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Chapter 10

Chemical Quantities

10.1 The Mole: A Measurement of Matter

10.2 Mole-Mass and Mole-Volume Relationships

10.3 Percent Composition and Chemical Formulas

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How can you calculate the moles of a substance in a given mass

or volume?

CHEMISTRY & YOU

Guess how many pennies are in the container. In a similar way, chemists use the relationships between the mole and quantities such as mass, volume, and number of particles to solve problems in chemistry.

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The Mole-Mass Relationship

How do you convert the mass of a substance to the number of moles of the substance?

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The Mole-Mass Relationship

In some situations the term molar mass may be unclear.

Suppose you were asked for the molar mass of oxygen.

You can avoid confusion such as this by using the formula of the substance, in this case O₂ or O.

If you assume molecular oxygen (O₂), then the molar mass is 32.0 g/mol (2 × 16.0 g/mol).
If you assume that the question is asking for the mass of a mole of oxygen atoms (O), then the answer is 16.0 g/mol.

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The Mole-Mass Relationship

Use the molar mass of an element or compound to convert between the mass of a substance and the moles of the substance.

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The Mole-Mass Relationship

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

molar mass

and

The conversion factors for these calculations are based on the relationship molar mass = 1 mol.

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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 (Al₂O₃). This tough, resistant coating prevents any further corrosion. What is the mass, in grams, of 9.45 mol of aluminum oxide?

Sample Problem 10.5

Converting Moles to Mass

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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 Al₂O₃��UNKNOWN�mass = ? g Al₂O₃

Sample Problem 10.5

Analyze List the known and the unknown.

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First determine the mass of 1 mol of Al₂O₃.

Sample Problem 10.5

Calculate Solve for the unknown.

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2 mol Al × = 54.0 g Al

3 mol O × = 48.0 g O

1 mol Al₂O₃ = 54.0 g Al + 48.0 g O = 102.0 g Al₂O₃

27.0 g Al

1 mol Al

16.0 g O

1 mol O

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Identify the conversion factor relating moles of Al₂O₃ to grams of Al₂O₃.

1 mol Al₂O₃

102.0 g Al₂O₃

Use the relationship�1 mol Al₂O₃ = 102.0 g Al₂O_3.

Sample Problem 10.5

Calculate Solve for the unknown.

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Multiply the given number of moles by the conversion factor.

Sample Problem 10.5

Calculate Solve for the unknown.

2

9.45 mol Al₂O₃ ×

102.0 g Al₂O₃

1 mol Al₂O₃

= 964 g Al₂O₃

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The number of moles of Al₂O₃ 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

Evaluate Does the result make sense?

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When iron is exposed to air, it corrodes to form a red-brown rust. Rust is iron(III) oxide (Fe₂O₃). How many moles of iron(III) oxide are contained in 92.2 g of pure Fe₂O₃?

Converting Mass to Moles

Sample Problem 10.6

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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 Fe₂O_3��UNKNOWN�number of moles = ? mol Fe₂O₃

Sample Problem 10.6

Analyze List the known and the unknown.

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First determine the mass of 1 mol of Fe₂O₃.

1 mol Fe₂O₃ = 111.6 g Fe + 48.0 g O = 159.6 g Fe₂O₃

2 mol Fe ×

= 111.6 g Fe

55.8 g Fe

1 mol Fe

3 mol O ×

= 48.0 g O

16.0 g O

1 mol O

Sample Problem 10.6

Calculate Solve for the unknown.

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Identify the conversion factor relating grams of Fe₂O₃ to moles of Fe₂O₃.

159.6 g Fe₂O₃

1 mol Fe₂O₃

Note that the known unit (g) is in the denominator and the unknown unit (mol) is in the numerator.

Sample Problem 10.6

Calculate Solve for the unknown.

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Multiply the given mass by the conversion factor.

92.2 g Fe₂O₃ ×

1 mol Fe₂O₃

159.6 g Fe₂O₃

= 0.578 mol Fe₂O₃

Sample Problem 10.6

Calculate Solve for the unknown.

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The given mass (about 90 g) is slightly larger than the mass of one-half mole of Fe₂O₃ (about 80 g), so the answer should be slightly larger than one-half (0.5) mol.

Sample Problem 10.6

Evaluate Does the result make sense?

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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?

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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?

You also need to know the molar mass, which you can calculate using the molecular formula and the molar masses of the constituent elements listed in the periodic table of elements.

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The Mole-Volume Relationship

How do you convert the volume of a gas at STP to the number of moles of the gas?

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The Mole-Volume Relationship

Notice that the volumes of one mole of different solid and liquid substances are not the same.

The volumes of one mole of glucose (blood sugar) and one mole of parachlorobenzene (moth crystals) are much larger than the volume of one mole of liquid water.

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The Mole-Volume Relationship

Unlike liquids and solids, the volumes of moles of gases, measured under the same physical conditions, are much more predictable.

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The Mole-Volume Relationship

Avogadro’s hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

Avogadro’s Hypothesis

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The Mole-Volume Relationship

The particles that make up different gases are not the same size.

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 particles.

Avogadro’s Hypothesis

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The Mole-Volume Relationship

Whether the particles are large or small, large expanses of space exist between individual particles of gas.

Avogadro’s Hypothesis

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The Mole-Volume Relationship

The volume of a gas varies with a change in temperature or a change in pressure.

Avogadro’s Hypothesis

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The Mole-Volume Relationship

The volume of a gas varies with a change in temperature or a change in pressure.

Avogadro’s Hypothesis

Due to these variations with temperature and pressure, the volume of a gas is usually measured at standard temperature and pressure.

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The Mole-Volume Relationship

The volume of a gas varies with a change in temperature or a change in pressure.

Avogadro’s Hypothesis

Due to these variations with temperature and pressure, the volume of a gas is usually measured at standard temperature and pressure.
Standard temperature and pressure (STP) means a temperature of 0°C and a pressure of 101.3 kPa, or 1 atmosphere (atm).

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The Mole-Volume Relationship

At STP, 1 mol, or 6.02 × 10²³ 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.

Avogadro’s Hypothesis

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The Mole-Volume Relationship

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

22.4 L

1 mol

22.4 L

and

The conversion factors for these calculations are based on the relationship 22.4 L = 1 mol at STP.

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The Mole-Volume Relationship

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.

Calculating the Volume and Moles of a Gas at STP

22.4 L

1 mol

22.4 L

and

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Sulfur dioxide (SO₂) 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 SO₂ gas at STP.

Sample Problem 10.7

Calculating Gas Quantities at STP

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Since SO₂ is a gas, the volume at STP can be calculated from the known number of moles.

KNOWNS�number of moles = 0.60 mol SO₂

1 mol SO₂ = 22.4 L SO₂ at STP_��UNKNOWN�volume = ? L SO₂

Sample Problem 10.7

Analyze List the knowns and the unknown.

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First identify the conversion factor relating moles of SO₂ to volume of SO₂ at STP.

22.4 L SO₂

1 mol SO₂

The following relationship applies for gases at STP: 22.4 L = 1 mol.

Sample Problem 10.7

Calculate Solve for the unknown.

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Multiply the given number of moles by the conversion factor.

Sample Problem 10.7

Calculate Solve for the unknown.

2

0.60 mol SO₂ ×

22.4 L SO₂

1 mol SO₂

= 13 L SO₂

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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

Evaluate Does the result make sense?

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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

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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 moles of gas in a given volume at STP by using the relationship 22.4 L = 1 mol at STP.

CHEMISTRY & YOU

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The Mole-Volume Relationship

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

Different gases have different densities.
Usually the density of a gas is measured in grams per liter (g/L) and at a specific temperature.

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The Mole-Volume Relationship

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 to calculate the density of a gas at STP.

Calculating Molar Mass and Density

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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

Calculating the Molar Mass of a Gas at STP

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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_��UNKNOWN�molar mass = ? g/mol

Sample Problem 10.8

Analyze List the knowns and the unknown.

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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 =

g

mol

=

g

L

×

22.4 L

1 mol

Calculate Solve for the unknown.

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Multiply the given density by the conversion factor.

Sample Problem 10.8

Calculate Solve for the unknown.

2

= 44.0 g/mol

1.964 g

1 L

22.4 L

1 mol

×

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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

Evaluate Does the result make sense?

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The Mole-Volume Relationship

The mole is at the center of your chemical calculations.

To convert from one unit to another, you must use the mole as an intermediate step.

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Why does one mole of any gas occupy the same volume (22.4 L) at standard temperature and pressure?

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Why does one mole of any gas occupy the same volume (22.4 L) at standard temperature and pressure?

Gas molecules do vary in size, just like molecules of solids and liquids, but the particles in a gas are always so far apart that the change in volume of the molecules doesn’t change the volume the gas occupies at STP.

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Key Concepts

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.

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Glossary Terms

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)
molar volume: the volume occupied by 1 mole of a gas at standard temperature and pressure (STP); 22.4 L

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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

The Mole and Quantifying Matter

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END OF 10.2

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