Type: Single Date: Kinetic Theory of Gases. Homework: Read (14.1), Do CONCEPT Q. # (1), Do PROBLEMS # (2, 3, 5) Ch. 14

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1 Type: Single Date: Objective: Kinetic Theory of Gases Homework: Read (14.1), Do CONCEPT Q. # (1), Do PROBLEMS # (2, 3, 5) Ch. 14

2 AP Physics Mr. Mirro Kinetic Theory of Gases Date Unlike the condensed phases of matter solid and liquid the atoms or molecules that make up a gas DO NOT move around relatively fixed positions. Rather, the molecules of a gas move freely and rapidly in a chaotic swarm. A confined gas exerts a force on the walls of its container, because the molecules are zipping around inside the container, striking the walls and rebounding. The magnitude of the force per unit area, also known as pressure, is expressed as the familiar: P = F measured in N/m 2 or Pa A Often we wish to compare the mass of one atom with another. To facilitate the comparison, the atomic mass scale relates the mass of an atom s atomic mass unit (u or amu) to its equivalent SI units in kilograms (kg). That is, 1 amu 1 u = 1.66 x kg For example, a Magnesium atom (Mg) has an atomic mass of u, while the atomic mass for a lithium atom (Li) is u. Thus, atomic Magnesium is more massive than atomic Lithium by a factor of: Ratio [Mg/Li] = Macroscopic amounts of materials contain large numbers of atoms or molecules. Even in a small volume of gas, the number of molecules is enormous. Therefore, it is convenient to group and express such large numbers of molecules in terms of moles. One gram-mole of a substance contains as many particles, atoms or molecules as there are atoms in 12 grams of the isotope of carbon-12. Experiments have consistently shown that 12 grams of carbon-12 contain x number of atoms per mole is known as Avogadro s Number (N A ). atms/mol. The Thus, the number of moles (n) contained in any sample is the number of particles (N) in the sample, divided by the number of particles per mole (N A ). # moles = # of particles N = n Avogadro s # N A Although defined in terms of carbon atoms, the concept of a mole can be applied to ANY collection of objects by noting that one mole contains Avogadro s Number of objects. one mole (1 mol) of atomic sulfur contains x sulfur atoms one mole (1 mol) of water contains x H 2 O molecules one mole (1 mol) of sand contains x grains of sand

3 Technically speaking, by definition, 12 grams of Carbon-12 (C 12 ) have x say that Carbon-12 has a molar mass of 12 grams per mole. atoms, therefore we However, practically, speaking, one mole of any substance has a mass in grams that defines its atomic or molecular mass. For example, the mass of a carbon-12 atom has a mass of exactly 12 atomic mass units (amu s), and a mole of these atoms has a mass of 12 grams. C 6 Notice that the atomic mass of Carbon-12 is 12 amu or 12 u Similarly, considering the molar mass of Helium-4 (He 4 ). That is, there are g for every 1-mole of the substance (He 4 ) He By contrast, it can be shown that one mole (mol) of carbon dioxide has a mass of 44 grams: Each CO 2 molecule consists of one Carbon and two Oxygen atoms. Since Oxygen has an atomic mass of 16, it has a gram-molecular weight of 16 grams per mole. Therefore, combining the gram-molecular weights of both the Carbon and the Oxygen, we have: Thus, gram-molecular weight = 12 g/mol + 2(16 g/mol) = ( ) g/mol = 44 grams per mol This is useful in that we can now determine the mass of a mole of gas in grams (g) and ultimately in kilograms (kg). The Mass of a Mole of Ideal Gas The mass (m) of a substance is related to the number of moles (n) of that substance by the expression: m = n M Where M is the molar mass, usually expressed in grams per mole (g/mol). For example, two moles (2 mol) of neon (Ne) gas [m = u] have mass, m Neon = n M = (2 mol) * g = g Since 1 kg = 1000 g = kg

4 AP Physics Mr. Mirro Kinetic Theory of Gases Date Ex 1: Sodium (Na) has an atomic mass of u, while the atomic mass for a Beryllium atom (Be) is u. By what factor is Sodium more atomically massive than Beryllium? [General] Ex 2: How many particles (N) are there in 5.5 moles of any substance? [General] Ex 3: If x molecules of a certain substance exist, how many moles are in this sample? [General] Ex 4: If hydrogen has an atomic mass of u, [Giancoli13.14] a) Determine the mass of one mole (molar mass) of hydrogen in kilograms per mole. b) What is the mass of a single hydrogen atom in kilograms? FTBO

5 Ex 5: The Rosser Reeves ruby (138 carats), primarily consists of aluminum oxide (Al 2 O 3 ). If one carat is equivalent to a mass of grams, and the atomics masses of Aluminum and Oxygen are u and u respectively, determine the number of aluminum oxide molecules in the ruby. [Cutnell14.1]

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