dcs 08 the mole

8/10/2019 DCS 08 The Mole

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The Mole


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Copyright 2006-2011 Marshall Cavendish International (Singapore) Pte. Ltd.

How can we measure the mass of anatom?

Chemists often compare masses of different atoms

with the carbon-12 atom(an isotope of carbon).

Atoms also have very small masses,

so it is not practical to use the actual masses of

atoms in calculations.

The masses of all other atoms are compared with

one-twelfth the mass of one carbon-12 atom.


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Relative Atomic Mass

The relative atomic massof any atom is

the number of times the mass of one atom

of an element is greater than 1/12 of the

mass of one carbon-12 atom.

Relative atomic mass =Mass of 1/12 of an atom of carbon-12

Mass of one atom of the element


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Relative Atomic Mass

The symbolfor relative atomic mass is Ar.

Relative atomic mass is a ratio and has no unit.

The relative atomic mass of each element is

given in the Periodic Table.


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Relative Atomic Mass of Some Elements

Some Ar values are not whole numbers.

35.5Chlorine

16Oxygen

12Carbon

1Hydrogen

Relative atomic mass, ArElement


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Why are some Arvalues not wholenumbers?

This is because such elements occur as

mixtures of isotopes.

For example, chlorine exists in two isotopic

forms: chlorine-35and chlorine-37.


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How do we derive the Arof chlorine?

Hence, relative atomic mass of chlorine

= (0.75 35) + (0.25 37)

= 26.25 + 9.25= 35.5

A sample of chlorine is made up of

75% ofchlorine-35atoms and

25% of chlorine-37atoms.


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Relative Molecular Mass

Many elements and compounds exist as molecules.

For example, chlorine exists as molecules.

Cl

Cl

Hence, we use relative molecularmass

instead of relative atomic mass.


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The relative molecular mass(Mr) of an element or

compound is the mass of a molecule, compared to

1/12 the mass of one atom of carbon-12.

Like Ar, it is a ratio and therefore has no unit.

Relative Molecular Mass

MrMass of 1 molecule

Mass of 1/12 of a carbon-12 atom=


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How do we calculate the relativemolecular mass of ammonia (NH3)?

Arof N = 14 Arof H = 1

Mrof NH3= 14 + 1 3 = 17


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How do we calculate the relativemolecular mass of ethanoic acid

(CH3COOH)?

Arof C = 12

Arof H = 1

Mrof CH3COOH

= 12 + 1 3 + 12 + 16 + 16 + 1= 17

Arof O = 16


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(2 x 12) + (6 x 1) + (1 x 16) = 462 C; 6 H; 1 OC2H5OHEthanol

(2 x 1) + (1 x 16) = 182 H; 1 OH2OWater

(1 x 12) + (2 x 16) = 441 C ; 2 OCO2Carbon dioxide

(1 x 14) + (3 x 1) = 171 N; 3 HNH3Ammonia

2 x 14 = 282 NN2Nitrogen

Calculating MrNumber ofatoms in onemolecule

Chemicalformula

Molecule


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Relative Formula Mass

Many substances such as water are covalent and exist asmolecules.

However, substances like sodium chloride are ionicand

do not exist as molecules.

The relative molecular mass of an ionic compound

is more accurately known as relative formula mass.


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Relative Formula Mass

Like relative molecular mass,

relative formula mass has the symbol Mrand

relative formula mass has no units.

For example, the relative formula mass of sodium

chloride (NaCl) is 23 + 35.5 = 58.5.


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Calculating Mrof MgSO4

Arof Mg = 24

Arof S = 32

Mrof MgSO4= 24 + 32 + (16 4) = 120

Arof O = 16


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Calculating Mrof CuSO4 . 5H2O

Arof Cu = 64

Arof S = 32

Mrof CuSO4.5H2O

= 64 + 32 + (16 4) + 5 (2 1 + 16) = 250

Arof O = 16

Arof H = 1

The dot means plus

in calculation.

5 needs to be multiplied

to entire Mrof water.


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Molecule ChemicalFormula

Number ofatoms inonemolecule

Calculating Mr

Magnesium

sulphate

MgSO4 1 Mg; 1 S;

4 O

(1 x 24) + (1 x 32) + (4 x 16)

= 120

Calciumcarbonate

CaCO3 1 Ca; 1 C;3 O

(1 x 40) + (1 x 12) + (3 x 16)= 100

Calcium nitrate Ca(NO3)2 1 Ca ; 2 N;

6 O

(1 x 40) + (2 x 14) + (6 x 16)

= 164

Copper(II)

sulphate

crystals

CuSO4 . 5H2O 1 Cu; 1 S;

9 O; 10 H

(1 x 64) + (1 x 32) + (9 x 16) +

(10 x 1) = 250


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The Mole

Atoms are too small and numerous to be counted

one at a time.

Instead, the quantity of atoms is measured by mass.

The unit of measurement for atoms and molecules is

the mole.

The symbol for the mole is mol.


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The Mole

A moleof substance contains the same number of

particles as the number of atoms in 12 g of carbon-12.

12 g of carbon-12 contain approximately

6 1023carbon atoms.


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How many particles are there in amole?

There are approximately 6 1023particles in

one moleof substance.

6 1023is called the Avogadros constant orAvogadrosnumber.

One mole of particles means 6 1023particles.The particles could be atoms, molecules, ions or electrons.


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How do we convert between numberof moles and number of particles?

Number of molesNumber of particles

6 1023=


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Example 1: Convert 1 1023neon atomsto moles of neon atoms

Number of moles of neon atoms

Number of moles of neon atoms6 1023

=

1 1023

6 1023=

= 0.167 mol


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Example 2: How many iron atoms arethere in 0.5 mol of iron?

Number of iron atoms

Number of moles 6 1023=

= 3 1023

In 1 mole of iron, there are 6 1023iron atoms.

0.5 6 1023=


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Example 3:How many hydrogen atoms arethere in 3 moles of hydrogen gas?

Hydrogen gas is made up of hydrogen molecules (H2).

In 3 moles of H2molecules, there are 3 2 = 6 moles of H atoms.

In 1 mole of H2molecules, there are 2 moles of H atoms.

Number of hydrogen atoms

Number of moles 6 1023=

= 3.6 1024

6 6 1023

=


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How is the mole related to chemicalequations?

2 particles

(atoms) of

sodium

1 particle(molecule) of

chlorine

2 moles of

sodium atoms

1 mole of chlorine

molecules

Na + Cl2 NaCl22

OR OR

2 units of sodiumchloride

2 moles of sodium

chloride

OR


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The molar mass of an element is the mass

of one moleof atoms of the element.

What is the mass of one mole ofatoms of an element?

Do you notice a

relationship between the

value of Arand the molar

mass of a substance?

Element Ar Molarmass

Aluminium 27 27 g

carbon 12 12 g

Neon 20 20 g

Oxygen 16 16 g


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What is the relationship betweenmole and molar mass?

The number of moles of an element can be

calculated using the formula:

Number of moles

of an element

Massof element (g)

Arof element

=


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Example 1 Determine the number ofmoles in 0.196 kg of iron. (Ar: Fe = 56)

Number of moles of iron

mass of iron in gramsArof iron

=

0.196 1000

56=

= 3.5mol


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Example 2a) How many moles of lead are there in 1.204

1022

atoms of lead?b) What is the mass of 1.204 1022atoms oflead? (Ar: Pb = 207)

a) Number of moles of lead

number of atoms of lead

Avogadros constant=

1.204 1022

6 1023

=

= 0.02mol


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Example 2 (continued)a) How many moles of lead are there in 1.204

1022

atoms of lead?b) What is the mass of 1.204 1022atoms oflead? (Ar: Pb = 207)

b) Mass of lead

= number of moles Arof lead

= 0.02 207

= 4.14 g


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What is the mass of one mole ofmolecules or one mole of a compound?

One mole of a substance has a mass equal its Mr.

18 g(2 1) + 16

= 18

H2OWater

40 g24 + 16 = 40MgOMagnesiumoxide

254 g2 127 = 160I2Iodine

32 g2 16 = 32O2Oxygen

Molar massMrFormulaSubstance


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The number of moles of a substance can becalculated using the following formulae:

Number of moles

Mass of substance (g)

Mr=

or

Number of particles

6 1023=


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Example 1A conical flask contains 68.4 g of octane (C8H18).

How many molecules of octane are there in theflask?

Number of moles of octane

Mass of octane

Mrof octane=

6.84

114

=

= 0.6mol


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Example 1(continued)A conical flask contains 68.4 g of octane (C8H18).

How many molecules of octane are there in theflask?

Number of molecules of octane= number of moles Avogadros constant

= 0.6 6 1023

= 3.6 1023


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Example 2How many ions are there in 20 g of magnesium

oxide (MgO)?

Number of moles of MgO

Mass of magnesium oxideMrof magnesium oxide

=

20

40=

= 0.5mol


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Example 2 (continued)How many ions are there in 20 g of magnesium

oxide (MgO)?

MgO Mg2+ + O2

1 mol of MgO1 mol of Mg2+ions and 1 mol of O2ions.

0.5 mol of MgO0.5 mol of Mg2+ions and

0.5 mol of O2ions.

Hence, 0.5 mol of MgO contains 1 mol of ions.

Number of ions = 1 6 1023= 6 1023


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Molar Gas Volume

Unlike solids and liquids, gases weigh very

little.

It is easier to measure the volume of a gas

than its mass.

Is there a way to relate moles to the volumesof gases?


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Molar Gas Volume

One mole of any gasoccupies 24 dm3(24 000 cm3)

at room temperature and pressure (r.t.p.).

24 dm3is called the molar volumeof a gas.


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This means that at r.t.p.

1 mol of oxygen occupies 24 dm3,

1 mol of carbon dioxide occupies 24 dm3,

2 mol of oxygen occupy 2 24 = 48 dm3,

2 mol of carbon dioxide occupy 2 24 = 48 dm

3

.

how many dm3?

how many dm3?

how many dm3?

how many dm3

?2

24 = 48 dm3

24 dm3

2 24 = 48 dm3

24 dm3


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How can we calculate the number ofmoles of a gas?

The number of moles of a gas can be measured in 2 ways:

Number of moles of gas =Mrof gas

Mass of gas in grams

Number of moles of gas =24 000 cm3

Volume of gas in cm3at r.t.p


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Example 1 What is the volume, in dm3, of 8 g

of oxygen gas (O2) at r.t.p.?

Relative molecular mass of oxygen = 2 16 = 32

Volume of oxygen= number of moles of oxygen 24

= 24

= 6 dm3

32

8


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Number of moles of carbon dioxide given off

Number of molecules of carbon dioxide given off

= number of moles Avogadros constant= 3.33 103 6 1023= 2.00 1021

Example 2 In an experiment, hydrochloric acidwas reacted with calcium carbonate at r.t.p.

80 cm3

of carbon dioxide was produced. Calculatethe number of molecules of carbon dioxide givenoff.

= = 3.33 103mol00024

80


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Example 3 Calculate the mass of oxygen gas(O2) in a room that measures 4 m high, 8 m wide

and 10 m long. Assume that air contains 20%oxygen. (1 m3= 106cm3)

Volume of air in room = 4 x 8 x 10 = 320 m3= 320 x 106cm3

Volume of oxygen in room = 20% x 320 x 106= 64 x 106cm3

Mass of oxygen =

24 000 cm3

Volume of oxygen

Number of moles of oxygen x Mr

Molar volume=

=

x 32

64 x 106cm3

8.53 x 104g

= x 32


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Do the balloons of the same volume containthe same number of particles?

According to Avogadros Law, each ofthese balloons contains the same number

of gaseous particles since they have the

same volume.

Yes, they do!


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Do the balloons of the same masscontain the same number of

particles?No, they dont!

Same mass but different number of moles.

Gas Mass (g) Aror Mr Number of moles= mass / Aror Mr

Helium (He) 0.18 4

Hydrogen(H2)

0.18 2

Methane(CH4)

0.18 16= 0.011

16

0.18

= 0.0902

0.18

= 0.0454

0.18

dcs 08 the mole

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