CHEM 205 lecture 13

• Gas

  Substance normally in gaseous state at ambient temperature and pressure
• Vapour


  Gaseous form of substance that is normally a solid or liquid at ambient temperature and pressure
• Particles in a gas

  • Very far apart
  • Lowest density state of matter
  • Particles can be squeezed closer together (compressible)
  • Particles don't interact much with each other (simple behaviours)
• Gas pressure


  Force caused by gas particles colliding with container walls
• Pressure


  Force per unit area
• Calculating force


  Force = mass x acceleration

  = mass x (velocity change/ unit time)

  1 Newton = 1 kg x (m/s2)
• Unit of pressure


  Pascals: 1 Pa = 1 N/m2
• Atmospheric pressure
• Measuring pressure with a barometer

  Dish or Hg open to atmosphere

  Evacuated tube inverted into Hg

  Hg rises until PHg(gravity) = Patm

  P = height of Hg column
• Measuring pressure with a manometer

  1. tube with Hg

  Sealed on one end

  Gas flask on other end

  P = difference in height of two ends
• Ideal gas law


  PV=nRT

  P = pressure

  V = volume

  n = number moles

  R = gas constant = 8.314 J/mol-1K-1 or 0.08206 L atm mol-1K-1

  T = temperature
• Gases behave ideally if their particles don't interact much
• In gases, the kinetic energy of the particles is directly related to the temperature of the gas. As the temperature of a gas increases, the motion of its particles increases, which means their kinetic energy increases. This is because the higher the temperature, the more energy the particles have to move.

  
• Ideal behaviour for a gas occurs at low temperatures (low concentration of particles) and high temperatures (particles moving quickly)
• Boyle's law


  P1V1=P2V2 when n and T are constant
• Charles' law


  V1/T1=V2/T2 when n and P are constant
• Dalton's law of partial pressure

  For mixture of gases in containers Ptotal = P1 + P2 + P3 ... each gas contributes to total pressure

  Partial pressure of each gas is the same as if alone in container

  P1 depends only on number of moles of gas 1 (use PV=nRT)
• Real gases show non-ideal behaviours at high pressure, smaller volume, and low temperature
• Reasons for non-ideal gas behaviour

  High pressure or small volume: Particles are closer together, polar molecules attract each other fairly strongly, nonpolar molecules interactions are small but significant

  Low temperature: Particles are only moving slowly, if not enough thermal energy to break away from intermolecular interactions, gas will not behave ideally

  
• Van der Waals equation

  Accurately describes real gas behaviour

  V2 = compensate for intermolecular forces: real gas particles waste some energy by interacting with each other, observed pressure is lower than if behaving ideally

  nb = volume of particles correction: real gas particles do not each have zero volume, total volume occupied by real gas sample therefore larger than predicted for ideal gas

  
• Kinetic molecular theory of gases

  • Gases consist of particles (atoms, molecules), separated by distances much greater than size of particles

  Particles in constant, random, rapid motion, collide with each other and walls of container

  Temperature determines the average kinetic energy of particles

  
• Kinetic energy


  1/2 m u2

  m = mass

  u = average velocity (speed)
• Distribution of molecular velocities at a given temperature: some have high kinetic energy, most have average, others have low
• Heavier molecules are slower than lighter molecules at the same temperature
• Diffusion


  Mixing of gases due to random molecular motions

  Heavier molecules diffuse and effuse more slowly

  
• Graham's law


  Rate for A / rate for B
• Effusion


  Movement of gas through tiny holes, faster for lighter molecules since they hit the barrier more often
• Balloons: Molecules effuse through holes in rubber, rate (moles/time) is proportional to temperature but inversely proportional to molar mass
• Reducing greenhouse gases by capturing carbon dioxide
• Greenhouse gases prevent heat from leaving the atmosphere, leading to global warming
• Industrial activity produces more carbon dioxide than plants can consume
• Charles' Law


  Describes the relationship between the volume (V) and temperature (T) of a gas, assuming the pressure (P) and number of moles (n) are constant
• Charles' Law


  1. V1/T1 = V2/T2

  2. If the temperature of a gas increases, the volume of the gas will also increase, and vice versa
• Boyle's Law


  Describes the relationship between the volume (V) and pressure (P) of a gas, assuming the temperature (T) and number of moles (n) are constant
• Boyle's Law


  1. P1V1 = P2V2

  2. If the pressure of a gas increases, the volume of the gas will decrease, and vice versa
• Charles' Law

  Deals with the relationship between volume and temperature
• Boyle's Law


  Deals with the relationship between volume and pressure
• Both Charles' Law and Boyle's Law assume that the number of moles and the other variable are constant
• Bohr's model


  A model of the atom that was proposed by Niels Bohr in 1913
• Bohr's model


  • It is a relatively simple model that describes the behavior of electrons in an atom