THE MOLE Unit 7

THE MOLEUnit 7

THE MOLEUnit 7

• One way to measure how much substance available is to count the # of particles in that sample–However, atoms & molecules are extremely small

–Also, the # of individual particles in even a small sample is very large

–Therefore, counting the # of particles is not a practical measure of amount

• To solve this problem, scientists developed the concept of the mole– It’s the “chemical counting unit”

• One way to measure how much substance available is to count the # of particles in that sample–However, atoms & molecules are extremely small

–Also, the # of individual particles in even a small sample is very large

–Therefore, counting the # of particles is not a practical measure of amount

• To solve this problem, scientists developed the concept of the mole– It’s the “chemical counting unit”

How Scientists Keep Track of Atoms

How Scientists Keep Track of Atoms

• Just as a dozen eggs equals 12 eggs, a mole = 602,000,000,000,000,000,000,000– It is equal to that number no matter what kind of particles you’re talking about

– It could be represent marbles, pencils, or bikes

– usually deals with atoms and molecules•The word “mole” was introduced

about 1896 by Wilhelm Oswald, who derived the term from the latin word moles meaning a “heap” or “pile.”

•The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance.

• Just as a dozen eggs equals 12 eggs, a mole = 602,000,000,000,000,000,000,000– It is equal to that number no matter what kind of particles you’re talking about

– It could be represent marbles, pencils, or bikes

– usually deals with atoms and molecules•The word “mole” was introduced

about 1896 by Wilhelm Oswald, who derived the term from the latin word moles meaning a “heap” or “pile.”

•The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance.

• The mole, as a unit, is only used to count very small items– Represents a # of items, so, we can know exactly how many items are in 1 mole

• The experimentally determined number a mole is called, Avogadro’s Number.–Or 6.02x1023

• The term representative particle refers to the species present in a substance– Usually atoms– Molecules– Or formula units (ions)

• The mole, as a unit, is only used to count very small items– Represents a # of items, so, we can know exactly how many items are in 1 mole

• The experimentally determined number a mole is called, Avogadro’s Number.–Or 6.02x1023

• The term representative particle refers to the species present in a substance– Usually atoms– Molecules– Or formula units (ions)

REPRESENTATIVE PARTICLES & REPRESENTATIVE PARTICLES & MOLESMOLES

ATOMIC ATOMIC NITROGENNITROGEN ATOMATOM NN

6.02x106.02x1022

33

NITROGEN NITROGEN GASGAS MOLECMOLEC.. NN22

6.02x106.02x1022

33

WATERWATER MOLEC.MOLEC. HH22006.02x106.02x1022

33

CALCIUM CALCIUM IONION IONION CaCa2+2+ 6.02x106.02x1022

33

CALCIUM CALCIUM FLUORIDEFLUORIDE

FORMULA FORMULA UNITUNIT CaFCaF22

6.02x106.02x1022

33

How Do We Use The Mole?How Do We Use The Mole?• We’d never use the mole to describe

macroscopic or real world objects. – 1 mole (6.02x1023) of watermelon seeds would be found inside a watermelon the size of the moon.

– 1 mole (6.02x1023) of donut holes would cover the earth and would be 5 miles deep.

• Since the mole is such a huge number of items, it is only used to describe the amount of things that are very, very small.– 1 mole (6.02x1023) of water molecules would barely fill a shot glass

• We’d never use the mole to describe macroscopic or real world objects. – 1 mole (6.02x1023) of watermelon seeds would be found inside a watermelon the size of the moon.

– 1 mole (6.02x1023) of donut holes would cover the earth and would be 5 miles deep.

• Since the mole is such a huge number of items, it is only used to describe the amount of things that are very, very small.– 1 mole (6.02x1023) of water molecules would barely fill a shot glass

Using the mole in calculations #1


What number of moles of Mg is equivalent to 1.806x1024 atoms of Mg?

What number of moles of Mg is equivalent to 1.806x1024 atoms of Mg?

*Remember*1 mol Mg = 6.02x1023 atoms

Mg

*Remember*1 mol Mg = 6.02x1023 atoms

Mg

6.02x1023 atoms Mg

6.02x1023 atoms Mg

1 mole Mg1 mole Mg X mole MgX mole Mg

1.806x1024 atoms Mg1.806x1024 atoms Mg

==

(6.02x1023 atoms Mg)(X mole Mg) =(6.02x1023 atoms Mg)(X mole Mg) =(1.806x1024 atoms Mg)(1

mole Mg)(1.806x1024 atoms Mg)(1

mole Mg)(6.02x1023atmMg)(X)=(1.806x1024atms•molsMg)

(6.02x1023atmMg)(X)=(1.806x1024atms•molsMg)

(6.02x1023atmMg)(6.02x1023atmMg) (6.02x1023atmMg)(6.02x1023atmMg)X = 3.0 molesX = 3.0 molesX = 3.0 molesX = 3.0 moles


Using the mole in calculations #2If we had 2.5 moles of sugar, how many

molecules of sugar is that equal to?If we had 2.5 moles of sugar, how many

molecules of sugar is that equal to?

*Remember*1 mol sugar = 6.02x1023 molecules

sugar

*Remember*1 mol sugar = 6.02x1023 molecules

sugar

6.02x1023molec sugar

6.02x1023molec sugar

1 mole sugar1 mole sugar 2.5 moles sugar

2.5 moles sugar

X molec sugarX molec sugar==

(1mole sugar)(X molec sugar) =(1mole sugar)(X molec sugar) =(6.02x1023 molecs sugar)(2.5

mole sugar)(6.02x1023 molecs sugar)(2.5

mole sugar)(1molsugar)(X) = (1.505x1024molecs•mols sugar)

(1molsugar)(X) = (1.505x1024molecs•mols sugar)

(1molsugar)(1molsugar) (1molsugar)(1molsugar)X = 1.51x10X = 1.51x102424 molecules of molecules of

sugarsugarX = 1.51x10X = 1.51x102424 molecules of molecules of

sugarsugar

•What if I asked you how many atoms are in a mole of a compound?–you must know how many atoms are in a representative particle or cluster of the compound.

•To do this you must know the chem formula–For example, each molecule of CO2 is composed of 1 C + 2 O’s = 3 atoms

•1 mole of carbon dioxide molecules contains avogadro’s number of carbon dioxide molecules.–Thus a mole of CO2 contains three times avogadro’s number of atoms

•What if I asked you how many atoms are in a mole of a compound?–you must know how many atoms are in a representative particle or cluster of the compound.

•To do this you must know the chem formula–For example, each molecule of CO2 is composed of 1 C + 2 O’s = 3 atoms

•1 mole of carbon dioxide molecules contains avogadro’s number of carbon dioxide molecules.–Thus a mole of CO2 contains three times avogadro’s number of atoms

•To find the # of atoms in a mol of a compound, –You 1st determine the # of atoms in a representative particle of that compound

–And then multiply that # of atoms by avogadro’s #

•To find the # of atoms in a mol of a compound, –You 1st determine the # of atoms in a representative particle of that compound

–And then multiply that # of atoms by avogadro’s #Using the mole in

calculations #3Using the mole in calculations #3

How many atoms of carbon are in 2.12 mols of propane molecules (C3H8)?

How many atoms of carbon are in 2.12 mols of propane molecules (C3H8)?

Useful Info:1 mol C3H8 = 6.02x1023 molecules C3H8

1molecule C3H8 = 3 atoms of C

Useful Info:1 mol C3H8 = 6.02x1023 molecules C3H8

1molecule C3H8 = 3 atoms of C

1st we need to see how many molecules of propane we have if

we have 2.12 moles.

1st we need to see how many molecules of propane we have if

we have 2.12 moles.

6.02x1023molec C3H8

6.02x1023molec C3H8

1 mole C3H81 mole C3H8 2.12 moles C3H8

2.12 moles C3H8X molec C3H8X molec C3H8

==

X = 1.276x1024 molecules of C3H8

X = 1.276x1024 molecules of C3H8

(1molecC3H8)(X)=(1.276x1024molec•molsC3H8)

(1molecC3H8)(X)=(1.276x1024molec•molsC3H8)(1 molec C3H8)(1 molec C3H8) (1 molec C3H8)(1 molec C3H8)

2nd we need to see how many atoms of C if we have 1.276x1024

molecs of C3H8.

2nd we need to see how many atoms of C if we have 1.276x1024

molecs of C3H8.

3 atoms of C3 atoms of C

1 molecule C3H8

1 molecule C3H8

1.276x1024 molec C3H8

1.276x1024 molec C3H8X atoms CX atoms C

==

X = 3.83x1024 atoms of Carbon

X = 3.83x1024 atoms of Carbon

(1molec C3H8)(X)=(3.83x1024molec •

atoms C)(1molec C3H8)(X)=(3.83x1024molec •

atoms C)(1 molec C3H8)(1 molec C3H8) (1 molec C3H8)(1 molec C3H8)

•Do you know how to measure out 3 moles of sugar or salt or water?–The mole is a counting unit, so we would have to count out 6.02x1023 particles of each substance. (no thank you)

•There are 2 ways we can use to measure out a number of moles of a substance.–Measure it in grams (a mass)–Or measure it in liters (a volume)

•Do you know how to measure out 3 moles of sugar or salt or water?–The mole is a counting unit, so we would have to count out 6.02x1023 particles of each substance. (no thank you)

•There are 2 ways we can use to measure out a number of moles of a substance.–Measure it in grams (a mass)–Or measure it in liters (a volume)

How we measure moles…How we measure moles…

•One of the units we can use to measure out a particular amount of moles is to weigh it out in grams?–The only problem with this method is that 1 mol of books will weigh more than 1 mol of pencils, since each book is heavier.

–What if 1 mol of pencils weighs 500Gtons and 1 mol of books weighs 1x106Gtons.

•How much would 3.0 mols of pencils and 3 mols of books weigh? –500 Gtons * 3 mols = 1500 Gtons pencils

–1x106 Gtons * 3 mols = 3x106 Gtons

•One of the units we can use to measure out a particular amount of moles is to weigh it out in grams?–The only problem with this method is that 1 mol of books will weigh more than 1 mol of pencils, since each book is heavier.

–What if 1 mol of pencils weighs 500Gtons and 1 mol of books weighs 1x106Gtons.

•How much would 3.0 mols of pencils and 3 mols of books weigh? –500 Gtons * 3 mols = 1500 Gtons pencils

–1x106 Gtons * 3 mols = 3x106 Gtons

Using mass to measure moles…




• To be able to measure out 1 mol of a substance we would need access to the known mass in grams of 1 mol of any substance in question– We would need a data table that provided all of these masses since every substance involved would have its own mass.

• Remember, we don’t use the mole to count anything but atoms, molecules, etc.– So we need a table that provides the mass 1 mole would weigh for every combination of atoms known to man.

• To be able to measure out 1 mol of a substance we would need access to the known mass in grams of 1 mol of any substance in question– We would need a data table that provided all of these masses since every substance involved would have its own mass.

• Remember, we don’t use the mole to count anything but atoms, molecules, etc.– So we need a table that provides the mass 1 mole would weigh for every combination of atoms known to man.



• It just so happens that the periodic table provides us with some of that information.–The masses of each atom on the table is the equivalent to the mass of 1 mole of that atom

–Every type of atom known to humankind is on that table.

•The mass on the periodic table is called the molar mass (units of g/mol), because it represents the mass of 1 mol of that atom–1 mole of Mg atoms weighs 24.305 g–1 mole of C atoms weighs 12.011 g

• It just so happens that the periodic table provides us with some of that information.–The masses of each atom on the table is the equivalent to the mass of 1 mole of that atom

–Every type of atom known to humankind is on that table.

•The mass on the periodic table is called the molar mass (units of g/mol), because it represents the mass of 1 mol of that atom–1 mole of Mg atoms weighs 24.305 g–1 mole of C atoms weighs 12.011 g



•That works well for atoms off of the periodic table, but how do we deal the molar masses of molecules and compounds?–Each of those compounds and molecules is composed of a combination of atoms

–We have the molar masses for all of the atoms on the periodic table

•We need to be able to add up the total weight of all of the atoms in the compound or molecule given its formula.–For ex, what is the molar mass of H2O?

•That works well for atoms off of the periodic table, but how do we deal the molar masses of molecules and compounds?–Each of those compounds and molecules is composed of a combination of atoms

–We have the molar masses for all of the atoms on the periodic table

•We need to be able to add up the total weight of all of the atoms in the compound or molecule given its formula.–For ex, what is the molar mass of H2O?

•We just add the molar masses of each of the atoms that make up the molecule

•From the PT, we find that the molar mass of 1 mole of Hydrogen atoms is 1.0079 g.–We have 2 Hydrogen atoms per molecule of H2O, so our Hydrogen atoms total 2 * 1.0079 g or 2.0158 g per mole

•The mass of 1 mole of oxygen atoms is 15.999 g.–We have only 1 atom of oxygen per mole-cule of H2O so our total mass of oxygen is 1 * 15.999 g or just 15.999 g per mol

•Therefore 1 mole of H2O molecs would weigh, 2.0158g+15.999g= 18.0148g

•We just add the molar masses of each of the atoms that make up the molecule

•From the PT, we find that the molar mass of 1 mole of Hydrogen atoms is 1.0079 g.–We have 2 Hydrogen atoms per molecule of H2O, so our Hydrogen atoms total 2 * 1.0079 g or 2.0158 g per mole

•The mass of 1 mole of oxygen atoms is 15.999 g.–We have only 1 atom of oxygen per mole-cule of H2O so our total mass of oxygen is 1 * 15.999 g or just 15.999 g per mol

•Therefore 1 mole of H2O molecs would weigh, 2.0158g+15.999g= 18.0148g

What is the mass of 1 mole of C6H12O6?

What is the mass of 1 mole of C6H12O6?

Ex #2: Calculating molar masses using chemical formulas

Ex #2: Calculating molar masses using chemical formulas

•The overall mass of 1 mole of C6H12O6 will be the molar mass of 6 Carbons + the molar mass of 12 Hydrogens + the molar mass of 6 Oxygens.

•The overall mass of 1 mole of C6H12O6 will be the molar mass of 6 Carbons + the molar mass of 12 Hydrogens + the molar mass of 6 Oxygens.6 Carbons =6 Carbons = 12.011

g 12.011 g

6 *6 *

12 Hydrogens =12 Hydrogens = 1.0079 g 1.0079 g

12 *12 *

= 72.066 g

= 72.066 g = 12.095 g

= 12.095 g

6 Oxygens =6 Oxygens = 15.999 g 15.999 g

6 *6 * = 95. 994 g = 95. 994 g

180.16 g/mole 180.16 g/mole

• Even though for compounds and molecules we have to calculate a molar mass using the periodic table, they are considered given or known values.

• We can use these molar masses in calculations in which we are either give moles and asked for its mass equivalent or given mass and asked for its mole equivalent.– If we are given an element we just use the mass from the periodic table

– If we are given a formula instead we just calculate the molar mass of the molecule using the masses from the periodic table.

• Even though for compounds and molecules we have to calculate a molar mass using the periodic table, they are considered given or known values.

• We can use these molar masses in calculations in which we are either give moles and asked for its mass equivalent or given mass and asked for its mole equivalent.– If we are given an element we just use the mass from the periodic table

– If we are given a formula instead we just calculate the molar mass of the molecule using the masses from the periodic table.


Using the mole in calculations #4How much would

9.45 moles of N2O3 weigh?How much would

9.45 moles of N2O3 weigh?

2(14.007g)+3(15.999g)2(14.007g)

+3(15.999g)

1 mole N2O31 mole N2O3 9.45 moles N2O3

9.45 moles N2O3X g N2O3X g N2O3

==


Using the mole in calculations #4How much would

9.45 moles of N2O3 weigh?How much would

9.45 moles of N2O3 weigh?

76.011g N2O376.011g N2O3

1 mole N2O31 mole N2O3 9.45 moles N2O3

9.45 moles N2O3X g N2O3X g N2O3

==

(1mole N2O3)(X g N2O3) =(1mole N2O3)(X g N2O3) =(9.45 moles N2O3)(76.011g N2O3)(9.45 moles N2O3)(76.011g N2O3)

X = 718 grams of N2O3X = 718 grams of N2O3

(1mol N2O3)(X) = (718 g • mols N2O3)

(1mol N2O3)(X) = (718 g • mols N2O3)(1 mol N2O3)(1 mol N2O3) (1 mol N2O3)(1 mol N2O3)



1(55.847g)+1(15.999g)1(55.847g)

+1(15.999g)

1 mole FeO1 mole FeO X mols FeOX mols FeO

92.2 g FeO92.2 g FeO==

We have 92.2g of FeO, how many moles is the equivalent of the

given mass?


given mass?


given mass?


given mass?



71.846 g FeO71.846 g FeO

1 mole FeO1 mole FeO X mols FeOX mols FeO

92.2 g FeO92.2 g FeO==

(71.846g FeO)(X mols FeO) =(71.846g FeO)(X mols FeO) = (1 mole FeO)(92.2 g FeO)(1 mole FeO)(92.2 g FeO)

X = 1.28 moles of FeOX = 1.28 moles of FeO

(71.846gFeO)(X) = (92.2 g•mols FeO)

(71.846gFeO)(X) = (92.2 g•mols FeO)

(71.846gFeO)(71.846gFeO) (71.846gFeO)(71.846gFeO)

• The other unit we can use to measure out mols is to measure a gas in Liters– There is a standard volume that 1 mol of any gas will occupy called molar volume.

– If we had 1 mol of Ne and 1 mol of CO2 they would each contain 6.02x1023

particles, and occupy the same volume under standard conditions (0°C, 1 atm).

• At STP or standard temp & press; 1 mol of any gas occupies 22.4 Liters of space– 1 mol of He = 22.4 L of space– 1 mol of N2 = 22.4 L of space

• The other unit we can use to measure out mols is to measure a gas in Liters– There is a standard volume that 1 mol of any gas will occupy called molar volume.

– If we had 1 mol of Ne and 1 mol of CO2 they would each contain 6.02x1023

particles, and occupy the same volume under standard conditions (0°C, 1 atm).

• At STP or standard temp & press; 1 mol of any gas occupies 22.4 Liters of space– 1 mol of He = 22.4 L of space– 1 mol of N2 = 22.4 L of space

Using volume to measure moles…

Using volume to measure moles…


Using the mole in calculations #6What volume, in Liters,

would .500 mols of CO gas occupy at STP?

What volume, in Liters, would .500 mols of CO gas

occupy at STP?

22.4 L CO22.4 L CO

1 mole CO1 mole CO .500 mol CO.500 mol CO

X L COX L CO==

*Remember*1 mol CO = 22.4 L CO

*Remember*1 mol CO = 22.4 L CO

(1mol CO)(X L CO)= (.500 mol CO)(22.4 L CO(1mol CO)(X L CO)= (.500 mol CO)(22.4 L CO

(1mol CO)(1mol CO)

(1mol CO)(1mol CO)

X = 12.2 L of COX = 12.2 L of CO

If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are in

this piece of metal?

If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are in

this piece of metal?•You are given mass and asked for number of particles•Let’s get some strategy

•You are given mass and asked for number of particles•Let’s get some strategy



We are We are given a given a massmass




We are We are asked for asked for

atomsatoms

We are We are asked for asked for

atomsatoms •It’s going to take It’s going to take us 2 conversions, us 2 conversions, we just need to we just need to follow the follow the arrowsarrows

• 11stst we must convert our given mass we must convert our given mass of Chromium to moles of Chromiumof Chromium to moles of Chromium– So we need to use the periodic table So we need to use the periodic table

to calculate the mass of 1 mole of to calculate the mass of 1 mole of ChromiumChromium

• 11stst we must convert our given mass we must convert our given mass of Chromium to moles of Chromiumof Chromium to moles of Chromium– So we need to use the periodic table So we need to use the periodic table

to calculate the mass of 1 mole of to calculate the mass of 1 mole of ChromiumChromium

51.996g Cr51.996g Cr

1 mole Cr1 mole Cr X mol CrX mol Cr

35.67g Cr35.67g Cr==

(51.996gCr)(X mol Cr) =(51.996gCr)(X mol Cr) =(35.67gCr)(1 mol

Cr)(35.67gCr)(1 mol

Cr)X = .6860 mol CrX = .6860 mol Cr

• 22ndnd we must convert our newly we must convert our newly found moles of Cr to atoms of Crfound moles of Cr to atoms of Cr– So we need to remember that 1 So we need to remember that 1

mole of anything there are mole of anything there are 6.02x106.02x102323 particles particles

• 22ndnd we must convert our newly we must convert our newly found moles of Cr to atoms of Crfound moles of Cr to atoms of Cr– So we need to remember that 1 So we need to remember that 1

mole of anything there are mole of anything there are 6.02x106.02x102323 particles particles

6.02x1023 atoms Cr

6.02x1023 atoms Cr1 mole Cr1 mole Cr

X atoms Cr

X atoms Cr

.6860 mol Cr

.6860 mol Cr

==

(1 mol Cr)(X atoms Cr) =(1 mol Cr)(X atoms Cr) =(6.02x1023 atoms Cr)

(.6860 mol Cr)(6.02x1023 atoms Cr)

(.6860 mol Cr)

X = 4.13x1023 atoms Cr

X = 4.13x1023 atoms Cr

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THE MOLE Unit 7