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How do you calculate the partial pressure of each component?

Published in Chemistry 3 mins read

The partial pressure of a gas component within a mixture can be calculated using the ideal gas law or by using mole fractions if the total pressure is known.

Here's a breakdown of the methods:

1. Using the Ideal Gas Law:

This method directly applies the ideal gas law to each individual component of the gas mixture. The ideal gas law is:

  • PV = nRT

Where:

  • P = Pressure
  • V = Volume
  • n = Number of moles
  • R = Ideal gas constant
  • T = Temperature

To calculate the partial pressure (Pi) of a specific component i in the mixture:

  • Pi = ni * R * T / V

    • ni is the number of moles of component i.
    • R is the ideal gas constant (its value depends on the units used for pressure, volume, and temperature).
    • T is the absolute temperature (in Kelvin).
    • V is the volume of the gas mixture.

    Important Note: The temperature (T) and volume (V) are the same for each component of the gas mixture.

Example:

Imagine a container with a volume of 10 L at a temperature of 300 K. The container holds 2 moles of nitrogen (N2) and 1 mole of oxygen (O2). Calculate the partial pressures of nitrogen and oxygen. (R = 0.0821 L atm / (mol K))

  • Partial pressure of Nitrogen (PN2):

    • PN2 = (2 mol 0.0821 L atm / (mol K) 300 K) / 10 L
    • PN2 = 4.926 atm

  • Partial pressure of Oxygen (PO2):

    • PO2 = (1 mol 0.0821 L atm / (mol K) 300 K) / 10 L
    • PO2 = 2.463 atm

2. Using Mole Fractions and Total Pressure (Dalton's Law of Partial Pressures):

Dalton's Law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas. This leads to another way to calculate partial pressures:

  • First, calculate the mole fraction (χi) of component i:

    • χi = ni / ntotal

      • ni is the number of moles of component i.
      • ntotal is the total number of moles of all gases in the mixture.

  • Then, calculate the partial pressure of component i:

    • *Pi = χi Ptotal**

      • Ptotal is the total pressure of the gas mixture.

Example (Continuing from the previous example):

The total number of moles is 2 (N2) + 1 (O2) = 3 moles. Suppose the total pressure is measured to be 7.389 atm.

  • Mole fraction of Nitrogen (χN2):

    • χN2 = 2 mol / 3 mol = 0.667

  • Mole fraction of Oxygen (χO2):

    • χO2 = 1 mol / 3 mol = 0.333

  • Partial pressure of Nitrogen (PN2):

    • PN2 = 0.667 * 7.389 atm = 4.92 atm

  • Partial pressure of Oxygen (PO2):

    • PO2 = 0.333 * 7.389 atm = 2.46 atm

In summary, you can calculate the partial pressure of each component using either the ideal gas law directly or by determining the mole fraction of the component and multiplying it by the total pressure of the gas mixture.

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