abundance) X-30 ( amu, 3.09% abundance). Calculate the atomic weight of X.

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B. Relating Mass to the number of Atoms

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It is impractical to get caught up into working with 1 atom’s mass because usually you working with a large number of atoms.It is impractical to get caught up into working with 1 atom’s mass because usually you working with a large number of atoms. Scientists were challenged to figure out a way to define a collection of particlesScientists were challenged to figure out a way to define a collection of particles –And which could still be described in terms of a relative mass

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1. The average C atom with an atomic mass of 12.0 amus is 12 times heavier than the average H atom a.So 100 C atoms are 12 times heavier than 100 H atoms b. any # of C atoms would be 12 times heavier than the same # of H atom b. any # of C atoms would be 12 times heavier than the same # of H atom

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If we assume we can relate the relative masses from the PT in the terms of gramsIf we assume we can relate the relative masses from the PT in the terms of grams –With the literal masses of an atom (g) for each atom we use we seem to get the same number of atoms

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Counting Atoms

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The number of atoms that are in the relative masses of elements identical in grams to the atomic masses on the PT is called Avogadro’s NumberThe number of atoms that are in the relative masses of elements identical in grams to the atomic masses on the PT is called Avogadro’s Number And is defined as a moleAnd is defined as a mole Counting Atoms The mole becomes a counting unit much like the dozen.The mole becomes a counting unit much like the dozen. –1 dozen eggs = 12 eggs –1 mole of eggs =

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The word “mole” was introduced by Wilhelm Oswald, who derived the term from the word moles meaning a “heap” or “pile.”The word “mole” was introduced by Wilhelm Oswald, who derived the term from the word moles meaning a “heap” or “pile.” –We are just defining the pile as con- taining 6.02x10 23 items –Because it is such a huge number of items we usually reserve the mole for atoms or molecules Counting Atoms 1 mole is always = 6.02 x items

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The mole, whose abbreviation is “mol”, is the SI base unit for meas- uring amount of a pure substance.The mole, whose abbreviation is “mol”, is the SI base unit for meas- uring amount of a pure substance. –The mole is the chemist’s six-pack or dozen. Many objects in our everyday lives come in similar counting units. 1 ream = 500 sheets of paper1 ream = 500 sheets of paper 1 pair of socks = 2 socks1 pair of socks = 2 socks 1 cube = 24 cans1 cube = 24 cans Counting Atoms

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REPRESENTATIVE PARTICLES & MOLES Atomic Nitrogen AtomN 6.02x10 23 Nitrogen gas Molec. N2N2N2N2 6.02x10 23 WaterMolec. H2OH2OH2OH2O Calcium ion Ion Ca 2+ Ca x10 23 Calcium Fluoride Formula unit CaF x10 23

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We will learn in the near future that when a chemist reasons through a chemical reaction (recipe) they think in terms of X number of mols of this compound reacts with Y number of mols of this compound.We will learn in the near future that when a chemist reasons through a chemical reaction (recipe) they think in terms of X number of mols of this compound reacts with Y number of mols of this compound. –So we need to know how to calculate the number of molecules or atoms are involved in that X number of mols Counting Atoms

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Using the mole in calculations #1 Counting Atoms How many moles of Magnesium is 1.25 x atoms of Magnesium? unit equality: 1 mol Mg = 6.02 x atoms Mg

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The desired conversion is: atoms moles Counting Atoms 6.02x10 23 atoms Mg 1 mole Mg 1.25x10 23 atoms Mg =.208 mol Mg

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Your Turn: To make sure adequate amounts of product AB is being made during a rxn you might need 3.33 mols of A reacting with 2.68 mols of B. How many atoms of A are reacting with how many atoms of B?To make sure adequate amounts of product AB is being made during a rxn you might need 3.33 mols of A reacting with 2.68 mols of B. How many atoms of A are reacting with how many atoms of B? If you burn sugar (C 12 H 22 O 11 ) in pure oxygen you produce carbon dioxide and water as products. To burn 6.02x10 23 molecules of sugar you also need 7.22x10 24 molecules of oxygen and you produce 6.62x10 24 molecules of water and 7.22x10 24 molecules of carbon dioxide. How many mols are reacted or produced for each component of the rxn?If you burn sugar (C 12 H 22 O 11 ) in pure oxygen you produce carbon dioxide and water as products. To burn 6.02x10 23 molecules of sugar you also need 7.22x10 24 molecules of oxygen and you produce 6.62x10 24 molecules of water and 7.22x10 24 molecules of carbon dioxide. How many mols are reacted or produced for each component of the rxn?

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Now suppose you want to determine how many atoms are in a mol of a compound or moleculeNow suppose you want to determine how many atoms are in a mol of a compound or molecule –To do this you must know how many atoms are involved in the molecule. To determine the number of atoms represented in a molecule requires knowing the chemical formulaTo determine the number of atoms represented in a molecule requires knowing the chemical formula –Eg, each molecule of Carbon Dioxide (CO 2 ) is composed of 3 atoms Counting Atoms

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1 mole of Carbon Dioxide contains Avogadro’s number of Carbon Dioxide molecules.1 mole of Carbon Dioxide contains Avogadro’s number of Carbon Dioxide molecules. –Thus a mole of CO 2 contains three times Avogadro’s # of atoms Counting Atoms

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Using the mole in calculations #2 Counting Atoms How many atoms of Carbon are in 2.12 mols of Propane (C 3 H 8 )? unit equalities: 1 mol C 3 H 8 = 6.02x10 23 molecules C 3 H 8 1 molecule C 3 H 8 = 3 atoms C

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6.02x10 23 molecules C 3 H 8 1 mole C 3 H 8 The desired conversions are: 2.12 mols C 3 H 8 3 atoms C 1 molecule C 3 H 8 =3.83x10 24 atoms C Counting Atoms moles molecules atoms

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Your Turn: Back to burning sugar, 1 mol of sugar (C 12 H 22 O 11 ) was burned with 12 mols of oxygen (O 2 ) to produce 11 mols of water (H 2 O) and 12 mols of Carbon dioxide (CO 2 ). How many total atoms of oxygen are burned in the reaction (reactants), and how many total atoms of oxygen are produced in the reaction (products)?Back to burning sugar, 1 mol of sugar (C 12 H 22 O 11 ) was burned with 12 mols of oxygen (O 2 ) to produce 11 mols of water (H 2 O) and 12 mols of Carbon dioxide (CO 2 ). How many total atoms of oxygen are burned in the reaction (reactants), and how many total atoms of oxygen are produced in the reaction (products)?

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We can also relate mass to the number of atoms and the mole.We can also relate mass to the number of atoms and the mole. –Relative atomic masses and the mol can be used to develop a method of measuring the amount of a sample. If we had a pile of C atoms that weighed 12 g and a pile of H atoms that weighed 1gIf we had a pile of C atoms that weighed 12 g and a pile of H atoms that weighed 1g –each pile would contain the same number of atoms or 6.02x10 23 atoms Counting Atoms

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The gram atomic masses of any 2 elements (since they are relative to C) must contain the same # of atomsThe gram atomic masses of any 2 elements (since they are relative to C) must contain the same # of atoms –A pile of any atom that corresponds to its average atomic mass from the PT contains exactly 6.02x10 23 atoms of that element. And is equal to how much 1 mole of that sample would weigh in gramsAnd is equal to how much 1 mole of that sample would weigh in grams Counting Atoms

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What this allows us to do is to use the mass off of the periodic table to represent the mass of 1 mole (or 6.02x10 23 atoms) of that elementWhat this allows us to do is to use the mass off of the periodic table to represent the mass of 1 mole (or 6.02x10 23 atoms) of that element –1 mol of C atoms weighs g –1 mol of H atoms weighs g –1 mol of W atoms weigh g Counting Atoms

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This new version of mass from the periodic table is called the gram molar mass, or molar mass.This new version of mass from the periodic table is called the gram molar mass, or molar mass. –Molar Mass = mass of 1 mole of atoms/molecules/or formula units in grams abbreviated = MMabbreviated = MM units = grams/molunits = grams/mol Counting Atoms

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We get the mass of 1 mole of any element off of the Periodic TableWe get the mass of 1 mole of any element off of the Periodic Table So how do we figure out the mass of a mole of a compound rather than just an element?So how do we figure out the mass of a mole of a compound rather than just an element? –To answer that question you must have the formula of the compound. Counting Atoms

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ModelFormulaModelFormula The formula of a compound tells you how many atoms of each element combine to make the representative particle of that compound. Counting Atoms What is the mass of 1 mole of Sulfur Trioxide (SO 3 ) A.K.A. Molar Mass?

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You can calculate the mass of a mol- ecule of SO 3 by adding the MM of each of the atoms in the moleculeYou can calculate the mass of a mol- ecule of SO 3 by adding the MM of each of the atoms in the molecule –The mass of 1 mole of S is 32.1g. –The mass of 3 atoms of O is 3 times the MM of a single O atom, or (3)(15.99g) = 47.97g –So MM of 1 molecule of SO 3 is 32.1g g = 80.1 g/mol Counting Atoms

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(6C’S)(12.011g/mol) = 180.1g/mol (12H’S)(1.008 g/mol) = (6O’S)(15.99 g/mol) = 1 mole of C 6 H 12 O 6 or 6.02x10 23 molecules of the compound – it would weigh 180 grams g/mol g/mol 95.94g/mol Counting Atoms What is the MM of glucose (C 6 H 12 O 6 )?

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Practice Time: Determine the mass of 1 mole (Molar mass) of each of the following:Determine the mass of 1 mole (Molar mass) of each of the following: –Zn –Gd –Zn(C 2 H 3 O 2 ) 2 –(NH 4 ) 3 PO 4 –C 12 H 22 O 11

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How many grams are in 9.45 mol of Dinitrogen Trioxide (N 2 O 3 ) The only connection to N 2 O 3 and its mass is how much 1 mol of the compound weighs. But, using it as a comparison we can calculate the mass of 9.45 mol. Counting Atoms Using the mole in calculations:

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Counting Atoms Step 1: Determine the mass of 1 mol of N 2 O g (2N’s)(14.01g) = 28.02g (3O’s)(15.99g) = 75.99g If 1 mole of N 2 O 3 weighs 75.99g than how much will 9.45 mols of N 2 O 3 weigh?

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1 mol N 2 O g N 2 O mol N 2 O 3 =718 g N 2 O 3 Counting Atoms Step 2: Convert the given moles to grams using the Molar mass equality.

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Find the number of moles of 92.2g of Iron (III) Oxide (Fe 2 O 3 ) The only connection to the mass of Fe 2 O 3 and how that corresponds to mols is how that 1 mol of the compound weighs a certain # of grams. Using that we can figure out how many moles weigh 92.2 g Counting Atoms

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47.97g (2Fe’s)(55.85g) = 111.7g (3O’s)(15.99g) = g If 1 mole of Fe 2 O 3 weighs g than how many mols will weigh 92.2 g of Fe 2 O 3 ? Counting Atoms Step 1: Determine the mass of 1 mol of Fe 2 O 3

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g Fe 2 O 3 1 mol Fe 2 O g Fe 2 O 3 =.577mol Fe 2 O 3 Counting Atoms Step 2: Convert the given mass to mols using the Molar mass equality

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Practice Time: Vitamin C (C 6 H 8 O 6 ), cannot be stored by the body and therefore, must be present in the diet. If an orange contains 70 mg of Vit C how many oranges are necessary to consume 2.5 mols of Vit C?Vitamin C (C 6 H 8 O 6 ), cannot be stored by the body and therefore, must be present in the diet. If an orange contains 70 mg of Vit C how many oranges are necessary to consume 2.5 mols of Vit C?

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Another generality about the mole is that with matter in the gas phase we can develop another equality.Another generality about the mole is that with matter in the gas phase we can develop another equality. –Under the same conditions, equal volumes of gases contain equal numbers of particles. –1 mol of a gas will occupy the same volume as 1 mol of any other gas under the same conditions. Counting Atoms

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1 mole of any gas under the specific conditions of 0°C and 1 atm (STP) will occupy a volume of 22.4 L. 6.02x10 23 molecules of O x10 23 molecules of CO 2 Molar Volume of a Gas

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What volume, in Liters, does 0.60 mol of SO 2 gas occupy at STP? The only connection to the volume of any gas and how that corresponds to mols is that 1 mol of a gas occupies 22.4 Liters of space. Using that we can figure out the volume of 0.60 mols of a gas at STP. Counting Atoms

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1 mole SO L SO moles SO 2 = 13 L SO 2 Step 1: Use the equality 1 mol = 22.4 L to do the conversion Counting Atoms

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Practice Time: The Snoopy balloon featured at the Macy’s Thanksgiving Day Parade has a volume of ft 3. How many moles of Helium are required to fill it STP?The Snoopy balloon featured at the Macy’s Thanksgiving Day Parade has a volume of ft 3. How many moles of Helium are required to fill it STP?

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If you have a 35.67g piece of Chro- mium metal on your car, how many atoms of Chromium do you have? If you have a 35.67g piece of Chro- mium metal on your car, how many atoms of Chromium do you have? You are given mass and asked for number of particlesYou are given mass and asked for number of particles Let’s get some strategyLet’s get some strategy Counting Atoms

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1 st convert given mass into moles1 st convert given mass into moles To do this we use the molar mass (MM) of Cr which on the PT is g/molTo do this we use the molar mass (MM) of Cr which on the PT is g/mol Then we need to convert from mols to atoms using Avogadro’s number.Then we need to convert from mols to atoms using Avogadro’s number. Counting Atoms 35.67g Cr g Cr 1 mole Cr 6.02x10 23 atoms = 4.130x10 23 atoms of Cr

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Calculate the Missing Info… Formula Molar Mass MolesMassParticles Gas STP CH mol H 2 SO g CO 9.03x10 23 molecules Cu(NO 3 ) g

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