A Container Holds 6.4 Moles Of Gas. Hydrogen Gas Makes Up $25\%$ Of The Total Moles In The Container. If The Total Pressure Is 1.24 Atm, What Is The Partial Pressure Of Hydrogen?Use $\frac{P_e}{P_T}=\frac{n_e}{n_T}$.A. 0.31 Atm B.
Understanding the Problem
To find the partial pressure of hydrogen in the container, we need to use the concept of partial pressures and the given information about the total moles of gas and the total pressure. The partial pressure of a gas is the pressure that the gas would exert if it were the only gas present in the container.
Given Information
- Total moles of gas in the container: 6.4 moles
- Hydrogen gas makes up $25%$ of the total moles in the container
- Total pressure: 1.24 atm
Using Dalton's Law of Partial Pressures
Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas. Mathematically, this can be expressed as:
where is the total pressure, and , , ..., are the partial pressures of each gas.
Finding the Partial Pressure of Hydrogen
We can use the formula to find the partial pressure of hydrogen. In this formula, is the partial pressure of the gas of interest (hydrogen), is the total pressure, is the number of moles of the gas of interest (hydrogen), and is the total number of moles.
Calculating the Number of Moles of Hydrogen
Since hydrogen gas makes up $25%$ of the total moles in the container, we can calculate the number of moles of hydrogen as follows:
Substituting the given value of moles, we get:
n_e = 0.25 \times 6.4 = 1.6$ moles ## Calculating the Partial Pressure of Hydrogen Now that we have the number of moles of hydrogen, we can use the formula $\frac{P_e}{P_T}=\frac{n_e}{n_T}$ to find the partial pressure of hydrogen: $\frac{P_e}{1.24} = \frac{1.6}{6.4}
Solving for , we get:
P_e = 0.3125$ atm ## Conclusion The partial pressure of hydrogen in the container is 0.3125 atm, which can be rounded to 0.31 atm. ## Final Answer The final answer is: $\boxed{0.31}{{content}}lt;br/> # A container holds 6.4 moles of gas. Hydrogen gas makes up $25\%$ of the total moles in the container. If the total pressure is 1.24 atm, what is the partial pressure of hydrogen? ## Understanding the Problem To find the partial pressure of hydrogen in the container, we need to use the concept of partial pressures and the given information about the total moles of gas and the total pressure. The partial pressure of a gas is the pressure that the gas would exert if it were the only gas present in the container. ## Given Information * Total moles of gas in the container: 6.4 moles * Hydrogen gas makes up $25\%$ of the total moles in the container * Total pressure: 1.24 atm ## Using Dalton's Law of Partial Pressures Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas. Mathematically, this can be expressed as: $P_T = P_1 + P_2 + ... + P_n
where is the total pressure, and , , ..., are the partial pressures of each gas.
Finding the Partial Pressure of Hydrogen
We can use the formula to find the partial pressure of hydrogen. In this formula, is the partial pressure of the gas of interest (hydrogen), is the total pressure, is the number of moles of the gas of interest (hydrogen), and is the total number of moles.
Calculating the Number of Moles of Hydrogen
Since hydrogen gas makes up $25%$ of the total moles in the container, we can calculate the number of moles of hydrogen as follows:
Substituting the given value of moles, we get:
n_e = 0.25 \times 6.4 = 1.6$ moles ## Calculating the Partial Pressure of Hydrogen Now that we have the number of moles of hydrogen, we can use the formula $\frac{P_e}{P_T}=\frac{n_e}{n_T}$ to find the partial pressure of hydrogen: $\frac{P_e}{1.24} = \frac{1.6}{6.4}
Solving for , we get:
P_e = 0.3125$ atm ## Conclusion The partial pressure of hydrogen in the container is 0.3125 atm, which can be rounded to 0.31 atm. ## Final Answer The final answer is: $\boxed{0.31}$ ## Q&A ### Q: What is the partial pressure of hydrogen in a container with 6.4 moles of gas, where hydrogen makes up 25% of the total moles, and the total pressure is 1.24 atm? A: The partial pressure of hydrogen is 0.31 atm. ### Q: How do you calculate the partial pressure of a gas in a mixture? A: You can use the formula $\frac{P_e}{P_T}=\frac{n_e}{n_T}$, where $P_e$ is the partial pressure of the gas of interest, $P_T$ is the total pressure, $n_e$ is the number of moles of the gas of interest, and $n_T$ is the total number of moles. ### Q: What is Dalton's Law of Partial Pressures? A: Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas. ### Q: How do you calculate the number of moles of a gas in a mixture? A: You can use the formula $n_e = 0.25 \times n_T$, where $n_e$ is the number of moles of the gas of interest, and $n_T$ is the total number of moles. ### 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 each gas. ### Q: How do you calculate the partial pressure of a gas in a mixture using the formula $\frac{P_e}{P_T}=\frac{n_e}{n_T}$? A: You can substitute the values of $P_e$, $P_T$, $n_e$, and $n_T$ into the formula and solve for $P_e$. ## Example Problems ### Problem 1 A container holds 8 moles of gas. Nitrogen gas makes up 30% of the total moles in the container. If the total pressure is 1.56 atm, what is the partial pressure of nitrogen? ### Solution Using the formula $\frac{P_e}{P_T}=\frac{n_e}{n_T}$, we can calculate the partial pressure of nitrogen as follows: $\frac{P_e}{1.56} = \frac{0.3 \times 8}{8}
P_e = 0.0565$ atm ### Problem 2 A container holds 10 moles of gas. Oxygen gas makes up 20% of the total moles in the container. If the total pressure is 1.8 atm, what is the partial pressure of oxygen? ### Solution Using the formula $\frac{P_e}{P_T}=\frac{n_e}{n_T}$, we can calculate the partial pressure of oxygen as follows: $\frac{P_e}{1.8} = \frac{0.2 \times 10}{10}
P_e = 0.036$ atm