Chemistry

• Matter exists in three states: solid, liquid and gaseous
• Gaseous state


  • Molecules are separated wide apart in empty space
  • Molecules are free to move about throughout the container
• Characteristics of a gas

  • Expansibility
  • Compressibility
  • Diffusibility
  • Ability to exert Pressure
• Parameters of a gas

  • Volume (V)
  • Pressure (P)
  • Temperature (T)
  • Number of moles (n)
• Boyle's Law


  At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure
• If the pressure is doubled

  The volume is halved
• Charles's Law


  At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature
• If the temperature is doubled

  The volume is doubled
• Ideal Gas


  Any gas that obeys the equation of state PV = nRT
• Ideal Gas Equation


  PV = nRT
• The ideal gas equation is called an equation of state for a gas because it contains all the variables (T,P,V and n) which describe completely the condition or state of any gas sample
• Molar gas constant (R)

  0.0821 atmLmol-1K-1 or 8.314 Jmol-1K-1
• Calculating the number of moles (n)

  n = mass / molar mass
• Dalton's Law of Partial Pressure

  The total pressure (P) of a mixture of gases is equal to the sum of the partial pressures of all the gases present
• Total Pressure, PT


  PT = P1 + P2 + ... Pn
• Mole Fraction


  The ratio of the number of moles of a component to the total number of moles of all components in a mixture
• Partial Pressure, Mole Fraction and Total Pressure

  PA = XA Ptotal
• Kinetic Molecular Theory (KMT) of Gases

  • Gas consists of extremely small discrete particles called molecules
  • Molecules are in constant random motion with high velocities
  • Molecules move in straight lines with uniform velocity and change direction on collision
  • Molecules can move freely, independent of each other
  • Collisions are perfectly elastic
  • Pressure is caused by the hits recorded by molecules on the walls of the container
  • Average kinetic energy of gas molecules is directly proportional to absolute temperature
• Kinetic Gas Equation


  PV = 1/3 mNu2
• Collisions


  • Perfectly elastic
  • No loss of kinetic energy during collision
• Pressure of a gas

  Caused by the hits recorded by molecules on the walls of the container
• Average kinetic energy of gas molecules

  • Directly proportional to absolute temperature
  • Same at a given temperature
• Fundamental Equation for the Pressure of a Gas (PV= 1/3mNu2)
• Kinetic Gas Equation in terms of Kinetic Energy

  PV = 2/3Ne = 2/3E
• General ideal gas equation is PV= nRT
• For one mole of a gas, the kinetic energy of N molecules is E = 3RT/2
• Deduction of Gas Laws from the Kinetic Gas Equation

  1. Boyle's Law

  2. Charles' Law

  3. Avogadro's Law

  4. Graham's Law of Diffusion
• Differences between Ideal and Real gases

  • Ideal gas is infinitely compressible, real gas will condense to a liquid
  • Ideal gas loses no energy to container, real gas conducts and radiates heat
  • No attraction between ideal gas molecules, real gas has particle attractions
  • Ideal gas follows PV=nRT, real gas does not
• Compressibility Factor (Z)


  • Explains the extent to which a real gas departs from ideal behaviours
  • For ideal gas, Z=1
  • For real gas, Z can be <1 or >1
  • Difference between 1 and Z determines deviation from ideality
• At low pressures and fairly high temperatures, real gases show nearly ideal behavior
• At low temperatures and sufficiently high pressures, a real gas deviates significantly from ideality
• The closer the gas is to the liquefaction point, the larger the deviation from ideal behavior
• Van der Waals Equation

  • Corrects the pressure (P) and volume (V) factors in the ideal gas equation to make it applicable to real gases
  • Volume correction: (V-nb) where b is the excluded volume
  • Pressure correction: P = Pideal - x where x is determined by the force of attraction between molecules
• Excluded volume


  Not equal to the actual volume of the gas molecules
• Pressure Correction


  1. Molecule in the interior of a gas is attracted by other molecules on all sides, but a molecule about to strike the wall is attracted by molecules on one side only, resulting in reduced velocity and actual pressure P being less than ideal pressure Pideal

  2. P = Pideal - x

  3. x = an^2/V^2, where a is a proportionality constant and n is the total number of gas molecules in volume V
• Vander Waals equation


  (P + an^2/V^2)(V - nb) = nRT, where a and b are Vander Waals constants characteristic of each gas
• Determination of a and b

  1. a = (pressure)(volume)^2/(mole)^2 = Nm4mol-2

  2. b = volume/mole = m3mol-1
• Vander Waals equation explains satisfactorily the general behaviour of real gases, but fails to give exact agreement with experimental data at very high pressures and low temperatures
• Excluded volume is not equal to the actual volume of the gas molecules
• Pressure correction is due to attractive forces between molecules striking the wall and molecules pulling them inward