1/7/14. Measuring Matter. How can you convert among the count, mass, and volume of something? Apples can be measured in three different ways.

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1 Chapter 10 Chemical Quantities 102 Mole-Mass and Mole-Volume Relationships 103 Percent Composition and Chemical Formulas 1 Measuring Matter Measuring Matter How can you convert among the count, mass, and volume of something? 2 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 3 1

2 Measuring Matter Each of these different ways to measure apples can be equated to a dozen apples By count: 1 dozen apples = 12 apples By mass: 1 dozen apples = ~ 20 kg By volume: 1 dozen apples = ~ 020 bushel 4 Measuring Matter Knowing how the count, mass, and volume of an item relate to a common unit allows you to convert among these units 1 dozen apples 12 apples 20 kg apples 1 dozen apples 1 dozen apples 020 bushel apples 5 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? 6 2

3 Sample Problem 101 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 7 Calculate Solve for the unknown Sample Problem dozen apples 20 kg apples 90 apples = 15 kg apples 12 apples 1 dozen apples The units apples and dozen apples cancel, so the answer has the unit kg 8 Sample Problem 101 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 9 3

4 How do chemists count the number of atoms, molecules, or formula units in a substance? 10 Recall that matter is composed of atoms, molecules, and ions These particles are extremely small, so counting one by one is not practical 11 Think about counting eggs It s easier when the eggs are grouped into dozens A dozen is a specified number (12) of things 12 4

5 Counting with Moles Chemists also use a unit that is a specified number of particles The unit is called the mole 1 mole (mol) = representative particles of that substance SI unit for measuring the amount of a substance Avogadro s number 13 Counting with Moles The term representative particle refers to the species present in a substance, usually atoms, molecules, or formula units Elements atoms Compounds molecules or formula units 14 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 Interpret Data 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

6 Converting Between Number of Particles and Moles 1 mol representative particles and representative particles 1 mol 16 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? 17 2 Calculate Solve for the unknown Sample Problem 102 First state the relationship between moles and number of representative particles 1 mol Mg = atoms Mg 18 6

7 2 Calculate Solve for the unknown Sample Problem 102 Multiply the number of atoms of Mg by the conversion factor atoms Mg 1 mol Mg atoms Mg = 0208 mol Mg 19 Sample Problem Evaluate Does the result make sense? The given number of atoms ( ) is less than Avogadro s number ( ), so the answer should be less than 1 The answer should have three significant figures 20 Converting Between Number of Particles and Moles Carbon dioxide (CO 2 ) one molecule of carbon dioxide is composed of three atoms: one C atom and two O atoms 1 mole of CO 2 contains Avogadro s number of CO 2 molecules Each molecule contains 3 atoms So a mole of carbon dioxide contains 3x Avogadro s number of atoms 21 7

8 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 )? 22 Sample Problem 103 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 23 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 24 8

9 How do you determine the molar mass of an element and of a compound? The atomic mass of an element (the mass of a single atom) is expressed in atomic mass units (amu) 25 The Mass of a Mole of an Element The mass of 1 mole of an element is its molar mass For carbon, the molar mass is 120 g For atomic hydrogen, the molar mass is 101 g 26 The Mass of a Mole of an Element 1 mol of S atoms = 321 g 1 mol of C atoms = 120 g 1 mol of Fe atoms = 558 g 27 9

10 The Mass of a Mole of a Compound The molecular mass of SO 3 is 321 amu amu = 801 amu 28 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 29 The Mass of a Mole of a Compound 1 mol of paradichlorobenzene (C 6 H 4 Cl 2 ) molecules (moth crystals) = 147 g 1 mol of glucose (C 6 H 12 O 6 ) molecules (blood sugar) = 180 g 30 1 mol of water (H 2 O) molecules = 180 g 10

11 Sample Problem 104 Finding the 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? 31 Sample Problem g H 2 mol H = 20 g H 1 mol H 160 g O 2 mol O = 320 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 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 32 Sample Problem