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Chapter 14: The Ideal Gas Law and Kinetic Theory Fluids – Chapter 11 - cover 14.1: Molecular Mass, the Mole and Avogadro’s Number. 14.2: The Ideal Gas Law. 14.3: Kinetic Theory of Gases. 14.1 Molecular Mass, the Mole, and Avogadro’s Number To facilitate comparison of the mass of one atom with another, a mass scale known as the atomic mass scale has been established. Fluids – Chapter 11 The unit is called the atomic mass unit (symbol u). Based on the mass of a reference element : the most abundant isotope of carbon, (“carbon-12”), whose atomic mass is defined to be exactly 12u. 1 u 1.6605 10 27 kg The atomic mass is given in atomic mass units. For example, a Li atom has a mass of 6.941u. 14.1 Molecular Mass, the Mole, and Avogadro’s Number One mole of a substance contains as many particles as there are atoms in 12 grams of the isotope carbon-12. Fluids – Chapter 11 The number of atoms per mole is known as Avogadro’s number, NA. N A 6.022 10 mol 23 number of moles 1 number of atoms N n NA 14.1 Molecular Mass, the Mole, and Avogadro’s Number The number of moles contained in a sample can be found from its mass: Fluids – Chapter 11 n mparticle N mparticle N A m Mass per mole The mass per mole (in g/mol) of a substance has the same numerical value as the atomic or molecular mass of the substance (in atomic mass units). For example Hydrogen has an atomic mass of 1.00794 g/mol, while the mass of a single hydrogen atom is 1.00794 u. (1.00794 is the “gram molecular weight” of H) 14.1 Molecular Mass, the Mole, and Avogadro’s Number Example 1 The Hope Diamond and the Rosser Reeves Ruby Fluids – Chapter 11 The Hope diamond (44.5 carats) is almost pure carbon. The Rosser Reeves ruby (138 carats) is primarily aluminum oxide (Al2O3). One carat is equivalent to a mass of 0.200 g. Determine (a) the number of carbon atoms in the Hope diamond. m 44.5 carats0.200 g 1 carat n 0.741 mol Mass per mole 12.011 g mol N nN A 0.741 mol 6.022 10 23 mol1 4.46 10 23 atoms 14.1 Molecular Mass, the Mole, and Avogadro’s Number Example 1 The Hope Diamond and the Rosser Reeves Ruby Fluids – Chapter 11 The Hope diamond (44.5 carats) is almost pure carbon. The Rosser Reeves ruby (138 carats) is primarily aluminum oxide (Al2O3). One carat is equivalent to a mass of 0.200 g. Determine (b) the number of Al2O3 molecules in the ruby. Mass/mole (Al2O3 ) = 2 x Mass/mole (Al) + 3 x Mass/mole (O) N nN A 0.271 mol 6.022 10 23 mol1 1.63 10 23 atoms Chapter 14: The Ideal Gas Law and Kinetic Theory Fluids – Chapter 11 - cover 14.1: Molecular Mass, the Mole and Avogadro’s Number. 14.2: The Ideal Gas Law. 14.3: Kinetic Theory of Gases. 14.2The Ideal Gas Law An ideal gas is an idealized model for real gases that have sufficiently low densities. Fluids – Chapter 11 The condition of low density means that the molecules are so far apart that they do not interact except during collisions, which are effectively elastic. Observations: At constant volume the pressure is proportional to the temperature. 14.2The Ideal Gas Law An ideal gas is an idealized model for real gases that have sufficiently low densities. Fluids – Chapter 11 The condition of low density means that the molecules are so far apart that they do not interact except during collisions, which are effectively elastic. Observations: Pumping up a tire (approximately constant temperature and volume): Adding more gas molecules increases the pressure. 14.2The Ideal Gas Law An ideal gas is an idealized model for real gases that have sufficiently low densities. Fluids – Chapter 11 The condition of low density means that the molecules are so far apart that they do not interact except during collisions, which are effectively elastic. Observations: Pressure of an ideal gas can be increased by reducing the volume of the container. (1 bar = 100 kPa) 14.2The Ideal Gas Law THE IDEAL GAS LAW Fluids – Chapter 11 The absolute pressure of an ideal gas is directly proportional to the Kelvin temperature and the number of moles of the gas and is inversely proportional to the volume of the gas. Universal gas constant: R 8.31 J mol K 14.2The Ideal Gas Law THE IDEAL GAS LAW (Alternative) Fluids – Chapter 11 The absolute pressure of an ideal gas is directly proportional to the Kelvin temperature and the number of molecules of the gas and is inversely proportional to the volume of the gas. R T NkT PV nRT N NA n N NA Boltzmann’s constant: 8.31 J mol K R 23 1 . 38 10 J K k 23 1 N A 6.022 10 mol