Nitrogen's Partial Pressure: Unveiling Gas Mixtures At STP

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Hey there, chemistry enthusiasts! Let's dive into a fascinating problem that blends the concepts of gas mixtures, partial pressures, and the ever-so-handy Standard Temperature and Pressure (STP) conditions. We're going to break down how to find the partial pressure of nitrogen (Nâ‚‚) in a gaseous mixture containing both nitrogen and oxygen (Oâ‚‚). Ready to put on your thinking caps? Let's get started!

Decoding the Problem: What We Know

Alright, guys, let's start by unpacking what the question throws at us. We've got a gaseous mixture, and in this mixture, we know a few key things:

  • The Gases: Nitrogen (Nâ‚‚) and oxygen (Oâ‚‚) are hanging out together. Think of them as roommates in a shared container.
  • The Conditions: We're dealing with STP. Remember, STP is a big deal in chemistry. It sets the playing field with specific temperature and pressure values. STP means a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm). This is super important because it gives us a baseline to work with.
  • The Volume Percentage: The mixture contains 20% oxygen by volume. This is our golden ticket to understanding the proportions of each gas in the mixture. Knowing the percentage by volume directly tells us the mole fraction, thanks to Avogadro's Law which we will discuss later.
  • The Goal: We need to find the partial pressure of Nâ‚‚. This is the pressure that nitrogen gas would exert if it occupied the container alone. It's like asking, "Hey Nâ‚‚, what's your contribution to the total pressure?"

So, to recap, our mission is to figure out the partial pressure of nitrogen, given that it's mixed with oxygen, and everything is at STP.

Grasping the Concepts: The Building Blocks

Before we jump into the calculations, let's brush up on the key concepts that make this problem tick. Understanding these ideas is crucial for solving the problem and for building a strong foundation in chemistry.

STP: The Standard Playground

As mentioned earlier, STP (Standard Temperature and Pressure) is a set of defined conditions. It's like a benchmark that chemists use to compare gas properties. At STP:

  • Temperature (T) = 0°C or 273.15 K
  • Pressure (P) = 1 atm

STP provides a standard reference point, simplifying calculations because we know the total pressure of the gas mixture at the outset. This means the total pressure of the Nâ‚‚ and Oâ‚‚ mixture is 1 atm.

Partial Pressure: Each Gas's Contribution

Imagine a container filled with several types of gas. Each gas contributes to the total pressure of the system. Partial pressure is the pressure exerted by a single gas in a mixture. Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of each gas component. Mathematically:

  • Ptotal = P1 + P2 + P3 + ...

Where Ptotal is the total pressure, and P1, P2, P3, and so on are the partial pressures of each gas. In our case:

  • Ptotal = PNâ‚‚ + POâ‚‚

Mole Fraction: The Key to Gas Ratios

The mole fraction (χ) of a gas in a mixture is the ratio of the number of moles of that gas to the total number of moles of all the gases in the mixture. The mole fraction is a dimensionless quantity that represents the proportion of a specific gas in the mixture. Here's the formula:

  • χi = ni / ntotal

Where:

  • χi is the mole fraction of gas i.
  • ni is the number of moles of gas i.
  • ntotal is the total number of moles of all gases.

Since volume percent and mole percent are equivalent for ideal gases, the 20% oxygen by volume translates directly to a 20% mole fraction for oxygen.

Linking Mole Fraction and Partial Pressure: Raoult's Law

Raoult's Law links the partial pressure of a gas to its mole fraction and the total pressure of the mixture:

  • Pi = χi * Ptotal

Where:

  • Pi is the partial pressure of gas i.
  • χi is the mole fraction of gas i.
  • Ptotal is the total pressure of the mixture.

This is the secret weapon we need to calculate the partial pressure of nitrogen.

Solving the Puzzle: Step-by-Step

Alright, now for the fun part – putting everything together to solve the problem! Here's a step-by-step approach to finding the partial pressure of N₂.

Step 1: Determine the Mole Fraction of Oxygen (Oâ‚‚)

We know that the mixture contains 20% oxygen by volume. Because we're working with ideal gases (which is a good assumption for this problem), volume percentages are directly proportional to mole percentages. So, the mole fraction of O₂ (χO₂) is 0.20.

Step 2: Determine the Mole Fraction of Nitrogen (Nâ‚‚)

Since the mixture consists of only Nâ‚‚ and Oâ‚‚, the sum of their mole fractions must equal 1. Therefore:

  • χNâ‚‚ + χOâ‚‚ = 1
  • χNâ‚‚ = 1 - χOâ‚‚
  • χNâ‚‚ = 1 - 0.20
  • χNâ‚‚ = 0.80

This tells us that nitrogen makes up 80% of the gas mixture by moles.

Step 3: Calculate the Partial Pressure of Nitrogen (Nâ‚‚)

Now, let's apply Raoult's Law. We know the mole fraction of N₂ (χN₂ = 0.80) and the total pressure at STP (Ptotal = 1 atm). So:

  • PNâ‚‚ = χNâ‚‚ * Ptotal
  • PNâ‚‚ = 0.80 * 1 atm
  • PNâ‚‚ = 0.80 atm

Step 4: The Answer

The partial pressure of nitrogen (Nâ‚‚) in the mixture is 0.80 atm. Therefore, the correct answer is D) 0.8 atm.

Why This Matters: The Real-World Connection

Understanding partial pressures isn't just a theoretical exercise. It has real-world applications in many areas. For example:

  • Scuba Diving: Divers breathe a mixture of gases, often including nitrogen and oxygen. At greater depths, the increased pressure affects the partial pressures of these gases, which can have physiological effects on the diver, such as nitrogen narcosis.
  • Medicine: In hospitals, oxygen therapy uses specific oxygen concentrations to treat respiratory conditions. Understanding the partial pressure of oxygen in the lungs is crucial for effective treatment.
  • Industrial Processes: Many industrial processes involve gas mixtures. Controlling the partial pressures of gases is essential for reactions to occur efficiently and safely.

Conclusion: You Did It!

Way to go, you guys! You've successfully navigated the problem of finding the partial pressure of nitrogen in a gas mixture at STP. You've now seen how to use the concepts of STP, partial pressure, mole fraction, and Raoult's Law to solve this type of problem. Keep up the great work, and happy chemistry-ing!

Remember to review these concepts, practice similar problems, and always strive to understand the underlying principles. Happy studying!