Calculating Partial Pressure Of Helium In A Noble Gas Mixture Dalton's Law

In the fascinating realm of chemistry, understanding the behavior of gas mixtures is crucial. This article delves into a specific scenario: a mixture of three noble gases – neon, argon, and helium – and the calculation of helium's partial pressure within this mixture. We'll explore the fundamental principles governing gas behavior, particularly Dalton's Law of Partial Pressures, and apply them to solve this problem. This exploration will not only enhance your understanding of gas mixtures but also highlight the importance of partial pressures in various chemical and physical processes.

Dalton's Law of Partial Pressures: The Foundation

At the heart of this calculation lies Dalton's Law of Partial Pressures. This law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas. In simpler terms, each gas in a mixture behaves independently and contributes to the overall pressure as if it were the only gas present. Mathematically, this is represented as:

$$P_T = P_1 + P_2 + P_3 + ... + P_n$$

Where:

• $P_T$ is the total pressure of the gas mixture.
• $P_1$, $P_2$, $P_3$, and so on, represent the partial pressures of each individual gas in the mixture.
• $P_n$ represents the partial pressure of the nth gas in the mixture.

This law is a cornerstone in understanding gas behavior, especially in mixtures. It allows us to predict and calculate the pressure contributions of individual gases within a complex system. Dalton's Law assumes that the gases in the mixture do not react with each other, which is a valid assumption for noble gases due to their inert nature. Understanding Dalton's Law is paramount to grasp the concept of partial pressures and their application in various fields, including chemistry, physics, and engineering. For instance, in respiratory physiology, the partial pressures of oxygen and carbon dioxide in the lungs and blood are critical for understanding gas exchange. Similarly, in industrial processes involving gas mixtures, Dalton's Law is used to control and optimize reaction conditions. The law's simplicity and broad applicability make it an indispensable tool for scientists and engineers working with gases.

Problem Statement: Unveiling Helium's Contribution

Let's revisit the problem at hand. We have a mixture of three noble gases: neon, argon, and helium. The total pressure of this mixture is given as 1.25 atm. We also know the individual partial pressures of neon (0.68 atm) and argon (0.35 atm). Our objective is to determine the partial pressure of helium within this mixture. This problem provides a practical application of Dalton's Law, allowing us to see how the principle works in a real-world scenario. The noble gases, with their inherent stability, make for an ideal system to demonstrate Dalton's Law. Since they do not readily react with each other, the total pressure is a straightforward sum of their individual partial pressures. This problem-solving exercise will not only reinforce our understanding of Dalton's Law but also highlight the importance of carefully considering the properties of the gases involved in a mixture. By isolating the partial pressure of helium, we gain a deeper understanding of its contribution to the overall pressure of the mixture. This is crucial in many applications, such as gas blending for specific industrial processes or analyzing the composition of atmospheric gases. Moreover, the problem underscores the analytical approach required to tackle gas mixture problems, involving the identification of known variables and the strategic application of relevant laws and equations.

Solution: Applying Dalton's Law

To find the partial pressure of helium, we can directly apply Dalton's Law of Partial Pressures. We know the total pressure ($P_T$) and the partial pressures of neon ($P_{Ne}$) and argon ($P_{Ar}$). We can represent the partial pressure of helium as $P_{He}$. The equation becomes:

$$P_T = P_{Ne} + P_{Ar} + P_{He}$$

Now, we can plug in the given values:

$$1.25 ext{ atm} = 0.68 ext{ atm} + 0.35 ext{ atm} + P_{He}$$

To isolate $P_{He}$, we subtract the partial pressures of neon and argon from the total pressure:

$$P_{He} = 1.25 ext{ atm} - 0.68 ext{ atm} - 0.35 ext{ atm}$$

Performing the subtraction, we get:

$$P_{He} = 0.22 ext{ atm}$$

Therefore, the partial pressure of helium in the mixture is 0.22 atm. This straightforward calculation demonstrates the power and simplicity of Dalton's Law. By knowing the total pressure and the partial pressures of other components in a mixture, we can easily determine the partial pressure of the remaining gas. This principle is not only useful in academic settings but also has significant implications in various industrial and scientific applications. For instance, in the design of diving equipment, understanding the partial pressures of gases in the breathing mixture is critical to ensure the safety and well-being of divers. Similarly, in the chemical industry, controlling the partial pressures of reactants is essential for optimizing reaction rates and yields. The calculation we performed highlights the quantitative aspect of chemistry, where mathematical equations and physical laws are used to solve real-world problems. This approach is fundamental to scientific inquiry and allows us to make accurate predictions and informed decisions in various fields.

Conclusion: The Significance of Partial Pressures

In conclusion, the partial pressure of helium in the given mixture of noble gases is 0.22 atm. This result, obtained through the application of Dalton's Law of Partial Pressures, underscores the importance of understanding gas behavior in mixtures. Partial pressure is not just a theoretical concept; it has practical implications in numerous fields, including chemistry, physics, engineering, and even medicine. The ability to calculate and manipulate partial pressures allows us to control and optimize various processes, from industrial chemical reactions to the delivery of therapeutic gases in healthcare settings. By understanding how individual gases contribute to the overall pressure of a mixture, we gain a deeper insight into the complex world of gas dynamics. This knowledge is essential for scientists, engineers, and healthcare professionals who work with gases on a daily basis. The principles we've discussed here form the foundation for more advanced concepts in gas behavior, such as gas diffusion and effusion. As we continue to explore the properties of gases, we'll find that the concept of partial pressure remains a crucial tool for understanding and predicting their behavior. The example we've worked through serves as a reminder of the power of simple scientific laws to explain complex phenomena. Dalton's Law, with its straightforward application and broad applicability, is a testament to the elegance and utility of fundamental scientific principles.

FAQ Section

What is partial pressure?

Partial pressure is the pressure exerted by an individual gas in a mixture of gases. It's the pressure the gas would exert if it occupied the same volume alone.

How is partial pressure calculated?

Partial pressure can be calculated using Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas.

Why is partial pressure important?

Partial pressure is important because it helps us understand the behavior of gases in mixtures and their contribution to the overall pressure. It has applications in various fields, including chemistry, physics, engineering, and medicine.

What is Dalton's Law of Partial Pressures?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.

Can Dalton's Law be applied to reacting gases?

Dalton's Law is strictly applicable to non-reacting gases. If gases react, the partial pressures will change as the reaction proceeds, and Dalton's Law cannot be directly applied.

What are some real-world applications of partial pressure?

Real-world applications of partial pressure include gas blending for specific industrial processes, understanding gas exchange in respiratory physiology, designing diving equipment, and controlling reaction conditions in the chemical industry.