Gases

Key Ideas

  • Kinetic energy: the energy of all motion
  • Elastic collision: the conservation of kinetic energy during collisions

Kinetic Molecular Theory

Gases are in continuous, chaotic motion and, except during elastic collisions, are widely separated from each other

  • Gases are widely separated with no intermolecular bonding between molecules
  • Rapid, chaotic, random movement in straight lines until they collide with another particle or the wall of the container
  • When gases collide, kinetic energy can be transferred from one particle to another, but no energy is lost

Pressure

Pressure is the measure of the force exerted by the particles on the walls of the container during collisions.
Pressure \(=\frac{Force}{Area}\) (The force per unit area of the container)

Unit Symbol Conversion to kPa
Kilopascal kPa 1
Pascal Pa 1000 Pa
Atmosphere atm 0.987 atm
Bar bar 1 bar
Millimeters of Mercury mmHg 750 mmHg

The Universal Gas Equation

For all gas equations, units must be kept constant

  • P: Pressure is in kPa
  • V: Volume is in L
  • n: mol is in mol
  • T: Temperature is in Kelvin (\(0K\approx -273^oC\))
  • R: The gas constant is \(=8.31\,J\,K^{-1}\,mol^{-1}\)

Volume and Pressure

  • Given an amount of gas at a constant temperature, the volume will be inversely proportional to the pressure
  • \(P\propto \frac{1}{V}\)
  • \(P_1V_1=P_2V_2\)

Volume and Temperature

  • Given an amount of gas at a constant pressure, the volume of the gas will be directly proportional to the temperature
  • \(V\propto T\)
  • \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)

Combined Gas Law

  • \(\frac{P_1\times V_1}{n_1\times T_1}=\frac{P_2\times V_2}{n_2\times T_2}\)

Universal Gas Equation

  • \(P\times V=n\times R\times T\)

Molar Volume of Gas

  • If an amount of gas has a constant pressure and a constant temperature, the volume of the gas will be the same. If the gas is at SLC - Standard Laboratory Conditions (\(100kPa,\,25^oC\)) then \(1\,\text{mol}\) of gas occupies \(24.8L\)

Dalton's Law of Partial Pressure

The total pressure exerted by a mixture of gases is equal to the sun of all the partial pressures of the constituent gases

  • \(P_{TOTAL}=P_1+P_2+P_3+P_{...}\)