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The Mole Concept Unit VII

Dr. PasserChemistry Department

Bronx Community College

Version 1.1 © John Wiley and Sons, IncVersion 1.1

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Unit Outline5.11 Atomic Mass

7.1 The Mole

7.2 The Molar Mass of Compounds

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Atomic Mass

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The mass of a single atom is too small to measure on a balance.

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Using a mass spectrometer, the mass of one hydrogen atom was determined to be 1.673 x 10-24 g.

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smallsmallsmallsmall

This number is very small.

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Numbers of this size are too small for practical use. To overcome this problem a system of relative atomic masses using “atomic mass units” was devised to express the masses of elements using simple numbers.

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126C

The standard to which the masses of all other atoms are compared to was chosen to be the most abundant isotope of carbon.

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126C

A mass of exactly 12 atomic mass units (amu) was assigned to

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1 amu is defined as exactly equal to the mass of a carbon-12 atom 12

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126C

1 amu = 1.6606 x 10-24 g

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HAverage atomic mass 1.00797 amu.

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KAverage atomic mass 39.098 amu.

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UAverage atomic mass 238.029 amu.

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Average RelativeAtomic Mass

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• Most elements occur as mixtures of isotopes.

• Isotopes of the same element have different masses.

• The listed atomic mass of an element is the average relative mass of the isotopes of that element compared to the mass of carbon-12 (exactly 12.0000…amu).

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To calculate the atomic mass multiply the atomic mass of each isotope by its percent abundance and add the results.

(62.9298 amu) 0.6909 = 43.48 amu(64.9278 amu) 0.3091 = 20.07 amu

63.55 amu

Isotope Isotopic mass (amu)

Abundance (%)

Average atomic mass

(amu)

62.9298 69.09

64.9278 30.91 63.55

6329 Cu6529 Cu

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The MoleThe Mole

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The mass of a single atom is too small to measure on a balance.

mass of hydrogen atom = 1.673 x 10-24 g

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This is an

infinitesimal

mass1.673 x 10-24 g

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• Chemists have chosen a unit for counting atoms.

• That unit is the

• Chemists require a unit for counting which can express large numbers of atoms using simple numbers.

MOLE

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1 mole = 6.022 x 1023 objects

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LARGE6.022 x 1023

is a very

number

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6.022 x 1023

is

number

Avogadro’s Number

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If 10,000 people started to count Avogardro’s number and counted at the rate of 100 numbers per minute each minute of the day, it would take over 1 trillion years to count the total number.

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1 mole of any element contains

6.022 x 1023

particles of that element.

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The atomic mass in grams

of any element23

contains 1 mole of atoms

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This is the same number of particles6.022 x 1023

as there are in exactly 12 grams of

C126

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ExamplesExamples

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Species

Quantity

Number of H atoms

H

1 mole

6.022 x 1023

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Species

Quantity

Number of H2 molecules

H2

1 mole

6.022 x 1023

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Species

Quantity

Number of Na atoms

Na

1 mole

6.022 x 1023

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Species

Quantity

Number of Fe atoms

Fe

1 mole

6.022 x 1023

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Species

Quantity

Number of C6H6 molecules

C6H6

1 mole

6.022 x 1023

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1 mol of atoms = 6.022 x 1023 atoms

6.022 x 1023 molecules

6.022 x 1023 ions

1 mol of molecules =

1 mol of ions =

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• The molar mass of an element is its atomic mass in grams.

• It contains 6.022 x 1023 atoms (Avogadro’s number) of the element.

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Element Atomic mass Molar mass Number of atoms

H 1.008 amu 1.008 g 6.022 x 1023

Mg 24.31 amu 24.31 g 6.022 x 1023

Na 22.99 amu 22.99 g 6.022 x 1023

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The Mole and Mass

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The molar mass is the mass of Avogadro’s number of atoms, ions or molecules.

6.022 x 1023

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The mass of one mole of a substance is equal to the molar mass in grams of the substance.

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Examples of theMolar Mass of an Element

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element

atomicmass

molar mass

H

1.01

1.01 g

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element

atomicmass

molar mass

Cu

63.546

63.546 g

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element

atomicmass

molar mass

K

39.0983

39.0983 g

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Examples of the Molar Massof a Molecular Compound

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molecule

molecular mass

molar mass

H2O

18.02

18.02 g

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molecule

molecular mass

molar mass

SO2

64.05

64.05 g

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molecule

molecular mass

molar mass

N2O5

108.01

108.01 g

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Examples of the Molar Massof an Ionic Compound

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formula unit

formula weight

molar mass

NaCl

58.44

58.44 g

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formula unit

formula weight

molar mass

BaF2

175.33

175.33 g

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formula unit

formula weight

molar mass

Mg3(PO4)2

167.88

167.88 g

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ProblemsProblems

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Atomic mass iron = 55.85

How many moles of iron does 25.0 g of iron represent?

Conversion sequence: grams Fe → moles Fe

1 mol Fe(grams Fe)55.85 g Fe

1 mol Fe(25.0 g Fe)55.85 g Fe

0.448 mol Fe

Set up the calculation using a conversion factor between moles and grams.

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Atomic mass iron = 55.85

Conversion sequence: grams Fe → atoms Fe

236.022 x 10 atoms Fe(grams Fe)55.85 g Fe

How many iron atoms are contained in 25.0 grams of iron?

236.022 x 10 atoms Fe(25.0 g Fe)55.85 g Fe

232.70 x 10 atoms Fe

Set up the calculation using a conversion factor between atoms and grams.

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Molar mass Na = 22.99 g

Conversion sequence: atoms Na → grams Na

2322.99 g Na(Na atoms)

6.022 x 10 Na atoms

What is the mass of 3.01 x 1023 atoms of sodium (Na)?

2323

22.99 g Na(3.01 x 10 Na atoms)6.022 x 10 Na atoms

11.5 g Na

Set up the calculation using a conversion factor between grams and atoms.

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Atomic mass tin = 118.7

What is the mass of 0.365 moles of tin?

Conversion sequence: moles Sn → grams Sn

1 molar mass Sn(moles Sn)1 mole Sn

118.7 g Sn(0.365 moles Sn)1 mole Sn

43.3 g Sn

Set up the calculation using a conversion factor between grams and atoms.

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2(2.00 mol O )23

2

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6.022 x 10 molecules O1 mol O

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2 atoms O1 molecule O

Conversion sequence: moles O2 → molecules O2 → atoms O

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2

6.022 x 10 molecules O1 mol O

How many oxygen atoms are present in 2.00 mol of oxygen molecules?

Two conversion factors are needed:

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2 atoms O1 molecule O

24= 2.41 x10 atoms O

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Molar Mass of Molar Mass of CompoundsCompounds

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The molar mass of a compound can be determined by adding the molar masses of all of the atoms in its formula.

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2 C = 2(12.01 g) = 24.02 g6 H = 6(1.01 g) = 6.06 g1 O = 1(16.00 g) = 16.00 g

46.08 g

Calculate the molar mass of C2H6O.

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1 Li = 1(6.94 g) = 6.94 g1 Cl = 1(35.45 g) = 35.45 g4 O = 4(16.00 g) = 64.00 g

106.39 g

Calculate the molar mass of LiClO4.

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Calculate the molar mass of (NH4)3PO4 .

3 N = 3(14.01 g) = 42.03 g12 H = 12(1.01 g) = 12.12 g

1 P = 1(30.97 g) = 30.97 g4 O = 4(16.00 g) = 64.00 g

149.12 g

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6.022 x 1023

Particles

Molar Mass

1 MOLE

Avogadro’s Number of Particles

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1 MOLE Ca

Avogadro’s Number ofCa atoms

40.078 g Ca

6.022 x 1023 Ca atoms

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1 MOLE H2O

Avogadro’s Number of

H2O molecules

18.02 g H2O

6.022 x 1023 H2O molecules

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In dealing with diatomic elements (H2, O2, N2, F2, Cl2, Br2, and I2), distinguish between one mole of atoms and one mole of molecules.

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Calculate the molar mass of 1 mole of H atoms.

1 H = 1(1.01 g) = 1.01 g

Calculate the molar mass of 1 mole of H2 molecules.

2 H = 2(1.01 g) = 2.02 g

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MoleConversions

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To convert from grams of a substance to moles of a substance use the molar mass of the substance.

grams moles

molarmass

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To convert from moles of a substance into atoms (or molecules) of the substance (and vice versa) we have to use Avogadro’s number.

moles molecules

Avogadro’s Number

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To convert from moles of a substance into molecules of the substance we use the molar mass and Avogadro’s number.

grams moles molecules(or atoms)

Molarmass

Avogadro’sNumber

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Definition

The molar mass of any substance is the number of grams contained in one mole of that substance.

grams substancemolar mass1 mole substance

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ProblemsProblems

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How many moles of benzene, C6H6, are present in 390.0 grams of benzene?

Conversion sequence: grams C6H6 → moles C6H6

6 6

6 6

1 mole C HUse the conversion factor: 78.12 grams C H

6 6

6 6

1 mole C H 78.12 g C H

6 6(390.0 g C H ) 6 6= 5.000 moles C H

The molar mass of C6H6 is 78.12 g.

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How many grams of (NH4)3PO4 are contained in 2.52 moles of (NH4)3PO4?

Conversion sequence: moles (NH4)3PO4

→ grams (NH4)3PO4

4 3 4

4 3 4

149.12 grams (NH ) POUse the conversion factor: 1 mole (NH ) PO

4 3 4(2.52 mol (NH ) PO ) 4 3 4

4 3 4

149.12 g (NH ) PO1 mol (NH ) PO

4 3 4= 376g (NH ) PO

The molar mass of (NH4)3PO4 is 149.12 g.

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2(56.04 g N ) 2

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1 mol N28.02 g N

232

2

6.022 x 10 molecules N 1 mol N

56.04 g of N2 contains how many N2 molecules?

The molar mass of N2 is 28.02 g.

Conversion sequence: g N2 → moles N2 → molecules N2

Use the conversion factor

2

2

1 mol N 28.02 g N

242= 1.204 x 10 molecules N

232

2

6.022 x 10 molecules N 1 mol N

Use the conversion factor

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2

2

1 mol N28.02 g N

2(56.04 g N )23

2

2

6.022 x 10 molecules N 1 mol N

56.04 g of N2 contains how many nitrogen atoms?

The molar mass of N2 is 28.02 g.Conversion sequence: g N2 → moles N2 → molecules N2

→ atoms NUse the conversion factor

2

2

1 mol N 28.02 g N

24= 2.409 x 10 atoms N2

2 atoms N1 molecule N

232

2

6.022 x 10 molecules N 1 mol N

Use the conversion factor

2

2 atoms N 1 molecule N

Use the conversion factor

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