Dalton's Law of Partial Pressures Overview

Containers and Gases

• Three identical containers, each holding different gases:
  • Container 1: Contains Gas A
  • Pressure: $10$
  • Container 2: Contains Gas B
  • Pressure: $5$
  • Container 3: Contains both Gas A and Gas B
  • Total Pressure: $15$

Pressure Contributions

• To find the fraction of total pressure contributed by each gas:
  • Total Pressure: $P_{total} = 15$
  • Fractions:
  • Gas A:
    • Fraction = $\frac{P<em>A}{P</em>{total}} = \frac{10}{15}$
    • Simplifies to $\frac{2}{3}$
    • Percentage: $66.67\%$
  • Gas B:
    • Fraction = $\frac{P<em>B}{P</em>{total}} = \frac{5}{15}$
    • Simplifies to $\frac{1}{3}$
    • Percentage: $33.33\%$

Mole Fraction

• To calculate the mole fraction, count the number of particles in Container 3:
  • Total Particles = $15$
  • Particles from Gas A = $10$
  • Particles from Gas B = $5$
• Fractions for moles (same as pressures):
  • Gas A:
  • Mole Fraction: $\frac{10}{15}$ (same as pressure fraction)
  • Mole Percentage: $66.67\%$
  • Gas B:
  • Mole Fraction: $\frac{5}{15}$ (same as pressure fraction)
  • Mole Percentage: $33.33\%$

Key Takeaways

• The relationship between pressure and moles:
  • Dalton's Law of Partial Pressures states:
  • Partial Pressure and Moles are Equivalent:
    • The percentage derived from pressure calculations directly translates to mole percentages.
  • Total Pressure is the sum of partial pressures:
    • $P<em>{total} = P</em>A + P_B$
• When performing calculations:
  • The method involves identifying total pressure and contributions from each gas and confirming that insights into pressure also apply to moles without needing separate calculations.

Calculation Steps

1. Find the total pressure.
2. Calculate individual gas pressures as fractions.
3. Convert those fractions to percentages and validate with particle counts (if applicable).
4. Remember that mole fractions will mirror pressure contributions.
5. Total pressure equals the sum of individual pressures.