# C H A P T E R 14 The Ideal Gas Law and Kinetic Theory .

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C H A P T E R   14 The Ideal Gas Law and Kinetic Theory. 14.1  The Mole, Avogadro's Number, and Molecular Mass . Atomic Mass Unit, U.
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﻿C H A P T E R   14 The Ideal Gas Law and Kinetic Theory

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14.1  The Mole, Avogadro\'s Number, and Molecular Mass

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Atomic Mass Unit, U By global assention, the reference component is been the most copious sort of carbon, called carbon-12, and its nuclear mass is characterized to be precisely twelve nuclear mass units, or 12 u.

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Molecular Mass The sub-atomic mass of a particle is the entirety of the nuclear masses of its iotas. For example, hydrogen and oxygen have nuclear masses of 1.007 94 u and 15.9994 u, separately. The atomic mass of a water particle (H 2 O) is: 2(1.007 94 u) + 15.9994 u = 18.0153 u.

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Avogadro\'s Number N A The quantity of iotas per mole is known as Avogadro\'s number N A , after the Italian researcher Amedeo Avogadro (1776–1856):

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Number of Moles, n The quantity of moles n contained in any example is the quantity of particles N in the specimen partitioned by the quantity of particles per mole N An (Avogadro\'s number): The quantity of moles contained in a specimen can likewise be found from its mass.

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14.2  The Ideal Gas Law A perfect gas is an admired model for genuine gasses that have adequately low densities.

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The Ideal Gas Law A perfect gas is an admired model for genuine gasses that have adequately low densities. The state of low thickness implies that the atoms of the gas are so far separated that they don\'t collaborate (aside from amid crashes that are successfully flexible).

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The Ideal Gas Law A perfect gas is a romanticized display for genuine gasses that have adequately low densities. The state of low thickness implies that the atoms of the gas are so far separated that they don\'t associate (with the exception of amid impacts that are viably versatile). The perfect gas law communicates the relationship between the supreme weight (P) , the Kelvin temperature (T) , the volume (V), and the quantity of moles (n) of the gas. Where R is the widespread gas consistent. R = 8.31 J/(mol · K).

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The Ideal Gas Law The steady term R/N An is alluded to as Boltzmann\'s consistent, to pay tribute to the Austrian physicist Ludwig Boltzmann (1844–1906), and is spoken to by the image k : PV = NkT

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14.3  Kinetic Theory of Gasses

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Kinetic Theory of Gasses The weight that a gas applies is created by the effect of its particles on the dividers of the holder.

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Kinetic Theory of Gasses The weight that a gas applies is brought about by the effect of its atoms on the dividers of the holder. It can be demonstrated that the normal translational dynamic vitality of a particle of a perfect gas is given by, where k is Boltzmann\'s consistent and T is the Kelvin temperature.

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Derivation of, Consider a gas atom impacting flexibly with the right mass of the holder and bouncing back from it.

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The compel on the particle is gotten utilizing Newton\'s second law as takes after,

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The drive on one of the atom, According to Newton\'s law of action–reaction, the constrain on the divider is equivalent in greatness to this esteem, however oppositely coordinated. The drive applied on the divider by one atom,

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If N is the aggregate number of particles, since these particles move haphazardly in three measurements, 33% of them on the normal strike the right divider. In this manner, the aggregate compel is: V rms = root-mean-square speed.

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Pressure is drive per unit region, so the weight P following up on a mass of region L 2 is

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Pressure is compel per unit zone, so the weight P following up on a mass of zone L 2 is Since the volume of the crate is V = L 3 , the condition above can be composed as,

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PV = NkT

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EXAMPLE 6 The Speed of Molecules in Air is principally a blend of nitrogen N 2 (sub-atomic mass = 28.0 u) and oxygen O 2 (sub-atomic mass = 32.0 u). Accept that each carries on as a perfect gas and decide the rms speed of the nitrogen and oxygen atoms when the temperature of the air is 293 K.

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The Internal Energy of a Monatomic Ideal Gas

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