Chapter 10 Chemical Quantities

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1 Chapter 10 Chemical Quantities 101 The Mole: A Measurement 102 Mole-Mass and Mole-Volume Relationships 103 Percent Composition and Chemical Formulas 1 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

2 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? Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

3 Measuring Matter Measuring Matter How can you convert among the count, mass, and volume of something? 3 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

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 4 At an orchard, you can buy apples by volume bushel Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

5 If you know the mass of a bushel of apples and the mass of a single apple, what other information can you calculate? 5 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

6 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 6 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

7 What Is a Mole? What Is a Mole? How do chemists count the number of atoms, molecules, or formula units in a substance? 7 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

8 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 8 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

9 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 9 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

10 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 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, , is called Avogadro s number 10 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

11 Mole movie 11 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

12 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 12 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

13 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 13 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

14 Counting with Moles What Is a Mole? For ionic compounds, such as calcium chloride, the representative particle is the formula unit CaCl 2 14 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

15 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 representative particles 15 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

16 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 Atomic nitrogen Atom N Nitrogen gas Molecule N Water Molecule H 2 O Calcium ion Ion Ca Calcium fluoride Formula unit CaF Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

17 CHEMISTRY & YOU What are the different ways you can measure the amount of sand in a sand sculpture? 17 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

18 What Is a Mole? Converting Between Number of Particles and Moles The relationship 1 mol = 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 representative particles and representative particles 1 mol Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

19 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 atoms of magnesium? 19 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

20 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 20 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

21 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 21 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

22 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 22 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

23 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 representative particles/1 mol Then multiply the number of representative particles by the number of atoms in each molecule or formula unit 23 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

24 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 )? 24 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

25 Sample Problem 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 = molecules C 3 H 8 1 molecule C 3 H 8 = 11 atoms (3 carbon atoms and 8 hydrogen atoms) UNKNOWN number of atoms =? atoms 25 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

26 Sample Problem Calculate Solve for the unknown First write the conversion factor to convert from moles to molecules 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 26 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

27 Sample Problem 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 27 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

28 Sample Problem Calculate Solve for the unknown Multiply the moles of C 3 H 8 by the conversion factors 212 mol C 3 H molecules C 3 H 8 1 mol C 3 H 8 11 atoms 1 molecule C 3 H 8 = atoms Be sure to check sig figs 28 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

29 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 29 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

30 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 30 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

31 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 = 559 g This figure shows one mole of carbon, sulfur, and iron 31 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

32 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 atoms of that element 32 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

33 Molar Mass 33 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 atoms of magnesium) has a mass of 243 g Molar mass is the mass of 1 mol of atoms of any element Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

34 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 34 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

35 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): amu = 480 amu So, the molecular mass of SO 3 is 321 amu amu = 801 amu 35 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

36 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 molecules of SO 3 36 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

37 Molar Mass 37 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 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

38 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 38 1 mol of water (H 2 O) molecules = 180 g Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

39 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? 39 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

40 Sample Problem 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 40 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

41 Sample Problem Calculate Solve for the unknown Convert moles of hydrogen and oxygen to grams of hydrogen and oxygen 10 g H 2 mol H = 20 g H 1 mol H 2 mol O = 20 g O 160 g O 1 mol 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 41 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

42 Sample Problem Calculate Solve for the unknown Add the results mass of 1 mol H 2 O 2 = 20 g H g O = 340 g molar mass of H 2 O 2 = 340 g/mol 42 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

43 Sample Problem 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 43 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

44 Complete the following analogy: Molar mass is to moles of a substance as atomic/molecular mass is to 44 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

45 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 45 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

46 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 46 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

47 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 47 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

48 Glossary Terms mole (mol): the amount of a substance that contains representative particles of that substance Avogadro s number: the number of representative particles contained in one mole of a substance; equal to 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 48 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

49 BIG IDEA The Mole and Quantifying Matter The mole is an important measurement in chemistry 49 Copyright Pearson Education, Inc, or its affiliates All Rights Reserved

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