Kinetic theory of gases

• The kinetic theory of gases?states that molecules in gases are constantly moving
• The theory makes the following assumptions:
  • That gas molecules are moving very fast and randomly
  • That molecules hardly have any volume
  • That gas molecules do not attract or repel each other (no?intermolecular forces)
  • No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)
  • The temperature of the gas is related to the average kinetic energy of the molecules

   

• Gases that follow the kinetic theory of gases are called?ideal gases
• However, in reality gases do not fit this description exactly?but?may come very close and are called?real gases

Ideal gases

• The volume that an ideal gas occupies depends on:
  • Its pressure
  • Its temperature

   

• When a gas is?heated?(at constant pressure) the particles gain more?kinetic energy?and undergo more?frequent collisions?with the container wall
• To keep the?pressure constant, the molecules must get further apart and therefore the?volume increases
• The?volume?is therefore?directly proportional?to the?temperature?(at constant pressure)

The volume of a gas increases upon heating to keep a constant pressure (a); volume is directly proportional to the temperature (b)

Limitations of the ideal gas law

• At very?low?temperatures?and?high?pressures?real gases do not obey the kinetic theory as under these conditions:
  • Molecules are close to each other
  • There are instantaneous dipole- induced dipole or permanent dipole- permanent dipole forces between the molecules
  • These attractive forces pull the molecules away from the container wall
  • The volume of the molecules is not negligible

   

• Real gases therefore do not obey the following kinetic theory?assumptions?at low temperatures and high pressures:
  • There is zero attraction between molecules (due to attractive forces, the?pressure?is?lower?than expected for an ideal gas)
  • The volume of the gas molecules can be ignored (volume?of the gas is?smaller?than expected for an ideal gas)

   

Ideal gas equation

• The?ideal gas equation?shows the relationship between pressure, volume, temperature and number of moles of gas of an ideal gas:

PV = nRT

P = pressure (pascals, Pa)

V = volume (m3)

n = number of moles of gas (mol)

R = gas constant (8.31 J K-1?mol-1)

T = temperature (kelvin, K)

Answer

Step 1:?Rearrange the ideal gas equation to find volume of gas

Step 2:?Calculate the volume the oxygen gas occupies

• • P?= 220 kPa = 220 000 Pa
  • n?= 0.781 mol
  • R?= 8.31 J K-1?mol-1
  • T?= 21?oC = 294 K

Answer

Step 1:?Rearrange the ideal gas equation to find the number of moles of gas

Step 2:?Calculate the number of moles of gas

p = 300 kPa = 300 000 Pa

V = 1000 cm3?= 1 dm3?= 0.001 m3

R = 8.31 J K-1?mol-1

T = 23?oC = 296 K

Step 3:?Calculate the molar mass using the number of moles of gas