Chapter 10 Notes- Gases

10.1 Characteristics of Gases [p.394]

  1. All substances which are gases have similar characteristics while maintaining their individual physical and chemical properties.
  2. Examples of gases
  3. Monoatomic gases (noble gases)
  4. Diatomic gases (hydrogen, nitrogen, oxygen, fluorine, chlorine)
  5. Low molar mass molecular compounds such as methane, carbon dioxide, ammonia, see others on p.394
  6. Vapors- gaseous state above a liquid
  7. Characteristics
  8. Gases expand to fit container (volume of gas = volume of container)
  9. Compressible
  10. From homogeneous mixtures regardless of the component gases
  11. Maintain individual properties because particles in gas phase are far apart

10.2 Pressure[p.395]

  1. General Definitions
  2. Pressure – force that pushes on something
  3. Basic formula
  1. Atmospheric Pressure and the Barometer
  2. Atmospheric pressure is the result of gases molecules being pulled to earth by gravitational forces
  3. KE of gas particles prevent the molecules from piling up on the earth surface
  4. Result of gas molecules tiny masses
  5. Atmospheric pressure is based on F=ma where “m” stands for the mass of an object and “a” is gravitational acceleration (9.8 m/s2)
  6. Unit used is N/m2 or Pascal (Pa)
  7. Named after Blaise Pascal
  8. Derived unit bar = 105 Pa
  9. Atmospheric pressure at sea level is about 100 kPa or 1 bar
  10. Atmospheric pressure varies with altitude and weather
  11. Barometer- measures atmospheric pressure
  12. Standard atmospheric pressure

1 atm = 760 mm Hg= 760 torr = 1.01325 x 105 Pa = 101.325 kPa = 14.7 psi

  1. Manometer- instrument used to measure pressure of an enclosed gas

10.3 The Gas Laws [p. 399]

  1. Four variables needed to define physical condition of a gas
  2. Temperature
  3. Pressure
  4. Volume
  5. Amount of gas
  6. The Pressure-Volume Relationship: Boyle’s Law
  7. Volume of a gas is inversely proportional to the pressure when temperature and amount are held constant
  8. Equation
  9. PV = constant
  10. P1V1=P2V2
  11. The Temperature-Volume Relationship: Charles’ Law
  12. Volume of gas is directly proportional to its absolute temperature
  13. Must use Kelvin scale
  14. 0 K = -273.25°C = absolute zero
  15. Equation
  16. V = constant x T
  17. The Quantity-Volume Relationship: Avogadro’s Law
  18. Based on research performed by Gay-Lussac and Avogadro
  19. Law of combining volumes- numbers of combined gases are whole number ratios
  20. Avogadro’s Hypothesis- equal volumes at equal temperatures and pressures contain equal number of molecules
  21. Avogadro’s Law volume of gas is proportional to amount of particles if temperature and pressure are constant
  22. Equation

V= constant x n

10.4 The Ideal-Gas Equation [p.402]

  1. General Information
  2. Combined Gas Law: combines Boyle’s, Charles’, and Avogadro’s Law
  1. If you add the proportionally constant you get
  1. Ideal –gas law equation

PV = nRT

  1. Ideal gas – hypothetical gas whose pressure, volume, amount, and temperature can be described by the ideal-gas law
  2. “R” is the gas constant
  3. Multiple values depending on units used
  4. Temp is always in Kelvin
  5. Most common unit is R=0,08206 L-atm/ mol-K or R= 8.314 J/mol-K
  1. Under ideal conditions 1 mole of gas = 22.14 L
  2. “STP” stands for standard temperature and pressure 0°C or 100 K and 1atm or 101.325 kPa
  1. Relating the Ideal-Gas Equation and the Gas Laws

10.5Further Applications of the Ideal-Gas Equation [p.406]

  1. Gas Densities and Molar Mass
  2. Can use ideal gas law and molar mass to solve for density

Where “M” is the molar mass

Then

Where “d” is density

  1. Rearrange density equation above to solve for molar mass
  1. Volumes of Gases in Chemical Reactions can be found using mole relationships and ideal gas law

10.6_Gas Mixtures and Partial Pressures [p.410]

  1. General Information
  2. Dalton’s Law of partial pressures- the pressure of a misxyure is equal to the sun of the partial pressures for each component gas
  3. Pt= P1 + P2 + P3 + …
  4. Equation implies that each gas acts independently
  5. Total pressure can be found by using the ideal gas law along with the sum of the moles of each component gas
  1. Partial Pressures and Mole Fractions
  2. Mole fraction (Xt) = the moles of an individual gas per total moles of gases in a mixture (n1/n2)
  3. Equation
  1. Collecting Gases over Water

Ptotal = Pgas + Pwater

10.7 Kinetic Molecular Theory [p. 414]

  1. Kinetic Molecular Theory explains the behavior of gases as conditions change
  2. Gases consist of large numbers of particles that are in continuous, random motion.
  3. Negligible volume relative to total volume of container
  4. Negligible attractive and repulsive forces between particles
  5. Collisions are elastic
  6. Average KE is proportional to the absolute temperature
  7. Distribution of Molecular Speed
  8. Particles of gas in a contained sample vary in speed due to collisions
  9. The average kinetic energy “ε” = the average rate of all the particles
  10. Root- mean-square (rms) “u” = the speed of a molecule possessing the average KE

ε = ½ mu2

  1. Both Average KE and Root-mean- square increase in speed with an increase in temperature
  1. Application to the Gas Laws
  2. Effects of volume increase at a constant temperature- average KE and rms remain constant, therefore an increase in the size of the container will result in fewer collisions decreasing the pressure
  3. Effects of temperature increase at constant volume- inc. temp, increases ave KE and rms resulting in more collisions with the walls of the container leading to an increase in pressure

10.8 Molecular Effusion and Diffusion [p. 417]

  1. Equation showing that lower molar mass gases have a higher root mean square speed
  1. Graham’s Law of Effusion
  2. Effusion- escape of gas through a tiny hole
  3. Rate of escaping gas is inversely proportional to the molar mass of the gas
  4. High molar mass = lower rate
  5. Equation
  1. Diffusion and Mean Free Path
  2. Spreading a gas throughout an area
  3. Lower molar mass gases diffuse at a higher rate
  4. Rate of diffusion can be affected by the number of particles in the container
  5. Higher the number the shorter the mean free path (lots of collisions slows motion down)
  6. Lower the number of particles the longer the mean free path

10.9 Real Gases: Deviations from Ideal Behavior [p. 420]

  1. Deviations of a real gas increase from ideal behavior when:
  2. High pressure ( particles collide more often)
  3. Low temperature (particles are too close)
  4. Real gases behave more ideally at low pressure and high temperatures
  5. The van der Waals Equation
  6. Accounts for the particle attraction of a real gas “a” and the finite volume of a real gas “b”
  7. Equation

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