atomic masses & the mole…. neon is a gas that can be found in the atmosphere.neon is a gas...

Atomic Masses & the MOLE…Atomic Masses & the MOLE…

• Neon is a gas that can be found in Neon is a gas that can be found in the atmosphere.the atmosphere.– Dry air contains about 0.002% NeDry air contains about 0.002% Ne– That’s 500,000,000,000,000,000 That’s 500,000,000,000,000,000

atoms of neon every breathatoms of neon every breath• Scientists can deal with atoms quant-Scientists can deal with atoms quant-

itatively because they know itatively because they know some some fundamental properties of the atoms fundamental properties of the atoms of each elementof each element

• Masses of atoms expressed in grams Masses of atoms expressed in grams are extremely small.are extremely small.– An atom of Oxygen -16An atom of Oxygen -16literally weighsliterally weighs0.0000000000000000000000266 g0.0000000000000000000000266 g

--For most calcs in chemistry For most calcs in chemistry it is easier to use a relative it is easier to use a relative atomic mass.atomic mass.

- For relative masses, an - For relative masses, an atom was arbitrarily chosen as atom was arbitrarily chosen as the standard, by which all other the standard, by which all other masses are comparedmasses are compared

--For most calcs in chemistry For most calcs in chemistry it is easier to use a relative it is easier to use a relative atomic mass.atomic mass.

- For relative masses, an - For relative masses, an atom was arbitrarily chosen as atom was arbitrarily chosen as the standard, by which all other the standard, by which all other masses are comparedmasses are compared

I. Atomic MassA. Relative Mass is when you

measure the mass of all atoms based on the measurement of one particular atom.

1.1.C-12 atom acts as the standard to C-12 atom acts as the standard to compare all other atoms compare all other atoms

2.2. A single C-12 atom was assigned A single C-12 atom was assigned a mass of 12 a mass of 12 atomic mass units atomic mass units (amu)(amu)– 1 amu is exactly 1/12 of the mass of 1 amu is exactly 1/12 of the mass of

a C-12 atom a C-12 atom – Carbon has 12 nucleons therefore, Carbon has 12 nucleons therefore,

the mass of a proton = 1 amuthe mass of a proton = 1 amu

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

amusamus

A proton weighs 1.007276 amu

A neutron weighs 1.008665 amu

A. Most elements exist in nature as A. Most elements exist in nature as isotopesisotopes• 75% of all of the Cl atoms found in 75% of all of the Cl atoms found in

nature are the isotope Cl-35 nature are the isotope Cl-35 • 25% of the all of the Cl atoms found 25% of the all of the Cl atoms found

in nature are the isotope Cl-37in nature are the isotope Cl-37

II. Average Atomic Mass

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

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?

2. 2. Calculating average atomic masses:Calculating average atomic masses:

a. Cua. Cu69.17% Cu-63 has a mass of 63 amu, 69.17% Cu-63 has a mass of 63 amu, 30.83% Cu-65 has a mass of 65 amu.30.83% Cu-65 has a mass of 65 amu.

• It’s calculated by multiplying the atomic It’s calculated by multiplying the atomic mass of each isotope by its abundance mass of each isotope by its abundance and adding the results.and adding the results.

• The reported average atomic mass of The reported average atomic mass of naturally occurring Cu is 63.55 amu.naturally occurring Cu is 63.55 amu.

(0.6917)(63 amu)(0.6917)(63 amu)

63.6 amu63.6 amu

Cu-63Cu-63Cu-65Cu-65 + (0.3083)(65 amu) + (0.3083)(65 amu)

Your Turn:Your Turn:

b. Practice #1.b. Practice #1.

Gallium consists of two isotopes of masses Gallium consists of two isotopes of masses

• 68.95 amu and 70.95 amu with 68.95 amu and 70.95 amu with abundances of 60.16% and 39.84%, abundances of 60.16% and 39.84%, respectively. What is the average atomic respectively. What is the average atomic mass of gallium?mass of gallium?

c. Practice #2.

•Naturally occurring element X exists in Naturally occurring element X exists in three isotopic forms: three isotopic forms:

•X-28 (27.977 amu, 92.21% X-28 (27.977 amu, 92.21% abundance), abundance),

•X-29 (28.976 amu, 4.70% abundance), X-29 (28.976 amu, 4.70% abundance),

• X-30 (29.974 amu, 3.09% abundance)X-30 (29.974 amu, 3.09% abundance)

. Calculate the atomic weight of X.. Calculate the atomic weight of X.

•B. Relating Mass to the number of Atoms

• It is impractical to get caught up into It is impractical to get caught up into working with 1 atom’s mass because working with 1 atom’s mass because usually you working with a large usually you working with a large number of atoms. number of atoms.

• Scientists were challenged to figure Scientists were challenged to figure out a way to define a collection of out a way to define a collection of particles particles – And which could still be described in And which could still be described in

terms of a relative massterms of a relative mass

1.1. The average C atom with an atomic The average C atom with an atomic mass of 12.0 amus is 12 times mass of 12.0 amus is 12 times heavier than the average H atomheavier than the average H atoma.a.So 100 C atoms are 12 times So 100 C atoms are 12 times

heavier than 100 H atomsheavier than 100 H atoms b. any # of C atoms would be 12 b. any # of C atoms would be 12 times heavier than the same # of H times heavier than the same # of H atomatom

• If we assume we can relate the If we assume we can relate the relative masses from the PT in the relative masses from the PT in the terms of grams terms of grams – With the literal masses of an atom With the literal masses of an atom

(g) for each atom we use we seem (g) for each atom we use we seem to get the to get the same number of atomssame number of atoms

atoms10*0235.6g10*6561.2

atom 115.999g 23

23

atoms10*0231.6g10*6735.1

atom 11.00797g 23

24

atoms10*0235.6g10*9941.1

atom 112.0115g 23

23

Counting AtomsCounting Atoms

• The number of atoms that are in the The number of atoms that are in the relative masses of elements identical relative masses of elements identical in grams to the atomic masses on the in grams to the atomic masses on the PT is called PT is called Avogadro’s NumberAvogadro’s Number• And is defined as a And is defined as a molemole


• The mole becomes a The mole becomes a counting unitcounting unit much like the dozen.much like the dozen.– 1 dozen eggs = 12 eggs1 dozen eggs = 12 eggs– 1 mole of eggs = 1 mole of eggs =

• The word “mole” was introduced by The word “mole” was introduced by Wilhelm Oswald, who derived the Wilhelm Oswald, who derived the term from the word moles meaning term from the word moles meaning a a “heap” or “pile.”“heap” or “pile.”– We are just defining the pile as con-We are just defining the pile as con-

taining 6.02x10taining 6.02x102323 items items– Because it is such a huge number of Because it is such a huge number of

items we usually reserve the mole for items we usually reserve the mole for atoms or moleculesatoms or molecules


1 mole is always = 6.02 x 101 mole is always = 6.02 x 1023 23 itemsitems

• The mole, whose abbreviation is The mole, whose abbreviation is “mol”, is the SI base unit for meas-“mol”, is the SI base unit for meas-uring amount of a pure substance.uring amount of a pure substance.– The mole is the chemist’s six-pack or The mole is the chemist’s six-pack or

dozen. Many objects in our everyday dozen. Many objects in our everyday lives come in similar counting units.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


REPRESENTATIVE PARTICLES & MOLESREPRESENTATIVE PARTICLES & MOLES

Atomic Atomic NitrogenNitrogen AtomAtom NN 6.02x106.02x102323

Nitrogen Nitrogen gasgas MolecMolec.. NN22 6.02x106.02x102323

WaterWater Molec.Molec. HH22OO 6.02x106.02x102323

Calcium ionCalcium ion IonIon CaCa2+2+ 6.02x106.02x102323

Calcium Calcium FluorideFluoride

Formula Formula unitunit CaFCaF22 6.02x106.02x102323

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

the number of molecules or atoms the number of molecules or atoms are involved in that X number of molsare involved in that X number of mols


Using the mole in calculations #1Using the mole in calculations #1


How many moles of Magnesium How many moles of Magnesium is 1.25 x 10is 1.25 x 102323 atoms of Magnesium? atoms of Magnesium?

unit equality:unit equality:

1 mol Mg = 6.02 x 101 mol Mg = 6.02 x 102323 atoms Mg atoms Mg

The desired conversion is: The desired conversion is: atomsatoms moles moles


6.02x106.02x102323atoms Mgatoms Mg

1 mole Mg1 mole Mg1.25x101.25x102323 atoms Mg atoms Mg

= .208 mol Mg= .208 mol Mg

Your Turn:Your Turn:• To make sure adequate amounts of product AB To make sure adequate amounts of product AB

is being made during a rxn you might need is being made during a rxn you might need 3.33 mols of A reacting with 2.68 mols of B. 3.33 mols of A reacting with 2.68 mols of B. How many atoms of A are reacting with how How many atoms of A are reacting with how many atoms of B?many atoms of B?

• If you burn sugar (CIf you burn sugar (C1212HH2222OO1111) in pure oxygen ) in pure oxygen you produce carbon dioxide and water as you produce carbon dioxide and water as products. To burn 6.02x10products. To burn 6.02x102323 molecules of molecules of sugar you also need 7.22x10sugar you also need 7.22x102424 molecules of molecules of oxygen and you produce 6.62x10oxygen and you produce 6.62x102424 molecules molecules of water and 7.22x10of water and 7.22x102424 molecules of carbon molecules of carbon dioxide. How many mols are reacted or dioxide. How many mols are reacted or produced for each component of the rxn?produced for each component of the rxn?

• Now suppose you want to determine Now suppose you want to determine how many atoms are in a how many atoms are in a mol of a mol of a compound or moleculecompound or molecule– To do this you must know how many To do this you must know how many

atoms are involved in the molecule.atoms are involved in the molecule.• To determine the number of atoms To determine the number of atoms

represented in a molecule requires represented in a molecule requires knowing the knowing the chemical formulachemical formula– Eg, each molecule of Carbon Dioxide Eg, each molecule of Carbon Dioxide

((COCO22) is composed of ) is composed of 3 atoms3 atoms


• 1 mole of Carbon Dioxide contains 1 mole of Carbon Dioxide contains Avogadro’s number of Carbon Avogadro’s number of Carbon Dioxide molecules.Dioxide molecules.– Thus a mole of COThus a mole of CO22 contains three contains three

times Avogadro’s # of atomstimes Avogadro’s # of atoms


Using the mole in calculations #2Using the mole in calculations #2


How many atoms of Carbon are in How many atoms of Carbon are in 2.12 mols of Propane (C2.12 mols of Propane (C33HH88)?)?

unit equalities:unit equalities:

1 mol C1 mol C33HH88 = = 6.02x106.02x102323 molecules C molecules C33HH88

1 molecule C1 molecule C33HH88 = = 3 atoms C3 atoms C

6.02x106.02x1023 23

molecules Cmolecules C33HH88

1 mole C1 mole C33HH88

The desired conversions are: The desired conversions are:

2.12 2.12 mols mols CC33HH88

3 atoms C3 atoms C

1 molecule 1 molecule CC33HH88

=3.83x10=3.83x1024 24 atoms Catoms C


moles moles molecules molecules atoms atoms

Your Turn:Your Turn:

• Back to burning sugar, 1 mol of sugar Back to burning sugar, 1 mol of sugar (C(C1212HH2222OO1111) was burned with 12 mols of ) was burned with 12 mols of oxygen (Ooxygen (O22) to produce 11 mols of water ) to produce 11 mols of water (H(H22O) and 12 mols of Carbon dioxide O) and 12 mols of Carbon dioxide (CO(CO22). How many total atoms of oxygen ). How many total atoms of oxygen are burned in the reaction (reactants), are burned in the reaction (reactants), and how many total atoms of oxygen are and how many total atoms of oxygen are produced in the reaction (products)?produced in the reaction (products)?

• We can also relate mass to the We can also relate mass to the number of atoms and the mole. number of atoms and the mole. – Relative atomic massesRelative atomic masses and the mol and the mol

can be used to develop a method of can be used to develop a method of measuring the amount of a sample. measuring the amount of a sample.

• If we had a pile of C atoms that If we had a pile of C atoms that weighed 12 g and a pile of H atoms weighed 12 g and a pile of H atoms that weighed 1gthat weighed 1g– each pile would contain the same each pile would contain the same

number of atoms or number of atoms or 6.02x106.02x102323 atoms atoms


• The The gram atomic massesgram atomic masses of any of any 2 elements (since they are relative to 2 elements (since they are relative to C) must contain the same # of atomsC) must contain the same # of atoms– A pile of any atom that corresponds A pile of any atom that corresponds

to its average atomic mass from the to its average atomic mass from the PT contains exactly 6.02x10PT contains exactly 6.02x102323 atoms atoms of that element.of that element.• And is equal to how much 1 mole of that And is equal to how much 1 mole of that

sample would weigh in gramssample would weigh in grams


• What this allows us to do is to use the What this allows us to do is to use the mass off of the periodic table to mass off of the periodic table to represent the mass of 1 mole (or represent the mass of 1 mole (or 6.02x106.02x1023 23 atoms) of that elementatoms) of that element– 1 mol of C atoms weighs 1 mol of C atoms weighs 12.01 g12.01 g– 1 mol of H atoms weighs 1 mol of H atoms weighs 1.008 g1.008 g– 1 mol of W atoms weigh 1 mol of W atoms weigh 183.8 g183.8 g


• This new version of mass from the This new version of mass from the periodic table is called the periodic table is called the gram gram molar massmolar mass, or , or molar massmolar mass..– Molar Mass = mass of 1 mole of Molar Mass = mass of 1 mole of

atoms/molecules/or formula units in atoms/molecules/or formula units in gramsgrams• abbreviated = abbreviated = MMMM • units = units = grams/molgrams/mol


• We get the mass of 1 mole of any We get the mass of 1 mole of any element off of the Periodic Tableelement off of the Periodic Table

• So how do we figure out the mass of So how do we figure out the mass of a mole of a a mole of a compoundcompound rather than rather than just an just an elementelement??– To answer that question you must To answer that question you must

have the have the formulaformula of the of the compound.compound.


ModelModelFormulaFormulaModelModelFormulaFormula

The formula of a compound tells you how The formula of a compound tells you how many atoms of each element combine to many atoms of each element combine to make the representative particle of that make the representative particle of that compound.compound.

Counting AtomsCounting AtomsWhat is the mass of 1 mole of Sulfur What is the mass of 1 mole of Sulfur Trioxide (SOTrioxide (SO33) A.K.A. Molar Mass?) A.K.A. Molar Mass?

• You can calculate the mass of a mol-You can calculate the mass of a mol-ecule of SOecule of SO33 by adding the MM of by adding the MM of each of the atoms in the moleculeeach of the atoms in the molecule– The mass of 1 mole of S is The mass of 1 mole of S is 32.1g32.1g..– The mass of 3 atoms of O is 3 times The mass of 3 atoms of O is 3 times

the MM of a single O atom, the MM of a single O atom, or or (3)(15.99g) = 47.97g(3)(15.99g) = 47.97g

– So MM of 1 molecule of SOSo MM of 1 molecule of SO33 is is 32.1g + 47.97g = 80.1 g/mol32.1g + 47.97g = 80.1 g/mol


(6C’S)(12.011g/mol) =(6C’S)(12.011g/mol) =

180.1g/mol180.1g/mol

(12H’S)(1.008 g/mol) =(12H’S)(1.008 g/mol) =

(6O’S)(15.99 g/mol) =(6O’S)(15.99 g/mol) =

1 mole of C1 mole of C66HH1212OO6 6 or or 6.02x106.02x102323 molecules of the compound – molecules of the compound –

it would weigh 180 grams it would weigh 180 grams

72.066g/mol72.066g/mol12.096g/mol12.096g/mol

95.94g/mol95.94g/mol


What is the MM of glucose (CWhat is the MM of glucose (C66HH1212OO66)?)?

Practice Time:Practice Time:

• Determine the mass of 1 mole (Molar Determine the mass of 1 mole (Molar mass) of each of the following:mass) of each of the following:– ZnZn

– GdGd

– Zn(CZn(C22HH33OO22))22

– (NH(NH44))33POPO44

– CC1212HH2222OO1111

How many grams are in 9.45 mol How many grams are in 9.45 mol of Dinitrogen Trioxide (Nof Dinitrogen Trioxide (N22OO33))

The only connection to NThe only connection to N22OO33 and its mass and its mass is how much 1 mol of the compound is how much 1 mol of the compound

weighs. But, using it as a comparison weighs. But, using it as a comparison we can calculate the mass of 9.45 mol.we can calculate the mass of 9.45 mol.


Using the mole in calculations:Using the mole in calculations:


Step 1: Determine the mass of 1 mol Step 1: Determine the mass of 1 mol of Nof N22OO33

47.97g47.97g(2N’s)(14.01g) =(2N’s)(14.01g) = 28.02g28.02g

(3O’s)(15.99g) =(3O’s)(15.99g) =

75.99g75.99g

If 1 mole of NIf 1 mole of N22OO3 3 weighs 75.99g than how weighs 75.99g than how much will 9.45 mols of Nmuch will 9.45 mols of N22OO33 weigh? weigh?

1 mol N1 mol N22OO33

75.99 g N75.99 g N22OO339.45 mol N9.45 mol N22OO33

=718 g N=718 g N22OO33


Step 2: Convert the given moles to Step 2: Convert the given moles to grams using the Molar mass grams using the Molar mass equality.equality.

Find the number of moles of Find the number of moles of 92.2g of Iron (III) Oxide (Fe92.2g of Iron (III) Oxide (Fe22OO33))

The only connection to the mass of FeThe only connection to the mass of Fe22OO33 and how that corresponds to mols is how and how that corresponds to mols is how

that 1 mol of the compound weighs a certain that 1 mol of the compound weighs a certain # of grams. Using that we can figure out # of grams. Using that we can figure out

how many moles weigh 92.2 g how many moles weigh 92.2 g


47.97g47.97g(2Fe’s)(55.85g) =(2Fe’s)(55.85g) = 111.7g111.7g

(3O’s)(15.99g) =(3O’s)(15.99g) =

159.67g159.67g

If 1 mole of FeIf 1 mole of Fe22OO3 3 weighs 157.67g than how weighs 157.67g than how many mols will weigh 92.2 g of Femany mols will weigh 92.2 g of Fe22OO33??


Step 1: Determine the mass of 1 mol of Step 1: Determine the mass of 1 mol of FeFe22OO33

159.67 g Fe159.67 g Fe22OO33

1 mol Fe1 mol Fe22OO3392.2 g Fe92.2 g Fe22OO33

=.577mol Fe=.577mol Fe22OO33


Step 2: Convert the given mass to mols Step 2: Convert the given mass to mols using the Molar mass equalityusing the Molar mass equality


• Vitamin C (CVitamin C (C66HH88OO66), cannot be stored by ), cannot be stored by the body and therefore, must be present the body and therefore, must be present in the diet. If an orange contains 70 mg in the diet. If an orange contains 70 mg of Vit C how many oranges are necessary of Vit C how many oranges are necessary to consume 2.5 mols of Vit C?to consume 2.5 mols of Vit C?

• Another generality about the mole is Another generality about the mole is that with matter in the gas phase we that with matter in the gas phase we can develop another can develop another equalityequality..– Under the same conditions, Under the same conditions, equal equal

volumesvolumes of gases contain of gases contain equal equal numbersnumbers of particles. of particles.

– 1 mol of a gas will occupy the same 1 mol of a gas will occupy the same volume as 1 mol of any other gas volume as 1 mol of any other gas under the same conditions.under the same conditions.


1 mole of any gas 1 mole of any gas under the specific under the specific conditions of 0conditions of 0°°C C and 1 atm (STP) and 1 atm (STP)

will occupy a will occupy a volume of volume of 22.4 L22.4 L..

6.02x106.02x102323

molecules of Omolecules of O22

6.02x106.02x102323

molecules of COmolecules of CO22

Molar Volume of a GasMolar Volume of a Gas

What volume, in Liters, does 0.60 mol What volume, in Liters, does 0.60 mol of SOof SO22 gas occupy at STP? gas occupy at STP?

The only connection to the volume of any The only connection to the volume of any gas and how that corresponds to mols is gas and how that corresponds to mols is

that 1 mol of a gas occupies 22.4 Liters of that 1 mol of a gas occupies 22.4 Liters of space. Using that we can figure out the space. Using that we can figure out the volume of 0.60 mols of a gas at STP. volume of 0.60 mols of a gas at STP.


1 mole SO1 mole SO22

22.4 L SO22.4 L SO220.60 moles SO0.60 moles SO22

= 13 L SO= 13 L SO22

Step 1: Use the equality 1 mol = 22.4 L Step 1: Use the equality 1 mol = 22.4 L to do the conversionto do the conversion



• The Snoopy balloon featured at the The Snoopy balloon featured at the Macy’s Thanksgiving Day Parade has a Macy’s Thanksgiving Day Parade has a volume of 15650 ftvolume of 15650 ft33. How many moles of . How many moles of Helium are required to fill it up @ STP?Helium are required to fill it up @ STP?

If you have a 35.67g piece of Chro-If you have a 35.67g piece of Chro-mium metal on your car, how many mium metal on your car, how many atoms of Chromium do you have?atoms of Chromium do you have?

• You are given mass and asked for You are given mass and asked for number of particlesnumber of particles

• Let’s get some strategyLet’s get some strategy


• 11stst convert given mass into moles convert given mass into moles• To do this we use the molar mass (MM) To do this we use the molar mass (MM)

of Cr which on the PT is 51.996g/molof Cr which on the PT is 51.996g/mol• Then we need to convert from mols to Then we need to convert from mols to

atoms using Avogadro’s number.atoms using Avogadro’s number.


35.67g Cr35.67g Cr51.996g Cr51.996g Cr

1 mole Cr1 mole Cr

1 mole Cr1 mole Cr

6.02x106.02x1023 23 atomsatoms

= 4.130x10= 4.130x1023 23 atoms of Cratoms of Cr

Calculate the Missing Info…Calculate the Missing Info…

FormulaFormula Molar Molar MassMass MolesMoles MassMass ParticlesParticles Gas Vol. Gas Vol.

@ STP@ STP

CHCH441.5 1.5 molmol

HH22SOSO44 79.0 g79.0 g

COCO 9.03x109.03x1023 23

moleculesmolecules

Cu(NOCu(NO33))22 93.8 g93.8 g

atomic masses & the mole…. neon is a gas that can be found in the atmosphere.neon is a gas...

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