How to Calculate the Partial Pressure in a Gas Mixture?

The partial pressure of a gas in a mixture is calculated by multiplying the total pressure of the gas mixture by the mole fraction of that specific gas.

Understanding Partial Pressure

Partial pressure is a fundamental concept in understanding gas mixtures. It refers to the pressure exerted by a single gas component within a mixture of gases. Each gas in a mixture contributes to the total pressure, and its individual contribution is its partial pressure.

Calculation Method

According to the provided reference, the partial pressure of a gas is equal to the total pressure multiplied by the mole fraction of that gas. This can be expressed mathematically as:

• *P_i = P_total X_i**

Where:

• P_i is the partial pressure of gas 'i'.
• P_total is the total pressure of the gas mixture.
• X_i is the mole fraction of gas 'i'.

Determining Mole Fraction

The mole fraction (X_i) of a gas is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture. It's calculated as:

• X_i = n_i / n_total

Where:

• n_i is the number of moles of gas 'i'.
• n_total is the total number of moles of all gases in the mixture.

Step-by-Step Calculation

Here's how to calculate the partial pressure, step-by-step:

1. Determine the number of moles of each gas: If you are given the mass of each gas, convert it to moles using the molar mass of each gas.
2. Calculate the total number of moles: Add up the moles of all the individual gases to find the total moles of gas in the mixture.
3. Calculate the mole fraction of the gas of interest: Divide the number of moles of the specific gas by the total number of moles in the mixture.
4. Determine the total pressure of the mixture: This is usually measured using a pressure gauge.
5. Calculate the partial pressure: Multiply the total pressure of the mixture by the mole fraction of the gas of interest to get its partial pressure.

Example Calculation

Let's assume a gas mixture contains 2 moles of nitrogen (N₂) and 3 moles of oxygen (O₂), and the total pressure of the mixture is 10 atm. We want to find the partial pressure of oxygen.

1. Moles of gases:

   • n(O₂) = 3 moles
   • n(N₂) = 2 moles

2. Total moles:

   • n_total = 3 moles + 2 moles = 5 moles

3. Mole fraction of oxygen (O₂):

   • X(O₂) = 3 moles / 5 moles = 0.6

4. Total pressure:

   • P_total = 10 atm

5. Partial pressure of oxygen (O₂):

   • P(O₂) = P_total X(O₂) = 10 atm 0.6 = 6 atm

Therefore, the partial pressure of oxygen in this mixture is 6 atm.

Practical Insights

• Partial pressure calculations are vital in various fields such as chemistry, physics, and engineering, particularly in analyzing chemical reactions involving gases, understanding atmospheric conditions, and designing industrial processes.
• The total pressure of a gas mixture is the sum of the partial pressures of all the individual gases present, according to Dalton's law of partial pressures.
• Understanding partial pressures helps in predicting gas behavior under different conditions.