CHEM1010 L9.2.2

Gas Pressure and Phase Changes

Partial Pressure

  • Partial pressure is the pressure exerted by an individual gas in a mixture of gases.
  • The total pressure of a gas mixture is the sum of the partial pressures of each gas.
  • Dalton's Law of Partial Pressures
    • The total pressure (P<em>totalP<em>{total}) is the sum of the partial pressures of each gas: P</em>total=P<em>1+P</em>2+P3+P</em>{total} = P<em>1 + P</em>2 + P_3 + …
    • The partial pressure of a gas is determined by multiplying its mole fraction by the total pressure.
      • Mole fraction (X) is the number of moles of a gas divided by the total number of moles of gas in the container: X<em>i=n</em>intotalX<em>i = \frac{n</em>i}{n_{total}}
      • Partial pressure (Pi) = Mole fraction (Xi) * Total pressure (Ptotal): P<em>i=X</em>iPtotalP<em>i = X</em>i * P_{total}
      • This calculation determines how much of a particular gas is available in a mixture.
  • Example: At sea level, the mole fraction of oxygen in the air is 21% (0.21), and the atmospheric pressure is 10510^5 Pascals. Therefore, the partial pressure of oxygen is 0.21105=210.21 * 10^5 = 21 kilopascals.

Atmospheric Pressure

  • Atmospheric pressure is the pressure exerted by the weight of the atmosphere above us.
  • Measured in Pascals (Pa), which is Newtons per square meter (N/m2m^2).
  • One Pascal is equivalent to the force exerted by a $50 note on the palm of your hand.
  • One atmosphere is equivalent to 1.011051.01 * 10^5 Pascals.
  • Atmospheric pressure is measured using a barometer.
    • A barometer measures the height of a column of mercury supported by atmospheric pressure.
  • At sea level, atmospheric pressure is approximately 10510^5 Pascals or 100 kilopascals.
  • Examples of Pressure Variations:
    • Mount Everest: The mole fraction of oxygen is still 21%, but the total pressure is only 0.331050.33 * 10^5 Pascals, resulting in a partial pressure of oxygen of 7 kilopascals. Lower oxygen levels can lead to hypoxia and impaired cognitive function.
    • Mariana Trench: The deepest part of the ocean, with immense pressure due to the water above.
    • Underwater Pressure: Every 10 meters of depth increases the pressure by approximately 1 atmosphere (100 kilopascals).
      • At 30 meters underwater, the total pressure is 400 kilopascals (100 kPa atmosphere + 300 kPa water). The partial pressure of oxygen is 84 kilopascals (0.21 * 400 kPa), which can lead to oxygen toxicity if the gas mixture is not properly managed.
  • Changes in atmospheric pressure affect human physiology.
    • In space, where there is no atmospheric pressure, people grow taller.
    • Deep-sea diving requires careful management of gas mixtures to avoid oxygen toxicity and decompression sickness (“the bends”).

Phase Diagrams

  • Phase diagrams show the different phases of a substance (solid, liquid, gas) under various conditions of temperature and pressure.
  • Heating a substance adds energy to its molecules, causing them to move more.
    • Solids melt into liquids, and liquids vaporize into gases as temperature increases.
  • The state changes with temperature and pressure. For example, a solid turns into liquid at 273K, the liquid starts to get hotter, and then once the liquid reaches 373K it turns into a gas.
  • Increased pressure can hinder the transition from liquid to gas.
  • Decreased pressure can cause solids to sublimate directly into a gas
  • Key Features of Phase Diagrams
    • Lines indicate phase transitions (melting, boiling, sublimation).
    • Triple point: The specific temperature and pressure at which all three phases (solid, liquid, gas) coexist in equilibrium.
      • For water, the triple point is at 0.006 atmospheres and approximately 273 Kelvin.
      • Useful for calibrating thermometers and identifying unknown substances.
    • Critical point: The temperature and pressure above which a distinct liquid phase does not exist.
      • Above the critical point, a substance exists as a supercritical fluid, which has properties of both liquids and gases.
      • Supercritical fluids are used in extraction, purification, sterilization, and chemical reactions.
  • Phase Changes
    • Freezing: Liquid to solid.
    • Melting: Solid to liquid.
    • Vaporization: Liquid to gas.
    • Condensation: Gas to liquid.
    • Sublimation: Solid directly to gas.
    • Deposition: Gas directly to solid.
  • The solid-liquid line represents the melting/freezing point at different pressures.
  • The liquid-gas line represents the boiling/condensation point at different pressures.
  • The solid-gas line represents the sublimation/deposition point at different pressures.
  • Unique Properties of Water
    • The solid-liquid line of water has a negative slope, indicating that increasing pressure on ice will cause it to melt.
      • This is because ice has a lower density than liquid water due to hydrogen bonding, which creates intermolecular spaces.
      • Putting ice under pressure favors the formation of the denser liquid phase.
  • Phase diagrams can be complex for substances with multiple solid phases or crystalline structures, such as diamond and iron, due to different arrangements of molecules and intermolecular spaces.