A gas mixture containing oxygen, nitrogen, and helium exerts a total pressure of 925 Torr. If the partial pressures are oxygen 425 Torr and helium 75 Torr, what is the partial pressure, in torr, of the nitrogen in the mixture?

Answer

Understanding Partial Pressures in Gas Mixtures: A Guide Using Dalton’s Law

In chemistry and physical science, understanding how gases behave in mixtures is fundamental. Whether we’re analyzing the composition of air, studying respiration, or calculating pressure inside scuba tanks, knowing how to compute the pressure contributed by each gas becomes essential.

One of the foundational concepts in this area is known as Dalton’s Law of Partial Pressures. This law enables us to determine how much pressure is exerted by individual gases in a mixture based on their proportion and presence.

📘 What is Dalton’s Law of Partial Pressures?

Dalton’s Law, named after the English chemist John Dalton, states that the total pressure of a gas mixture is the sum of the partial pressures of all the individual gases in the mixture.

Each P represents the partial pressure of a different gas component in the mixture.

🔍 What is a Partial Pressure?

A partial pressure is the pressure that one individual gas in a mixture would exert if it were alone in the same volume and temperature. In gas mixtures, each component gas acts independently when calculating pressure.

🧮 Step-by-Step Problem Breakdown

Let’s walk through the given values and apply Dalton’s Law to find the unknown:

• Total Pressure, P_total: 925 Torr
• Partial Pressure of Oxygen, P_O₂: 425 Torr
• Partial Pressure of Helium, P_He: 75 Torr
• Required: Partial Pressure of Nitrogen, P_N₂

Step 1: Substitute Known Values

Step 2: Simplify Inside the Parentheses

Step 3: Final Calculation

💡 Why Does This Make Sense?

Dalton’s Law assumes that all gases behave ideally — they do not interact or affect each other’s pressure contributions. The calculation shows that nitrogen contributes exactly what’s left over once we subtract the oxygen and helium’s pressures from the total.

Interestingly, in this case, the partial pressure of nitrogen turns out to be equal to that of oxygen. This doesn’t always happen, but it illustrates how gases balance each other in a mixture depending on their individual amounts and properties.

📈 Real-World Application of Dalton’s Law

Dalton’s Law is not just theory—it is used extensively in various fields:

• Medicine: Understanding oxygen mixtures for patients in hospitals and ventilators.
• Diving: Scuba divers use Dalton’s Law to prevent nitrogen narcosis by managing gas mixture pressures.
• Industrial: Gas pipelines and chemical plants depend on partial pressure monitoring for safety and process control.
• Laboratories: Scientists rely on it for gas chromatography and reaction control in controlled environments.

🧠 Deep Dive: Dalton’s Law and Mole Fractions

The partial pressure of a gas can also be calculated using its mole fraction in the mixture:

Where:

• X_gas is the mole fraction (moles of the gas ÷ total moles)
• P_total is the total pressure

If the mole quantities of the gases are known, you can calculate each partial pressure using this relationship, providing a deeper chemical context.

🧮 Practice Tip: Always Check Units

• Make sure all pressures are in the same units (Torr, atm, kPa)
• In this example, all pressures are already in Torr, so no conversion was needed
• Use the correct number of significant figures

📚 Recap & Final Thoughts

Here’s a quick recap of how we solved the problem using Dalton’s Law:

1. Write the formula: P_total = P_O₂ + P_He + P_N₂
2. Rearrange to solve for the unknown: P_N₂ = P_total − (P_O₂ + P_He)
3. Substitute and simplify
4. Result: P_N₂ = 425 Torr

Dalton’s Law of Partial Pressures is powerful in predicting how gases behave in mixtures. It’s straightforward, yet incredibly useful across various real-life scenarios — from respiratory care to deep-sea diving and industrial manufacturing.