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 in understanding various physical and chemical processes. One of the fundamental concepts in gas mixtures is the concept of partial pressure. The partial pressure of a gas in a mixture is the pressure that the gas would exert if it were the only gas present in the container. In this article, we will explore the concept of partial pressure and how to calculate it using the given total pressure and individual pressures of the gases in a mixture.

What are Noble Gases?

Noble gases are a group of elements that are chemically inert and are located in the far right column of the periodic table. They are also known as the inert gases. The six noble gases are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn). Noble gases are unreactive due to their full outer energy level, which makes them stable and non-reactive.

Partial Pressure of a Gas in a Mixture

The partial pressure of a gas in a mixture can be calculated using the following formula:

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

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

Calculating Partial Pressure of Helium

In this problem, we are given the total pressure of a mixture of three noble gases, which is 1.25 atm. We are also given the individual pressures exerted by neon and argon, which are 0.68 atm and 0.35 atm, respectively. We need to find the partial pressure of the third gas, helium.

Let's use the formula for partial pressure to calculate the partial pressure of helium:

$$P_T = P_1 + P_2 + P_3$$

where $P_T$ is the total pressure of the mixture, $P_1$ is the partial pressure of neon, $P_2$ is the partial pressure of argon, and $P_3$ is the partial pressure of helium.

We are given the following values:

• $P_T$ = 1.25 atm
• $P_1$ = 0.68 atm (partial pressure of neon)
• $P_2$ = 0.35 atm (partial pressure of argon)

We need to find the value of $P_3$, which is the partial pressure of helium.

Substituting Values into the Formula

Substituting the given values into the formula, we get:

$$1.25 = 0.68 + 0.35 + P_3$$

Solving for $P_3$

To solve for $P_3$, we need to isolate the variable $P_3$ on one side of the equation. We can do this by subtracting 0.68 and 0.35 from both sides of the equation:

$$1.25 - 0.68 - 0.35 = P_3$$

Simplifying the equation, we get:

$$0.22 = P_3$$

Therefore, the partial pressure of helium is 0.22 atm.

Conclusion

In conclusion, the partial pressure of a gas in a mixture can be calculated using the formula $P_T = P_1 + P_2 + P_3 + \ldots$. In this problem, we used the formula to calculate the partial pressure of helium in a mixture of three noble gases. We were given the total pressure of the mixture and the individual pressures exerted by neon and argon, and we were able to find the partial pressure of helium using the formula.

Real-World Applications

The concept of partial pressure is important in various real-world applications, such as:

• Chemical Engineering: Partial pressure is used to calculate the amount of gas that can be absorbed or released by a liquid or solid.
• Atmospheric Science: Partial pressure is used to calculate the amount of greenhouse gases in the atmosphere and their impact on global warming.
• Medical Applications: Partial pressure is used to calculate the amount of oxygen in the blood and its impact on respiratory health.

Limitations of the Formula

The formula for partial pressure assumes that the gases in the mixture are ideal gases and that there are no interactions between the gases. However, in real-world applications, the gases may not behave ideally, and there may be interactions between the gases. In such cases, the formula may not be accurate, and more complex calculations may be required.

Future Research Directions

Future research directions in the field of partial pressure include:

• Developing more accurate models: Developing more accurate models that take into account the interactions between the gases and the non-ideal behavior of the gases.
• Applying partial pressure to new fields: Applying the concept of partial pressure to new fields, such as biology and medicine.
• Improving measurement techniques: Improving measurement techniques to accurately measure the partial pressure of gases in various applications.
  A Mixture of Three Noble Gases: Q&A =====================================

Q: What is the total pressure of the mixture of three noble gases?

A: The total pressure of the mixture of three noble gases is 1.25 atm.

Q: What are the individual pressures exerted by neon and argon in the mixture?

A: The individual pressures exerted by neon and argon in the mixture are 0.68 atm and 0.35 atm, respectively.

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

A: The partial pressure of a gas in a mixture can be calculated using the formula:

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

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

Q: What is the partial pressure of helium in the mixture?

A: The partial pressure of helium in the mixture is 0.22 atm.

Q: How do you calculate the partial pressure of helium in the mixture?

A: To calculate the partial pressure of helium in the mixture, we need to subtract the individual pressures of neon and argon from the total pressure of the mixture. The formula is:

$$P_3 = P_T - P_1 - P_2$$

where $P_3$ is the partial pressure of helium, $P_T$ is the total pressure of the mixture, $P_1$ is the partial pressure of neon, and $P_2$ is the partial pressure of argon.

Q: What are some real-world applications of partial pressure?

A: Some real-world applications of partial pressure include:

• Chemical Engineering: Partial pressure is used to calculate the amount of gas that can be absorbed or released by a liquid or solid.
• Atmospheric Science: Partial pressure is used to calculate the amount of greenhouse gases in the atmosphere and their impact on global warming.
• Medical Applications: Partial pressure is used to calculate the amount of oxygen in the blood and its impact on respiratory health.

Q: What are some limitations of the formula for partial pressure?

A: Some limitations of the formula for partial pressure include:

• Ideal Gas Assumption: The formula assumes that the gases in the mixture are ideal gases, which may not be the case in real-world applications.
• Interactions between Gases: The formula does not take into account interactions between the gases, which may affect the partial pressure of each gas.

Q: What are some future research directions in the field of partial pressure?

A: Some future research directions in the field of partial pressure include:

• Developing more accurate models: Developing more accurate models that take into account the interactions between the gases and the non-ideal behavior of the gases.
• Applying partial pressure to new fields: Applying the concept of partial pressure to new fields, such as biology and medicine.
• Improving measurement techniques: Improving measurement techniques to accurately measure the partial pressure of gases in various applications.

Q: What is the significance of partial pressure in chemistry?

A: Partial pressure is a fundamental concept in chemistry that is used to calculate the amount of gas that is present in a mixture. It is an important tool for understanding the behavior of gases and their interactions with other substances.