Chapter 10 Chemical Quantities 101 The Mole: A Measurement 102 Mole-Mass and Mole-Volume Relationships 103 Percent Composition and Chemical Formulas 1
CHEMISTRY & YOU How can you quantify the amount of sand in a sand sculpture? 2 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?
Measuring Matter Measuring Matter How can you convert among the count, mass, and volume of something? 3
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 4
Measuring Matter Apples can be measured in three different ways At a fruit stand, they are often sold by the count In a supermarket, you usually buy apples by weight or mass At an orchard, you can buy apples by volume 5
Measuring Matter Each of these different ways to measure apples can be equated to a dozen apples By count: 1 dozen apples = 12 apples For average-sized apples, the following approximations can be used By mass: 1 dozen apples = 20 kg apples By volume: 1 dozen apples = 020 bushel apples 6
Measuring Matter Knowing how the count, mass, and volume of an item relate to a common unit allows you to convert among these units For example, based on the unit relationship, you could calculate the mass of a bushel of apples or the mass of 90 average-sized apples using conversion factors such as the following: 1 dozen apples 12 apples 20 kg apples 1 dozen apples 1 dozen apples 020 bushel apples 7
Sample Problem 101 Finding Mass from a Count What is the mass of 90 average-sized apples if 1 dozen of the apples has a mass of 20 kg? 8
Sample Problem 101 1 Analyze List the knowns and the unknown Use dimensional analysis to convert the number of apples to the mass of apples KNOWNS number of apples = 90 apples 12 apples = 1 dozen apples 1 dozen apples = 20 kg apples UNKNOWN mass of 90 apples =? kg 9
2 Calculate Solve for the unknown First identify the sequence of conversions needed to perform the calculation number of apples dozens of apples mass of apples Sample Problem 101 10
2 Calculate Solve for the unknown Write the conversion factor to convert from number of apples to dozens of apples 1 dozen apples 12 apples Sample Problem 101 Write the conversion factor to convert from dozens of apples to mass of apples 20 kg apples 1 dozen apples 11
2 Calculate Solve for the unknown Sample Problem 101 Multiply the number of apples by these two conversion factors to get the answer in kilograms 90 apples 1 dozen apples 12 apples 20 kg apples = 15 kg apples 1 dozen apples The units apples and dozen apples cancel, so the answer has the unit kg 12
Sample Problem 101 3 Evaluate Does the result make sense? A dozen apples has a mass of 20 kg, and 90 apples is less than 10 dozen apples, so the mass should be less than 20 kg of apples (10 dozen x 20 kg/dozen) 13
If you know the mass of a bushel of apples and the mass of a single apple, what other information can you calculate? 14
If you know the mass of a bushel of apples and the mass of a single apple, what other information can you calculate? You can calculate the number of apples in a bushel by setting up the information you have as units with a common unit kg apples will be the common unit 15
What Is a Mole? What Is a Mole? How do chemists count the number of atoms, molecules, or formula units in a substance? 16
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 17
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 18
Counting with Moles Chemists also use a unit that is a specified number of particles The unit is called the mole What Is a Mole? A mole (mol) of a substance is 602 10 23 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, 602 10 23, is called Avogadro s number 19
Counting with Moles What Is a Mole? 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 20
Counting with Moles What Is a Mole? Seven elements normally exist as diatomic molecules (H 2, N 2, O 2, F 2, Cl 2, Br 2, and I 2 ) The representative particle of these elements and of all molecular compounds is the molecule The molecular compounds water (H 2 O) and sulfur dioxide (SO 2 ) are composed of H 2 O and SO 2 molecules, respectively 21
Counting with Moles What Is a Mole? For ionic compounds, such as calcium chloride, the representative particle is the formula unit CaCl 2 22
Counting with Moles What Is a Mole? 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 602 10 23 representative particles 23
Interpret Data Counting with Moles The table below summarizes the relationship between representative particles and moles of substances Substance Representative Particles and Moles Representative particle Chemical formula Representative particles in 100 mol Copper Atom Cu 602 10 23 Atomic nitrogen Atom N 602 10 23 Nitrogen gas Molecule N 2 602 10 23 Water Molecule H 2 O 602 10 23 Calcium ion Ion Ca 2+ 602 10 23 Calcium fluoride Formula unit CaF 2 602 10 23 24
CHEMISTRY & YOU What are the different ways you can measure the amount of sand in a sand sculpture? 25
CHEMISTRY & YOU What are the different ways you can measure the amount of sand in a sand sculpture? 26 You can measure the amount of sand in a sand sculpture by count (for example, number of buckets of sand in the sculpture), by mass (which can be calculated by multiplying the number of buckets of sand by how much each bucket weighs), or by volume (which can be calculated by multiplying the number of buckets by the volume the bucket holds)
What Is a Mole? Converting Between Number of Particles and Moles The relationship 1 mol = 602 10 23 representative particles 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 602 10 23 representative particles and 27 602 10 23 representative particles 1 mol
Sample Problem 102 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 125 10 23 atoms of magnesium? 28
Sample Problem 102 1 Analyze List the known and the unknown The desired conversion is atoms moles KNOWN number of atoms = 125 10 25 atoms Mg UNKNOWN moles =? mol Mg 29
2 Calculate Solve for the unknown Sample Problem 102 First state the relationship between moles and number of representative particles 1 mol Mg = 602 10 23 atoms Mg 30
2 Calculate Solve for the unknown Sample Problem 102 Write the conversion factors you get based on this relationship 1 mol Mg 602 10 23 atoms Mg and 602 10 23 atoms Mg 1 mol Mg Identify the conversion factor needed to convert from atoms to moles 31 1 mol Mg 602 10 23 atoms Mg
2 Calculate Solve for the unknown Sample Problem 102 Multiply the number of atoms of Mg by the conversion factor 125 10 23 atoms Mg = 0208 mol Mg 1 mol Mg 602 10 23 atoms Mg 32
Sample Problem 102 3 Evaluate Does the result make sense? The given number of atoms (125 10 23 ) is less than one-fourth of Avogadro s number (602 10 23 ), so the answer should be less than one-fourth (025) mol of atoms The answer should have three significant figures 33
Converting Between Number of Particles and Moles Suppose you want to determine how many atoms are in a mole of a compound What Is a Mole? 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 34
The number of marbles in a dozen cups is (6 12) or 72 marbles Similarly, a mole of molecules contains more than a mole of atoms What Is a Mole? Converting Between Number of Particles and Moles 35
What Is a Mole? Converting Between Number of Particles and Moles In the formula for carbon dioxide (CO 2 ), 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 CO 2 molecules Each molecule contains three atoms, so a mole of carbon dioxide contains three times Avogadro s number of atoms 36
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 602 10 23 representative particles/1 mol Then multiply the number of representative particles by the number of atoms in each molecule or formula unit 37
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 602 10 23 animalmoles is 873 10 22 kg 38
What Is a Mole? The Size of 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, 602 10 23 animal-moles would stretch from Earth to the nearest star, Alpha Centauri, more than two million times 39
Sample Problem 103 Converting Moles to Number of Atoms Propane is a gas used for cooking and heating How many atoms are in 212 mol of propane (C 3 H 8 )? 40
Sample Problem 103 1 Analyze List the knowns and the unknown The desired conversion is: moles molecules atoms KNOWNS number of moles = 212 mol C 3 H 8 1 mol C 3 H 8 = 602 10 23 molecules C 3 H 8 1 molecule C 3 H 8 = 11 atoms (3 carbon atoms and 8 hydrogen atoms) 41 UNKNOWN number of atoms =? atoms
Sample Problem 103 2 Calculate Solve for the unknown First write the conversion factor to convert from moles to molecules 602 10 23 molecules C 3 H 8 1 mol C 3 H 8 Remember to write the conversion factors so that the unit in the denominator cancels the unit in the numerator of the previous factor 42
Sample Problem 103 2 Calculate Solve for the unknown Write the conversion factor to convert from molecules to atoms 11 atoms 1 molecule C 3 H 8 There are 3 atoms of carbon and 8 atoms of hydrogen in 1 molecule of propane 43
Sample Problem 103 2 Calculate Solve for the unknown Multiply the moles of C 3 H 8 by the conversion factors 212 mol C 3 H 8 602 10 23 molecules C 3 H 8 1 mol C 3 H 8 11 atoms 1 molecule C 3 H 8 = 140 10 23 atoms 44
Sample Problem 103 3 Evaluate Does the result make sense? 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 45
How is a mole similar to a dozen? 46
How is a mole similar to a dozen? Both mole and dozen are quantities made of a specified number of representative particles They both refer to multiple objects or particles that are now being thought of as a single object or particle with multiple parts 47
Molar Mass Molar Mass How do you determine the molar mass of an element and of a compound? 48
Interpret Data Remember that the atomic mass of an element (the mass of a single atom) is expressed in atomic mass units (amu) 49
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 50
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 120 g For atomic hydrogen, the molar mass is 10 g 51
Molar Mass The Mass of a Mole of an Element 1 mol of sulfur atoms = 321 g 1 mol of carbon atoms = 120 g 1 mol of iron atoms = 120 g This figure shows one mole of carbon, sulfur, and iron 52
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 602 10 23 atoms of that element 53
Molar Mass 54 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 120 g of carbon-12 You know that 120 g is the molar mass of carbon-12, so 120 g of carbon is 1 mol of carbon atoms Similarly, 243 g is the molar mass of magnesium, so 1 mol (or 602 10 23 atoms of magnesium) has a mass of 243 g Molar mass is the mass of 1 mol of atoms of any element
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 SO 3 is composed of one atom of sulfur and three atoms of oxygen You can calculate the mass of a molecule of SO 3 by adding the atomic masses of the atoms making up the molecule 55
Molar Mass The Mass of a Mole of a Compound From the periodic table, the atomic mass of sulfur (S) is 321 amu The mass of three atoms of oxygen is three times the atomic mass of a single oxygen atom (O): 3 160 amu = 480 amu So, the molecular mass of SO 3 is 321 amu + 480 amu = 801 amu 56
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 SO 3 1 mol of SO 3 has a mass of 801 g This is the mass of 602 x 10 23 molecules of SO 3 57
Molar Mass 58 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
Molar Mass The Mass of a Mole of a Compound 1 mol of paradichlorobenzene (C 6 H 4 Cl 2 ) molecules (moth crystals) = 1470 g 1 mol of glucose (C 6 H 12 O 6 ) molecules (blood sugar) = 1800 g 59 1 mol of water (H 2 O) molecules = 180 g
Sample Problem 104 Finding the Molar Mass of a Compound The decomposition of hydrogen peroxide (H 2 O 2 ) provides sufficient energy to launch a rocket What is the molar mass of hydrogen peroxide? 60
Sample Problem 104 1 Analyze List the knowns and the unknown 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 = H 2 O 2 mass of 1 mol H = 10 g H mass of 1 mol O = 160 g O UNKNOWN molar mass =? g/mol 61
Sample Problem 104 2 Calculate Solve for the unknown Convert moles of hydrogen and oxygen to grams of hydrogen and oxygen 2 mol H 10 g H 1 mol H = 20 g H 2 mol O 160 g O 1 mol O = 20 g O One mole of H 2 O 2 has 2 mol of H atoms and 2 mol of O atoms, so multiply the molar mass of each element by 2 62
Sample Problem 104 2 Calculate Solve for the unknown Add the results mass of 1 mol H 2 O 2 = 20 g H + 320 g O = 340 g molar mass of H 2 O 2 = 340 g/mol 63
Sample Problem 104 3 Evaluate Does the result make sense? The answer is the sum of two times the molar mass of hydrogen and oxygen (170 g) The answer is expressed to the tenths place because the numbers being added are expressed to the tenths place 64
Complete the following analogy: Molar mass is to moles of a substance as atomic/molecular mass is to 65
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 66
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 67
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 68
Glossary Terms mole (mol): the amount of a substance that contains 602 10 23 representative particles of that substance Avogadro s number: the number of representative particles contained in one mole of a substance; equal to 602 10 23 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 69
BIG IDEA The Mole and Quantifying Matter The mole is an important measurement in chemistry 70
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