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Topic | Discussion | Learning Aids
Atomic mass unit Molecular mass | 14.1 MOLECULAR MASS, THE MOLE, AND AVOGADRO’S NUMBER Each element in the periodic table is assigned an atomic mass. One atomic mass unit (u) is exactly one-twelfth the mass of an atom of carbon-12. The molecular mass of a molecule is the sum of the atomic masses of its atoms. |
Number of moles | The number of moles n contained in a sample is equal to the number of particles N (atoms or molecules) in the sample divided by the number of particles per mole NA

Avogadro’s number Number of moles | where NA is called Avogadro’s number and has a value of . The number of moles is also equal to the mass m of the sample (expressed in grams) divided by the mass per mole (expressed in grams per mole):

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 one of its particles (in atomic mass units). |
Mass of a particle | The mass mparticle of a particle (in grams) can be obtained by dividing the mass per mole (in g/mol) by Avogadro’s number:

Ideal gas law | 14.2 THE IDEAL GAS LAW The ideal gas law relates the absolute pressure P, the volume V, the number n of moles, and the Kelvin temperature T of an ideal gas according to

| (14.1)

Universal gas constant Ideal gas law | where is the universal gas constant. An alternative form of the ideal gas law is

| (14.2)

Boltzmann’s constant | where N is the number of particles and is Boltzmann’s constant. A real gas behaves as an ideal gas when its density is low enough that its particles do not interact, except via elastic collisions. |
Boyle’s law | A form of the ideal gas law that applies when the number of moles and the temperature are constant is known as Boyle’s law. Using the subscripts “i”and “f” to denote, respectively, initial and final conditions, we can write Boyle’s law as

| (14.3)

Charles’ law | A form of the ideal gas law that applies when the number of moles and the pressure are constant is called Charles’ law:

| (14.4)

Maxwell speed distribution Average translational kinetic energy | 14.3 KINETIC THEORY OF GASES The distribution of particle speeds in an ideal gas at constant temperature is the Maxwell speed distribution (see Figure 14-9). The kinetic theory of gases indicates that the Kelvin temperature T of an ideal gas is related to the average translational kinetic energy of a particle according to

| (14.6)

Root-mean-square speed | where vrms is the root-mean-square speed of the particles. |
Internal energy | The internal energy U of n moles of a monatomic ideal gas is

| (14.7)

The internal energy of any type of ideal gas (e.g., monatomic, diatomic) is proportional to its Kelvin temperature.
Fick’s law of diffusion | 14.4 DIFFUSION Diffusion is the process whereby solute molecules move through a solvent from a region of higher solute concentration to a region of lower solute concentration. Fick’s law of diffusion states that the mass m of solute that diffuses in a time t through the solvent in a channel of length L and cross-sectional area A is

| (14.8)

where is the solute concentration difference between the ends of the channel and D is the diffusion constant.
Use Self-Assessment Test 14.1 to evaluate your understanding of Sections 14.1–14.4.

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