Calculating the Partial Pressure of Gas Y

Oct 13, 2025 by wbrum.org 102 views

Introduction

In a gas mixture, the partial pressure of a component is the pressure that the component would exert if it were the only component present in the container. The partial pressure of a gas can be calculated using the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$, where $$P_a$$ is the partial pressure of the gas, $$P_T$$ is the total pressure of the gas mixture, $$n_a$$ is the number of moles of the gas, and $$n_T$$ is the total number of moles of the gas mixture.

Understanding the Problem

In this problem, we are given a gas cylinder containing 2.0 mol of gas $$X$$ and 6.0 mol of gas $$Y$$ at a total pressure of 2.1 atm. We need to calculate the partial pressure of gas $$Y$$. To do this, we can use the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$.

Calculating the Partial Pressure of Gas Y

First, we need to identify the values given in the problem. We have:

Total pressure ($$P_T$$) = 2.1 atm
Number of moles of gas $$X$$ ($$n_X$$) = 2.0 mol
Number of moles of gas $$Y$$ ($$n_Y$$) = 6.0 mol

We can now use the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$ to calculate the partial pressure of gas $$Y$$. We know that the total number of moles ($$n_T$$) is the sum of the number of moles of gas $$X$$ and gas $$Y$$, which is 2.0 mol + 6.0 mol = 8.0 mol.

Applying the Formula

Now, we can plug in the values into the formula: $$\frac{P_Y}{2.1}=\frac{6.0}{8.0}$$

To solve for $$P_Y$$, we can multiply both sides of the equation by 2.1: $$P_Y=\frac{6.0}{8.0}\times2.1$$

Calculating the Partial Pressure of Gas Y

Now, we can calculate the partial pressure of gas $$Y$$: $$P_Y=\frac{6.0}{8.0}\times2.1=0.7875\times2.1=1.65$$

Conclusion

Therefore, the partial pressure of gas $$Y$$ is 1.65 atm.

Discussion

The partial pressure of a gas is an important concept in chemistry, as it can be used to calculate the concentration of a gas in a mixture. In this problem, we used the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$ to calculate the partial pressure of gas $$Y$$. This formula is a useful tool for chemists and physicists to calculate the partial pressure of a gas in a mixture.

Answer

The partial pressure of gas $$Y$$ is 1.65 atm.

Final Answer

The final answer is: $\boxed{1.65}$

Introduction

In our previous article, we discussed how to calculate the partial pressure of a gas in a mixture using the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$. We used this formula to calculate the partial pressure of gas $$Y$$ in a gas cylinder containing 2.0 mol of gas $$X$$ and 6.0 mol of gas $$Y$$ at a total pressure of 2.1 atm.

Q&A

Q: What is the partial pressure of a gas in a mixture?

A: 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.

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

A: You can use the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$, where $$P_a$$ is the partial pressure of the gas, $$P_T$$ is the total pressure of the gas mixture, $$n_a$$ is the number of moles of the gas, and $$n_T$$ is the total number of moles of the gas mixture.

Q: What is the total pressure of a gas mixture?

A: The total pressure of a gas mixture is the sum of the partial pressures of all the gases present in the mixture.

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

A: You can use the formula: $$P_T=P_1+P_2+...+P_n$$, where $$P_T$$ is the total pressure of the gas mixture, and $$P_1$$, $$P_2$$, ..., $$P_n$$ are the partial pressures of the individual gases.

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

A: The partial pressure of a gas is the pressure that the gas would exert if it were the only gas present in the container, while the total pressure of a gas mixture is the sum of the partial pressures of all the gases present in the mixture.

Q: Can I use the formula: $$\frac{P_a}{P_T}=\frac{n_a}{n_T}$$ to calculate the partial pressure of a gas in a mixture if I don't know the total pressure?

A: No, you need to know the total pressure of the gas mixture to use this formula.

Q: Can I use the formula: $$P_T=P_1+P_2+...+P_n$$ to calculate the total pressure of a gas mixture if I don't know the partial pressures?

A: No, you need to know the partial pressures of all the gases present in the mixture to use this formula.

Conclusion

Calculating the partial pressure of a gas in a mixture is an important concept in chemistry, and it can be used to calculate the concentration of a gas in a mixture. We hope that this Q&A article has helped you to understand how to calculate the partial pressure of a gas in a mixture.

Final Answer

The final answer is: $\boxed{1.65}$