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

Avogadro's Number NA The number of atoms per mole is known as Avogadro's number NA, after the Italian scientist Amedeo Avogadro (1776–1856): NA = 6.0221415 x 1023 mol-1

Atomic Mass Unit, U By international agreement, the reference element is chosen to be the most abundant type of carbon, called carbon-12, and its atomic mass is defined to be exactly twelve atomic mass units, or 12 u. 1 u = 1/(Avagadro’s Number) grams 1 u = 1/(6.0221415 x 1023) grams

Number of Moles, n 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 NA (Avogadro's number): The number of moles contained in a sample can also be found from its mass.

The Ideal Gas Law An ideal gas is an idealized model for real gases that have sufficiently low densities. The condition of low density means that the molecules of the gas are so far apart that they do not interact (except during collisions that are effectively elastic). The ideal gas law expresses the relationship between the absolute pressure (P), the Kelvin temperature (T), the volume (V), and the number of moles (n) of the gas. Where R is the universal gas constant. R = 8.31 J/(mol · K).

The Ideal Gas Law The constant term R/NA is referred to as Boltzmann's constant, in honor of the Austrian physicist Ludwig Boltzmann (1844–1906), and is represented by the symbol k: PV = NkT

Kinetic Theory of Gases The pressure that a gas exerts is caused by the impact of its molecules on the walls of the container. It can be shown that the average translational kinetic energy of a molecule of an ideal gas is given by, where k is Boltzmann's constant and T is the Kelvin temperature.

Derivation of, Consider a gas molecule colliding elastically with the right wall of the container and rebounding from it. Derivation Video

EXAMPLE 6 The Speed of Molecules in Air Air is primarily a mixture of nitrogen N2 (molecular mass = 28.0 u) and oxygen O2 (molecular mass = 32.0 u). Assume that each behaves as an ideal gas and determine the rms speed of the nitrogen and oxygen molecules when the temperature of the air is 300 K.

Distribution of Molecular Speeds The Maxwell distribution curves for molecular speeds in oxygen gas at temperatures of 300 and 1200 K.

The Internal Energy of a Monatomic Ideal Gas