A Mixture Of Three Noble Gases Has A Total Pressure Of 1.25 Atm. The Individual Pressures Exerted By Neon And Argon Are 0.68 Atm And 0.35 Atm, Respectively. What Is The Partial Pressure Of The Third Gas, Helium? Use $P_T = P_1 + P_2 + P_3 + \ldots

Introduction

In chemistry, the study of gases and their behavior is crucial for understanding various physical and chemical phenomena. One of the fundamental concepts in gas chemistry is the partial pressure, which is the pressure exerted by a specific gas in a mixture of gases. In this article, we will explore the concept of partial pressure and use it to determine the partial pressure of helium in a mixture of three noble gases.

What are Partial Pressures?

Partial pressures are the pressures exerted by individual gases in a mixture of gases. The total pressure of a gas mixture is the sum of the partial pressures of each gas present in the mixture. The concept of partial pressure is based on Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas present in the mixture.

Mathematical Representation of Partial Pressures

The mathematical representation of partial pressures is given by the equation:

$$P_T = P_1 + P_2 + P_3 + \ldots$$

where $P_T$ is the total pressure of the gas mixture, and $P_1$, $P_2$, $P_3$, etc. are the partial pressures of each gas present in the mixture.

Calculating Partial Pressures

To calculate the partial pressure of a gas in a mixture, we need to know the total pressure of the mixture and the partial pressures of the other gases present in the mixture. Let's consider a mixture of three noble gases: neon, argon, and helium. The total pressure of the mixture is given as 1.25 atm, and the individual pressures exerted by neon and argon are 0.68 atm and 0.35 atm, respectively.

Determining the Partial Pressure of Helium

To determine the partial pressure of helium, we need to subtract the partial pressures of neon and argon from the total pressure of the mixture. The partial pressure of helium can be calculated as follows:

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

where $P_{He}$ is the partial pressure of helium, $P_T$ is the total pressure of the mixture, $P_{Ne}$ is the partial pressure of neon, and $P_{Ar}$ is the partial pressure of argon.

Substituting Values

Substituting the given values, we get:

$$P_{He} = 1.25\, \text{atm} - 0.68\, \text{atm} - 0.35\, \text{atm}$$

Simplifying the Equation

Simplifying the equation, we get:

$$P_{He} = 0.22\, \text{atm}$$

Conclusion

In conclusion, the partial pressure of helium in a mixture of three noble gases can be determined by subtracting the partial pressures of neon and argon from the total pressure of the mixture. The partial pressure of helium is 0.22 atm.

Applications of Partial Pressures

Partial pressures have numerous applications in various fields, including chemistry, physics, and engineering. Some of the applications of partial pressures include:

• Gas Mixtures: Partial pressures are used to determine the composition of gas mixtures.
• Chemical Reactions: Partial pressures are used to predict the rates of chemical reactions.
• Gas Separation: Partial pressures are used to separate gases based on their partial pressures.
• Gas Storage: Partial pressures are used to determine the storage capacity of gases.

Limitations of Partial Pressures

While partial pressures are a powerful tool for understanding gas mixtures, they have some limitations. Some of the limitations of partial pressures include:

• Assumptions: Partial pressures assume that the gases in the mixture are ideal gases, which may not be the case in real-world scenarios.
• Interactions: Partial pressures do not take into account the interactions between the gases in the mixture.
• Temperature and Pressure: Partial pressures are sensitive to temperature and pressure changes.

Future Directions

In conclusion, partial pressures are a fundamental concept in gas chemistry, and their applications are numerous. However, they have some limitations, and future research should focus on developing more accurate models that take into account the interactions between gases and the effects of temperature and pressure changes.

References

• Dalton's Law of Partial Pressures: A fundamental concept in gas chemistry that states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas present in the mixture.
• Ideal Gas Law: A mathematical equation that describes the behavior of ideal gases.
• Gas Mixtures: A mixture of gases that can be composed of any number of gases.

Glossary

• Partial Pressure: The pressure exerted by a specific gas in a mixture of gases.
• Total Pressure: The sum of the partial pressures of each gas present in a mixture of gases.
• Dalton's Law of Partial Pressures: A fundamental concept in gas chemistry that states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas present in the mixture.
• Ideal Gas Law: A mathematical equation that describes the behavior of ideal gases.
  A Mixture of Noble Gases: Q&A ================================

Introduction

In our previous article, we explored the concept of partial pressures in a mixture of noble gases. We calculated the partial pressure of helium in a mixture of three noble gases: neon, argon, and helium. In this article, we will answer some frequently asked questions related to partial pressures and gas mixtures.

Q: What is the difference between total pressure and partial pressure?

A: The total pressure of a gas mixture is the sum of the partial pressures of each gas present in the mixture. The partial pressure of a gas is the pressure exerted by that gas in the mixture.

Q: How do I calculate the partial pressure of a gas in a mixture?

A: To calculate the partial pressure of a gas in a mixture, you need to know the total pressure of the mixture and the partial pressures of the other gases present in the mixture. You can use the equation:

$$P_{gas} = P_T - P_{other\, gases}$$

where $P_{gas}$ is the partial pressure of the gas, $P_T$ is the total pressure of the mixture, and $P_{other\, gases}$ is the sum of the partial pressures of the other gases present in the mixture.

Q: What is Dalton's Law of Partial Pressures?

A: Dalton's Law of Partial Pressures is a fundamental concept in gas chemistry that states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas present in the mixture.

Q: What are some applications of partial pressures?

A: Partial pressures have numerous applications in various fields, including chemistry, physics, and engineering. Some of the applications of partial pressures include:

• Gas Mixtures: Partial pressures are used to determine the composition of gas mixtures.
• Chemical Reactions: Partial pressures are used to predict the rates of chemical reactions.
• Gas Separation: Partial pressures are used to separate gases based on their partial pressures.
• Gas Storage: Partial pressures are used to determine the storage capacity of gases.

Q: What are some limitations of partial pressures?

A: While partial pressures are a powerful tool for understanding gas mixtures, they have some limitations. Some of the limitations of partial pressures include:

• Assumptions: Partial pressures assume that the gases in the mixture are ideal gases, which may not be the case in real-world scenarios.
• Interactions: Partial pressures do not take into account the interactions between the gases in the mixture.
• Temperature and Pressure: Partial pressures are sensitive to temperature and pressure changes.

Q: How do I determine the composition of a gas mixture?

A: To determine the composition of a gas mixture, you can use the partial pressures of the gases present in the mixture. You can use the equation:

$$P_{gas} = P_T \times \frac{n_{gas}}{n_{total}}$$

where $P_{gas}$ is the partial pressure of the gas, $P_T$ is the total pressure of the mixture, $n_{gas}$ is the number of moles of the gas, and $n_{total}$ is the total number of moles of the mixture.

Q: What is the difference between an ideal gas and a real gas?

A: An ideal gas is a gas that obeys the ideal gas law, which is a mathematical equation that describes the behavior of ideal gases. A real gas, on the other hand, is a gas that does not obey the ideal gas law and has non-ideal behavior.

Q: How do I calculate the number of moles of a gas in a mixture?

A: To calculate the number of moles of a gas in a mixture, you can use the equation:

$$n_{gas} = \frac{P_{gas} \times V}{R \times T}$$

where $n_{gas}$ is the number of moles of the gas, $P_{gas}$ is the partial pressure of the gas, $V$ is the volume of the gas, $R$ is the gas constant, and $T$ is the temperature of the gas.

Conclusion

In conclusion, partial pressures are a fundamental concept in gas chemistry, and their applications are numerous. However, they have some limitations, and future research should focus on developing more accurate models that take into account the interactions between gases and the effects of temperature and pressure changes.

References

• Dalton's Law of Partial Pressures: A fundamental concept in gas chemistry that states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas present in the mixture.
• Ideal Gas Law: A mathematical equation that describes the behavior of ideal gases.
• Gas Mixtures: A mixture of gases that can be composed of any number of gases.

Glossary

• Partial Pressure: The pressure exerted by a specific gas in a mixture of gases.
• Total Pressure: The sum of the partial pressures of each gas present in a mixture of gases.
• Dalton's Law of Partial Pressures: A fundamental concept in gas chemistry that states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas present in the mixture.
• Ideal Gas Law: A mathematical equation that describes the behavior of ideal gases.