10.1 The Mole: A Measurement of Matter Read the lesson title aloud to students.

Measuring Matter There are a number of different ways to measure the amount of matter in something. Review with students the different ways to measure the amount of something. Ask: What are some different ways to measure the fruits? Answer: determining their volume, determining their mass, counting them Ask: If you know the mass or volume of one apple, how could you determine the mass or volume of multiple apples? Answer: using a conversion factor

Dimensional Analysis What is the mass of 90 average-sized apples if 1 dozen of the apples has a mass of 2.0 kilograms? Tell students: We can use dimensional analysis to convert between measurements. Have students identify the knowns and unknowns for the problem. Click to reveal the knowns and unknowns. Ask: How can we convert from the number of apples to the mass of apples? Answer: use conversion factors Click to reveal the strategy for calculating the mass of apples.

Dimensional Analysis, cont. What is the mass of 90 average-sized apples if 1 dozen of the apples has a mass of 2.0 kilograms? Review the steps needed to convert number to dozens and dozens to mass. Ask: What is the conversion factor used to convert number of apples to dozens of apples? Answer: 12 apples in 1 dozen Click to reveal the conversion factor. Ask: What is the conversion factor for converting dozens of apples to mass of apples? Answer: 2.0 kilograms for 1 dozen apples Click to reveal the conversion equation. Point out where each conversion factor shows up in the equation. Emphasize how units in the numerator and denominator cancel during calculation. Click to show each of the cancellations (two clicks). Ask: Why can you cancel units in different conversion factors? Answer: because they are in the numerator and the denominator of the final value Ask: How can you confirm that you have set up the conversion factors correctly? Answer: The correct unit remains after the other units have been cancelled. Ask a volunteer to write the answer to the conversion. Click to reveal the answer. 15 kg apples

The Mole Avogadro’s number is the number of representative particles in one mole of a substance. Review the table with students. Point out that although the substances have different representative particles and chemical formulas, 1.00 mole of each substance contains Avogadro’s number of particles. Encourage students to think of other examples of counting units that express the number of a certain type of object. Suggest kilobytes of information, pairs of socks, and six-packs of soda as familiar examples. Show students a packaged ream of paper and explain that a ream refers to the number of sheets of paper in the package. Ask: How many sheets of paper are in a ream? Answer: 500 sheets Ask: Why is counting paper by reams more convenient than counting by sheets? Answer: You could easily lose count when counting by sheets. Explain that the mole is based on measurements for carbon-12. The mole is defined as the amount of substance that contains as many representative particles as there are atoms in 12 grams of carbon-12. As a visual aid, tell students that a 4-centimeter lump of charcoal, which is largely carbon-12, has a mass of about 12 grams.

Converting Between Atoms and Moles How many moles of magnesium is 1.25 × 1023 atoms of magnesium? Tell students: Avogadro’s number is the conversion factor for converting between number of atoms and number of moles. Have students identify the knowns and unknowns for the problem. Click to reveal the knowns and unknowns. Ask students to describe the two possible conversion factors that could be used to convert between atoms and moles. Click to reveal the conversion factors.

Calculating Number of Moles How many moles of magnesium is 1.25 × 1023 atoms of magnesium? Review the two possible conversion factors for converting between moles and atoms. Ask: If we are given the number of atoms and must determine the number of moles, which conversion factor should we use? Answer: the first one Click to highlight the correct conversion factor. If necessary, explain that whatever unit we need to solve for must end up in the numerator of the conversion equation. Therefore, we must use the conversion factor with moles in the numerator. Click to reveal the conversion equation. Emphasize how units in the numerator and denominator cancel during calculation. Click to show the cancellation. Ask a volunteer to write the answer to the conversion. Click to reveal the answer. Ask: Why does the correct answer have three significant figures? Answer: because the known quantity was expressed to three significant figures If necessary, remind students that conversion factors such as Avogadro’s number are considered to be exact units and therefore do not affect the precision of the final answer. = 0.208 mol Mg

Calculating Number of Atoms Calculate the number of atoms in 2.12 moles of propane (C3H8). Tell students: Avogadro’s number is the conversion factor for converting between number of atoms and number of moles. Have students identify the knowns and unknowns for the problem. Click to reveal the knowns and unknowns.

Calculating Number of Atoms, cont. Calculate the number of atoms in 2.12 moles of propane (C3H8). Ask: What are the two conversions that must be performed to solve this problem? Answer: moles to number of molecules and number of molecules to number of atoms Ask: How can you convert from moles of propane to molecules of propane? Answer: Use Avogadro’s number. Click to reveal the conversion between molecules and moles. Ask: How can you convert from molecules of propane to atoms? Answer: Use the chemical formula of propane to determine the number of atoms in each propane molecule. Ask: How many total atoms are in a molecule of propane? Answer: 11 Click to reveal the conversion factor between atoms and molecules. If necessary, review with students how to use subscripts to determine the number of atoms in a molecule. Click to reveal the calculation for molecules of propane. Emphasize the importance of writing a unit for every quantity in a calculation and carrying the units through the calculation. Click to show how each of the units cancels (two clicks). Ask a volunteer to write the answer on the board. Click to reveal the correct answer. = 1.40 × 1025 atoms

Molar Mass The molar mass of a substance is the mass in grams of one mole of representative particles of the substance. 1 mol S = 32.1 g Remind students of some of the other unit quantities they have discussed in this lesson. Ask: Does one dozen apples have the same mass as one dozen strawberries? Answer: No. Ask: Do all atoms have the same atomic mass? Explain that because atoms of each element have unique atomic masses, one mole of an element will have a different mass than one mole of a different element. The molar mass of an element is therefore unique to that element. Click to reveal each of the molar masses of three different substances (three clicks). As the molar mass of each element is revealed, point out that although the mass of one mole of the element is unique, each mole still contains exactly Avogadro’s number of atoms. 1 mol Fe = 55.8 g 1 mol C = 12.0 g

Calculating Molar Mass for a Compound The molar mass of a compound is equal to the sum of the molar masses of all of the elements in the compound. = Remind students that a molecule is made up of atoms bonded together. Ask: How can you determine the molar mass of an element? Answer: by looking on the periodic table Ask: How is the atomic mass listed on the periodic table related to the molar mass of an element? Answer: The molar mass in g/mol is equal to the atomic mass in amu. Ask: How will the molar mass of SO3 compare to the molar masses of S and O? Answer: The molar mass of SO3 should be greater than the molar mass of S or O. Click to reveal how to calculate the molar mass of SO3. =

Molar Mass of a Compound You can calculate the molar mass of a compound from its chemical formula. 1 mol C6H4Cl2 = 147.0 g 1 mol C6H12O6 = 180.0 g Ask: Can the mass of a mole of an element be found directly on the periodic table? Answer: Yes. Ask: Can the mass of a mole of a compound be found directly on the periodic table? Explain. Answer: No; the masses must be found by adding the masses of each atom in a representative unit of the compound. Click to reveal the molar mass of each compound (three clicks). For each compound, have students verify that the molar mass given is equal to the sum of the molar masses of the atoms in the compound. 1 mol H2O = 18.0 g