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Atomic Masses & the MOLE…

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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 O-16 literally weighs g For most calcs in chemistry it is easier to use a relative atomic mass.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 Counting Atoms

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The mass of all the other atoms are then expressed in relation to the standardThe mass of all the other atoms are then expressed in relation to the standard –C-12 atom acts as the standard A single C-12 atom was assigned a mass of 12 atomic mass units (amu)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 Counting Atoms

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The masses of all other atoms are based on the mass of 1 amuThe masses of all other atoms are based on the mass of 1 amu –Hydrogen has 1 proton therefore, it weighs 1 amu –Helium has 2 protons and 2 neutrons therefore, it weighs 4 amus Most elements occur naturally as a mixture of isotopes.Most elements occur naturally as a mixture of isotopes. –For instance in the two isotopes of Chlorine (Cl-35 & Cl-37) Counting Atoms

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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-37 Cl-35 atoms are naturally more abundant than Cl-37Cl-35 atoms are naturally more abundant than Cl-37 –Therefore, the average mass of Cl (taking into account isotopic abun- dance) should be closer to 35 than to the median of 36. Counting Atoms

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Masses on the PT are weighted aver- ages of all of the naturally occurring isotopes of an elementMasses on the PT are weighted aver- ages of all of the naturally occurring isotopes of an element –The average atomic mass on the PT is reflective of both the mass numbers of each isotope & the abundance of each isotope Here’s how the masses were calculated on the Periodic Table: Counting Atoms

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Calculating average atomic masses: Naturally occurring copper consists of 69.17% Cu-63, which has a mass of amu, and 30.83% Cu-65, with a mass of amu. The average atomic mass of Cu is calculated by multiplying the atomic mass of each isotope by its abundance and adding the results.The average atomic mass of Cu is calculated by multiplying the atomic mass of each isotope by its abundance and adding the results. Counting Atoms

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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. Counting Atoms (0.6917)( amu) amu Cu-63 Cu-65 + (0.3083)( amu) amu

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Your Turn: 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?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? Naturally occurring element X exists in three isotopic forms: X-28 ( amu, 92.21% abundance), X-29 ( amu, 4.70% abundance), and X-30 ( amu, 3.09% abundance). Calculate the atomic weight of X.Naturally occurring element X exists in three isotopic forms: X-28 ( amu, 92.21% abundance), X-29 ( amu, 4.70% abundance), and X-30 ( amu, 3.09% abundance). Calculate the atomic weight of X.

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It is impractical to get caught up into working with 1 atom or 1 atom’s mass.It is impractical to get caught up into working with 1 atom or 1 atom’s mass. –It makes more sense to work with a collection of atoms rather than individually Counting 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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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 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 –Any time we are counting how many we have and we want to describe it in terms of moles than… 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 measuring amount of a pure substance.The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance. –It’s used exclusively for counting atoms, molecules, ions, or other things that are extremely small –It’s 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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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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Using the mole in calculations #2 Counting Atoms How many atoms of Gold do we have if we have.0327 moles of Gold? unit equality: 1 mol Au = 6.02 x atoms Au

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The desired conversion is: moles atoms Counting Atoms 6.02x10 23 atoms Au 1 mole Au.0327 mole Au = 2.23x10 22 atoms Au

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Your Turn: Fill in the missing information in the following table, be sure to show your work. Moles Atoms or molecules mols Al(OH) x molecules H 2 O x atoms W.2116 mols Al +3

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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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Using the mole in calculations #3 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: Moles Atoms or molecules # of ____ atoms mols Al(OH) x10 24 molecules # of O atoms 3.350x mols H 2 O x molecules H 2 O # of total atoms 9.995x10 18 mols W x atoms W.2116 mols Al x10 23 ions Al +3 Fill in the missing information in the following table, be sure to show your work.

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We can’t literally count the number of atoms in a sample, but we can count them by massWe can’t literally count the number of atoms in a sample, but we can count them by mass –So, there needs to be a connection between the mass of a sample and the number of moles in that sample –If we weigh out a particular mass of a substance, that can represent a particular number of mols If we weighed out g of CarbonIf we weighed out g of Carbon –It will represent 1 mole of Carbon and/or 6.02x10 23 Carbon atoms Counting Atoms

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This allows us to use the mass off of the periodic table to represent the mass of 1 mole (or 6.02x10 23 atoms) of that elementThis allows us 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 understanding of mass from the periodic table is known as the gram molar mass, or molar mass.This new understanding of mass from the periodic table is known as the gram molar mass, or molar mass. –Molar Mass = mass of 1 mole of atoms in grams –We have a list of every possible molar mass for any given element on the periodic table This mass can be used as a conversion factor…1 mole = g H, etc.This mass can be used as a conversion factor…1 mole = g H, etc. Counting Atoms

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So what if we have a compound instead of an element?So what if we have a compound instead of an element? How do we figure out the mass of a mole of a compound?How do we figure out the mass of a mole of a compound? –This would be called a molecular mass, formula mass, or still can be called a molar mass –All we need is the formula for a representative particle of the compound and the periodic table. Counting Atoms

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For instance how do we calculate the mass of 1 mole of Ca(OH) 2 ?For instance how do we calculate the mass of 1 mole of Ca(OH) 2 ? You can calculate the mass of a mol- ecule of Ca(OH) 2 by breaking it up into individual piecesYou can calculate the mass of a mol- ecule of Ca(OH) 2 by breaking it up into individual pieces We can start with Calcium, then 2 oxygens, then 2 hydrogens… until we run out of piecesWe can start with Calcium, then 2 oxygens, then 2 hydrogens… until we run out of pieces Counting Atoms Ca: (1)(40.09 g/mol) = O: (2)(15.99 g/mol) = H: (2)(1.008 g/mol) = g/mol

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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 – weighs 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: Molar Mass Moles Atoms or molecules # of ____ atoms mols Al(OH) x10 24 molecules # of O atoms x10 25 atoms O 3.350x mols H 2 O x molecules H 2 O # of total atoms 6.051x10 12 atoms 9.995x10 18 mols W x atoms W.2116 mols Al x10 23 ions Al +3

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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 molar mass 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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Aspartame is an artificial sweetener that is 160 times sweeter than sugar when dissolved in water. It is marketed as Nutra-Sweet (C 14 H 18 N 2 O 5 ). 1.What number of molecules are in 5.0 mg of aspartame? 2.What number of atoms of nitrogen are in 1.2 g of aspartame? 3.What is the mass in g of 1 molecule of aspartame? Counting Atoms

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Your Turn: What is the mass of 7.21x10 21 molecules of silver acetate (AgC 2 H 3 O 2 )?What is the mass of 7.21x10 21 molecules of silver acetate (AgC 2 H 3 O 2 )? How many grams of neon gas will fill a room with a volume of 4000L at STP?How many grams of neon gas will fill a room with a volume of 4000L at STP? How many molecules are there in 122 g of Cu(NO 3 ) 2 ?How many molecules are there in 122 g of Cu(NO 3 ) 2 ? Which has the greater mass?Which has the greater mass? a.9.5x10 24 atoms of C a.9.5x10 24 atoms of C b.2.1 mol Br 2 c.1.86x10 22 molecules of CCl 4 d.59.5g Hg

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