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Chemists need a convenient method for counting accurately the number of atoms, molecules, or formula units in a sample of a substance. MOLE The Mole: Basic Concepts As you know, atoms and molecules are extremely small. There are so many of them in even the smallest sample that it’s impossible to actually count them. That’s why chemists created their own counting unit called the mole. Topic 14 Topic 14

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The mole, commonly abbreviated mol, is the SI base unit used to measure the amount of a substance. Measuring Matter It is the number of representative particles, carbon atoms, in exactly 12 g of pure carbon-12. The Mole: Basic Concepts Topic 14 Topic 14 Click box to view movie clip.

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Through years of experimentation, it has been established that a mole of anything contains 6.022 136 7 x 10 23 representative particles. Measuring Matter A representative particle is any kind of particle such as atoms, molecules, formula units, electrons, or ions. The Mole: Basic Concepts Topic 14 Topic 14

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The number 6.022 136 7 x 10 23 is called Avogadro’s number in honor of the Italian physicist and lawyer Amedeo Avogadro who, in 1811, determined the volume of one mole of a gas. Measuring Matter In this book, Avogadro’s number will be rounded to three significant figures— 6.02 x 10 23. The Mole: Basic Concepts Topic 14 Topic 14

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If you write out Avogadro’s number, it looks like this. Measuring Matter 602 000 000 000 000 000 000 000 The Mole: Basic Concepts Topic 14 Topic 14

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One-mole quantities of three substances are shown, each with a different representative particle. Measuring Matter The representative particle in a mole of water is the water molecule. The Mole: Basic Concepts Topic 14 Topic 14

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The representative particle in a mole of copper is the copper atom. Measuring Matter The Mole: Basic Concepts Topic 14 Topic 14

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The representative particle in a mole of sodium chloride is the formula unit. Measuring Matter The Mole: Basic Concepts Topic 14 Topic 14

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Suppose you want to determine how many particles of sucrose are in 3.50 moles of sucrose. You know that one mole contains 6.02 x 10 23 representative particles. Converting Moles to Particles Therefore, you can write a conversion factor, Avogadro’s number, that relates representative particles to moles of a substance. The Mole: Basic Concepts Topic 14 Topic 14

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You can find the number of representative particles in a number of moles just as you found the number of roses in 3.5 dozen. Converting Moles to Particles For sucrose, the representative particle is a molecule, so the number of molecules of sucrose is obtained by multiplying 3.50 moles of sucrose by the conversion factor, Avogadro’s number. The Mole: Basic Concepts Topic 14 Topic 14

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There are 2.11 x 10 24 molecules of sucrose in 3.50 moles. Converting Moles to Particles The Mole: Basic Concepts Topic 14 Topic 14

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Now, suppose you want to find out how many moles are represented by a certain number of representative particles. Converting Particles to Moles You can use the inverse of Avogadro’s number as a conversion factor. The Mole: Basic Concepts Topic 14 Topic 14

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Zinc is used as a corrosion-resistant coating on iron and steel. It is also an essential trace element in your diet. Converting Particles to Moles Calculate the number of moles that contain 4.50 x 10 24 atoms of zinc (Zn). The Mole: Basic Concepts Topic 14 Topic 14

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Multiply the number of zinc atoms by the conversion factor that is the inverse of Avogadro’s number. Converting Particles to Moles The Mole: Basic Concepts Topic 14 Topic 14

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The relative scale of atomic masses uses the isotope carbon-12 as the standard. The Mass of a Mole Each atom of carbon-12 has a mass of 12 atomic mass units (amu). The atomic masses of all other elements are established relative to carbon-12. The Mole: Basic Concepts Topic 14 Topic 14

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For example, an atom of hydrogen-1 has a mass of 1 amu. The Mass of a Mole The mass of an atom of helium-4 is 4 amu. Therefore, the mass of one atom of hydrogen-1 is one-twelfth the mass of one atom of carbon-12. The mass of one atom of helium-4 is one- third the mass of one atom of carbon-12. The Mole: Basic Concepts Topic 14 Topic 14

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You can find atomic masses on the periodic table, but notice that the values shown are not exact integers. The Mass of a Mole For example, you’ll find 12.011 amu for carbon, 1.008 amu for hydrogen, and 4.003 amu for helium. These differences occur because the recorded values are weighted averages of the masses of all the naturally occurring isotopes of each element. The Mole: Basic Concepts Topic 14 Topic 14

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You know that the mole is defined as the number of representative particles, or carbon- 12 atoms, in exactly 12 g of pure carbon-12. The Mass of a Mole Thus, the mass of one mole of carbon-12 atoms is 12 g. What about other elements? Whether you are considering a single atom or Avogadro’s number of atoms (a mole), the masses of all atoms are established relative to the mass of carbon-12. The Mole: Basic Concepts Topic 14 Topic 14

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The mass of a mole of hydrogen-1 is one- twelfth the mass of a mole of carbon-12 atoms, or 1.0 g. The Mass of a Mole The mass of a mole of helium-4 atoms is one-third the mass of a mole of carbon-12 atoms, or 4.0 g. The Mole: Basic Concepts Topic 14 Topic 14

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The Mass of a Mole The mass in grams of one mole of any pure substance is called its molar mass. The molar mass of any element is numerically equal to its atomic mass and has the units g/mol. The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass to Moles A roll of copper wire has a mass of 848 g. How many moles of copper are in the roll? Use the atomic mass of copper given on the periodic table to apply a conversion factor to the mass given in the problem. The Mole: Basic Concepts Topic 14 Topic 14

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Converting Moles to Mass Calculate the mass of 0.625 moles of calcium. Use the molar mass of calcium to apply a conversion factor to the number of moles given in the problem. According to the periodic table, the atomic mass of calcium is 40.078 amu, so the molar mass of calcium is 40.078 g. The Mole: Basic Concepts Topic 14 Topic 14

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Converting Moles to Mass The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass to Number of Particles Calculate the number of atoms in 4.77 g lead. To find the number of atoms in the sample, you must first determine how many moles are in 4.77 g lead. The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass to Number of Particles According to data from the periodic table, the molar mass of lead is 207.2 g/mol. Apply a conversion factor to convert mass to moles. The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass to Number of Particles Now use a second conversion factor to convert moles to number of particles. The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass to Number of Particles You can also convert from number of particles to mass by reversing the procedure above and dividing the number of particles by Avogadro’s number to determine the number of moles present. The Mole: Basic Concepts Topic 14 Topic 14

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Moles of Compounds Recall that a mole is Avogadro’s number (6.02 x 10 23 ) of particles of a substance. If the substance is a molecular compound, such as ammonia (NH 3 ), a mole is 6.02 x 10 23 molecules of ammonia. If the substance is an ionic compound, such as baking soda (sodium hydrogen carbonate, NaHCO 3 ), a mole is 6.02 x 10 23 formula units of sodium hydrogen carbonate. The Mole: Basic Concepts Topic 14 Topic 14

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Moles of Compounds In either case, a mole of a compound contains as many moles of each element as are indicated by the subscripts in the formula for the compound. For example, a mole of ammonia (NH 3 ) consists of one mole of nitrogen atoms and three moles of hydrogen atoms. The Mole: Basic Concepts Topic 14 Topic 14

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Molar mass of a compound The molar mass of a compound is the mass of a mole of the representative particles of the compound. Because each representative particle is composed of two or more atoms, the molar mass of the compound is found by adding the molar masses of all of the atoms in the representative particle. The Mole: Basic Concepts Topic 14 Topic 14

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Molar mass of a compound In the case of NH 3, the molar mass equals the mass of one mole of nitrogen atoms plus the mass of three moles of hydrogen atoms. The Mole: Basic Concepts Topic 14 Topic 14

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Molar mass of a compound You can use the molar mass of a compound to convert between mass and moles, just as you used the molar mass of elements to make these conversions. Molar mass of NH 3 = molar mass of N + 3(molar mass of H) Molar mass of NH 3 = 14.007 g + 3(1.008 g) = 17.031 g/mol The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass of a Compound to Moles At 4.0°C, water has a density of 1.000 g/mL. How many moles of water are in 1.000 kg of water (1.000 L at 4.0°C)? The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass of a Compound to Moles The Mole: Basic Concepts Topic 14 Topic 14 Before you can calculate moles, you must determine the molar mass of water (H 2 O). A mole of water consists of two moles of hydrogen atoms and one mole of oxygen atoms.

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Converting Mass of a Compound to Moles Now you can use the molar mass of water as a conversion factor to determine moles of water. Notice that 1.000 kg is converted to 1.000 x 10 3 g for the calculation. molar mass H 2 O = 2(molar mass H) + molar mass O The Mole: Basic Concepts Topic 14 Topic 14

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Converting Mass of a Compound to Moles The Mole: Basic Concepts Topic 14 Topic 14

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Basic Assessment Questions Question 1 Calculate the number of molecules in 15.7 mol carbon dioxide. Topic 14 Topic 14

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Basic Assessment Questions Answer 9.45 x 10 24 molecular CO 2 Topic 14 Topic 14

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Basic Assessment Questions Question 2 Calculate the number of moles in 9.22 x 10 23 atom iron. Topic 14 Topic 14

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Basic Assessment Questions Answer 1.53 mol Fe Topic 14 Topic 14

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Basic Assessment Questions Question 3 Calculate the mass of 6.89 mol antimony. Topic 14 Topic 14

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Basic Assessment Questions Answer 839g Sb Topic 14 Topic 14

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Basic Assessment Questions Question 4 A chemist needs 0.0700 mol selenium for a reaction. What mass of selenium should the chemist use? Topic 14 Topic 14

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Basic Assessment Questions Answer 5.53g Se Topic 14 Topic 14

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Basic Assessment Questions Question 5 Calculate the number of moles in 17.2 g of benzene (C 6 H 6 ). Topic 14 Topic 14

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Basic Assessment Questions Answer 0.220 mol C 6 H 6 Topic 14 Topic 14

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The Mole: Additional Concepts Topic 14 Topic 14 Additional Concepts

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Molecular formulas For many compounds, the empirical formula is not the true formula. Chemists have learned, though, that acetic acid is a molecule with the formula C 2 H 4 O 2, which is the molecular formula for acetic acid. A molecular formula tells the exact number of atoms of each element in a molecule or formula unit of a compound. The Mole: Additional Concepts Topic 14 Topic 14

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