Calculating Nitrogen Partial Pressure In A Balloon A Chemistry Problem

Jul 14, 2025 by ADMIN 71 views

Understanding Partial Pressure of Nitrogen in a Balloon A Comprehensive Guide

#title: Calculating Partial Pressure of Nitrogen in a Balloon A Chemistry Guide

In the realm of chemistry, grasping the concept of partial pressure is paramount, especially when dealing with gaseous mixtures. This article delves into a practical problem involving partial pressure calculation, offering a step-by-step solution and a comprehensive explanation to enhance your understanding. Let's explore how to determine the partial pressure of nitrogen in a balloon containing a mix of oxygen and nitrogen gases.

The Problem: Determining Nitrogen's Partial Pressure

We are presented with a scenario involving a 2.0-liter balloon at a temperature of 25°C. This balloon contains 0.1 mol of oxygen and 0.4 mol of nitrogen. The core question we aim to answer is: What is the partial pressure of nitrogen in this gaseous mixture?

To tackle this problem effectively, we'll navigate through the fundamental principles of partial pressure and leverage the ideal gas law. The options provided for the answer are:

A. 1.22 atmospheres B. 4.89 atmospheres C. 1 atmosphere D. 6.11 atmospheres E. 0.5 atmosphere

Decoding Partial Pressure: A Key Concept

Partial pressure is a crucial concept in understanding the behavior of gas mixtures. In a mixture of gases, each individual gas exerts a pressure as if it were the only gas present in the container. This individual pressure exerted by a gas is termed its partial pressure. The total pressure of the mixture is simply the sum of the partial pressures of all the component gases. This principle is mathematically expressed by Dalton's Law of Partial Pressures:

P_total = P₁ + P₂ + P₃ + ...

Where P_total is the total pressure of the gaseous mixture, and P₁, P₂, P₃, and so on represent the partial pressures of the individual gases in the mixture.

In essence, partial pressure allows us to analyze and predict the behavior of individual gases within a mixture, which is vital in various fields, including chemistry, physics, and engineering. Understanding partial pressure helps us in diverse applications, from predicting reaction rates in chemical processes to understanding the mechanics of respiration in living organisms.

The Ideal Gas Law: A Cornerstone of Gas Calculations

To accurately calculate the partial pressure of nitrogen in our balloon scenario, we need to employ the ideal gas law. The ideal gas law is a fundamental equation in thermodynamics that describes the state of a theoretical ideal gas. This law relates the pressure (P), volume (V), amount of substance (n), and temperature (T) of a gas through the equation:

PV = nRT

Where:

P is the pressure of the gas (in atmospheres)
V is the volume of the gas (in liters)
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L atm / (mol K))
T is the temperature of the gas (in Kelvin)

The ideal gas law is a powerful tool for predicting the behavior of gases under a wide range of conditions. It assumes that gas molecules have negligible volume and do not interact with each other, which is a close approximation for many real gases under normal conditions. This law allows us to establish a direct relationship between the macroscopic properties of a gas (pressure, volume, and temperature) and the amount of gas present, making it essential for gas calculations.

Solving the Problem: Step-by-Step Calculation

Now, let's apply our understanding of partial pressure and the ideal gas law to solve the problem at hand. We want to determine the partial pressure of nitrogen in the balloon.

Step 1: Convert Temperature to Kelvin

The ideal gas law requires temperature to be in Kelvin. We are given the temperature in Celsius (25°C), so we need to convert it to Kelvin using the formula:

T(K) = T(°C) + 273.15

T(K) = 25°C + 273.15 = 298.15 K

Step 2: Apply the Ideal Gas Law for Nitrogen

To find the partial pressure of nitrogen (P_N2), we'll use the ideal gas law, focusing solely on nitrogen:

P_N2V = n_N2RT

We have:

V = 2.0 L (volume of the balloon)
n_N2 = 0.4 mol (moles of nitrogen)
R = 0.0821 L atm / (mol K) (ideal gas constant)
T = 298.15 K (temperature in Kelvin)

Now, we can rearrange the ideal gas law equation to solve for P_N2:

P_N2 = (n_N2RT) / V

Step 3: Calculate the Partial Pressure of Nitrogen

Plug in the values we have:

P_N2 = (0.4 mol * 0.0821 L atm / (mol K) * 298.15 K) / 2.0 L

P_N2 = (9.78 L atm) / 2.0 L

P_N2 = 4.89 atm

Therefore, the partial pressure of nitrogen in the balloon is 4.89 atmospheres.

The Correct Answer and Why

Based on our calculations, the correct answer is:

B. 4.89 atmospheres

This result aligns perfectly with the principles of partial pressure and the ideal gas law. We correctly applied the ideal gas law using the number of moles of nitrogen, the volume of the balloon, the ideal gas constant, and the temperature in Kelvin to accurately determine the partial pressure exerted by nitrogen.

Analyzing the Incorrect Options

To further solidify our understanding, let's examine why the other options are incorrect:

A. 1.22 atmospheres: This value is significantly lower than the calculated partial pressure. It might be a result of incorrectly using the total moles of gas or a misunderstanding of the ideal gas law.
C. 1 atmosphere: This is the standard atmospheric pressure, but it doesn't account for the specific conditions and the amount of nitrogen in the balloon.
D. 6.11 atmospheres: This value is higher than the calculated partial pressure and might be due to an error in calculation or an incorrect application of the ideal gas law.
E. 0.5 atmosphere: This value is also significantly lower than the correct answer and may indicate a misunderstanding of the relationship between moles, pressure, and volume.

By analyzing the incorrect options, we gain a deeper appreciation for the correct methodology and the importance of accurate calculations in chemistry.

Practical Implications of Partial Pressure

The concept of partial pressure is not just a theoretical construct; it has numerous practical applications in various fields. Here are a few examples:

Respiration: In biology, partial pressure plays a critical role in understanding respiration. The exchange of oxygen and carbon dioxide in the lungs and blood is driven by differences in partial pressures. Oxygen moves from the lungs, where its partial pressure is high, to the blood, where its partial pressure is lower. Similarly, carbon dioxide moves from the blood to the lungs due to a partial pressure gradient.
Diving: Scuba divers need to understand partial pressure to avoid nitrogen narcosis and decompression sickness (the bends). At increased depths, the partial pressures of gases in the breathing mixture increase, which can lead to these conditions. Divers must carefully manage their gas mixtures and ascent rates to prevent these issues.
Industrial Chemistry: In chemical reactions involving gases, partial pressure can influence reaction rates and equilibrium. Understanding and controlling partial pressures is crucial for optimizing industrial processes, such as the Haber-Bosch process for ammonia synthesis.
Weather Forecasting: Partial pressure of water vapor in the atmosphere is a key factor in weather forecasting. It helps meteorologists predict humidity, cloud formation, and precipitation.
Anesthesia: In medicine, the partial pressure of anesthetic gases is carefully controlled to achieve the desired level of anesthesia while minimizing side effects.

These examples highlight the broad applicability of partial pressure in diverse scientific and practical contexts. Grasping this concept empowers us to understand and address real-world challenges in fields ranging from medicine to engineering.

Conclusion: Mastering Partial Pressure

In conclusion, determining the partial pressure of nitrogen in a balloon containing a mixture of gases is a problem that elegantly demonstrates the power of the ideal gas law and the importance of understanding partial pressure. By meticulously applying the ideal gas law and considering the specific conditions provided in the problem, we arrived at the correct answer: 4.89 atmospheres.

This exercise underscores the significance of careful calculations, a solid grasp of fundamental principles, and the ability to apply these concepts to practical scenarios. Partial pressure is a cornerstone concept in chemistry and physics, with far-reaching implications across various disciplines.

By mastering concepts like partial pressure, you'll be well-equipped to tackle a wide array of challenges in chemistry and beyond. Keep exploring, keep questioning, and keep learning!