ChemC10.2.ppt

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10.2 Mole-Mass and Mole-

Volume Relationships

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Chapter 10 Chemical Quantities

10.1 The Mole: A Measurement of

Matter

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10.2 Mole-Mass and Mole-

Volume Relationships

>

How can you calculate the moles of a

substance in a given mass

or volume?

CHEMISTRY

&

YOU

CHEMISTRY

&

YOU

Guess how many pennies are

in the container. In a similar

way, chemists use the

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10.2 Mole-Mass and Mole-

Volume Relationships

>

The Mole-Mass Relationship

How do you convert the mass of a

substance to the number of moles of

the substance?

The Mole-Mass

Relationship

(4)

10.2 Mole-Mass and Mole-

Volume Relationships

>

In some situations the term

molar mass

may

be unclear.

• Suppose you were asked for the molar mass of

oxygen.

The Mole-Mass

Relationship

– If you assume molecular oxygen (O

₂

), then the

molar mass is 32.0 g/mol (2 × 16.0 g/mol).

(5)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Use the molar mass of an element or

compound to convert between the mass

of a substance and the moles of the

substance.

The Mole-Mass

Relationship

(6)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Use the molar mass of an element or

compound to convert between the mass

of a substance and the moles of the

substance.

molar mass

1 mol

The Mole-Mass

Relationship

• The conversion factors for these

(7)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Items made out of aluminum, such

as aircraft parts and cookware, are

resistant to corrosion because the

aluminum reacts with oxygen in the

air to form a coating of aluminum

oxide (Al

₂

O

₃

). This tough, resistant

coating prevents any further

Sample

Problem 10.5

Sample

Problem 10.5

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10.2 Mole-Mass and Mole-

Volume Relationships

>

The mass of the compound is calculated from

the known number of moles of the compound.

The desired conversion is moles → mass.

KNOWN

number of moles

= 9.45 mol Al

₂

O

₃

UNKNOWN

Sample

Problem 10.5

Sample

Problem 10.5

Analyze

List the known and the unknown.

(9)

10.2 Mole-Mass and Mole-

Volume Relationships

>

First determine the mass of 1 mol of Al

₂

O

₃

.

Sample

Problem 10.5

Sample

Problem 10.5

Calculate

Solve for the unknown.

2 2 mol Al × = 54.0 g Al

3 mol O × = 48.0 g O

27.0 g Al

1 mol Al

16.0 g O

(10)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Identify the conversion factor relating

moles of Al

₂

O

₃

to grams of Al

₂

O

₃

.

1 mol Al

₂

O

₃

102.0 g Al

₂

O

₃

Use the relationship

1 mol Al

₂

O

₃

= 102.0 g Al

₂

O

_3.

Sample

Problem 10.5

Sample

Problem 10.5

Calculate

Solve for the unknown.

(11)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Multiply the given number of moles

by the conversion factor.

Sample

Problem 10.5

Sample

Problem 10.5

Calculate

Solve for the unknown.

2

(12)

10.2 Mole-Mass and Mole-

Volume Relationships

>

• The number of moles of Al

₂

O

₃

is

approximately 10, and each has a mass

of approximately 100 g.

• The answer should be close to 1000 g.

• The answer has been rounded to the

correct number of significant figures.

Sample

Problem 10.5

Sample

Problem 10.5

Evaluate

Does the result make sense?

(13)

10.2 Mole-Mass and Mole-

Volume Relationships

>

When iron is exposed to air,

it corrodes to form a

red-brown rust. Rust is iron(III)

oxide (Fe

₂

O

₃

). How many

moles of iron(III) oxide are

contained in 92.2 g of pure

Converting Mass to Moles

Sample

Problem 10.6

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10.2 Mole-Mass and Mole-

Volume Relationships

>

The number of moles of the compound is

calculated from the known mass of the

compound. The conversion is mass → moles.

KNOWN

mass

= 92.2 g Fe

₂

O

₃

UNKNOWN

number of moles = ? mol Fe

₂

O

₃

Sample

Problem 10.6

Sample

Problem 10.6

Analyze

List the known and the unknown.

(15)

10.2 Mole-Mass and Mole-

Volume Relationships

>

First determine the mass of 1 mol of Fe

₂

O

₃

.

2 mol Fe ×

55.8 g Fe

= 111.6 g Fe

1 mol Fe

3 mol O ×

16.0 g O

= 48.0 g O

1 mol O

Sample

Problem 10.6

Sample

Problem 10.6

Calculate

Solve for the unknown.

(16)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Identify the conversion factor relating

grams of Fe

₂

O

₃

to moles of Fe

₂

O

₃

.

159.6 g Fe

₂

O

₃

1 mol Fe

₂

O

₃

Note that the known unit (g) is in the denominator

and the unknown unit (mol) is in the numerator.

Sample

Problem 10.6

Sample

Problem 10.6

Calculate

Solve for the unknown.

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10.2 Mole-Mass and Mole-

Volume Relationships

>

Multiply the given mass by the

conversion factor.

92.2 g Fe

₂

O

₃

×

1 mol Fe

2 O

3 159.6 g Fe

₂

O

₃

Sample

Problem 10.6

Sample

Problem 10.6

Calculate

Solve for the unknown.

(18)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The given mass (about 90 g) is slightly

larger than the mass of one-half mole of

Fe

₂

O

₃

(about 80 g), so the answer should

be slightly larger than one-half (0.5) mol.

Sample

Problem 10.6

Sample

Problem 10.6

Evaluate

Does the result make sense?

(19)

10.2 Mole-Mass and Mole-

Volume Relationships

>

You know how many grams of a

substance you have and want to find

(20)

10.2 Mole-Mass and Mole-

Volume Relationships

>

You know how many grams of a

substance you have and want to find

out how many moles this is. What other

information do you need to know, and

where can you find it?

(21)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The Mole-Volume Relationship

How do you convert the volume of a

gas at STP to the number of moles of

the gas?

The Mole-Volume

Relationship

(22)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Notice that the volumes of one mole of

different solid and liquid substances are not

the same.

The Mole-Volume

Relationship

• The volumes of one

mole of glucose (blood

sugar) and one mole of

parachlorobenzene

(23)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Unlike liquids and solids, the volumes of

moles of gases, measured under the

same physical conditions, are much

more predictable.

The Mole-Volume

Relationship

(24)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Avogadro’s hypothesis

states that

equal volumes of gases at the same

temperature and pressure contain equal

numbers of particles.

The Mole-Volume

Relationship

(25)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The particles that make up different

gases are not the same size.

The Mole-Volume

Relationship

• However, particles in all gases are so far

apart that a collection of relatively large

particles does not require much more space

than the same number of relatively small

(26)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Whether the particles are large or small,

large expanses of space exist between

individual particles of gas.

Avogadro’s Hypothesis

The Mole-Volume

Relationship

(27)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The volume of a gas varies with a change

in temperature or a change in pressure.

The Mole-Volume

Relationship

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10.2 Mole-Mass and Mole-

Volume Relationships

>

The volume of a gas varies with a change

in temperature or a change in pressure.

The Mole-Volume

Relationship

Avogadro’s Hypothesis

• Due to these variations with temperature and

pressure, the volume of a gas is usually

(29)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The volume of a gas varies with a change

in temperature or a change in pressure.

The Mole-Volume

Relationship

Avogadro’s Hypothesis

• Due to these variations with temperature and

pressure, the volume of a gas is usually

(30)

10.2 Mole-Mass and Mole-

Volume Relationships

>

At STP, 1 mol, or 6.02 × 10

23 representative particles, of any gas

occupies a volume of 22.4 L.

• The quantity, 22.4 L, is called the

molar

volume

of a gas.

The Mole-Volume

Relationship

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10.2 Mole-Mass and Mole-

Volume Relationships

>

The molar volume is used to convert

between the number of moles of gas

and the volume of the gas at STP.

Calculating the Volume and Moles of a

Gas at STP

The Mole-Volume

Relationship

• The conversion factors for these

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10.2 Mole-Mass and Mole-

Volume Relationships

>

• You can use these conversion factors to

convert a known number of moles of gas to

the volume of the gas at STP.

• Similarly, you can convert a known volume of

gas at STP to the number of moles of the gas.

The Mole-Volume

Relationship

(33)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Sulfur dioxide (SO

₂

) is a gas

produced by burning coal. It is

an air pollutant and one of the

causes of acid rain. Determine

the volume, in liters, of 0.60

mol SO

gas at STP.

Sample

Problem 10.7

Sample

Problem 10.7

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10.2 Mole-Mass and Mole-

Volume Relationships

>

Since SO

₂

is a gas, the volume at STP can be

calculated from the known number of moles.

KNOWNS

number of moles

= 0.60 mol SO

₂

1 mol SO

₂

= 22.4 L SO

₂

at STP

UNKNOWN

volume = ? L SO

Sample

Problem 10.7

Sample

Problem 10.7

Analyze

List the knowns and the unknown.

(35)

10.2 Mole-Mass and Mole-

Volume Relationships

>

First identify the conversion factor

relating moles of SO

₂

to volume of SO

₂

at STP.

22.4 L SO

₂

1 mol SO

₂

The following relationship applies for gases at

Sample

Problem 10.7

Sample

Problem 10.7

Calculate

Solve for the unknown.

(36)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Multiply the given number of moles by

the conversion factor.

Sample

Problem 10.7

Sample

Problem 10.7

Calculate

Solve for the unknown.

2 0.60 mol SO

₂

×

22.4 L SO

2 1 mol SO

₂

(37)

10.2 Mole-Mass and Mole-

Volume Relationships

>

• One mole of any gas at STP has a

volume of 22.4 L, so 0.60 mol should

have a volume slightly larger than

one-half of a mole or 11.2 L.

• The answer should have two significant

figures.

Sample

Problem 10.7

Sample

Problem 10.7

Evaluate

Does the result make sense?

(38)

10.2 Mole-Mass and Mole-

Volume Relationships

>

How can you calculate the moles of a

substance in a given mass? How can you

calculate the moles of a gas in a given

volume at STP?

CHEMISTRY

&

YOU

(39)

10.2 Mole-Mass and Mole-

Volume Relationships

>

How can you calculate the moles of a

substance in a given mass? How can you

calculate the moles of a gas in a given

volume at STP?

You can calculate the moles of a substance

in a given mass by using the relationship

molar mass = 1 mol. You can calculate the

CHEMISTRY

&

YOU

(40)

10.2 Mole-Mass and Mole-

Volume Relationships

>

A gas-filled air balloon will either sink or

float in the air depending on whether

the density of the gas inside the balloon

is greater or less than the density of the

surrounding air.

Calculating Molar Mass and Density

The Mole-Volume

Relationship

• Different gases have different densities.

(41)

10.2 Mole-Mass and Mole-

Volume Relationships

>

• The density of a gas at STP and the

molar volume at STP (22.4 L/mol) can

be used to calculate the molar mass of

the gas.

• Similarly, the molar mass of a gas and

the molar volume at STP can be used

The Mole-Volume

Relationship

(42)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The density of a gaseous

compound containing

carbon and oxygen is found

to be 1.964 g/L at STP. What

is the molar mass of the

compound?

Sample

Problem 10.8

Sample

Problem 10.8

(43)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The molar mass of the compound is calculated

from the known density of the compound and

the molar volume at STP.

KNOWNS

density

= 1.964 g/L

1 mol of gas at STP = 22.4 L

Sample

Problem 10.8

Sample

Problem 10.8

Analyze

List the knowns and the unknown.

(44)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Sample

Problem 10.8

First identify the conversion factor needed

to convert density to molar mass.

22.4 L

1 mol

Use the density and molar volume at STP to

calculate the molar mass.

molar mass =

_{mol =}

g

_{L ×}

22.4 L

Calculate

Solve for the unknown.

(45)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Multiply the given density by the

conversion factor.

Sample

Problem 10.8

Sample

Problem 10.8

Calculate

Solve for the unknown.

2 = 44.0 g/mol

1.964 g

1 L

(46)

10.2 Mole-Mass and Mole-

Volume Relationships

>

• The ratio of the calculated mass (44.0 g)

to the volume (22.4 L) is about 2, which is

close to the known density.

• The answer should have three significant

figures.

Sample

Problem 10.8

Sample

Problem 10.8

Evaluate

Does the result make sense?

(47)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The mole is at the center

of your chemical

calculations.

The Mole-Volume

Relationship

(48)

10.2 Mole-Mass and Mole-

Volume Relationships

>

(49)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Why does one mole of any gas occupy

the same volume (22.4 L) at standard

temperature and pressure?

(50)

10.2 Mole-Mass and Mole-

Volume Relationships

>

Use the molar mass of an element or

compound to convert between the

mass of a substance and the moles

of the substance.

The molar volume is used to convert

between the number of moles of gas

and the volume of the gas at STP.

Key Concepts

(51)

10.2 Mole-Mass and Mole-

Volume Relationships

>

• Avogadro’s hypothesis

: equal volumes of

gases at the same temperature and pressure

contain equal numbers of particles

• _{standard temperature and pressure (STP)}

_:

the conditions under which the volume of a gas

is usually measured; standard temperature is

0°C, and standard pressure is 101.3 kPa, or 1

atmosphere (atm)

Glossary Terms

(52)

10.2 Mole-Mass and Mole-

Volume Relationships

>

The mole allows you to convert among

the amount of representative particles in

a substance, the mass of a substance,

and the volume of a gas at STP.

BIG

IDEA

BIG

IDEA

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10.2 Mole-Mass and Mole-

Volume Relationships

>

END OF 10.2