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 quantify the amount of sand in a sand sculpture?
CHEMISTRY & YOU
How can you quantify the amount of sand in a sand sculpture?
You could measure the amount of sand in a sculpture by counting the grains of sand. Is there an easier way to measure the amount of sand?
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3. Measuring Matter
Measuring Matter
How can you convert among the count, mass, and volume of something?
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4. Chemistry is a quantitative science.
Measuring Matter
Chemistry is a quantitative science.
In your study of chemistry, you will analyze the composition of samples of matter and perform chemical calculations that relate quantities of the reactants in a chemical reaction to quantities of the products.
To solve these and other problems, you will have to be able to measure the amount of matter you have.
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5. What Is a Mole?
What Is a Mole?
How do chemists count the number of atoms, molecules, or formula units in a substance?
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6. Recall that matter is composed of atoms, molecules, and ions.
What Is a Mole?
Recall that matter is composed of atoms, molecules, and ions.
These particles are much, much smaller than grains of sand, and an extremely large number of them are in a small sample of a substance.
Obviously, counting particles one by one is not practical.
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7. Think about counting eggs.
What Is a Mole?
Think about counting eggs.
It’s easier when the eggs are grouped into dozens.
A dozen is a
specified number
(12) of things.
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8. Chemists also use a unit that is a specified number of particles.
What Is a Mole?
Counting with Moles
Chemists also use a unit that is a specified number of particles.
The unit is called the mole.
A mole (mol) of a substance is 6.02 × 1023 representative particles of that substance and is the SI unit for measuring the amount of a substance.
The number of representative particles in a mole, 6.02 × 1023, is called Avogadro’s number.
What SI unit is used to measure the number of representative particles in a substance?
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9. What Is a Mole?
Counting with Moles
The term representative particle refers to the species present in a substance, usually atoms, molecules, or formula units.
The representative particle of most elements is the atom.
Iron is composed of iron atoms. Helium is composed of helium atoms.
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10. What Is a Mole?
Counting with Moles
Seven elements normally exist as diatomic molecules (H2, N2, O2, F2, Cl2, Br2, and I2).
The representative particle of these elements and of all molecular compounds is the molecule.
The molecular compounds water (H2O) and sulfur dioxide (SO2) are composed of H2O and SO2 molecules, respectively.
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11. What Is a Mole?
Counting with Moles
For ionic compounds, such as calcium chloride, the representative particle is the formula unit CaCl2.
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12. What Is a Mole?
Counting with Moles
The mole allows chemists to count the number of representative particles in a substance.
A mole of any substance contains Avogadro’s number of representative particles, or 6.02 × 1023 representative particles.
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13. Representative Particles and Moles
Interpret Data
Counting with Moles
The table below summarizes the relationship between representative particles and moles of substances.
Representative Particles and Moles
Substance
Representative particle
Chemical formula
Representative particles in 1.00 mol
Copper
Atom Cu
6.02 × 1023
Atomic nitrogen N
Nitrogen gas
Molecule N2
Water
H2O
Calcium ion
Ion
Ca2+
Calcium fluoride
Formula unit
CaF2
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14. Converting Between Number of Particles and Moles
What Is a Mole?
Converting Between Number of Particles and Moles
The relationship 1 mol = 6.02 × 1023 representative particles (atoms, molecules, ions, etc….) is the basis for the following conversion factors that you can use to convert numbers of representative particles to moles and moles to number of representative particles.
1 mol
6.02 × 1023 representative particles
and
6.02 × 1023 representative particles
1 mol
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15. Converting Number of Atoms to Moles
Sample Problem 10.2
Converting Number of Atoms to Moles
Magnesium is a light metal used in the manufacture of aircraft, automobile wheels, and tools. How many moles of magnesium is 1.25 × 1023 atoms of magnesium?
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16. Analyze List the known and the unknown.
Sample Problem 10.2
Analyze List the known and the unknown. 1
The desired conversion is atoms → moles.
KNOWN
number of atoms = 1.25 × 1025 atoms Mg
UNKNOWN moles = ? mol Mg
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17. Calculate Solve for the unknown.
Sample Problem 10.2
Calculate Solve for the unknown. 2
First state the relationship between moles and number of representative particles.
1 mol Mg = 6.02 × 1023 atoms Mg
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18. Calculate Solve for the unknown.
Sample Problem 10.2
Calculate Solve for the unknown. 2
Write the conversion factors you get based on this relationship.
1 mol Mg
6.02 × 1023 atoms Mg
and
Identify the conversion factor needed to convert from atoms to moles.
6.02 × 1023 atoms Mg
1 mol Mg
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19. Calculate Solve for the unknown.
Sample Problem 10.2
Calculate Solve for the unknown. 2
Multiply the number of atoms of Mg by the conversion factor.
6.02 × 1023 atoms Mg
1 mol Mg
1.25 × 1023 atoms Mg ×
= mol Mg
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20. Evaluate Does the result make sense?
Sample Problem 10.2
Evaluate Does the result make sense? 3
The given number of atoms (1.25 × 1023) is less than one-fourth of Avogadro’s number (6.02 × 1023), so the answer should be less than one-fourth (0.25) mol of atoms.
The answer should have three significant figures.
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21. Example #2: Determine the number of moles in 7
Example #2: Determine the number of moles in 7.9 x 1024 formula units of Na2CO3?
7.9 x 1024 units Na2CO3 1 mol Na2CO x 1023 units Na2CO3
=13.1 mol Na2CO3

22. How many moles is 2.80 x1024 atoms of Silicon?
How many moles is 2.17 x1023 molecules of Bromine?

23. Converting Between Number of Particles and Moles
What Is a Mole?
Converting Between Number of Particles and Moles
Suppose you want to determine how many atoms are in a mole of a compound.
To do this, you must know how many atoms are in a representative particle of the compound.
This number is determined from the chemical formula.
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24. Converting Between Number of Particles and Moles
What Is a Mole?
Converting Between Number of Particles and Moles
In the formula for carbon dioxide (CO2), the subscripts show that one molecule of carbon dioxide is composed of three atoms: one carbon atom and two oxygen atoms.
A mole of carbon dioxide contains Avogadro’s number of CO2 molecules.
Each molecule contains three atoms, so a mole of carbon dioxide contains three times Avogadro’s number of atoms.
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25. Converting Between Number of Particles and Moles
What Is a Mole?
Converting Between Number of Particles and Moles
To find the number of atoms in a given number of moles of a compound, you must first determine the number of representative particles.
To convert the number of moles of a compound to the number of representative particles (molecules or formula units), multiply the number of moles by 6.02 × 1023 representative particles/1 mol.
Then multiply the number of representative particles by the number of atoms in each molecule or formula unit.
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26. What Is a Mole?
The Size of a Mole
The SI unit, the mole, is not related to the small burrowing animal of the same name.
Assume that an average animal-mole is 15 cm long, 5 cm tall, and has a mass of 145 g.
Based on this information, the mass of 6.02 × 1023 animal-moles is 8.73 × 1022 kg.
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27. The Size of a Mole What Is a Mole?
The mass of Avogadro’s number of animal-moles is equal to more than 60 times the combined mass of Earth’s oceans.
If spread over the entire surface of Earth, Avogadro’s number of animal-moles would form a layer more than 8 million animal-moles thick.
If lined up end-to-end, 6.02 × 1023 animal-moles would stretch from Earth to the nearest star (other than the sun), Alpha Centauri, more than two million times.
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28. Converting Moles to Number of Atoms
Sample Problem 10.3
Converting Moles to Number of Atoms
Propane is a gas used for cooking and heating. How many atoms are in 2.12 mol of propane (C3H8)?
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29. moles → molecules → atoms.
Sample Problem 10.3
Analyze List the knowns and the unknown. 1
The desired conversion is:
moles → molecules → atoms.
KNOWNS number of moles = 2.12 mol C3H8 1 mol C3H8 = 6.02 × 1023 molecules C3H8 1 molecule C3H8 = 11 atoms (3 carbon atoms and 8 hydrogen atoms)
UNKNOWN number of atoms = ? atoms
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30. Calculate Solve for the unknown.
Sample Problem 10.3
Calculate Solve for the unknown. 2
First write the conversion factor to convert from moles to molecules.
6.02 × 1023 molecules C3H8
1 mol C3H8
Remember to write the conversion factors so that the unit in the denominator cancels the unit in the numerator of the previous factor.
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31. Calculate Solve for the unknown.
Sample Problem 10.3
Calculate Solve for the unknown. 2
Write the conversion factor to convert from molecules to atoms.
11 atoms
1 molecule C3H8
There are 3 atoms of carbon and 8 atoms of hydrogen in 1 molecule of propane.
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32. Calculate Solve for the unknown.
Sample Problem 10.3
Calculate Solve for the unknown. 2
Multiply the moles of C3H8 by the conversion factors.
1 molecule C3H8
2.12 mol C3H8 ×
6.02 × 1023 molecules C3H8
1 mol C3H8 ×
11 atoms
= 1.40 × 1025 atoms
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33. Evaluate Does the result make sense?
Sample Problem 10.3
Evaluate Does the result make sense? 3
There are 11 atoms in each molecule of propane and more than 2 mol of propane, so the answer should be more than 20 times Avogadro’s number of propane molecules.
The answer has three significant figures, based on the three significant figures in the given measurement.
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34. II. Particles & Moles Example: How many formula units are
in 3 moles of Zn(NO3)2?
3 mol Zn(NO3) x units Zn(NO3) mol Zn(NO3)2
= x units Zn(NO3)2

35. II. Particles & Moles Example: How many atoms are
in 1.14 moles of SO3?

36. II. Particles & Moles Example: How many carbon atoms are
in 2.12 moles of C3H8? How many hydrogen atoms?

37. How do you determine the molar mass of an element and of a compound?
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38. Interpret Data
Remember that the atomic mass of an element (the mass of a single atom) is expressed in atomic mass units (amu).
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39. The Mass of a Mole of an Element
Molar Mass
The Mass of a Mole of an Element
The atomic mass of an element expressed in grams is the mass of a mole of the element.
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40. The Mass of a Mole of an Element
Molar Mass
The Mass of a Mole of an Element
The mass of a mole of an element is its molar mass.
For carbon, the molar mass is 12.0 g.
For atomic hydrogen, the molar mass is 1.0 g.
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41. The Mass of a Mole of an Element
Molar Mass
The Mass of a Mole of an Element
1 mol of sulfur atoms = 32.1 g
1 mol of carbon atoms = 12.0 g
1 mol of iron atoms = g
This figure shows one mole of carbon, sulfur, and iron.
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42. The Mass of a Mole of an Element
Molar Mass
The Mass of a Mole of an Element
How many atoms are contained in the molar mass of an element?
The molar mass of an element contains 1 mol or 6.02 × 1023 atoms of that element.
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43. The Mass of a Mole of an Element
Molar Mass
The Mass of a Mole of an Element
The mole can now be further defined as the amount of substance that contains the same number of representative particles as the number of atoms in 12.0 g of carbon-12.
You know that 12.0 g is the molar mass of carbon-12, so 12.0 g of carbon is 1 mol of carbon atoms.
Similarly, 24.3 g is the molar mass of magnesium, so 1 mol (or 6.02 × 1023 atoms of magnesium) has a mass of 24.3 g.
Molar mass is the mass of 1 mol of atoms of any element.
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44. The Mass of a Mole of a Compound
Molar Mass
The Mass of a Mole of a Compound
To find the mass of a mole of a compound, you must know the formula of the compound.
A molecule of SO3 is composed of one atom of sulfur and three atoms of oxygen.
You can calculate the mass of a molecule of SO3 by adding the atomic masses of the atoms making up the molecule.
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45. The Mass of a Mole of a Compound
Molar Mass
The Mass of a Mole of a Compound
From the periodic table, the atomic mass of sulfur (S) is 32.1 amu.
The mass of three atoms of oxygen is three times the atomic mass of a single oxygen atom (O): 3 × 16.0 amu = 48.0 amu.
So, the molecular mass of SO3 is 32.1 amu amu = 80.1 amu.
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46. The Mass of a Mole of a Compound
Molar Mass
The Mass of a Mole of a Compound
Now substitute the unit grams for atomic mass units to find the molar mass of SO3.
1 mol of SO3 has a mass of 80.1 g.
This is the mass of 6.02 x 1023 molecules of SO3.
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47. The Mass of a Mole of a Compound
Molar Mass
The Mass of a Mole of a Compound
To calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound. Then add the masses of the elements in the compound.
This method for calculating molar mass applies to any compound, molecular or ionic.
The molar masses in the following slide were obtained in this way.
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48. The Mass of a Mole of a Compound
Molar Mass
The Mass of a Mole of a Compound
1 mol of paradichlorobenzene (C6H4Cl2) molecules (moth crystals)
= g
1 mol of glucose (C6H12O6) molecules (blood sugar)
= g
1 mol of water (H2O) molecules = 18.0 g
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49. Finding the Molar Mass of a Compound
Sample Problem 10.4
Finding the Molar Mass of a Compound
The decomposition of hydrogen peroxide (H2O2) provides sufficient energy to launch a rocket. What is the molar mass of hydrogen peroxide?
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50. Analyze List the knowns and the unknown.
Sample Problem 10.4
Analyze List the knowns and the unknown. 1
Convert moles of atoms to grams by using conversion factors (g/mol) based on the molar mass of each element. The sum of the masses of the elements is the molar mass.
KNOWNS molecular formula = H2O2 mass of 1 mol H = 1.0 g H mass of 1 mol O = 16.0 g O
UNKNOWN molar mass = ? g/mol
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51. Calculate Solve for the unknown.
Sample Problem 10.4
Calculate Solve for the unknown. 2
Convert moles of hydrogen and oxygen to grams of hydrogen and oxygen.
2 mol H ×
= 2.0 g H
1.0 g H
1 mol H
2 mol O ×
= 2.0 g O
16.0 g O
1 mol O
One mole of H2O2 has 2 mol of H atoms and 2 mol of O atoms, so multiply the molar mass of each element by 2.
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52. Calculate Solve for the unknown.
Sample Problem 10.4
Calculate Solve for the unknown. 2
Add the results.
mass of 1 mol H2O2 = 2.0 g H g O = 34.0 g
molar mass of H2O2 = 34.0 g/mol
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53. Evaluate Does the result make sense?
Sample Problem 10.4
Evaluate Does the result make sense? 3
The answer is the sum of two times the molar mass of hydrogen and oxygen (17.0 g).
The answer is expressed to the tenths place because the numbers being added are expressed to the tenths place.
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54. Molar Mass What is the Molar mass of : H2
1.008 g/mol g/mol = g/mol
2. Ca (OH)2
 (2 x 16) + (2 x 1.008)=74.1 g/mol

55. Atomic Mass & Formula Mass
What is the molar mass of :
SO2
64 g/mol
C6H12O6
180 g/mol
Ba(OH)2
 g/mol

56. Complete the following analogy:
Molar mass is to moles of a substance as atomic/molecular mass is to _____.
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57. Complete the following analogy:
Molar mass is to moles of a substance as atomic/molecular mass is to one atom or molecule of a substance.
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58. Key Concepts
Knowing how the count, mass, and volume of an item relate to a common unit allows you to convert among these units.
The mole allows chemists to count the number of representative particles in a substance.
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59. Key Concepts
The atomic mass of an element expressed in grams is the mass of a mole of the element.
To calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound. Then add the masses of the elements in the compound.
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60. Glossary Terms
mole (mol): the amount of a substance that contains 6.02 × 1023 representative particles of that substance
Avogadro’s number: the number of representative particles contained in one mole of a substance; equal to 6.02 × 1023 particles
representative particle: the smallest unit into which a substance can be broken down without a change in composition, usually atoms, molecules, or ions
molar mass: a term used to refer to the mass of a mole of any substance
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61. The Mole and Quantifying Matter
BIG IDEA
The Mole and Quantifying Matter
The mole is an important measurement in chemistry.
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62. How many hydrogen atoms are in 5 molecules of C6H12O6?
If a dozen apples have a mass of 800 g, what will be the mass of 15 apples?
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