Concept Summary

The Gas Phase

• Gases are the least dense phase of matter.
• Gases are fluids and therefore conform to the shapes of their containers.
• Gases are easily compressible.
• Gas systems are described by the variables temperature (T), pressure (P), volume (V), and number of moles (n).
• Important pressure equivalencies include 1 atm = 760 mmHg ≡ 760 torr = 101.325 kPa.
• A simple mercury barometer measures incident (usually atmospheric) pressure. As pressure increases, more mercury is forced into the column, increasing its height. As pressure decreases, mercury flows out of the column under its own weight, decreasing its height.

Ideal Gases

• Standard temperature and pressure (STP) is 273 K (0°C) and 1 atm.
• Equations for ideal gases assume negligible mass and volume of gas molecules.
• Regardless of the identity of the gas, equimolar amounts of two gases will occupy the same volume at the same temperature and pressure. At STP, one mole of an ideal gas occupies 22.4 L.
• The ideal gas law describes the relationship between the four variables of the gas state for an ideal gas.
• Avogadro’s principle is a special case of the ideal gas law for which the pressure and temperature are held constant; it shows a direct relationship between the number of moles of gas and volume.
• Boyle’s law is a special case of the ideal gas law for which temperature and number of moles are held constant; it shows an inverse relationship between pressure and volume.
• Charles’s law is a special case of the ideal gas law for which pressure and number of moles are held constant; it shows a direct relationship between temperature and volume.
• Gay-Lussac’s law is a special case of the ideal gas law for which volume and number of moles are held constant; it shows a direct relationship between temperature and pressure.
• The combined gas law is a combination of Boyle’s, Charles’s, and Gay-Lussac’s laws; it shows an inverse relationship between pressure and volume along with direct relationships between pressure and volume with temperature.
• Dalton’s law of partial pressures states that individual gas components of a mixture of gases will exert individual pressures in proportion to their mole fractions. The total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.
• Henry’s law states that the amount of gas dissolved in solution is directly proportional to the partial pressure of that gas at the surface of a solution.

Kinetic Molecular Theory

• The kinetic molecular theory attempts to explain the behavior of gas particles. It makes a number of assumptions about the gas particles:

  • Gas particles have negligible volume.
  • Gas particles do not have intermolecular attractions or repulsions.
  • Gas particles undergo random collisions with each other and the walls of the container.
  • Collisions between gas particles (and with the walls of the container) are elastic.
  • The average kinetic energy of the gas particles is directly proportional to temperature.

• Graham’s law describes the behavior of gas diffusion or effusion, stating that gases with lower molar masses will diffuse or effuse faster than gases with higher molar masses at the same temperature.

  • Diffusion is the spreading out of particles from high to low concentration.
  • Effusion is the movement of gas from one compartment to another through a small opening under pressure.

Real Gases

• Real gases deviate from ideal behavior under high pressure (low volume) and low temperature conditions.

  • At moderately high pressures, low volumes, or low temperatures, real gases will occupy less volume than predicted by the ideal gas law because the particles have intermolecular attractions.
  • At extremely high pressures, low volumes, or low temperatures, real gases will occupy more volume than predicted by the ideal gas law because the particles occupy physical space.
  • The van der Waals equation of state is used to correct the ideal gas law for intermolecular attractions (a) and molecular volume (b).