Atomic Masses & the MOLE…. Masses of atoms expressed in grams are extremely small.Masses of atoms...

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

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

0.0000000000000000000000266 g0.0000000000000000000000266 g• For most calcs in chemistry it is For most calcs in chemistry it is

easier to use a easier to use a relative atomic mass.relative atomic mass.– for relative masses, an atom was for relative masses, an atom was

arbitrarily chosen as the standard, arbitrarily chosen as the standard, by which by which all other masses are all other masses are comparedcompared

Counting AtomsCounting Atoms

• The mass of all the other atoms The mass of all the other atoms are then expressed in relation are then expressed in relation to the standardto the standard– C-12C-12 atom acts as the standard atom acts as the standard

• 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 (amu)atomic mass units (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 = the mass of a proton = 1 amu1 amu


• The masses of all other atoms are The masses of all other atoms are based on the mass of 1 amubased on the mass of 1 amu– Hydrogen has 1 proton therefore, Hydrogen has 1 proton therefore,

it weighs it weighs 1 amu1 amu– Helium has 2 protons and 2 neutrons Helium has 2 protons and 2 neutrons

therefore, it weighs therefore, it weighs 4 amus4 amus• Most Most elementselements occur naturally as a occur naturally as a

mixture of isotopesmixture of isotopes..– For instance in the two isotopes of For instance in the two isotopes of

Chlorine (Cl-35 & Cl-37)Chlorine (Cl-35 & Cl-37)


• 75%75% of all of the Cl atoms found in of all of the Cl atoms found in nature are the isotope Cl-35 nature are the isotope Cl-35 – 25%25% of the all of the Cl atoms found of the all of the Cl atoms found

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

• Cl-35 atoms are naturally more Cl-35 atoms are naturally more abundant than Cl-37abundant than Cl-37 – Therefore, the average mass of Cl Therefore, the average mass of Cl

(taking into account isotopic abun-(taking into account isotopic abun-dance) should be closer to 35 than dance) should be closer to 35 than to the median of 36.to the median of 36.


• Masses on the PT are weighted aver-Masses on the PT are weighted aver-ages of all of the naturally occurring ages of all of the naturally occurring isotopes of an elementisotopes of an element– The average atomic mass on the PT The average atomic mass on the PT

is reflective of both the is reflective of both the mass mass numbersnumbers of each isotope & the of each isotope & the abundanceabundance of each isotope of each isotope

Here’s how the masses were Here’s how the masses were calculated on the Periodic Table:calculated on the Periodic Table:


Calculating average atomic masses:Calculating average atomic masses:

Naturally occurring copper consists Naturally occurring copper consists of 69.17% Cu-63, which has a mass of 69.17% Cu-63, which has a mass

of 62.9296011 amu, and 30.83% Cu-65, of 62.9296011 amu, and 30.83% Cu-65, with a mass of 64.9277937 amu. with a mass of 64.9277937 amu.

• The average atomic mass of Cu is The average atomic mass of Cu is calculated by multiplying the atomic 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 The reported average atomic mass of naturally occurring Cu is 63.55 amu.of naturally occurring Cu is 63.55 amu.


(0.6917)(62.9296011 amu)(0.6917)(62.9296011 amu)

63.54564387858 amu63.54564387858 amu

Cu-63Cu-63Cu-65Cu-65 + (0.3083)(64.9277937 amu) + (0.3083)(64.9277937 amu)

63.55 amu63.55 amu

Your Turn:Your Turn:

• Gallium consists of two isotopes of Gallium consists of two isotopes of masses 68.95 amu and 70.95 amu with masses 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?

• Naturally occurring element X exists in Naturally occurring element X exists in three isotopic forms: X-28 (27.977 amu, three isotopic forms: X-28 (27.977 amu, 92.21% abundance), X-29 (28.976 amu, 92.21% abundance), X-29 (28.976 amu, 4.70% abundance), and X-30 (29.974 4.70% abundance), and X-30 (29.974 amu, 3.09% abundance). Calculate the amu, 3.09% abundance). Calculate the atomic weight of X.atomic weight of X.

• It is impractical to get caught up into It is impractical to get caught up into working with 1 atom or 1 atom’s mass.working with 1 atom or 1 atom’s mass.– It makes more sense to work with It makes more sense to work with

a collection of atoms rather than a collection of atoms rather than individuallyindividually


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

terms of a terms of a relative massrelative mass

• 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


• 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– Any time we are counting how many Any time we are counting how many

we have and we want to describe it we have and we want to describe it in terms of moles than…in terms of moles than…


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

• The mole, whose abbreviation is “mol”, The mole, whose abbreviation is “mol”, is the SI base unit for measuring is the SI base unit for measuring amount of a pure substance.amount of a pure substance.– It’s used exclusively for counting It’s used exclusively for counting

atoms, molecules, ions, or other things atoms, molecules, ions, or other things that are extremely smallthat are extremely small

– It’s the chemist’s six-pack or dozen. It’s the chemist’s six-pack or dozen. Many objects in our everyday lives Many objects in our everyday lives come in similar counting units.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


• 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



How many atoms of Gold do we have How many atoms of Gold do we have if we have .0327 moles of Gold?if we have .0327 moles of Gold?

unit equality:unit equality:

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

The desired conversion is: The desired conversion is: molesmoles atoms atoms


6.02x106.02x102323atoms Auatoms Au

1 mole Au1 mole Au.0327 mole Au.0327 mole Au

= 2.23x10= 2.23x102222 atoms Au atoms Au


Fill in the missing information in the following Fill in the missing information in the following table, be sure to show your work.table, be sure to show your work.

MolesMoles Atoms or moleculesAtoms or molecules

12.045 mols Al(OH)12.045 mols Al(OH)33

2.017 x 102.017 x 101212 molecules H molecules H22OO

6.017 x 106.017 x 104242 atoms W atoms W

.2116 mols Al.2116 mols Al+3+3

• 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




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


MolesMoles Atoms or Atoms or moleculesmolecules # of ____ atoms# of ____ atoms

12.045 12.045 mols Al(OH)mols Al(OH)33

7.2511x107.2511x102424 moleculesmolecules

# of O atoms# of O atoms

3.350x103.350x10-12-12 mols Hmols H22OO

2.017 x 102.017 x 101212 molecules Hmolecules H22OO

# of total atoms# of total atoms

9.995x109.995x101818 mols Wmols W

6.017 x 106.017 x 104242 atoms Watoms W

.2116 mols .2116 mols AlAl+3+3

1.274x101.274x102323 ions ions AlAl+3+3

Fill in the missing information in the following Fill in the missing information in the following table, be sure to show your work.table, be sure to show your work.

• We can’t literally count the number of We can’t literally count the number of atoms in a sample, but we can count atoms in a sample, but we can count them by massthem by mass– So, there needs to be a connection So, there needs to be a connection

between the mass of a sample and between the mass of a sample and the number of moles in that samplethe number of moles in that sample

– If we weigh out a particular mass If we weigh out a particular mass of a substance, of a substance, that can represent that can represent a particular number of mols a particular number of mols

• If we weighed out 12.011 g of CarbonIf we weighed out 12.011 g of Carbon– It will represent 1 mole of Carbon It will represent 1 mole of Carbon

and/or and/or 6.02x106.02x102323 Carbon atoms Carbon atoms


• This allows us to use the mass off This allows us to use the mass off of the periodic table to represent the of the periodic table to represent the mass of 1 mole (or 6.02x10mass of 1 mole (or 6.02x1023 23 atoms) atoms) of that elementof 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 understanding of mass from This new understanding of mass from the periodic table is known as the the periodic table is known as the gram gram molar massmolar mass, or , or molar massmolar mass..– Molar Mass = mass of 1 mole of atoms Molar Mass = mass of 1 mole of atoms

in gramsin grams– We have a list of every possible molar We have a list of every possible molar

mass for any given element on the mass for any given element on the periodic tableperiodic table • This mass can be used as a conversion This mass can be used as a conversion

factor…1 mole = 1.0079 g H, etc.factor…1 mole = 1.0079 g H, etc.


• So what if we have a compound So what if we have a compound instead of an element?instead of an element?

• How do we figure out the mass of a How do we figure out the mass of a mole of a mole of a compoundcompound??– This would be called a This would be called a molecular molecular

mass, formula massmass, formula mass, or still can be , or still can be called a molar masscalled a molar mass

– All we need is the All we need is the formula for a formula for a representative particle representative particle of the of the compound and the periodic table.compound and the periodic table.


• For instance how do we calculate the For instance how do we calculate the mass of 1 mole of Ca(OH)mass of 1 mole of Ca(OH)22??• You can calculate the mass of a mol-You can calculate the mass of a mol-

ecule of Ca(OH)ecule of Ca(OH)22 by breaking it up into by breaking it up into individual piecesindividual pieces

• We can start with Calcium, then We can start with Calcium, then 2 oxygens, then 2 hydrogens… 2 oxygens, then 2 hydrogens… until we run out of piecesuntil we run out of pieces


Ca: (1)(40.09 g/mol) =Ca: (1)(40.09 g/mol) =O: (2)(15.99 g/mol) =O: (2)(15.99 g/mol) =H: (2)(1.008 g/mol) =H: (2)(1.008 g/mol) =

40.0940.09+ 31.98+ 31.98+ 2.016+ 2.016

74.09 g/mol74.09 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 –

weighs 180.1 gramsweighs 180.1 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:

Molar Molar MassMass MolesMoles Atoms or Atoms or

moleculesmolecules# of ____ # of ____

atomsatoms

12.045 mols 12.045 mols

Al(OH)Al(OH)33

7.2511x107.2511x102424 moleculesmolecules

# of O atoms# of O atoms2.1753x102.1753x102525

atoms Oatoms O

3.350x103.350x10-12-12 mols Hmols H22OO

2.017 x 102.017 x 101212 molecules Hmolecules H22OO

# of total atoms# of total atoms6.051x106.051x101212

atomsatoms

9.995x109.995x101818 mols Wmols W

6.017 x 106.017 x 104242 atoms Watoms W

.2116 mols .2116 mols AlAl+3+3

1.274x101.274x102323 ions ions AlAl+3+3

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 molar mass in calculations:Using the molar mass 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 volumesequal volumes of gases contain of gases contain equal numbersequal numbers 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?

Aspartame is an artificial sweetener Aspartame is an artificial sweetener that is 160 times sweeter than sugar that is 160 times sweeter than sugar

when dissolved in water. It is marketed when dissolved in water. It is marketed as Nutra-Sweet (Cas Nutra-Sweet (C1414HH1818NN22OO55).).

1.1.What number of molecules are What number of molecules are in 5.0 mg of aspartame? in 5.0 mg of aspartame?2.2.What number of atoms of nitrogen What number of atoms of nitrogen are in 1.2 g of aspartame?are in 1.2 g of aspartame?3.3.What is the mass in g of 1 molecule What is the mass in g of 1 molecule of aspartame?of aspartame?



molecules 1.0x10

mole 1

molecules 6.02x10

g 294.37

mole 1

mg 1000

g 15.0mg

19

23

N atoms 4.9x10

molecule 1

N atoms 2

mole 1

molecules 6.02x10

g 294.37

mole 1 g 1.2

21

23

g 4.9x10mole 1

g 294.37

molecules 6.02x10

mole 1 molecule 1 22-

23

Your Turn:Your Turn:• What is the mass of 7.21x10What is the mass of 7.21x102121 molecules molecules

of silver acetate (AgCof silver acetate (AgC22HH33OO22)?)?• How many grams of neon gas will fill a How many grams of neon gas will fill a

room with a volume of 4000L at STP?room with a volume of 4000L at STP?• How many molecules are there in How many molecules are there in

122 g of Cu(NO122 g of Cu(NO33))22??• Which has the greater mass?Which has the greater mass?

a.a. 9.5x109.5x102424 atoms of C atoms of Cb.b. 2.1 mol Br2.1 mol Br22

c.c. 1.86x101.86x102222 molecules of CCl molecules of CCl44d.d. 59.5g Hg59.5g Hg

Atomic Masses & the MOLE…. Masses of atoms expressed in grams are extremely small.Masses of atoms...

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Transcript of Atomic Masses & the MOLE…. Masses of atoms expressed in grams are extremely small.Masses of atoms...