Pression partielle : Exemple de calcul

Introduction

This tutorial will guide you through the calculation of partial pressures of gases in a mixture, using the mass composition of the mixture. Understanding partial pressures is crucial in fields like chemistry and environmental science, where gas behaviors play a significant role in reactions and processes.

Step 1: Understanding the Concept of Partial Pressure

• Definition: Partial pressure refers to the pressure that a gas would exert if it occupied the entire volume alone.

• Dalton's Law: The total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.

• Formula: The partial pressure of a gas can be calculated using the formula:

  [ P_i = \frac{n_i}{n_{total}} \times P_{total} ]

  Where:

  • ( P_i ) = partial pressure of gas i
  • ( n_i ) = number of moles of gas i
  • ( n_{total} ) = total number of moles of all gases
  • ( P_{total} ) = total pressure of the gas mixture

Step 2: Gathering Required Information

• Identify the Gases: List all the gases present in the mixture.

• Determine Mass Composition: Find the mass of each gas in the mixture.

• Convert Mass to Moles: Use the molar mass of each gas to convert mass to moles using the formula:

  [ n = \frac{m}{M} ]

  Where:

  • ( n ) = number of moles
  • ( m ) = mass of the gas
  • ( M ) = molar mass of the gas

Step 3: Calculating Total Moles

• Sum up the moles of all gases from the previous step to get the total number of moles:

  [ n_{total} = n_1 + n_2 + n_3 + \ldots + n_n ]

Step 4: Calculating Partial Pressures

• With the total moles calculated and the total pressure known, apply the formula for each gas to find its partial pressure. Repeat for each gas in the mixture:

  [ P_i = \frac{n_i}{n_{total}} \times P_{total} ]

Step 5: Example Calculation

1. Consider a mixture of oxygen (O₂) and nitrogen (N₂).
   • Mass of O₂ = 32 g, Molar mass of O₂ = 32 g/mol
   • Mass of N₂ = 28 g, Molar mass of N₂ = 28 g/mol
2. Convert to moles:
   • ( n_{O_2} = \frac{32}{32} = 1 ) mol
   • ( n_{N_2} = \frac{28}{28} = 1 ) mol
3. Total moles: ( n_{total} = 1 + 1 = 2 ) mol
4. Assume total pressure ( P_{total} = 2 ) atm.
5. Calculate partial pressures:
   • ( P_{O_2} = \frac{1}{2} \times 2 = 1 ) atm
   • ( P_{N_2} = \frac{1}{2} \times 2 = 1 ) atm

Conclusion

In this tutorial, you learned how to calculate the partial pressures of gases in a mixture using their mass composition. By following these steps, you can apply this knowledge in various scientific and engineering contexts. For further practice, consider working on real-world gas mixtures or exploring how changes in temperature and volume affect gas behaviors.