Partial Pressure & Gas–Liquid Equilibrium

Concept Review: Partial Pressure

  • Partial pressure quantifies the contribution of a single gas species to the total pressure of a gaseous mixture.

  • It provides a way to describe “how much” of that gas is present—either

    • in the gas phase itself (e.g.
      atmospheric air), or

    • dissolved in a liquid that is in equilibrium with the overlying gas.

  • The idea dates back to Dalton’s Law of Partial Pressures, which states that the total pressure of a gas mixture equals the sum of the partial pressures of its individual components.

Atmospheric Example: Oxygen and Nitrogen

  • At sea level, atmospheric (barometric) pressure is P_{\text{atm}} = 760 \, \text{mm Hg}.

  • Composition of dry air (approximate):

    • Oxygen fraction: F{O2} = 0.21 (≈21 %)

    • Nitrogen fraction: F{N2} = 0.79 (≈79 %)

  • Formula for the partial pressure of a component:
    P_i = X_i \cdot P_{\text{total}}

  • Applying to oxygen:
    P{O2} = 760 \, \text{mm Hg} \times 0.21 \approx 160 \, \text{mm Hg}

  • A similar calculation for nitrogen would yield P{N2} \approx 760 \times 0.79 \approx 600 \, \text{mm Hg} (numerical value mentioned tangentially but not explicitly calculated in the transcript).

Thought Experiment: Interface Between Air and Water

  • Imagine a container of water open to the atmosphere:

    • The gas phase above the water contains oxygen molecules moving randomly.

    • Some O₂ molecules collide with the water surface and dissolve; others leave (escape) from the liquid back to the gas phase.

  • A dynamic equilibrium forms when the rate of O₂ molecules entering the water equals the rate of O₂ molecules leaving.

  • Under equilibrium, the amount of O₂ dissolved in the water can be characterized by the same partial pressure as that of the gas above it.

    • Hence, if P{O2} = 160 \, \text{mm Hg} in the air, we say the dissolved O₂ in water is also at P{O2} = 160 \, \text{mm Hg}.

    • The actual concentration (e.g.
      in \text{mL O}_2 / \text{L water} or \text{mmol/L}) would depend on Henry’s Law constant (not covered explicitly in this clip), but the partial pressure remains the key descriptor.

Key Takeaways & Connections

  • Partial pressure is a unifying language for gases in both gaseous and dissolved states.

  • Knowing P{O2} in air immediately informs you of the driving force for oxygen to dissolve in, or leave, a liquid—critical for physiology (e.g.
    oxygenation of blood, gas exchange in lungs).

  • The principle underpins practical fields such as scuba diving (gas loading/unloading in tissues), environmental science (oxygen content in aquatic systems), and clinical medicine (assessing arterial blood gases).