Geology

Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures exerted by each individual gas.

Core Formula

• Total Pressure Statement:
  $P<em>{\text{total}} = P</em>1 + P<em>2 + P</em>3 + \dots + P<em>n$ where $P</em>{\text{total}}$ is the total pressure of the system and $P<em>1, P</em>2, \dots, P_n$ represent the partial pressures of each individual gas.

Mole Fraction Relationship

• Mole Fraction ($\chi$): The share or fraction of a specific gas compared to the total moles of gas in the mixture.
  $\chi<em>i = \frac{n</em>i}{n_{\text{total}}}$

• Partial Pressure Calculation:
  $P<em>i = \chi</em>i \times P<em>{\text{total}}$ where $P</em>i$ is the partial pressure of gas $i$, $\chi<em>i$ is its mole fraction, and $P</em>{\text{total}}$ is the total pressure.

Example: Parcel of Air

• Given a parcel of air comprised of only nitrogen ($N<em>2$), oxygen ($O</em>2$), and water vapor ($H_2O$):

  • Composition by percentage:

  • $N_2 \rightarrow 78\%$

  • $O_2 \rightarrow 21\%$

  • $H_2O \rightarrow 1\%$

  • Total pressure equation:
    $P<em>{\text{total}} = P</em>{N<em>2} + P</em>{O<em>2} + P</em>{H_2O}$

Key Conditions

• The gases in the mixture must not react chemically with each other.

• The gases are assumed to behave ideally, meaning interactions between gas molecules are negligible.