15.1.3 Ideal Gas Equation

• The equation of state for an ideal gas (or the ideal gas equation) can be expressed as:

pV = nRT

• The ideal gas equation can also be written in the form:

pV = NkT

• An ideal gas is therefore defined as:

A gas which obeys the equation of state pV = nRT at all pressures, volumes and temperatures

Step 1:            Write down the ideal gas equation

Since the number of moles (n) is required, use the equation:

pV = nRT

Step 2:            Rearrange for the number of moles n

Step 3:            Substitute in values

V = 8.3 × 10³ cm³ = 8.3 × 10³ × 10^-6 = 8.3 × 10^-3 m³

T = 15 ^oC + 273.15 = 288.15 K

• The Boltzmann constant k is used in the ideal gas equation and is defined by the equation:

• Where:
  • R = molar gas constant
  • N_A = Avogadro’s constant

• Boltzmann’s constant therefore has a value of

• The Boltzmann constant relates the properties of microscopic particles (e.g. kinetic energy of gas molecules) to their macroscopic properties (e.g. temperature)
  • This is why the units are J K^-1

• Its value is very small because the increase in kinetic energy of a molecule is very small for every incremental increase in temperature