1. 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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2. How can you calculate the moles of a substance in a given mass
CHEMISTRY & YOU
How can you calculate the moles of a substance in a given mass
or volume?
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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3. 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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4. 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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5. 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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6. 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.
The conversion factors for these calculations are based on the relationship molar mass = 1 mol.
molar mass
1 mol
and
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7. Converting Moles to Mass
Sample Problem 10.5
Converting Moles to Mass
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?
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8. Analyze List the known and the unknown.
Sample Problem 10.5
Analyze List the known and the unknown. 1
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
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9. Calculate Solve for the unknown.
Sample Problem 10.5
Calculate Solve for the unknown. 2
First determine the mass of 1 mol of Al2O3.
2 mol Al × = 54.0 g Al
3 mol O × = 48.0 g O
1 mol Al2O3 = 54.0 g Al g O = g Al2O3
27.0 g Al
1 mol Al
16.0 g O
1 mol O
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10. Calculate Solve for the unknown.
Sample Problem 10.5
Calculate Solve for the unknown. 2
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 = g Al2O3.
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11. Calculate Solve for the unknown.
Sample Problem 10.5
Calculate Solve for the unknown. 2
Multiply the given number of moles by the conversion factor.
9.45 mol Al2O3 ×
102.0 g Al2O3
1 mol Al2O3
= 964 g Al2O3
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12. Evaluate Does the result make sense?
Sample Problem 10.5
Evaluate Does the result make sense? 3
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.
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13. Converting Mass to Moles
Sample Problem 10.6
Converting Mass to Moles
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?
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14. Analyze List the known and the unknown.
Sample Problem 10.6
Analyze List the known and the unknown. 1
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 Fe2O3 UNKNOWN number of moles = ? mol Fe2O3
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15. Calculate Solve for the unknown.
Sample Problem 10.6
Calculate Solve for the unknown. 2
First determine the mass of 1 mol of Fe2O3.
2 mol Fe ×
= g Fe
55.8 g Fe
1 mol Fe
3 mol O ×
= 48.0 g O
16.0 g O
1 mol O
1 mol Fe2O3 = g Fe g O = g Fe2O3
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16. Calculate Solve for the unknown.
Sample Problem 10.6
Calculate Solve for the unknown. 2
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.
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17. Calculate Solve for the unknown.
Sample Problem 10.6
Calculate Solve for the unknown. 2
Multiply the given mass by the conversion factor.
92.2 g Fe2O3 ×
1 mol Fe2O3
159.6 g Fe2O3
= mol Fe2O3
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18. Evaluate Does the result make sense?
Sample Problem 10.6
Evaluate Does the result make sense? 3
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.
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19. 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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20. 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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21. 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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22. 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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23. 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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24. The Mole-Volume Relationship
Avogadro’s Hypothesis
Avogadro’s hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
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25. The Mole-Volume Relationship
Avogadro’s Hypothesis
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.
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26. The Mole-Volume Relationship
Avogadro’s Hypothesis
Whether the particles are large or small, large expanses of space exist between individual particles of gas.
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27. The Mole-Volume Relationship
Avogadro’s Hypothesis
The volume of a gas varies with a change in temperature or a change in pressure.
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28. The Mole-Volume Relationship
Avogadro’s Hypothesis
The volume of a gas varies with a change in temperature or a change in pressure.
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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29. The Mole-Volume Relationship
Avogadro’s Hypothesis
The volume of a gas varies with a change in temperature or a change in pressure.
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 kPa, or 1 atmosphere (atm).
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30. The Mole-Volume Relationship
Avogadro’s Hypothesis
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.
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31. The Mole-Volume Relationship
Calculating the Volume and Moles of a Gas at STP
The molar volume is used to convert between the number of moles of gas and the volume of the gas at STP.
The conversion factors for these calculations are based on the relationship 22.4 L = 1 mol at STP.
22.4 L
1 mol
and
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32. The Mole-Volume Relationship
Calculating the Volume and Moles of a Gas at STP
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.
22.4 L
1 mol
and
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33. Calculating Gas Quantities at STP
Sample Problem 10.7
Calculating Gas Quantities at STP
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.
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34. Analyze List the knowns and the unknown.
Sample Problem 10.7
Analyze List the knowns and the unknown. 1
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
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35. Calculate Solve for the unknown.
Sample Problem 10.7
Calculate Solve for the unknown. 2
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.
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36. Calculate Solve for the unknown.
Sample Problem 10.7
Calculate Solve for the unknown. 2
Multiply the given number of moles by the conversion factor.
0.60 mol SO2 ×
22.4 L SO2
1 mol SO2
= 13 L SO2
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37. Evaluate Does the result make sense?
Sample Problem 10.7
Evaluate Does the result make sense? 3
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.
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38. CHEMISTRY & YOU
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?
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39. CHEMISTRY & YOU
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.
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40. The Mole-Volume Relationship
Calculating Molar Mass and Density
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.
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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41. The Mole-Volume Relationship
Calculating Molar Mass and Density
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.
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42. Calculating the Molar Mass of a Gas at STP
Sample Problem 10.8
Calculating the Molar Mass of a Gas at STP
The density of a gaseous compound containing carbon and oxygen is found to be g/L at STP. What is the molar mass of the compound?
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43. Analyze List the knowns and the unknown.
Sample Problem 10.8
Analyze List the knowns and the unknown. 1
The molar mass of the compound is calculated from the known density of the compound and the molar volume at STP.
KNOWNS density = g/L 1 mol of gas at STP = 22.4 L UNKNOWN molar mass = ? g/mol
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44. Calculate Solve for the unknown.
Sample Problem 10.8
Calculate Solve for the unknown. 2
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 = L ×
22.4 L
1 mol
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45. Calculate Solve for the unknown.
Sample Problem 10.8
Calculate Solve for the unknown. 2
Multiply the given density by the conversion factor.
= 44.0 g/mol
1.964 g
1 L
22.4 L
1 mol ×
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46. Evaluate Does the result make sense?
Sample Problem 10.8
Evaluate Does the result make sense? 3
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.
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47. 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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48. Why does one mole of any gas occupy the same volume (22
Why does one mole of any gas occupy the same volume (22.4 L) at standard temperature and pressure?
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49. Why does one mole of any gas occupy the same volume (22
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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50. 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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51. 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 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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52. The Mole and Quantifying Matter
BIG IDEA
The Mole and Quantifying Matter
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.
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53. END OF 10.2
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