15 Ideal Gas (A2)

15.1 The Mole

  • Amount of substance is an SI base quantity with the base unit mol. It is used to express the number of particles (atoms, molecules, or ions) in a substance.

  • Molar quantities are used where one mole of any substance is the amount containing a number of particles of that substance equal to the Avogadro constant, NA, which is approximately equal to 6.022 x 1023 particles/mol.

  • Molar mass is the mass of one mole of a substance and is given in grams per mole (g/mol).

  • The number of moles of a substance is equal to its mass divided by its molar mass.

  • The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas. It is given by the formula PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the absolute temperature.

  • The gas constant R has a value of 8.31 J/mol K and relates the pressure, volume, temperature, and number of particles in a gas.

15.2 Equation of State

  • A gas that obeys the relationship pV ∝ T, where T is the thermodynamic temperature, is known as an ideal gas.

  • The equation of state for an ideal gas is expressed as pV = nRT, where p is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the absolute temperature.

  • The equation of state can also be expressed as pV = NkT, where N is the number of molecules and k is the Boltzmann constant, given by k = R/NA.

15.3 Kinetic Theory of Gases

  1. Gases are made up of a large number of small particles molecules or atoms that are in constant random motion.
  2. The volume of the molecules is negligible compared to the volume of the container
  3. The time of a collision is negligible compared to the time between collisions
  4. There are no forces of attraction or repulsion between the molecules

  • Molecular movement causes the pressure exerted by a gas. The relationship between pressure, volume, and temperature is derived from the kinetic theory of gases as pV = 1/3Nmc2, where N is the number of molecules, m is the mass of each molecule, and c2 is the mean-square speed of the molecules.

  • The root-mean-square speed r.m.s. of a molecule is given by pV = 1/3Nmc2. It is the square root of the average of the squares of the velocities of all the molecules in a gas.

  • Comparing the equations pV = 1/3Nmc2 and pV = NkT, we can deduce that the average translational kinetic energy of a molecule KE = 3/2 kT, where k is the Boltzmann constant and T is the absolute temperature.