Question

A balloon contains 0.76 mol N₂, 0.18 mol O₂, 0.031 mol He, and 0.026 mol H₂. What is the total pressure of the mixture if the partial pressure of O₂ is 140 mmHg? (R = 0.08206, 1 atm = 760 mmHg)

Answer 1

The total pressure of the gas mixture in the balloon is approximately 1.02 atm, calculated using Dalton's Law of Partial Pressures and the given partial pressure of O₂.

Step-by-step explanation:

To find the total pressure of the gas mixture in the balloon, we will use Dalton's Law of Partial Pressures. This states that the total pressure of a gas mixture is the sum of the partial pressures of each component of the gas. Given the partial pressure of O₂ (140 mmHg), we can find the mole fraction of O₂ and then use it to calculate the total pressure.

First, calculate the mole fraction of O₂:

• Moles of O₂ = 0.18 mol
• Total moles of gas = 0.76 mol N₂ + 0.18 mol O₂ + 0.031 mol He + 0.026 mol H₂ = 0.997 mol
• Mole fraction of O₂, X O₂= 0.18 mol / 0.997 mol = 0.1805

Now, find the total pressure using the mole fraction:

• XO₂ × Ptotal = Partial pressure of O₂ (140 mmHg)
• Ptotal = 140 mmHg / 0.1805 = 775.62 mmHg

Since 1 atm = 760 mmHg, divide the total pressure by 760 to convert to atmospheres:

• Ptotal (atm) = 775.62 mmHg / 760 mmHg/atm ≈ 1.02 atm

Therefore, the total pressure in the balloon is approximately 1.02 atm.